Gear Materials, Properties, And Manufacture

ASM International®Materials Park, OH 44073-0002

www.asminternational.org

GEAR MATERIALS,PROPERTIES, ANDMANUFACTURE

Edited by

J.R. DavisDavis & Associates

© 2005 ASM International. All Rights Reserved.Gear Materials, Properties, and Manufacture (#05125G)


Copyright © 2005by

ASM International®

All rights reserved

No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means,electronic, mechanical, photocopying, recording, or otherwise, without the written permission of the copyrightowner.

First printing, September 2005

Great care is taken in the compilation and production of this Volume, but it should be made clear that NO WAR-RANTIES, EXPRESS OR IMPLIED, INCLUDING, WITHOUT LIMITATION, WARRANTIES OF MER-CHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE, ARE GIVEN IN CONNECTION WITHTHIS PUBLICATION. Although this information is believed to be accurate by ASM, ASM cannot guaranteethat favorable results will be obtained from the use of this publication alone. This publication is intended for useby persons having technical skill, at their sole discretion and risk. Since the conditions of product or material useare outside of ASM’s control, ASM assumes no liability or obligation in connection with any use of this infor-mation. No claim of any kind, whether as to products or information in this publication, and whether or not basedon negligence, shall be greater in amount than the purchase price of this product or publication in respect ofwhich damages are claimed. THE REMEDY HEREBY PROVIDED SHALL BE THE EXCLUSIVE ANDSOLE REMEDY OF BUYER, AND IN NO EVENT SHALL EITHER PARTY BE LIABLE FOR SPECIAL,INDIRECT OR CONSEQUENTIAL DAMAGES WHETHER OR NOT CAUSED BY OR RESULTINGFROM THE NEGLIGENCE OF SUCH PARTY. As with any material, evaluation of the material under end-useconditions prior to specification is essential. Therefore, specific testing under actual conditions is recommended.

Nothing contained in this book shall be construed as a grant of any right of manufacture, sale, use, or reproduc-tion, in connection with any method, process, apparatus, product, composition, or system, whether or not cov-ered by letters patent, copyright, or trademark, and nothing contained in this book shall be construed as a defenseagainst any alleged infringement of letters patent, copyright, or trademark, or as a defense against liability forsuch infringement.

Comments, criticisms, and suggestions are invited, and should be forwarded to ASM International.

Prepared under the direction of the ASM International Technical Books Committee (2004-2005), Yip-Wah Chung, FASM, Chair.

ASM International staff who worked on this project include Scott Henry, Senior Manager of Product and Service Development; Madrid Tramble, Senior Production Coordinator, and Kathryn Muldoon, ProductionAssistant.

Library of Congress Cataloging-in-Publication Data

Gear materials, properties, and manufacture / edited by J.R. Davisp. cm.

Includes bibliographical references and indexISBN 0-87170-815-9

1. Gearing—Manufacture. I. Davis, J.R. (Joseph R.)

TJ184.G34715 2005621.8�33—dc22 2005050105

SAN:204-7586

ASM International®

Materials Park, OH 44073-0002www.asminternational.org

Printed in the United States of America



Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Introduction to Gear Technology

Chapter 1 Basic Understanding of Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Gear Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Types of Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Proper Gear Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Basic Applied Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Gear Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Gear Manufacturing Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Heat Treating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Through Hardening and Case Hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Chapter 2 Gear Tribology and Lubrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Gear Tribology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Lubrication Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Classification of Gear Tooth Failure Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Lubrication-Related Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Elastohydrodynamic Lubrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Lubricant Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Oil Lubricant Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Selection of Gear Lubricant Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Application of Gear Lubricants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Case History: Failure of a 24-Unit Speed-Increaser Gearbox . . . . . . . . . . . . . . . . 35

Gear Materials

Chapter 3 Ferrous and Nonferrous Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Wrought Gear Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Surface-Hardening Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Through-Hardening Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Gear Steel Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Processing Characteristics of Gear Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Bending Fatigue Strength of Carburized Steels . . . . . . . . . . . . . . . . . . . . . . . . . . 46Other Properties of Interest for Carburized Steels . . . . . . . . . . . . . . . . . . . . . . . . 62

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Other Ferrous Alloys for Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Nonferrous Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Chapter 4 Plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77General Characteristics of Plastic Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Classification of Plastics for Gear Applications . . . . . . . . . . . . . . . . . . . . . . . . . . 77Metals versus Plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Plastic Gear Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Plastic Gear Manufacture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Gear Manufacture

Chapter 5 Machining, Grinding, and Finishing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Machining Processes for Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Selection of Machining Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98Cutter Material and Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104Speed and Feed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Cutting Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Comparison of Steels for Gear Cutting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Computer Numerical Control (CNC) Milling and Hobbing Machines . . . . . . . . 113Grinding of Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Honing of Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Lapping of Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Superfinishing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Chapter 6 Casting, Forming, and Forging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Forging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

Chapter 7 Powder Metallurgy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139Capabilities and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140Gear Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142Gear Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Gear Design and Tooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144Gear Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Quality Control and Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Examples of P/M Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Heat Treatment of Gears

Chapter 8 Through Hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155Through-Hardening Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155Through-Hardened Gear Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157Hardness Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157Distortion of Through-Hardened Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Case History: Design and Manufacture of a Rack . . . . . . . . . . . . . . . . . . . . . . . 158

Chapter 9 Carburizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Gas Carburizing: Processing and Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Quenching and Hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

iv



Tempering of Carburized and Quenched Gears . . . . . . . . . . . . . . . . . . . . . . . . . 168Recarburizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169Cold Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169Selection of Materials for Carburized Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169Carbon Content and Case Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175Core Hardness of Gear Teeth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181Problems Associated with Carburizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184Heat Treat Distortion of Carburized and Hardened Gears . . . . . . . . . . . . . . . . . 188Grinding Stock Allowance on Tooth Flanks to Compensate for Distortion . . . . 201Shot Peening of Carburized and Hardened Gears . . . . . . . . . . . . . . . . . . . . . . . . 208Applications and Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211Vacuum Carburizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

Chapter 10 Nitriding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227The Gas Nitriding Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227Controlled Nitriding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240Ion Nitriding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

Chapter 11 Carbonitriding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245Applicable Steels and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246Depth of Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246Hardenability of Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246Quenching and Tempering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

Chapter 12 Induction and Flame Hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249Induction Hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249Flame Hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

Failure Analysis, Fatigue Life Prediction, and Mechanical Testing

Chapter 13 Gear Failure Modes and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257Classification of Gear Failure Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257Fatigue Failures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271Wear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273Scuffing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275Stress Rupture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276Causes of Gear Failures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276Conducting the Failure Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277Examples of Gear Failure Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

Chapter 14 Fatigue and Life Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293Gear Tooth Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293Gear Tooth Surface Durability and Breakage . . . . . . . . . . . . . . . . . . . . . . . . . . . 296Life Determined by Contact Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297Life Determined by Bending Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302Gear Tooth Failure by Breakage after Pitting . . . . . . . . . . . . . . . . . . . . . . . . . . . 304Flaws and Gear Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306Bores and Shafts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

v



Chapter 15 Mechanical Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311Common Modes of Gear Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311Stress Calculations for Test Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312Specimen Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315Tests Simulating Gear Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316Gear Power-Circulating (PC), or Four-Square, Tests . . . . . . . . . . . . . . . . . . . . . 323

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

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Preface

Gears, because of their unique contribution to the operation of so many machines and mechanicaldevices, have received special attention from the technical community for more than two millennia.New developments in gear technology, particularly from the materials point-of-view, have also beencovered in detail by ASM International for many years. Numerous forums, conference proceedings,books, and articles have been devoted to the understanding of gear performance by examining geartribology, failure modes, the metallurgy of ferrous gear materials, heat treatment, gear manufactur-ing methods, and testing. All of these important technical aspects of gear technology are broughttogether in the present offering, Gear Materials, Properties, and Manufacture.

Chapter 1, “Basic Understanding of Gears,” discusses the various types of gears used, importantgear nomenclature, and applied stresses and strength requirements associated with gears. It also pro-vides an overview of several important topics that are covered in greater detail in subsequent chap-ters, namely, gear materials, gear manufacture, and heat treatment. Gear tribology and lubrication iscovered in Chapter 2. Lubrication-related failures (pitting, wear, and scuffing), elastohydrodynamiclubrication, lubricant selection, and gear lubricant application are among the subjects described.

Chapters 3 and 4 describe both metallic (ferrous and nonferrous alloys) and plastic gear materials,respectively. Emphasis in Chapter 3 has been placed on the properties of carburized steels, the mate-rial of choice for high-performance power transmission gearing. The increasing use of plastics forboth motion-carrying and power transmission applications is covered in Chapter 4.

Chapters 5, 6, and 7 address methods for manufacturing gears including metal removal processes(machining, grinding, and finishing), casting, forming, and forging (including recent advances innear-net shape forging of gears), and powder metallurgy processing. Injection molding, anotherimportant method for the manufacture of plastic gears, is covered in Chapter 4.

The heat treatment of gears is reviewed in Chapters 8 through 12. Both through hardening and sur-face hardening methods are reviewed. Again, emphasis has been placed on carburizing, the mostcommon heat treatment applied to gear steels. It should be noted that some of the material presentedin these chapters was adapted, with the kind permission of the author, from Heat Treatment of Gears:A Practical Guide for Engineers, by A.K. Rakhit (ASM International, 2000). Dr. Rakhit’s book is anexcellent resource for those seeking a more in-depth reference guide to gear heat treatment.

Failure analysis, fatigue life prediction, and mechanical testing are examined in Chapters 13, 14,and 15, respectively. In Chapter 13, “Gear Failure Modes and Analysis,” emphasis has been placedon two of the most common types of gear failure—bending fatigue and contact fatigue. Bendingfatigue of carburized steels is also discussed in depth in Chapter 3.

In summary, this book is intended for gear metallurgists and materials specialists, manufacturingengineers, lubrication technologists, and analysts concerned with gear failures who seek a betterunderstanding of gear performance and gear life. It supplements other gear texts that emphasize thedesign, geometry, and theory of gears.

Joseph R. DavisDavis & AssociatesChagrin Falls, Ohio

vii



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CHAPTER 1

Basic Understanding of Gears

GEARS are machine elements that transmitrotary motion and power by the successiveengagements of teeth on their periphery. Theyconstitute an economical method for such trans-mission, particularly if power levels or accuracyrequirements are high. Gears have been in usefor more than three thousand years and they arean important element in all manner of machin-ery used in current times. Application areas forgears are diverse and include—to name a few:

• Small, low-cost gears for toys• Gears for office equipment• Bicycle gears• Appliance gears• Machine tool gears• Control gears• Automotive gears• Transportation gears• Marine gears

• Aerospace gears• Gears in the oil and gas industry• Gears for large mills that make cement,

grind iron ore, make rubber, or roll steel

Gears range in size from recently developedmicrometer-sized gears for electric motors nobigger than a grain of sand to gears as large as30 m (100 ft) in diameter. Gear materials rangefrom lightweight plastics to ultrahigh-strengthheat-treated steels.

Gear Nomenclature

Before discussing the various types of gearsused, this section will review some of the termsused in the gear industry to describe the designof gears and gear geometries. Figure 1 showsschematically typical gear nomenclature. It

Fig. 1 Schematic of typical gear tooth nomenclature

Gear Materials, Properties, and ManufactureJ.R. Davis, editor, p1-18 DOI:10.1361/gmpm2005p001

Copyright © 2005 ASM International® All rights reserved. www.asminternational.org

2 / Gear Materials, Properties, and Manufacture

Fig. 2 Nomenclature of gear contact areas and boundary zones

should be noted that only the most commonterms are discussed below. More detailed infor-mation on gear nomenclature can be found invarious standards published by the AmericanGear Manufacturers Association (AGMA),most notably AGMA 1012-F90, “Gear Nomen-clature, Definitions of Terms with Symbols.”active profile. The part of the gear tooth profile

that actually comes in contact with the profileof the mating gear while in mesh (Fig. 2).

addendum. The height of the tooth above thepitch circle (Fig. 1).

backlash. The amount by which the width of atooth space exceeds the thickness of theengaging tooth on the operating pitch circle(Fig. 3).

base circle. The circle from which the involutetooth profiles are generated (Fig. 1).

bottom land. The surface at the bottom of atooth space adjoining the fillet (Fig. 1 and 2).

center distance. The distance between theaxes of rotation between two mating gears.

circular pitch. Length of arc of the pitch circlebetween corresponding points on adjacentteeth (Fig. 1).

circular thickness. The length of arc be-tween the two sides of a gear tooth at thepitch circle.

dedendum. The depth of the tooth below thepitch circle (Fig. 1).

diametral pitch (DP). A measure of tooth sizein the English system. In units, it is the num-ber of teeth per inch of pitch diameter. As thetooth size increases, the diametral pitchdecreases (Fig. 4). Diametral pitches rangefrom 0.5 to 200. Coarse pitch gears are thosewith a diametral pitch of ≤20. Fine pitchgears are those with a diametral pitch of >20.Table 1 shows the various tooth dimensionsfor different diametral pitches of spur gears.

face width. The length of the gear teeth in anaxial plane (Fig. 1).

fillet radius. The radius of the fillet curve atthe base of the gear tooth (Fig. 2).

gear. A geometric shape that has teeth uni-formly spaced around the circumference. Ingeneral, a gear is made to mesh its teeth withanother gear.

gear blank. The workpiece used for the manu-facture of a gear, prior to machining the gearteeth.

gear pinion. When two gears mesh together,the smaller of the two is called the pinion; thelarger is called the gear (Fig. 5).

gear quality numbers. AGMA gear qualitynumbers ranging from 3 to 15 identify the

Chapter 1: Basic Understanding of Gears / 3

Fig. 3 Schematic of gear backlash. Source: Ref 1

Fig. 4 Tooth gage chart (for reference purposes only). Source: Boston Gear, Quincy, MA

accuracy level of the tooth element toler-ances permissible in the manufacture of aparticular gear in terms of its specialized use.The higher the number, the greater the levelof accuracy. Numbers 3 through 7 are forcommercial applications such as appliances,numbers 8 through 13 are for precision appli-cations, and numbers 14 and 15 are for ultra-precision applications. The permissible tol-

erances for the different quality numbersmay be obtained from the AGMA standards,which show the type of gear and the permis-sible tolerances and inspection dimensions.

gear ratio. The ratio of the larger to the smallernumber of teeth in a pair of gears.

helix angle. The angle between any helix andan element of its cylinder. In helical gearsand worms, it is at the standard pitch circleunless otherwise specified.

involute gear tooth. A gear tooth whose pro-file is established by an involute curve out-ward from the base circle (Fig. 6).

normal section. A section through a gear thatis perpendicular to the tooth at the pitch cir-cle (Fig. 2).

pitch circle. The circumference of a gearmeasured at the point of contact with themating gear (Fig. 1 and 7).

pitch diameter. The diameter of the pitch cir-cle.


Fig. 6 Schematic of an involute gear tooth. Source: Ref 1

Line of centers

Gearcenter Pitch

linePitchcircle

Pitchpoint

Fig. 7 Schematic of pitch nomenclature. Source: Ref 1Fig. 5 The pinion, gear, and rack portions of a spur gear.

Source: Ref 1

pitch line. In a cross section of a rack, the pitchline corresponds to the pitch circle in thecross section of the gear (Fig. 7).

pitch point. The tangency point of the pitchcircles of two mating gears (Fig. 7).

pitch radius. The radius of the pitch circle in across section of gear teeth in any plane otherthan a plane of rotation (Fig. 1).

pressure angle. The angle between a toothprofile and a radial line at its pitch point (Fig.1). The pressure angle of an involute gear

tooth is determined by the size ratio betweenthe base circle and the pitch circle (Fig. 8).Common pressure angles used by the gearindustry are 14.5, 20, and 25°.

rack. A rack is a gear having a pitch circle ofinfinite radius. Its teeth lie along a straightline on a plane. The teeth may be at rightangles to the edge of the rack and mesh witha spur gear (Fig. 5 and 9b), or the teeth on therack may be at some other angle and engagea helical gear (Fig. 10b).

Table 1 Gear cutting table showing varioustooth dimensions for different diametralpitches of spur gears

Diametralpitch

Circular pitch, in.

Thickness of tooth on

pitch line, in.

Depth to be cut in

gear(a), in.Addendum,

in.

3 1.0472 0.5236 0.7190 0.3333 4 0.7854 0.3927 0.5393 0.2500 5 0.6283 0.3142 0.4314 0.2000 6 0.5236 0.2618 0.3565 0.1667 8 0.3927 0.1963 0.2696 0.1250 10 0.3142 0.1571 0.2157 0.1000 12 0.2618 0.1309 0.1798 0.0833 16 0.1963 0.0982 0.1348 0.0625 20 0.1571 0.0785 0.1120 0.0500 24 0.1309 0.0654 0.0937 0.0417 32 0.0982 0.0491 0.0708 0.0312 48 0.0654 0.0327 0.0478 0.0208 64 0.0491 0.0245 0.0364 0.0156

(a) Hobbed gears. Source: Boston Gear, Quincy, MA


Fig. 8 Schematic of two common pressure angles. Source:Boston Gear, Quincy MA

Fig. 9 Sections of a spur gear (a) and a spur rack (b) Fig. 10 Sections of a helical gear (a) and a helical rack (b)

root circle. The root circle coincides with thebottoms of the tooth spaces (Fig. 1).

tooth thickness. The thickness of the toothmeasured at the pitch circle (Fig. 1).

top land. The surface of the top of a tooth (Fig.1 and 2).

transverse section. A section through a gearperpendicular to the axis of the gear (Fig. 2).

Types of Gears

There is a wide variety of types of gears inexistence, each serving a range of functions. Inorder to understand gearing, it is desirable toclassify the more important types in some way.One approach is by the relationship of the shaftaxes on which the gears are mounted. As listedin Table 2, shafts may be parallel, intersecting,or nonintersecting and nonparallel.

Types of Gears that Operate on Parallel Shafts

Spur gears (Fig. 5 and 9) are used to trans-mit motion between parallel shafts or between ashaft and a rack. The teeth of a spur gear areradial, uniformly spaced around the outerperiphery, and parallel to the shaft on which thegear is mounted. Contact between the matingteeth of a spur gear is in a straight line parallelto the rotational axes, lying in a plane tangent tothe pitch cylinders of the gears (a pitch cylinderis the imaginary cylinder in a gear that rollswithout slipping on a pitch cylinder or pitchplane of another gear).

Helical gears (Fig. 10a) are used to trans-mit motion between parallel or crossed shafts orbetween a shaft and a rack by meshing teeth thatlie along a helix at an angle to the axis of theshaft. Because of this angle, mating of the teethoccurs such that two or more teeth of each gearare always in contact. This condition permitssmoother action than that of spur gears. How-


Fig. 11 A typical one-piece herringbone gear. The opposedhelixes permit multiple-tooth engagement and elim-

inate end thrust.Fig. 12 Section of a spur-type internal gear (a) and relation

of internal gear with mating pinion (b)

Table 2 Types of gears in common use

Parallel axes

Spur external Spur internal Helical external Helical internal

Intersecting axes

Straight bevel Zerol bevel Spiral bevel Face gear

Nonintersecting and nonparallel axes

Crossed helical Single-enveloping worm Double-enveloping worm Hypoid Spiroid

ever, unlike spur gears, helical gears generateaxial thrust, which causes slight loss of powerand requires thrust bearings.

Herringbone gears (Fig. 11), sometimescalled double helical gears, are used to transmitmotion between parallel shafts. In herringbonegears, tooth engagement is progressive, and twoor more teeth share the load at all times. Becausethey have right-hand and left-hand helixes, her-ringbone gears are usually not subject to endthrust. Herringbone gears can be operated athigher pitch-line velocities than spur gears.

Internal gears are used to transmit motionbetween parallel shafts. Their tooth forms aresimilar to those of spur and helical gears exceptthat the teeth point inward toward the center ofthe gear. Common applications for internal gearsinclude rear drives for heavy vehicles, planetarygears, and speed-reducing devices. Internal

gears are sometimes used in compact designs be-cause the center distance between the internalgear and its mating pinion is much smaller thanthat required for two external gears. A typicalrelation between an internal gear and a matingpinion is shown in Fig. 12.

Types of Gears that Operate on Intersecting Shafts

Bevel gears transmit rotary motion betweentwo nonparallel shafts. These shafts are usuallyat 90° to each other.

Straight bevel gears (Fig. 13a) have straightteeth that, if extended inward, would intersect atthe axis of the gear. Thus, the action betweenmating teeth resembles that of two cones rollingon each other (see Fig. 14 for angles and termi-nology). The use of straight bevel gears is gener-ally limited to drives that operate at low speedsand where noise is not important.

Spiral bevel gears (Fig. 13b) have teeth thatare curved and oblique. The inclination of theteeth results in gradual engagement and contin-uous line contact or overlapping action; that is,more than one tooth will be in contact at alltimes. Because of this continuous engagement,the load is transmitted more smoothly from thedriving to the driven gear than with straightbevel gears. Spiral bevel gears also have greaterload-carrying capacity than their straight coun-terparts. Spiral bevel gears are usually preferredto straight bevel gears when speeds are greaterthan 300 m/min (1000 sfm), and particularly forvery small gears.

Zerol bevel gears (Fig. 13c) are curved-tooth bevel gears with zero spiral angle. Theydiffer from spiral bevel gears in that the teeth


Fig. 13 Three types of bevel gears and a hypoid gear

Fig. 14 Angles and terminology for straight bevel gears

Fig. 15 Face gear terminology. (a) Cross-sectional viewshowing gear and pinion positions. (b) Relationship

of gear teeth to gear axis

not ordinarily thought of as bevel gears, butfunctionally they are more akin to bevel gearsthan to any other type.

A spur pinion and a face gear are mounted(like bevel gears) on shafts that intersect andhave a shaft angle (usually 90°). The pinionbearings carry mostly radial load, while the gearbearings have both thrust and radial load. Themounting distance of the pinion from the pitch-cone apex is not critical, as it is in bevel orhypoid gears. Figure 15 shows the terminologyused with face gears.

The pinion that goes with a face gear is usu-ally made spur, but it can be made helical if nec-essary. The formulas for determining thedimensions of a pinion to run with a face gearare no different from those for the dimensions ofa pinion to run with a mating gear on parallelaxes. The pressure angles and pitches used aresimilar to spur gear (or helical gear) practice.

The gear must be finished with a shaper-cutter that is almost the same size as the pinion.Equipment for grinding face gears is not avail-able. The teeth can be lapped, and they can beshaved without too much difficulty, althoughordinarily shaving is not used.

The face gear tooth changes shape from oneend of the tooth to the other. The face width ofthe gear is limited at the outside end by theradius at which the tooth becomes pointed. Atthe inside end, the limit is the radius at which

are not oblique. They are used in the same wayas spiral bevel gears, and they have somewhatgreater tooth strength than straight bevel gears.

Face gears have teeth cut on the end face ofa gear, as the term face gear implies. They are


Fig. 16 Mating of worm gear (worm wheel) and worm in adouble-enveloping worm gear set

Fig. 17 Mating crossed-axes helical gears Fig. 18 Spiroid gear design

undercut becomes excessive. Due to practicalconsiderations, it is usually desirable to makethe face width somewhat short of these limits.The pinion to go with a face gear is usuallymade with a 20° pressure angle.

Types of Gears that Operate onNonparallel and Nonintersecting Shafts

Worm gear sets are usually right-angledrives consisting of a worm gear (or wormwheel) and a worm. A single-enveloping wormgear set has a cylindrical worm, but the gear isthroated (that is, the gear blank has a smallerdiameter in the center than at the ends of thecylinder, the concave shape increasing the areaof contact between them) so that it tends to wraparound the worm. In the double-enveloping

worm gear set, both members are throated, and both members wrap around each other. Adouble-enveloping worm gear set is shown inFig. 16. Worm gear sets are used where the ratioof the speed of the driving member to the speedof the driven member is large, and for a compactright-angle drive.

Crossed-helical gears are essentially non-enveloping worm gears, that is, both membersare cylindrical (Fig. 17). The action betweenmating teeth has a wedging effect, which resultsin sliding on tooth flanks. These gears have lowload-carrying capacity, but are useful whereshafts must rotate at an angle to each other.

Hypoid gears (Fig. 13d) are similar to spi-ral bevel gears in general appearance. Theimportant difference is that the pinion axis ofthe hypoid pair of gears is offset somewhat fromthe gear axis. This feature provides many designadvantages. In operation, hypoid gears run evenmore smoothly and quietly than spiral bevelgears and are somewhat stronger.

Spiroid gears consist of a tapered pinionthat somewhat resembles a worm (Fig. 18) and agear member that is a face gear with teeth curvedin a lengthwise direction; the inclination to thetooth is like a helix angle, but not a true helicalspiral. The combination of a high gear ratio incompact arrangements, low cost when mass pro-duced, and good load-carrying capacity makesthese gears attractive in many applications.

Proper Gear Selection

The first step in designing a set of gears is toselect the correct type. In many cases, the geo-metric arrangement of the apparatus that needsa gear drive will considerably affect the selec-


tion. If the gears must be on parallel axes, thenspur or helical gears are appropriate. Bevel andworm gears can be used if the axes are at rightangles, but they are not feasible with parallelaxes. If the axes are nonintersecting and non-parallel, then crossed-helical gears, hypoidgears, worm gears, or Spiroid gears can be used.Worm gears, though, are seldom used if the axesare not at right angles to each other.

There are no dogmatic rules that tell the de-signer which gear to use. The choice is oftenmade after weighing the advantages and disad-vantages of two or three types of gears. Somegeneralizations, though, can be made about gearselection.

External helical gears are generally usedwhen both high speeds and high horsepowersare involved. External helical gears have beenbuilt to carry as much as 45,000 kW (60,000 hp)of power on a single pinion and gear. Largerhelical gears could also be designed and built. Itis doubtful if any other type of gear could bebuilt and used successfully to carry this muchpower on a single mesh.

Bevel and Hypoid Gears. Bevel gears areordinarily used on right-angle drives when highefficiency is needed. These gears can usually bedesigned to operate with 98% or better effi-ciency. Hypoid gears do not have as good effi-ciency as bevel gears, but hypoid gears cancarry more power in the same space, providedthe speeds are not too high.

Worm gears are ordinarily used on right-angle drives when very high ratios (single-thread worm and gear) are needed. They arealso widely used in low-to-medium ratios(multiple-thread worm and gear) as packagedspeed reducers. Single-thread worms and wormgears are used to provide the mechanical index-ing accuracy on many machine tools. The criti-cal function of indexing hobbing machines andgear shapers is nearly always done by wormgear drive. Worm gears seldom operate at effi-ciencies above 90%.

Spur gears are relatively simple in designand in the machinery used to manufacture andcheck them. Most designers prefer to use themwherever design requirements permit.

Spur gears are ordinarily thought of as slow-speed gears, while helical gears are thought of ashigh-speed gears. If noise is not a serious designproblem, spur gears can be used at almost anyspeed that can be handled by other types of gears.Aircraft gas-turbine precision spur gears some-times operate at pitch-line speeds above 50 m/s

(10,000 sfm). In general, though, spur gears arenot used much above 20 m/s (4000 sfm).

Basic Applied Stresses (Ref 2)

The loads applied to one tooth by the action ofits mating tooth are at any moment of time a linecontact at the most; or, at the least, a point con-tact (more detailed information on gear toothcontact can be found in Chapter 14, “Fatigue andLife Prediction”). As the loads are increased, theline may lengthen or even broaden, or the pointmay expand to a rounded area.

The basic stresses applied to a gear toothinclude the six types listed in Fig. 19; often, acombination of two or three types are applied ata time. Commonly they are tensile, compres-sive, shear (slide), rolling, rolling-slide, and tor-sion. Each type of gear tooth will have its owncharacteristic stress patterns.

Spur Gear. As the contacting tooth movesup the profile of the loaded tooth, a sliding-rolling action takes place at the profile interface.At the pitchline, the stresses are pure rolling.Above the pitchline, the rolling-sliding actionagain takes over, but the sliding will be in theopposite direction. Keep in mind that the actionon the profile of the contacting tooth is exactlythe same as the loaded tooth except in reverse

Fig. 19 Basic stresses that are applied to gear teeth. Often,two or three are simultaneously applied to a specific

area. Source: Ref 2


Fig. 20 Diagramatic stress areas on basic spur gear tooth.Source: Ref 2

Fig. 21 Secondary stresses set up in associated parameters ofa helical gear due to the side thrust action of the

helix. Source: Ref 2

order (see Fig. 20). The sliding action of twosurfaces, when lubricated properly, will have noproblem. However, surface disparities, insuffi-cient lubrication, improper surface hardness,higher temperatures, and abrasive or adhesiveforeign particles will contribute to a breakdownduring a sliding contact. At the same time, thereis a tensile stress at the root radius of the loadedside of the tooth and a compressive stress at theroot radius of the opposite side.

Helical Gear. The helical gear tooth re-ceives the same contact action as the spur gear;i.e., a rolling-sliding action from the lowest pointof active profile up to the pitchline, rolling overthe pitchline, then sliding-rolling from the pitch-line over the addendum. An additional stress isbeing applied to the helical tooth; a lateral slid-ing action is applied at all contact levels, includ-ing the pitchline. The force component at 90° tothe direction of rotation increases as the helicalangle increases. Resultants of this side thrust areoften overlooked (see Fig. 21). The web betweenthe center shaft hub and the outer gear rim is con-stantly undergoing a cycle of bending stress; it isnot uncommon for a relatively thin web to fail inbending fatigue. If the hub of the gear facesagainst a thrust bearing, the bearing itself isunder a constant thrust load. The shaft carryingthe gear undergoes a continual rotation bendingstress. It is also not uncommon to have such ashaft fail by rotational bending fatigue. Theabove secondary stresses are found only in a gearof a single-helix pattern. A double-helical gearor a herringbone gear will not have a side thrustcomponent of stress; therefore, the entire stressload will be absorbed by the teeth.

One additional stress that should be discussedat this time is a stress common to all gearing

because it involves rolling surfaces. It is a shearstress running parallel to the surface at a distancefrom 0.18 to 0.3 mm (0.007 to 0.012 in.) belowthe surface. The distance below the surface givenabove is the average depth for a normal loadingcondition. The actual depth of maximum shearcould be deeper, depending on the radius of cur-vature of the mating surfaces and the tangentialforces being applied. In one instance there hasbeen evidence of rolling loads above the shearstrength as deep as 0.86 mm (0.034 in.). The sub-surface shear stress is most often the originator ofinitial line pitting along the pitchline of gearteeth, line pitting low on the profile due to toothtip interference, line pitting along the tooth tipdue to the same tooth tip interference, and sub-surface rolling contact fatigue. The subject ofrolling contact fatigue is discussed more fully inChapters 3, “Ferrous and Nonferrous Alloys”and 13, “Gear Failure Modes and Analysis.”

Straight Bevel Gear. The straight bevelgear undergoes the same stresses as discussedabove, including a very slight helical action lat-erally. The larger sliding action component isparallel to the axis of the gears and tends to push


the gears apart, causing a higher profile contact,and to exert a rotational bending stress in theweb of the part as well as in the shaft.

Spiral Bevel Gear. Aside from all thestresses applied above, a spiral bevel gear has aresultant peculiar to itself. As the rolling-slidingstress tends to move in a straight line laterally,the progression of the points along the stress linemoves in a bias across the profile of the tooth. Aslong as at least two teeth are in contact, theresulting load per unit area is well within reason-able limits. However, there are circumstances(and it may be only momentary) when there is a1-to-1 tooth contact. This very narrow line con-tact may be accepting an extremely high load perunit area, and a line of pitting will result early inthe life of the tooth. Careful attention should begiven to the design characteristics of these parts,such as spiral angle and pressure angle.

Hypoid Gear. The hypoid gearing has thesame applied stresses as those discussed for thespiral bevel, but sliding becomes the more pre-dominant factor. This predominance increasesas the axis of the pinion is placed farther fromthe central axis of the gear, and is maximumwhen the set becomes a high-ratio hypoid.

Strength (Ref 2)

The strength of any component is measured bythe amount of stress that can be tolerated beforepermanent strain (deformation) takes place.

Strain, or deflection under load, is a constantfor steel regardless of hardness or heat treatment.The amount of deflection under load of a thingear web or the shank of a pinion cannot bechanged by heat treatment or by use of a strongermaterial. Hooke’s law is the same: A change ofdeflection can be accomplished only by a changeof design.

Bending strength of a gear tooth is the amountof load per unit area acceptable at the root radiusto the point of permanent deformation. Perm-anent deformation of a carburized tooth is usu-ally accompanied by a crack at the root radius,whereas with a noncarburized tooth, actual bend-ing may occur. The root radius is mentioned asthe point of deformation because it is the area ofgreatest stress concentration in tension. Also,stress (load per unit area) calculations assumethat the load is applied at the pitchline or the mid-height of the tooth. Actually, the realistic stress atthe root radius varies from approximately one-half, when the load is applied low on the active

profile, to double, when the load is applied nearthe tooth tip. Bending strength of the root radiusis a function of the surface hardness and the phys-ical condition of the surface, such as smoothness,sharpness of radius, and/or corrosive pitting.

The strength of the core material—i.e., thebasic material under the carburized steel case—is generally to be considered as compressivestrength rather than tensile strength. It measuresthe ability to withstand surface pressures thatmay crush through the case and/or brinell (in-dent) the surface.

Torsional strength of a pinion shank or of ashaft is a bit more complex. The maximum ten-sile stress is at the surface in a direction 45° fromthe central axis or longitudinal direction. Themaximum shear stress, also at the surface, is lon-gitudinal (parallel to the central axis) and trans-verse (90° across the central axis) (see Fig. 22).The strength at the surface is a function of sur-face hardness; therefore, surface-originated tor-sional tensile failures of carburized parts are rareunless a specific type of stress raiser is present atthe surface. This is not so with through hardenedor non-heat treated parts since the strength is uni-form throughout the part. Under this condition,torsional tensile failure is expected to originateat the surface. In most instances of torsional fail-ure of carburized or induction hardened shaftsand pinion shanks, the initial fracture is along the

Fig. 22 Free-body diagram of maximum tensile and shearstress orientation on a surface element of a shaft in a

torsional mode. Both maximums are at the surface. Stress is con-sidered to be zero at the central axis. Source: Ref 2


Table 3 Recommended steels for various applications and gear typesTypical industrial application Gear design type Typical material choice

Differentials

Automotive Hypoid, spiral/straight bevel 4118, 4140, 4027, 4028, 4620, 8620, 8622, 8626 Heavy truck Hypoid, spiral/straight bevel 4817, 4820, 8625, 8822

Drives

Industrial Helical, spur rack and pinion, worm 1045, 1050, 4140, 4142, 4150, 4320, 4340, 4620 Tractor-accessory Crossed-axis helical, helical 1045, 1144, 4118, 4140

Engines

Heavy truck Crossed-axis helical, spur, worm 1020, 1117, 4140, 4145, 5140, 8620

Equipment

Earth moving Spiral/straight bevel, zerol 1045, 4140, 4150, 4340, 4620, 4820, 8620, 9310 Farming Face, internal, spiral/straight bevel, spur 4118, 4320, 4817, 4820, 8620, 8822 Mining, paper/steel mill Helical, herringbone, miter, spur, spur rack and pinion 1020, 1045, 4140, 4150, 4320, 4340, 4620, 9310

Starters

Automotive Spur 1045, 1050

Transmissions

Automotive Helical, spur 4027, 4028, 4118, 8620 Heavy Truck Helical, spur 4027, 4028, 4620, 4817, 5120, 8620, 8622, 9310 Marine Helical, helical conical, spiral bevel 8620, 8622 Off highway Helical, internal, spiral/straight bevel, spur 1118, 5130, 5140, 5150, 8620, 8822, 9310 Tractor Herringbone, internal, spur 4118, 4140, 8822

Source: Ref 3

shear plane (i.e., longitudinal or transverse), andnot at the 45° angle. This means that the shearstrength of the subsurface material is the control-ling factor. Shear strength is considered to beonly about 60% of the tensile strength. The areamost vulnerable to the origin of torsional shearfailure of a shaft is the transition zone betweenthe case and the core of either a carburized or aninduction hardened part. The maximum appliedstress often exceeds the shear strength of thematerial at this area and initiates a start of sub-surface failure.

Gear Materials

A variety of cast irons, powder-metallurgymaterials, nonferrous alloys, and plastics areused in gears, but steels, because of their highstrength-to-weight ratio and relatively low cost,are the most widely used gear materials forheavy duty, power transmission applications.Consequently, steel gears receive primary con-sideration in this chapter.

Among the through-hardening steels in wideuse are 1040, 1060, 4140, and 4340. These steelscan also be effectively case hardened by induc-tion heating. Among the carburizing steels usedin gears are 1018, 1524, 4026, 4118, 4320, 4620,4820, 8620, and 9310 (AMS 6260). Table 3 lists

specific application areas for commonly usedgear steels. Many high-performance gears arecarburized. Some special-purpose steel gears arecase hardened by either carbonitriding or nitrid-ing. Other special-purpose gears, such as thoseused in chemical or food-processing equip-ment, are made of stainless steels or nickel-basealloys because of their corrosion resistance, theirability to satisfy sanitary standards, or both.Gears intended for operation at elevated temper-atures may be made of tool steels or elevated-temperature alloys.

Most gears are made of carbon and low-alloysteels, including carburizing steels and the lim-ited number of low-alloy steels that respondfavorably to nitriding. In general, the steelsselected for gear applications must satisfy twobasic sets of requirements that are not alwayscompatible—those involving fabrication andprocessing and those involving service. Fabri-cation and processing requirements includemachinability, forgeability, and response to heattreatment as it affects fabrication and process-ing. Service requirements are related to the abil-ity of the gear to perform satisfactorily under theconditions of loading for which it was designedand thus encompass all mechanical-propertyrequirements, including fatigue strength andresponse to heat treatment (see the section“Selection Guidelines” presented below).


Because resistance to fatigue failure is partlydependent upon the cleanness of the steel andupon the nature of allowable inclusions, meltingpractice may also be a factor in steel selectionand may warrant selection of a steel producedby vacuum melting or electroslag refining. Themill form from which a steel gear is machined isanother factor that may affect its performance.Many heavy-duty steel gears are machined fromforged blanks that have been processed to pro-vide favorable grain flow consistent with loadpattern rather than being machined from blankscut from mill-rolled bar.

Selection Guidelines. In all gears the choiceof material must be made only after careful con-sideration of the performance demanded by theend-use application and total manufactured cost,taking into consideration such issues as machin-ing economics. Key design considerations re-quire an analysis of the type of applied load,whether gradual or instantaneous, and the de-sired mechanical properties, such as bending fa-tigue strength or wear resistance, all of which de-fine core strength and heat treating requirements.

Different areas in the gear tooth profile seedifferent service demands. Consideration mustbe given to the forces that will act on the gearteeth, with tooth bending and contact stress,resistance to scoring and wear, and fatigue issuesbeing paramount. For example, in the root area,good surface hardness and high residual com-pressive stress are desired to improve endurance,or bending fatigue life. At the pitch diameter, acombination of high hardness and adequate sub-

surface strength are necessary to handle contactstress and wear and to prevent spalling.

Numerous factors influence fatigue strength,including:

• Hardness distribution, as a function of casehardness, case depth, core hardness

• Microstructure, as a function of retained au-stenite percentage, grain size, carbides (size,type, distribution), nonmartensitic phases

• Defect control, as a function of residualcompressive stress, surface finish, geome-try, intergranular toughness

More detailed information on the factors thatinfluence the properties of gear steels can befound in Chapter 3, “Ferrous and NonferrousAlloys.”

Gear Manufacturing Methods

Gears can be made by a variety of manufac-turing processes. This section will brieflyreview these processes. For the manufacture ofmetal gears, the reader should consult Chapters5, “Machining, Grinding, and Finishing,” 6,“Casting, Forming and Forging,” and 7, “Pow-der Metallurgy.” Methods for making plasticgears are described in Chapter 4, “Plastics.”

Metal Removal Processes

As shown in Fig. 23, gear blanks can beshaped by a number of cutting (machining) andfinishing processes. Often blanks are processed

Fig. 23 Examples of various gear manufacturing processes. Source: Ref 3


Fig. 24 Typical gear manufacturing costs. Source: Ref 3

by a series of rough cutting and finishing opera-tions. Gears made by machining/finishing havethe highest AGMA quality tolerance levels thangears made by competing processes (see Table 1in Chapter 6). Machining and finishing pro-cesses make up about 60% of gear manufactur-ing costs (Fig. 24).

Broaching is a machining operation whichrapidly forms a desired contour in a workpiece bymoving a cutter, called a broach, entirely past theworkpiece. The broach has a long series of cut-ting teeth that gradually increase in height. Thebroach can be made in many different shapes toproduce a variety of contours. The last few teethof the broach are designed to finish the cut ratherthan to remove considerably more metal.Broaches are often used to cut internal gear teeth,racks, and gear segments on small gears, and usu-ally are designed to cut all teeth at the same time.

Grinding is a process that shapes the sur-face by passes with a rotating abrasive wheel.Grinding is not a practical way to remove largeamounts of metal, so it is used to make veryfine-pitch teeth, or to remove heat treat distor-tion from large gears that have been cut and thenfully hardened. Many different kinds of grind-ing operations are used in gear manufacture.

Hobbing. This is a gear cutting method thatuses a tool resembling a worm gear in appear-ance, having helically spaced cutting teeth. In asingle-pitch hob, the rows of teeth advanceexactly one pitch as the hob makes one revolu-tion. With only one hob, it is possible to cut in-terchangeable gears of a given pitch of any num-ber of teeth within the range of the hobbingmachine.

Honing is a low-speed finishing processused chiefly to produce uniform high dimen-sional accuracy and fine finish. In honing, verythin layers of stock are removed by simultane-ously rotating and reciprocating a bonded abra-sive stone or stick that is pressed against the sur-

face being honed with lighter force than is typi-cal of grinding.

Lapping is a polishing operation that usesabrasive pastes to finish the surfaces of gearteeth. Generally a toothed, cast iron lap is rolledwith the gear being finished.

Milling is a machining operation whichremoves the metal between two gear teeth bypassing a rotating cutting wheel across the gearblank.

Shaping is a gear cutting method in whichthe cutting tool is shaped like a pinion. Theshaper cuts while traversing across the face widthand rolling with the gear blank at the same time.

Shaving is a finishing operation that uses aserrated gear-shaped or rack-shaped cutter toshave off small amounts of metal as the gear andcutter are meshed at an angle to one another.The crossed axes create a sliding motion whichenables the shaving cutter to cut.

Skiving is a machining operation in whichthe cut is made with a form tool with its face soangled that the cutting edge progresses from oneend of the workpiece to the other as the toolfeeds tangentially past the rotating workpiece.

Casting, Forming, and Forging Processes

Casting is a process of pouring or injectingmolten metal into a mold so that the metal solid-ifies and hardens into the desired shape. Castingis often used to make gear blanks that will havecut teeth. Small gears are frequently cast com-plete with teeth by the die casting process,which uses a precision mold of tool steel andlow-melting-point alloys for the gears.

Stamping is a fast inexpensive method ofproducing small gears from thin sheets of metal.The metal is sheared by a punching die whichstamps through the sheet stock into a matinghole.

Gear rolling is a process which rapidlyshapes fine gear teeth or worm threads by high-pressure rolling with a toothed die.

Powder Metallurgy (P/M) Processing. Inits most basic and widely used form, the P/Mprocess consists of pressing a powder to thedesired shape, followed by heating (sintering) atan elevated temperature below its melting point.There are a number of variations of the P/Mprocess that are applicable to gears (see Fig. 1 inChapter 7). The P/M process is suitable for high-volume production of small gears. It is not eco-nomical for low-to-medium volume production.

Injection molding is a method of forming aplastic to the desired shape by forcing the heat-


softened plastic into a relatively cool cavity(die) under pressure. It is widely used for high-volume production of thermoplastic resin (e.g.,acetals and nylons) gears. Often lubricants areadded to the thermoplastic material to furtherimprove the inherent lubricity of the material.

Forging. The forging process has long beenused to create blanks that will be subsequentlyshaped into gears by metal removal methods.However, it is increasingly being used for theproduction of near-net shape and net shapegears for demanding applications where greatstrength and durability are required. The forgingprocess is carried out hot with metal preheatedto a desired temperature under intense pressureuntil it fills the die cavity. The resultant grainflow which smoothly follows gear tooth con-tours makes forged gears stronger than thosemade by other processes.

Alternative or Nontraditional Gear Manufacturing

Although the gear manufacturing processesdiscussed above are by far the most prevalentmethods for gear production, there are a numberof other processes that are being used increas-ingly by the gear industry.

Laser Machining. While sometimes slowerthan traditional machining techniques, depend-ing on the material, lasers can cut complexshapes such as gears with great precision andvery little material waste. This conservationcomes from the ability of the computerized-numerically-controlled (CNC) machines con-trolling the lasers to reuse cutting paths, gettingas many gears from a single sheet as possible.Also, the computer control means that lasermachining is also low maintenance. The setupand first runs are closely supervised, but theactual production runs don’t need any real super-vision due to the CNC programming.

Limitations of the laser machining processare as follows:

• Pieces cut with a laser have heat affectedzones, areas where the metal is heatedbeyond a critical transformation point, andrecast. These zones are limited, however, tothe edges of the cuts—minimizing, but noteliminating heat distortion and the need forfurther machining. Post production grindingand honing are common.

• Lasers are limited to cutting metals ≤19 mm(≤0.75 in.). Cutting thicker materials re-quires too much power.

• Lasers are limited to nonreflective or semi-reflective metals. Metals like aluminum andbrass that are highly reflective are difficult tocut.

• Lasers are limited, like stamping, to flatforms such as spur gears.

Electrical Discharge Machining (EDM).The EDM process uses electricity to melt orvaporize the material being cut. Many of theattributes and limitations outlined for lasermachining are also applicable to EDM.

Abrasive water jet machining is a hydro-dynamic machining process that uses a high-velocity stream of water laden with fine abra-sive particles as a cutting tool. The processtypically produces burr-free edges with heat-affected zones, can easily handle heat treatedmaterial, and, unlike lasers, can cut throughstacks of material to create multiple parts at thesame time, saving time and money. Abrasivewaterjets have been used to:

• Cut lapping machine gears made from diffi-cult-to-machine plastic composites

• Titanium rack and pinion components forcommercial jet pilot seats

• Process phenolics into machinery gear com-ponents

• Cut spring steel into gears with tightlyspaced teeth

Inspection

As noted at the bottom of Fig. 23, inspectionis an integral part of the gear manufacturingprocess. As with all manufactured products,gears must be checked to determine whether theresulting product meets design specificationsand requirements. Because of the irregularshape of gears and the number of factors thatmust be measured, such inspection is somewhatdifficult. Among the factors to be checked arethe linear tooth dimensions (thickness, spacing,depth, and so on), tooth profile, surface rough-ness, and noise. Several special devices, most ofthem automatic or semiautomatic, are used forthis inspection.

Gear tooth vernier calipers can be used tomeasure the thickness of gear teeth on the pitchcircle. However, inspection is usually done byspecial machines, which in one or a series ofoperations check several factors, includingeccentricity, variations in circular pitch, varia-tions in pressure angle, fillet interference, andlack of continuous action. The gear is usually


Fig. 25 Typical data obtained on charts generated by auto-mated gear-checking machines. (a) Tooth-to-tooth

pitch error. (b) Accumulated pitch error. (c) Spacing error

mounted and moved in contact with a mastergear. The movement of the latter is amplified andrecorded on moving charts, as shown in Fig. 25.

Noise level is important in many applica-tions, not only from the standpoint of noise pol-lution but also as an indicator of probable gearlife. Therefore, special equipment for its mea-surement is quite widely used, sometimes inte-grated into mass-production assembly lines.

Dimensional variations in gears result innoise, vibration, operational problems, reducedcarrying ability, and reduced life. These prob-lems are compounded at higher gear-operating

speeds. AGMA has incorporated the criticaldimensions of pitch, concentricity, tooth profile,tooth thickness, and tooth surface finish into anumber of standards which the interested readershould refer to. Additional information can alsobe found in Ref 4 and 5.

Heat Treating (Ref 3)

Heat treating is one of the most importantsteps in the manufacture of precision gearing.Its contribution is vitally important for cost con-trol, durability, and reliability. As shown in Fig.24, heat treating represents about 30% of a typ-ical gear manufacturing cost. If not properlyunderstood and controlled, it can have a signifi-cant impact on all aspects of the gear manufac-turing process. This section will briefly reviewthe following heat treating processing steps:prehardening processes, through hardening andcase hardening processes, applied energy hard-ening, and post-hardening processes. Moredetailed information on these processes can befound in the following chapters:

• Chapter 8, “Through Hardening”• Chapter 9, “Carburizing”• Chapter 10, “Nitriding”• Chapter 11, “Carbonitriding”• Chapter 12, “Induction and Flame Harden-

ing”

Prehardening Processes

Several heat treatments are normally per-formed during the gear manufacturing processto prepare the part for the intended manufactur-ing steps. These are essential to the manufactureof a quality gear.

Annealing consists of heating to and hold-ing at a suitable temperature followed by cool-ing at an appropriate rate, primarily intended tosoften the part and improve its machinability.Supercritical or full annealing involves heatinga part above the upper critical temperature(Ac3), that is the temperature at which austenitebegins to transform to ferrite during cooling,and then slowly cooling in the furnace to around315 °C (600 °F). Intercritical annealing in-volves heating the part to a temperature abovethe final transformation temperature (Ac1), thetemperature at which austenite begins to formduring heating. Subcritical annealing heats thepart to just below the Ac1 point followed by aslow cool in the furnace. The rate of softening


increases rapidly as the annealing temperatureapproaches the Ac1 point.

Normalizing involves heating the partabove the upper critical temperature and then aircooling outside the furnace to relieve residualstresses in a gear blank and for dimensional sta-bility. Normalizing is often considered fromboth a thermal and microstructural standpoint.In the thermal sense, normalizing is austenitiz-ing followed by cooling in still or slightly agi-tated air or nitrogen. In a microstructural sense,normalizing produces a more homogenousstructure. A normalized part is very machinablebut harder than an annealed part. Normalizingalso plays a significant role in the control ofdimensional variation during carburizing.

Stress relieving involves heating to a tem-perature below the lower transformation temper-ature, as in tempering, holding long enough to re-duce residual stress and cooling slowly enough,usually in air, to minimize the development ofnew residual stresses. Stress relief heat treating isused to relieve internal stresses locked in the gearas a consequence of a manufacturing step.

Through Hardening and Case Hardening

Various heat treatment processes are designedto increase gear hardness. These usually involveheating and cooling and are typically classifiedas through hardening, case hardening, and hard-ening by applied energy which will be discussedseparately in a subsequent section.

Through or direct hardening refers to heattreatment methods, which do not produce a case.Examples of commonly through hardened gearsteels are AISI 1045, 4130, 4140, 4145, 4340,and 8640. It is important to note that hardnessuniformity should not be assumed throughoutthe gear tooth. Since the outside of a gear iscooled faster than the inside, there will be a hard-ness gradient developed. The final hardness isdependent on the amount of carbon in the steel;the depth of hardness depends on the hardenabil-ity of the steel as well as the quench severity.

Through hardening can be performed eitherbefore or after the gear teeth are cut. When gearteeth will be cut after the part has been hardened,surface hardness and machinability becomeimportant factors especially in light of the factthat machining will remove some or most of thehigher hardness material at the surface. The hard-ness is achieved by heating the material into the

austenitic range, typically 815 to 875 °C (1500 to1600 °F), followed by quenching and tempering.

Case hardening produces a hard, wearresistant case or surface layer on top of a ductile,shock resistant interior, or core. The idea behindcase hardening is to keep the core of the geartooth at a level around 30 to 40 HRC to avoidtooth breakage while hardening the outer sur-face to increase pitting resistance. The higherthe surface hardness value, the greater the pit-ting resistance. Bending strength increases forsurface hardness up to about 50 HRC, afterwhich the increase in bending strength is offsetby an increase in notch sensitivity.

Carburizing is the most common of thecase hardening methods. A properly carburizedgear will be able to handle between 30% to 50%more load than a through hardened gear. Car-burizing steels are typically alloy steels withapproximately 0.10% to 0.20% carbon. Exam-ples of commonly carburized gear steels includeAISI 1018, 4320, 5120, 8620, and 9310 as wellas international grades such as 20MnCr5,16MnCr5, ZF-7B, 20MoCr4, and V2525.

Carburizing can be performed in the tempera-ture range of 800 to 1090 °C (1475 to 2000 °F).Common industry practice today finds the ma-jority of carburizing operations taking place at870 to 1010 °C (1600 to 1850 °F). Carburizingcase depths can vary over a broad range, 0.13 to8.25 mm (0.005 to 0.325 in.) being typical. How-ever, it is common to use the carbonitridingprocess for case depths below 0.4 mm (0.015 in.).

Carbonitriding is a modification of the car-burizing process, not a form of nitriding. Thismodification consists of introducing ammoniainto the carburizing atmosphere to add nitrogento the carburized case as it is being produced.Examples of gear steels that are commonly car-bonitrided include AISI 1018, 1117, and 12L14.

Typically, carbonitriding is done at a lowertemperature than carburizing, or between 700 to900 °C (1300 to 1650 °F), and for a shorter time.Because nitrogen inhibits the diffusion of car-bon, what generally results is a shallower casethan is typical for carburized parts. A carboni-trided case is usually between 0.075 to 0.75 mm(0.003 to 0.030 in.) deep.

Nitriding is another surface treatment pro-cess that increases surface hardness. Since rapidquenching is not required, dimensional changesare kept to a minimum, which is a major advan-tage. It is not suitable for all gear materials. Oneof its limitations is the extremely high surfacehardness or “white layer” produced, which has a


more brittle nature than the surface produced bycarburizing. Despite this, nitriding has proved tobe a viable alternative for numerous applications.Commonly nitrided gear steels include AISI4140, 4150, 4340, 7140, 8640, and AMS 6475(Nitralloy N).

Nitriding is typically done in the 495 to 565°C (925 to 1050 °F) range. Three factors that areextremely critical in producing superior andconsistent nitrided cases and predictable dimen-sional change are steel composition, prior struc-ture, and core hardness. Case depth and casehardness properties vary not only with the dura-tion and type of nitriding being performed but are also influenced by these factors. Typi-cally case depths are between 0.20 to 0.65 mm(0.008 to 0.025 in.) and take from 10 to 80 hoursto produce.

ACKNOWLEDGMENT

Portions of this article were adapted from T.J.Krenzer and J.W. Coniglio, Gear Manufacture,

Machining, Vol 16, ASM Handbook, ASMInternational, 1989, p 330–355

REFERENCES

1. Gear Nomenclature, Definitions of Termswith Symbols, ANSI/AGMA 1012-F90,American Gear Manufacturerers Associa-tion, 1990

2. L.E. Alban, Systematic Analysis of GearFailures, American Society for Metals,1985

3. F.J. Otto and D.H. Herring, Gear HeatTreatment: Part I, Heat Treating Progress,June 2002, p 55–59

4. D.W. Dudley, Handbook of Practical GearDesign, McGraw Hill Book Company,1984

5. D.P. Townsend, Ed., Dudley’s Gear Hand-book: The Design, Manufacture, and Ap-plication of Gears, 2nd ed., McGraw Hill,Inc., 1991

CHAPTER 2

Gear Tribology and Lubrication

GEAR PERFORMANCE is profoundlyinfluenced by tribology, which can be defined asthe science and technology of interacting sur-faces in relative motion, or, alternatively, thescience and technology of friction, lubrication,and wear. This chapter reviews current knowl-edge of the field of gear tribology and isintended for both gear designers and gear oper-ators. Gear tooth failure modes are discussedwith emphasis on lubrication-related failures.Equations for calculating lubricant film thick-ness which determines whether the gears oper-ate in the boundary, elastohydrodynamic, orfull-film lubrication range are given. Also givenis an equation for Blok’s flash temperature,which is used for predicting the risk of scuffing.In addition, recommendations for lubricantselection, viscosity, and method of applicationare discussed. Finally, a case history demon-strates how the tribological principles discussedin the chapter can be applied in a practical man-ner to avoid gear failure. Table 1 lists thenomenclature used in this chapter and the unitsrequired to calculate Eq 1 to 24.

Gear Tribology

Because gears are such common machinecomponents, they may be taken for granted. It isnot generally appreciated that they are complexsystems requiring knowledge from all the engi-neering disciplines for their successful design.Gear design is a process of synthesis in whichgear geometry, materials, heat treatment, manu-facturing methods, and lubrication are selected tomeet the requirements of a given application.The designer must design the gearset with ade-quate strength, wear resistance, and scuffingresistance. To do this, he or she must considergear tribology. The choice of lubricant and its ap-

plication method is as important as the choice ofsteel alloy and heat treatment. The interrelation-ship of the following factors must be considered:

• Gear tooth geometry• Gear tooth motion (kinematics)• Gear tooth forces (static and dynamic)• Gear tooth material and surface characteris-

tics (physical and chemical)• Lubricant characteristics (physical and

chemical)• Environmental characteristics (physical and

chemical)

Lubrication Regimes

Throughout this chapter a number of differenttypes of lubrication regimes are discussed.Lubrication regimes are the ranges of operatingconditions for lubricated tribological systemsthat can be distinguished by their frictional char-acteristics and/or by the manner and amount ofseparation of the contacting surfaces (Fig. 1). Abrief review of the various types of lubricationregimes is discussed below. More detailed infor-mation on this subject can be found in the article“Lubrication Regimes” in Friction, Lubrication,and Wear Technology, Vol 18, of the ASM Hand-book (see pages 89 to 97).

Terminology. When two surfaces are incontact with each other, the load is carried bymany high points, or asperities, on the surfaces.During sliding, the total tangential forcerequired to shear these asperity junctions is usu-ally high, causing unacceptable friction, wear,and surface damage. To reduce the frictionalforce and thus allow easier sliding, a lubricant isdeliberately introduced to separate the asperitieseither totally or partially (Fig. 1).

The use of liquid or gas lubricants is known asfluid-film lubrication. Full-film lubrication, also




Fig. 1 Schematic showing three lubrication regimes

Symbol Description Units Symbol Description Units

BM Thermal contact coefficient lbf/(in. · s0.5 · °F) WNr Normal operating load lbfbH Semiwidth of Hertzian contact band in. wNr Normal unit load lbf/in.c Constant (see Table 5) hp/(gal/min) X

w Welding factor . . .cM Specific heat per unit mass lbf · in./[lb · °F] X

Γ Load sharing factor . . .d Operating pitch diameter of pinion in. α Pressure-viscosity coefficient in.2/lbfE1 Modulus of elasticity of pinion lbf/in.2 λ Specific film thickness . . .E2 Modulus of elasticity of gear lbf/in.2 λmin Minimum specific film thickness . . .Er Reduced modulus of elasticity lbf/in.2 λM Heat conductivity lbf/[s · °F]hmin Minimum film thickness in. μm Mean coefficient of friction . . .Lmin Minimum contact length in. μ0 Absolute viscosity reyns (lbf · s/in.2)n Pinion speed rev/min ν1 Poisson’s ratio of pinion . . .P Transmitted power hp ν2 Poisson’s ratio of gear . . .q Oil flow rate gal/min ν40 Kinematic viscosity at 40 °C (105 °F) cStS Average root-mean-square (rms)

surface roughnessmin. ρ1

ρ2

Transverse radius of curvature of pinionTransverse radius of curvature of gear

in.in.

Tb Bulk temperature °F ρM Density lb/in.3Tbtest

Bulk temperature of test gears °F ρn Normal relative radius of curvature in.Tc

Tf

Contact temperatureFlash temperature

°F°F

σ Root-mean-square composite surface roughness

μin.

TftestMaximum flash temperature

of test gears°F σ

1 Root-mean-square surface roughness of pinion

μin.

Ts

VScuffing temperatureOperating pitch line velocity

°Fft/min

σ2 Root-mean-square surface roughness

of gearμin.

Ve Entraining velocity in./s ψb Base helix angle degreesω1 Angular velocity of pinion rad/sω2 Angular velocity of gear rad/s rad/s

Table 1 Nomenclature and units of measure used in this chapter to discuss friction, lubrication, and wear of gears

Vr1 Rolling velocity of pinion in./sVr2 Rolling velocity of gear in./s

known as thick-film lubrication, refers to thetotal separation of asperities by a lubricant filmthickness many times larger than the size of thelubricant molecules. If this condition exists onlypartially—that is, if part of the load is carried bythe fluid pressure and the rest is borne by con-tacting asperities separated by a molecularly thinlubricant film—the term thin-film lubrication isused. In the most severe form of thin-film lubri-cation, the entire load is carried by asperitieslubricated by surface films of molecularly thinliquids, gases, or solids; this condition is known

as boundary lubrication. The exclusive use ofsolid lubricants is called solid lubrication.

For highly loaded contacts, lubricant pressurecan cause elastic deformation of the surfacesthat is on the same order as the lubricant filmthickness. When this occurs, the influence of de-formation on lubrication performance becomesa significant parameter. Contacts operatingunder this condition are in the regime of elasto-hydrodynamic lubrication.

Lubricated contacts such as gear teeth androlling bearings have surface deformation com-

Chapter 2: Gear Tribology and Lubrication / 21

Table 2 Basic failure modes of gear teethNonlubrication-related failures Lubrication-related failures

Overload Bending fatigue Hertzian fatigue Wear Scuffing

Brittle fractureDuctile fracture

Low-cycle fatigue (≤1000cycles to failure)

PittingInitial

AdhesionNormal

ScoringGalling

Plastic deformationCold flow

SuperficialDestructive

Running-inMild

SeizingWelding

Hot flow Spalling Moderate SmearingIndentation Micropitting Severe Initial

Rolling Frosting Excessive ModerateBruising Gray staining Abrasion DestructivePeening Peeling ScoringBrinelling

Rippling (fish scaling)Ridging

Subcase fatigue (casecrushing)Plowing

ScratchingCuttingPlowing

Bending (yielding)CorrosionFretting corrosionElectrical discharge damagePolishing (burnishing)

High-cycle fatigue (>1000cycles to failure)

Tip-to-root interferenceGouging

parable to or exceeding the lubricant film thick-ness. Therefore, elastohydrodynamic (EHD)lubrication is extremely important in determin-ing friction and wear in many mechanical com-ponents and will be emphasized throughout thischapter (see, for example, the section “Elasto-hydrodynamic Lubrication”).

Classification of Gear Tooth Failure Modes

To obtain optimum minimum-weight gear-sets, the gear designer must be aware of the intri-cate details of many competing modes of failure.Erichello (Ref 1) has classified gear failures intotwo broad groups:

• Nonlubrication-related failure• Lubrication-related failure

As shown in Table 2, nonlubrication-relatedfailures include both overload and bendingfatigue types of failure. Lubrication-related fail-ures, the focal point in this chapter, includeHertzian fatigue, wear, and scuffing. Failuremodes are further discussed in Chapter 13,“Gear Failure Modes and Analysis,” and in Ref2 through 6.

Many gear failures are known by severalnames and qualifying terms, such as initial, mod-erate, destructive, and so on. The term “scoring”has been used in the past in the United States,

while the term “scuffing” is used in Europe todescribe the severe form of adhesive wear thatinvolves the welding and tearing of the surfacesof gear teeth. To agree with current usage, theterm scuffing will be used in this chapter whenreferring to this failure mode. The term scoringimplies scratching, and it will be used to describeabrasive wear rather than scuffing.

Lubrication-Related Failure

This chapter is concerned with gear toothfailures that are influenced by friction, lubrica-tion, and wear. Pitting or scuffing may cause thegear teeth to deteriorate and generate dynamicforces, which in turn cause the gear teeth to failby bending fatigue. In these cases, the bendingfailure is secondary and not directly related tolubrication, whereas pitting or scuffing are theprimary failure modes, and both are definitelyinfluenced by lubrication. The failure analystmust discern the difference between primaryand secondary failure modes because the wrongcorrective action is likely to be recommended ifa secondary failure mode is mistaken for the pri-mary failure mode. For example, increasing thesize of the gear teeth to prevent reoccurrence ofthe above-mentioned bending failure wouldonly make the situation worse by lowering thepitting and scuffing resistance. Godfrey (Ref 7)gives a good description of lubrication-relatedfailure modes.


On the basis of the above considerations, over-load and bending fatigue are judged to be unre-lated to lubrication and are eliminated from fur-ther discussion together with another category,subcase Hertzian fatigue. Although corrosion,fretting-corrosion, cavitation, and electrical dis-charge damage are influenced by lubrication,they will not be discussed in this chapter becausethese failure modes occur relatively rarely in gearteeth. Hence, only the following failure modesare discussed in this chapter:

• Hertzian fatigue (including pitting andmicropitting)

• Wear (including adhesion, abrasion, andpolishing)

• Scuffing

Hertzian FatiguePitting and micropitting are two lubrication-

related gear tooth failure modes caused byHertzian fatigue.

Pitting is a common failure mode for gearteeth because they are subjected to high Hertziancontact stresses and many stress cycles. Forexample, through-hardened gears are typicallydesigned to withstand contact stresses ofapproximately 700 MPa (100 ksi), while thecontact stresses on carburized gears may reach2100 MPa (300 ksi). In addition, a given tooth ona pinion that is revolving at 3600 rev/min accu-mulates over 5 × 106 stress cycles every 24 h.

Pitting is a fatigue phenomenon (Ref 8) thatoccurs when a fatigue crack initiates either atthe surface of the gear tooth or at a small depthbelow the surface. The crack usually propagatesfor a short distance in a direction roughly paral-lel to the tooth surface before turning or branch-ing to the surface. When the cracks have grownto the extent that they separate a piece of the sur-face material, a pit is formed. If several pitsgrow together, the resulting larger pit is oftenreferred to as a “spall.” There is no endurancelimit for Hertzian fatigue, and pitting occurseven at low stresses if the gears are operatedlong enough. Because there is no endurancelimit, gear teeth must be designed for a suitablefinite lifetime.

To extend the pitting life of a gearset, thedesigner must keep the contact stress low andthe material strength and lubricant specific filmthickness high. There are several geometric va-riables, such as diameter, face width, number ofteeth, pressure angle, and so on, that can be opti-mized to lower the contact stress. Steels andheat treatment are selected to obtain hard tooth

surfaces with high strength. Maximum pittingresistance is obtained with carburized gear teethbecause they have hard surfaces, and carburiz-ing induces beneficial compressive residualstresses that effectively lower the load stresses.The drawbacks to using carburized gear teethare that they are relatively expensive to produceand that they must be finished by grinding. Thedetails for obtaining high lubricant specific filmthickness will be explained later when EHDlubrication is discussed, but general recommen-dations are to use an adequate supply of cool,clean, and dry lubricant that has adequate vis-cosity and a high pressure-viscosity coefficient.

Pitting may initiate at the surface or at a sub-surface defect, such as a nonmetallic inclusion.With gear teeth, pits are most often of the sur-face-initiated type because the lubricant filmthickness is usually low, resulting in relativelyhigh metal-to-metal contact. The interactionbetween asperities or contacts at defects, such as nicks or furrows, creates surface-initiated,rather than subsurface-initiated cracks. For high-speed gears with smooth surface finishes, thefilm thickness is greater and subsurface-initiatedpitting, rather than surface-initiated, may pre-dominate. In these cases, pitting usually starts ata subsurface inclusion, which acts as a point ofstress concentration. Cleaner steels, such asthose produced by vacuum melting, prolong thepitting life by reducing the number of inclusions.

Contamination from water in the lubricant isbelieved to promote pitting through hydrogenembrittlement of the metal, and abrasive parti-cles in the lubricant cause pitting by indentingthe tooth surfaces, causing stress concentra-tions, and disrupting the lubricant film. At pres-ent, the influence of lubricant additives on pit-ting is unresolved.

Prevention of Pitting. The following rec-ommendations serve as guidelines for prevent-ing the onset of pitting in gearsets:

• Reduce contact stresses by reducing loads oroptimizing gear geometry

• Use clean steel, properly heat treated to highhardness, preferably by carburizing

• Use smooth tooth surfaces produced bycareful grinding or honing

• Use an adequate amount of cool, clean, anddry lubricant of adequate viscosity

Micropitting. On relatively soft gear toothsurfaces; such as those of through-hardenedgears, Hertzian fatigue forms large pits withdimensions on the order of millimeters. With


surface-hardened gears (for example, carbur-ized, nitrided, induction hardened, and flamehardened), pitting may occur on a much smallerscale, typically only 10 mm (400 min.) deep. Tothe naked eye, the areas where micropitting hasoccurred appear frosted, and “frosting” is a pop-ular term for micropitting. Japanese researchers(Ref 9) have referred to the failure mode as“gray staining” because the light-scatteringproperties of micropitting give the gear teeth agray appearance. With scanning electronmicroscopy (SEM), it is immediately evidentthat micropitting proceeds by the same fatigueprocess as classical pitting, except the pits areextremely small.

In many cases, micropitting is not destructiveto the gear tooth surface. It sometimes occursonly in patches and may stop after the tribolog-ical conditions have been improved by running-in. The micropits may actually be removed bymild polishing wear during running-in, in whichcase the micropitting is said to “heal.” However,there have been examples (Ref 9–11) wheremicropitting has escalated into full-scale pit-ting, leading to the destruction of the gear teeth.

The specific film thickness is the most impor-tant parameter that influences micropitting.Damage seems to occur most readily on gearteeth with rough surfaces, especially when theyare lubricated with low-viscosity lubricants.Gears finished with special grinding wheels to amirrorlike finish (Ref 12) have effectively elim-inated micropitting. Slow-speed gears are proneto micropitting because their film thickness islow.

Prevention of Micropitting. To preventmicropitting, the specific film thickness shouldbe maximized by using smooth gear tooth sur-faces, high-viscosity lubricants, and highspeeds. Experiments (Ref 10) have shown thatflame-hardened and induction-hardened gearshave less resistance to micropitting than car-burized gears of the same hardness. This isprobably due to the lower carbon content of the surface layers of the flame-hardened andinduction-hardened gears.

The following recommendations serve asguidelines for preventing the onset of micropit-ting in gearsets:


• Use an adequate amount of cool, clean, anddry lubricant of the highest viscosity per-missible

• Use high speeds if possible

• Use carburized steel with proper carboncontent in the surface layers

WearGearsets are susceptible to wear caused by

adhesion, abrasion, and polishing.Adhesion. Adhesive wear is classified as

“mild” if it is confined to the oxide layers of thegear tooth surfaces. If, however, the oxide lay-ers are disrupted and bare metal is exposed, thetransition to severe adhesive wear usuallyoccurs. Severe adhesive wear is termed scuffingand will be discussed in the section “Scuffing”in this chapter. Here we assume that scuffinghas been avoided through proper design of thegears, selection of the lubricant, and control ofthe running-in process.

When new gear units are first operated, thecontact between the gear teeth is not optimumbecause of unavoidable manufacturing inaccu-racies. If the tribological conditions are favor-able, mild adhesive wear occurs during running-in and usually subsides with time, resulting in asatisfactory lifetime for the gears. The wear thatoccurs during running-in is beneficial if itsmooths the tooth surfaces (thereby increasingthe specific film thickness) and if it increases thearea of contact by removing minor imperfec-tions through local wear. To ensure that thewear rate remains under control, new gearsetsshould be run-in by being operated for at leastthe first ten hours at one-half load.

The amount of wear considered tolerabledepends on the expected lifetime for the gearsand requirements for control of noise and vibra-tion. Wear is considered excessive when thetooth profiles wear to the extent that highdynamic loads occur or the tooth thickness isreduced to the extent that bending fatiguebecomes possible.

Many gears, because of practical limits onlubricant viscosity, speed, and temperature,must operate under boundary-lubricated condi-tions in which some wear is inevitable. Highlyloaded, slow speed (<30 m/min, or 100 ft/min),boundary-lubricated gears are especially proneto excessive wear. Tests with slow-speed gears(Ref 10) have shown that nitrided gears havegood wear resistance, whereas carburized andthrough-hardened gears have similar but lowerwear resistance. Winter and Weiss (Ref 10) con-cluded that lubricant viscosity has the greatesteffect on slow-speed adhesive wear, and thathigh-viscosity lubricants reduce the wear ratesignificantly. Winter and Weiss (Ref 10) also


found that sulfur-phosphorus additives can bedetrimental with slow-speed (<3 m/min, or 10ft/min) gears, giving very high wear rates.

A few gear units operate under ideal condi-tions with smooth tooth surfaces, high pitch linespeed, and high lubricant film thickness. Forexample, turbine gears that operated almostcontinuously at 9000 m/min (30,000 ft/min)pitch line speed still had the original machiningmarks on their teeth, even after operating for 20years. Most gears, however, operate betweenthe boundary and full-film lubrication regimes,under EHD conditions. In the EHD regime, withthe proper type and viscosity of lubricant, thewear rate usually reduces during running-in andadhesive wear virtually ceases once running-inis completed. If the lubricant is properly main-tained (cool, clean, and dry), the gearset shouldnot suffer an adhesive wear failure.

Prevention of Adhesive Wear. The fol-lowing recommendations serve as guidelinesfor preventing the onset of adhesive wear ingearsets:

• Use smooth tooth surfaces• If possible, run-in new gearsets by operating

the first 10 hours at one-half load• Use high speeds if possible. Otherwise, rec-

ognize that highly loaded slow-speed gearsare boundary lubricated and are especiallyprone to excessive wear. For these condi-tions, specify nitrided gears and the highestpermissible lubricant viscosity

• For very slow-speed gears (<3 m/min, or 10ft/min), avoid using lubricants with sulfur-phosphorus additives

• Use an adequate amount of cool, clean, anddry lubricant of the highest viscosity per-missible

Abrasion. Abrasive wear on gear teeth isusually caused by contamination of the lubri-cant by hard, sharp-edged particles. Contamina-tion enters gearboxes by being built-in, inter-nally generated, ingested through breathers andseals, or inadvertently added during mainte-nance.

Many gear manufacturers do not fully appre-ciate the significance of clean assembly; it is notuncommon to find sand, machining chips,grinding dust, weld splatter, or other debris innew gearboxes. To remove built-in contamina-tion, the gearbox lubricant should be drainedand flushed before start-up and again after thefirst 50 h of operation, refilled with the recom-

mended lubricant, and a new oil filter should beinstalled.

Internally generated particles are usuallywear debris from gears or bearings due to Hertz-ian fatigue pitting or adhesive and abrasivewear. The wear particles are especially abrasivebecause they become work-hardened when theyare trapped between the gear teeth. Internallygenerated wear debris can be minimized byusing accurate surface-hardened gear teeth(with high pitting resistance), smooth surfaces,and high-viscosity lubricants.

Breather vents are used on gearboxes to ventinternal pressure, which may occur when airenters through seals, or when air within thegearbox expands (or contracts) during the nor-mal heating and cooling of the gear unit. Thebreather vent should be located in a clean, non-pressurized area and should have a filter to pre-vent ingress of airborne contaminants. In espe-cially harsh environments, the gearbox can becompletely sealed, and the pressure variationcan be accommodated by an expansion chamberwith a flexible diaphragm.

All maintenance procedures that involveopening any part of the gearbox or lubricationsystem must be carefully performed to preventcontamination of the gearbox system.

Abrasive wear due to foreign contaminants,such as sand or internally generated wear debris,is called three-body abrasion and is a commonoccurrence. Two-body abrasion also occurswhen hard particles or asperities on one geartooth abrade the opposing tooth surface. Unlessthe tooth surfaces of a surface-hardened gear aresmoothly finished, they will act like files if themating gear is appreciably softer. This is thereason that a worm pinion is polished aftergrinding before it is run with a bronze wormwheel. Manufacturers of computer disk driveshave found that stainless steel pinions matedwith anodized aluminum racks have excessivelyhigh wear rates. The anodized layer of the alu-minum rack is extremely thin and brittle, and itbreaks up and impregnates the relatively softstainless steel pinion. The aluminum oxide par-ticles then act like emery paper and wear theteeth of the rack very quickly.

The lubrication system should be carefullymaintained and monitored to ensure that thegears receive an adequate amount of cool, clean,and dry lubricant. For circulating-oil systems,fine filtration removes contamination. Filters asfine as 3 mm (120 min.) have significantlyincreased gear life. For oil bath gearboxes, the


lubricant should be changed frequently toremove contamination. Under normal operatingconditions, the lubricant should be changed atleast every 2500 h of operation or every sixmonths, whichever occurs first. For criticalgearboxes, a regular program of lubricant mon-itoring can help prevent gear failures by show-ing when maintenance is required. The lubricantmonitoring should include spectrographic andferrographic analysis of contamination, alongwith analysis of acid number, viscosity, andwater content.

Prevention of Abrasive Wear. The fol-lowing guidelines should be observed to pre-vent abrasive wear in gearsets:

• Remove built-in contamination from newgearboxes by draining and flushing thelubricant before start-up and again after thefirst 50 h of operation. Refill with the rec-ommended lubricant and install a new filter

• Minimize internally generated wear debrisby using surface-hardened gear teeth,smooth tooth surfaces, and high-viscositylubricants

• Minimize ingested contamination by main-taining oil-tight seals and using filteredbreather vents located in clean, nonpressur-ized areas

• Minimize contamination that is added dur-ing maintenance by using good housekeep-ing procedures

• For circulating-oil systems, use fine filtra-tion

• For oil bath systems, change the lubricant atleast every 2500 h or every six months

• Monitor the lubricant with spectrographicand ferrographic analysis together withanalysis of acid number, viscosity, andwater content

Polishing Wear. If the extreme-pressure(EP) antiscuff additives in the lubricant are toochemically reactive, they may cause polishingof the gear tooth surfaces until they attain abright mirror finish. Although the polished gearteeth may look good, polishing wear is undesir-able because it generally reduces gear accuracyby wearing the tooth profiles away from theirideal form. Antiscuff additives used in lubri-cants to prevent scuffing, such as sulfur andphosphorus, will be covered when scuffing isdiscussed. They function by forming iron-sul-fide and iron-phosphate films on areas of thegear teeth where high temperatures occur. Ide-ally, the additives should react only at tempera-

tures where there is a danger of welding. If therate of reaction is too high, and there is a con-tinuous removal of the surface films caused byvery fine abrasives in the lubricant, the polish-ing wear may be excessive (Ref 13).

Prevention of Polishing Wear. Polishingwear can be prevented by using less chemicallyactive additives. As an alternative to sulfur-phosphorus additives, antiscuff lubricants areavailable with dispersions of potassium borate(Ref 14) that deposit EP films without chemi-cally reacting with the metal. Removing theabrasives in the lubricant by using fine filtrationor frequent oil changes is helpful.

In summary, the following guidelines shouldbe observed to prevent polishing wear ingearsets:

• Use less chemically active antiscuff addi-tives (for example, borate)

• Remove abrasives from the lubricant byusing fine filtration or frequent oil changes

ScuffingScuffing is defined as localized damage

caused by solid-phase welding between slidingsurfaces. It is accompanied by the transfer ofmetal from one surface to another due to weldingand tearing. It may occur in any sliding androlling contact where the oil film is not thickenough to separate the surfaces. The symptomsof scuffing are microscopically rough, matte,and torn surfaces. Surface analysis that showstransfer of metal from one surface to the other isproof of scuffing.

Scuffing can occur in gear teeth when theyoperate in the boundary lubrication regime. Ifthe lubricant film is insufficient to prevent sig-nificant metal-to-metal contact, the oxide layersthat normally protect the gear tooth surfacesmay be broken through, and the bare metal sur-faces may weld together. The sliding that occursbetween gear teeth results in tearing of thewelded junctions, metal transfer, and cata-strophic damage.

In contrast to pitting and bending fatigue,which only occur after a period of running time,scuffing may occur immediately upon start-up.In fact, gears are most vulnerable to scuffingwhen they are new and their tooth surfaces havenot yet been smoothed by running-in. For thisreason, it is wise to run-in a new gearbox underone-half load for at least 10 h to reduce the sur-face roughness of the teeth before applying fullload. The gear teeth can be coated with iron-


manganese phosphate or plated with copper orsilver to protect them from scuffing during thecritical running-in period.

The basic mechanism of scuffing is notclearly understood, but by general agreement itis believed to be caused by intense frictionalheating generated by the combination of highsliding velocity and intense surface pressure.Blok’s (Ref 15) critical temperature theory isbelieved to be the best criterion for predictingscuffing. It states that scuffing will occur in gearteeth that are sliding under boundary-lubricatedconditions when the maximum contact temper-ature of the gear teeth reaches a critical magni-tude. For mineral oils without antiscuff/EPadditives, each combination of oil and rubbingmaterials has a critical scuffing temperature thatis constant, regardless of the operating condi-tions (Ref 16). The critical scuffing tempera-tures are not constant for synthetic lubricantsand lubricants with antiscuff additives; theymust be determined from tests that closely sim-ulate the operating conditions of the gears.

Today, most antiscuff additives are sulfur-phosphorus compounds, which form boundary-lubricating films by chemically reacting with themetal surfaces of the gear teeth at local points ofhigh temperature. Antiscuff films help preventscuffing by forming solid films on the gear toothsurfaces and inhibiting true metal-to-metal con-tact. The films of iron sulfide and iron phosphatehave high melting points, allowing them toremain as solids on the gear tooth surfaces even athigh contact temperatures. The rate of reaction ofthe antiscuff additives is greatest where the geartooth contact temperatures are highest. Becauseof the rubbing action of the gear teeth, the surfacefilms are repeatedly scraped off and reformed. Ineffect, scuffing is prevented by substituting mildcorrosion in its place. Occasionally, antiscuffadditives (for example, sulfur) are too chemi-cally active, causing polishing wear and necessi-tating a change to less aggressive additives.Lubricants with antiscuff additives of potassiumborate do not cause polishing wear because theydeposit glasslike boundary films without react-ing with the metal.

For mineral oils without antiscuff additives,the critical scuffing temperature increases withincreasing viscosity and ranges from 150 to 300°C (300 to 570 °F). The increased scuffing resis-tance of high-viscosity lubricants is believed tobe due to differences in chemical compositionrather than increases in viscosity. However, a

viscosity increase also helps to reduce the riskof scuffing by increasing the lubricant filmthickness and reducing the contact temperaturegenerated by metal-to-metal contact.

Scuffing is controlled by the total contacttemperature, Tc, which consists of the sum ofthe gear bulk temperature, Tb, and the flash tem-perature, Tf:

(Eq 1)

The bulk temperature is the equilibrium tem-perature of the surface of the gear teeth beforethey enter the meshing zone. The flash tempera-ture is the local and instantaneous temperaturerise that occurs on the gear teeth due to the fric-tional heating as they pass through the meshingzone.

Anything that reduces either the bulk tempera-ture or the flash temperature will reduce the totalcontact temperature and lessen the risk of scuf-fing. Higher viscosity lubricants or smoothertooth surfaces help by increasing the specific filmthickness, which in turn reduces the frictionalheat and, therefore, the flash temperature. Also,the lubricant performs the important function ofremoving heat from the gear teeth. The lubricantmust be supplied to the gear teeth in such a waythat it removes heat rapidly and maintains a lowbulk temperature. A heat exchanger can be usedwith a circulating-oil system to cool the lubricantbefore it is sprayed at the gears.

Prevention of Scuffing. The gear designercan maximize scuffing resistance by optimizingthe gear geometry so that the gear teeth are assmall as possible, consistent with bendingstrength requirements, to reduce the tempera-ture rise caused by sliding. Figure 2 shows thatthe rolling velocity of the pinion, Vr1, and therolling velocity of the gear, Vr2, linearly increasefrom zero at the interference points to a maxi-mum at each end of the path of contact. Thesliding velocity is represented by the distancebetween the Vr1 and Vr2 lines. The amount ofsliding is proportional to the distance from thepitch point, P, and is zero when the gear teethcontact at the pitch point, and largest at the endsof the path. Addendum modification can beused to balance and minimize the temperaturerise that occurs in the addendum and dedendumof the gear teeth. The temperature rise may alsobe reduced by modifying the tooth profiles withslight tip and/or root relief to ease the load at thestart and end of the engagement path where thesliding velocities are the greatest. Also, the gear

Tc � Tb � Tf


Fig. 3 Regions of elastohydrodynamic contact between themating gear teeth of a gearset. (a) Schematic showing

three distinct regions on pinion and gear tooth surfaces and keyparameters determining oil film lubrication. (b) Plot of pressuredistribution within contact zone. bH, semiwidth of Hertzian contact band; h0, central film thickness; hmin, minimum filmthickness

Fig. 2 Graphical representation of rolling velocities of pinion(Vr1) and gear (Vr2) in relation to sliding velocity

teeth must be accurate and held rigidly in goodalignment to minimize tooth loading and, there-fore, the temperature rise.

Gear materials should be chosen with theirscuffing resistance in mind. Nitrided steels,such as Nitralloy 135M, are generally found tohave the highest resistance to scuffing, whereasstainless steels are liable to scuff even undernear-zero loads. The thin oxide layer on stain-less steel is hard and brittle and breaks up easilyunder sliding loads, exposing the bare metal andthus promoting scuffing. Like stainless steel,anodized aluminum has a low scuffing resis-tance. Hardness does not seem to be a reliableindication of scuffing resistance.

In summary, the following guidelines shouldbe observed to prevent scuffing in gearsets:


• Protect the gear teeth during the critical run-ning-in period by coating them with iron-manganese phosphate or plating them withcopper or silver. Run-in new gearsets byoperating the first 10 h at one-half load

• Use high-viscosity lubricants with antiscuffadditives, such as sulfur, phosphorus, orborate

• Cool the gear teeth by supplying an adequateamount of cool lubricant. For circulating-oilsystems, use a heat exchanger to cool thelubricant

• Optimize the gear tooth geometry by usingsmall teeth, addendum modification, andprofile modification

• Use accurate gear teeth, rigid gear mount-ings, and good helix alignment

• Use nitrided steels for maximum scuffingresistance. Do not use stainless steel or alu-minum for gears if there is a risk of scuffing

Elastohydrodynamic Lubrication

Gear teeth are subjected to enormous contactpressures on the order of the ultimate tensilestrength of hardened steel, yet they are quite suc-cessfully lubricated with oil films that are <1 mm(<40 min.) thick. This is possible because lubri-cants have a fortuitous property that causes theirviscosity to increase dramatically with increasedpressure. Figure 3 depicts the region of contactbetween mating gear teeth. It shows the shape ofthe elastically deformed teeth and the pressuredistribution developed within the contact zone.


The molecular adsorption of the lubricant ontothe gear tooth surfaces causes it to be draggedinto the inlet region of the contact, where its pres-sure is increased due to the convergence of thetooth surfaces. The viscosity increase of thelubricant caused by the increasing pressure helpsto entrain the lubricant into the contact zone.Once it is within the high-pressure Hertzianregion of the contact, the lubricant cannot escapebecause its viscosity has increased to the extentwhere the lubricant is virtually a rigid solid.

The following equation, from Dowson andHigginson (Ref 17) gives the minimum filmthickness that occurs near the exit of the contact.The minimum film thickness, hmin, is obtainedfrom:

(Eq 2)

where a is the pressure-viscosity coefficient(in.2/lbf), m0 is the absolute viscosity (reyns, orlbf · s/in.2), and Ve is the entraining velocity, inwhich:

(Eq 3)

where Vr1 and Vr2 are the rolling velocities ofpinion and gear, respectively, given by:

(Eq 4a)

(Eq 4b)

in which w1 and w2 are the angular velocities ofpinion and gear, respectively, and r1 and r2 arethe transverse radii of curvature of the pinionand gear, respectively.

The normal relative radius of curvature, rn, isgiven by:

(Eq 5)

where yb is the base helix angle. Referring backto Eq 2, XG is the load-sharing factor, and wNr isthe normal unit load given by:

(Eq 6)

in which WNr is the normal operating load andLmin is the minimum contact length.

Er is the reduced modulus of elasticity, givenby:

(Eq 7)Er � 2 a 1 � n21

E1�

1 � n22

E2b�1

wNr �WNr

Lmin

rn �r1r2

1r2 ; r1 2cos yb

Vr2 � w1 r2

Vr1 � �1 r2

Ve � Vr1 � Vr2

hmin �1.63a0.54 1m0Ve 2 0.7 r0.43

n

1XGwNr 2 0.13 E 0.03r

where n1 is the Poisson’s ratio of pinion, n2 isthe Poisson’s ratio of gear, E1 is the modulus ofelasticity of pinion, and E2 is the modulus ofelasticity of gear.

Figure 4 gives average values of absolute vis-cosity, m0, versus bulk temperature for typicalmineral gear lubricants with a viscosity index of 95.

The pressure-viscosity coefficient, a, rangesfrom 0.5 × 10–4 to 2 × 10–4 in.2/lbf for typicalgear lubricants. Data for pressure-viscositycoefficients versus bulk temperature for typicalgear lubricants are given in Fig 5.

The specific film thickness, λ, is given by:

(Eq 8)

where hmin is the minimum film thickness and sis the composite surface roughness given by:

(Eq 9)

in which s1 is the root-mean-square (rms) sur-face roughness of the pinion and s2 is the rmssurface roughness of the gear.

Load-Sharing Factor. The load-sharingfactor, XG, accounts for load sharing betweensucceeding pairs of teeth as affected by profilemodification (tip and root relief) and whetherthe pinion or gear is the driver. Figure 6 givesplots of the load-sharing factors for unmodifiedand modified tooth profiles.

As shown by the exponents in Eq 2, the filmthickness is essentially determined by theentraining velocity, lubricant viscosity, andpressure-viscosity coefficient; the elastic prop-erties of the gear teeth and the load have rela-tively small influences. In effect, the relativelyhigh stiffness of the oil film makes it insensitiveto load, and an increase in load simply increasesthe elastic deformation of the tooth surfaces andwidens the contact area, rather than decreasingthe film thickness.

Blok’s contact temperature theory (Ref15) states that scuffing will occur in gear teethwhich are sliding under boundary-lubricatedconditions when the maximum contact temper-ature of the gear teeth reaches a critical magni-tude. The contact temperature is the sum of twocomponents: the bulk temperature and the flashtemperature, as described in Eq 1.

Blok’s flash temperature equation as formu-lated in AGMA 2001-B88, Appendix A (Ref18) for spur and helical gears is:

s � 1s21 � s2

2 2 1>2

l �hmin

s


Fig. 4 Plot of absolute viscosity versus bulk temperature for selected mineral oil gear lubricants having a viscosity index of 95

(Eq 10)

where mm is the mean coefficient of friction, BMis the thermal contact coefficient, and bH is thesemiwidth of the Hertzian contact band.

Mean Coefficient of Friction. The follow-ing equation gives a typical value of 0.06 < mm< 0.18 for the mean coefficient of friction forgears operating in the partial EHD regime (l <1). It may give values too low for boundary-lubricated gears, where mm may be greater than0.2, or too high for gears in the full-film regime(l > 2), where mm may be less than 0.01:

(Eq 11a)

where:

(Eq 11b)

in which S is the average rms surface roughnessgiven by:

a 50

50 � Sb � 3.0

mm � 0.06 a 50

50 � Sb

Tf �0.8mmX�wNr�1Vr1 2 0.5 � 1Vr2 2 0.5�

BM1bH 2 0.5(Eq 12)

Thermal Contact Coefficient. The ther-mal contact coefficient, BM, is given by:

(Eq 13)

where lM is the heat conductivity, rM is the den-sity, and cM is the specific heat per unit mass.For typical gear steels, BM is ~43 lbf/(in. · s0.5 ·°F).

Semiwidth of the Hertzian ContactBand. The semiwidth of the Hertzian contactband, bH, is defined as:

(Eq 14)

Bulk Temperature. The gear bulk tempera-ture, Tb, is the equilibrium bulk temperature ofthe gear teeth before they enter the meshingzone. In some cases, the bulk temperature maybe significantly higher than the temperature ofthe oil supplied to the gear mesh. In a test withultrahigh-speed gears (Ref 19), the pinion bulk

bH � a 8X�wNr rn

pErb 0.5

BM � 1lMrMcM 2 0.5

S �s1 � s2

2


Fig. 5 Plot of pressure-viscosity coefficient versus bulk temperature for selected mineral oil gear lubricants

temperature was 135 °C (275 °F), which is 95°C (171 °F) hotter than the oil inlet temperature.For turbine gears at lower speeds, the bulk tem-perature rise of the gear teeth over the inlet oiltemperature may range from 11 °C (20 °F) at3700 m/min (1.2 × 104 ft/min) pitch line veloc-ity to 22 °C (40 °F) at 4900 m/min (1.6 × 104

ft/min). At similar speeds, the bulk temperaturerise of aircraft gears with less oil flow mayrange from 22 to 33 °C (40 to 60 °F).

Scuffing Temperature. The scuffing tem-perature, Ts, is the contact temperature at whichscuffing is likely to occur with the chosen com-bination of lubricant and gear materials.

For mineral oils without antiscuff additivesor for mineral oils with low concentrations ofantiscuff additives, the scuffing temperature isindependent of the operating conditions for afairly wide range. For these oils, the scuffingtemperature may be correlated with the compo-sition of the oil. The viscosity grade is a con-venient index of the composition and, thus, ofthe scuffing temperature.

For nonantiscuff mineral oils, the mean scuff-ing temperature (50% chance of scuffing) in °Fis given by:

(Eq 15)

where n40 is the kinematic viscosity at 40 °C(105 °F) in centistokes.

For mineral oils with low concentrations ofantiscuff additives, the mean scuffing tempera-ture in °F is given by:

(Eq 16)

The scuffing temperature determined fromForschungsstelle für Zahnräder und Getriebe-bau (FZG, or Technical Institute for the Studyof Gears and Drive Mechanisms) test gears formineral oils without antiscuff additives or withlow concentrations of antiscuff additives maybe extended to different gear steels, heat treat-ments, or surface treatments by introducing anempirical welding factor:

(Eq 17)Ts � Tbtest� XwTftest

Ts � 245 � 59 ln n40

Ts � 146 � 59 ln n40


Table 3 Welding factor for selected gear steelsMaterial Welding factor, XW

Through-hardened steel 1.00Phosphated steel 1.25Copper-plated steel 1.50Nitrided steel 1.50Carburized steel

Content of austenite < average 1.15Content of austenite = average 1.00Content of austenite > average 0.85

Stainless steel 0.45

Source: Ref 18

Table 4 Mean scuffing temperature forsynthetic lubricants typically used for operatingcarburized gears in aerospace applications

Mean scuffing temperature, Ts

Lubricant °C °F

MIL-L-6081 (grade 1005) 129 264MIL-L-7808 205 400MIL-L-23699 220 425DERD2487 225 440DERD2497 240 465DOD-L-85734 260 500Mobil SHC624 280 540Dexron II 290 550

Source: Ref 20

where Xw is the welding factor (see Table 3),Tbtest is the bulk temperature of the test gears,and Tftest is the maximum flash temperature ofthe test gears.

Scuffing temperatures for synthetic lubri-cants typically used with carburized gears in theaerospace industry are shown in Table 4.

For mineral oils with high concentrations ofantiscuff additives (for example, hypoid gearoils), research is still needed to determinewhether the scuffing temperature is dependent onthe materials and operating conditions. Special

attention has to be paid to the correlation betweentest conditions and actual or design conditions.

Lubricant Selection

The choice of lubricant depends on the typeof gearing and enclosure, operating speed andload, ambient temperature, and method of lubri-cant application. Most gears are lubricated withone of the following types:

• Oil• Synthetic lubricant• Grease• Adhesive open-gear lubricant• Solid lubricant

The optimum lubricant for any application is theproduct that is the least expensive, consideringboth initial cost and maintenance costs, andmeets the requirements.

Oil is the most widely used lubricantbecause it is readily distributed to gears andbearings and has both good lubricating andcooling properties. In addition, contaminationmay be readily removed by filtering periodi-cally or draining and replacing the oil. How-ever, it requires an oil-tight enclosure providedwith adequate shaft seals.

Synthetic lubricants are used for applica-tions (for example, aircraft gas turbines) wherethe oil must operate over a wide temperaturerange and have good oxidation stability at hightemperature. Ester and hydrocarbon syntheticlubricants have high viscosity indices, givingthem good fluidity or low viscosities at very lowtemperatures and acceptable viscosities at hightemperatures. The volatility of esters is lowerthan that of mineral oils of the same viscosity,

Fig. 6 Plot of load-sharing factor (XG) versus pinion roll angle. (a) Unmodified tooth profiles. (b) Modified tooth

profiles

Sub intable headis alreadynot italic—SBI


thus reducing oil loss at high temperature.Despite their long service life, the extra cost ofsynthetic lubricants generally cannot be justifiedfor oil-bath systems unless there are extremetemperatures involved, because the oil must bechanged frequently to remove contamination.

Grease is suitable only for low-speed, low-load applications because it does not circulatewell, and it is a relatively poor coolant. Grease-lubricated gears are generally boundary lubri-cated because the grease is either pushed asideor thrown from the gear teeth. Contaminationfrom wear particles or other debris is usuallytrapped in the grease and requires costly main-tenance to eliminate. Grease is often used toavoid leakage from enclosures that are not oiltight. However, if all the factors are considered,it is usually found that an oil lubricant is moreeconomical and reliable than a grease lubricantfor gear lubrication.

Open-gear lubricants are viscous adhesivesemifluids used on large low-speed open gears,such as those used in iron ore and cement mills,antenna drives, bridge drives, cranes, and so on.Gears in these applications run slowly, and theyare therefore boundary lubricated. The lubricantmust bond strongly to resist being thrown off thegear teeth. However, the squeezing and slidingaction of gear teeth tends to push the lubricantinto the roots of the gear teeth where it is rela-tively ineffective. These lubricants are appliedby hand brushing or by automatic systems thatdeliver an intermittent spray. Some open-gearlubricants are thinned with a quick-evaporatingsolvent/diluent to make them easier to apply.Open-gear lubricants share the disadvantages ofgrease lubrication, and they are especially costly(in addition to being messy) to maintain. Forthese reasons, the trend is away from open gearsand toward the use of enclosed oil-lubricatedgearboxes whenever possible.

Solid lubricants, usually in the form ofbonded dry films, are used when the followingconditions are encountered:

• The temperature is too high or too low for anoil or grease

• Leakage cannot be tolerated• The gears must operate in a vacuum

These lubricants are usually molybdenum disul-fide (MoS2) or graphite in an inorganic binder,which is applied to the gear teeth and cured toform a dry film coating. Polytetrafluoroethylene(PTFE) and tungsten disulfide (WS2) coatings

are also used. Solid lubricants are expensive toapply and have limited wear lives. However, inmany applications, such as spacecraft, they arethe only alternative and can provide excellentservice.

Oil Lubricant Applications

Of the above-mentioned lubricants, only oilwill be discussed in greater detail in this chap-ter. Oil should be used as the lubricant unlessthe operating conditions preclude its use. Gen-erally, the simplest and least expensive lubrica-tion system for gears is a totally enclosed oilbath of mineral oil.

Spur, Helical, and Bevel Gears. The lubri-cation requirements of spur, helical, straight-bevel, and spiral-bevel gears are essentially thesame. For this class of gears, the magnitudes ofthe loads and sliding speeds are similar, andrequirements for viscosity and antiscuff proper-ties are virtually identical. Many industrial spurand helical gear units are lubricated with rust andoxidation inhibited (R & O) mineral oils. Thelow-viscosity R & O oils, commonly called tur-bine oils, are used in many high-speed gear unitswhere the gear tooth loads are relatively low.Mineral oils without antiscuff additives are suit-able for high-speed lightly loaded gears wherethe high entraining velocity of the gear teethdevelops thick EHD oil films. In these cases, themost important property of the lubricant is vis-cosity. Antiscuff/EP additives are unnecessarybecause the gear teeth are separated, eliminatingmetal-to-metal contact and the scuffing mode offailure. Slower speed gears, especially carbur-ized gears, tend to be more heavily loaded. Thesegears generally require higher viscosity lubri-cants with antiscuff additives.

Hypoid gears, such as those used for automo-tive axles, are especially prone to scuffingbecause they are heavily loaded and have highsliding velocities. For these reasons, hypoidgear oils have the higher concentrations of anti-scuff additives.

For critical applications, the contact tempera-ture should be calculated with Blok’s equation(see Eq 1) (Ref 15) and compared to the scuff-ing temperature of the lubricant. This quantita-tive method is effective for selecting a lubricantwith adequate scuffing resistance.

Worm gears have high sliding velocity,which generates significant frictional losses.Fortunately, their tooth loads are relatively


light, and they are successfully lubricated withmineral oils that are compounded with lubricityadditives. These oils contain 3 to 10% fatty oil or low-acid tallow. The polar molecules ofthe additive form surface films by physicaladsorption or by reaction with the surface ox-ide to form a metallic soap that acts as a lowshear strength film, improving the “lubricity,”or friction-reducing property.

Selection of Gear Lubricant Viscosity

The recommendations of AGMA 250.04(Ref 21) should be followed when selectinglubricants for enclosed gear drives that operateat pitch line velocities ≤1500 m/min (≤5000ft/min). AGMA 421.06 (Ref 22) should be con-sulted for high-speed drives (>1500 m/min, or5000 ft/min).

Viscosity is one of the most important lubri-cant properties, and the higher the viscosity, thegreater the protection against the various geartooth failures. However, the viscosity must belimited to avoid excessive heat generation andpower loss from churning and shearing of thelubricant by high-speed gears or bearings. Theoperating temperature of the gear drive deter-mines the operating viscosity of the lubricant. Ifthe lubricant is too viscous, excessive heat isgenerated. The heat raises the lubricant temper-ature and reduces its viscosity, reaching a pointof diminishing returns where increasing thestarting viscosity of the lubricant leads to ahigher operating temperature and a higher oxi-dation rate, without a significant gain in operat-ing viscosity.

Gear drives operating in cold climates musthave a lubricant that circulates freely and doesnot cause high starting torques. A candidategear lubricant should have a pour point at least5 °C (9 °F) lower than the expected minimumambient start-up temperature. Typical pourpoints for mineral gear oils are –7 °C (20 °F),whereas synthetic gear lubricants have signifi-cantly lower pour points of about –40 °C (–40°F). Pour point depressants are used to tailorpour points of mineral lubricants for automotivehypoid gears to be as low as –40 °C (–40 °F).

The pitch line speed of the gears is a goodindex of the required viscosity. An empiricalequation for determining required viscosity is:

(Eq 18)n40 �7000

1V 2 0.5

where ν40 is the lubricant kinematic viscosity at40 °C (105 °F) (in cSt) and V is the operatingpitch line velocity (in ft/min) given by:

(Eq 19)

where d is the operating pitch diameter of pinion(in inches) and n is the pinion speed (rev/min).

Caution must be used when using AGMArecommendations for viscosity. For example,there was an application where two gear driveswere considered to be high speed. The pinionspeed was 3625 rev/min, qualifying the gearunits as high-speed gear drives per AGMA421.06. The gear drives were supplied with oilhaving the recommended viscosity (per AGMA421.06) of ISO 68. However, because the pinionwas relatively small, its pitch line velocity wasonly 1000 m/min (3000 ft/min). This qualifiesthe gear drives as slow speed per AGMA250.04, which recommends a viscosity of ISO150. Both gear drives failed within weeks ofstart-up because of pitting fatigue. The empiri-cal equation (Eq 18) for this application gives:

(Eq 20)

This indicates that the viscosity per AGMA421.06 (68 cSt, or 6.8 × 10–5 m2/s) is much toolow, and the viscosity per AGMA 250.04 (150cSt, or 1.5 × 10–4 m2/s) is appropriate. Hence, def-initions of high-speed versus slow-speed geardrives must be carefully considered, and pitchline velocity is generally a better index than shaftspeed. The gear drives were rebuilt with newgearsets and the ISO VG 68 oil was replaced withISO VG 150. The gear drives then operated with-out overheating, and the pitting was eliminated.

For critical applications, the specific filmthickness, λ, should be calculated with Dowsonand Higginson’s equation (see Eq 8) (Ref 16).The specific film thickness is a useful measure ofthe lubrication regime. It can be used with Fig. 7as an approximate guide to the probability ofwear-related surface distress. Figure 7 is basedon the data of Wellauer and Holloway (Ref 23),which were obtained from several hundred labo-ratory tests and field applications of gear drives.

Application of Gear Lubricants

The method of applying the lubricant to thegear teeth depends primarily on the pitch linevelocity.

n40 �7000

13000 2 0.5 � 128 cSt

V � 0.262 d # n


Fig. 7 Probability of wear distress as a function of specific film thickness and pitch line velocity (in ft/min). Source: Ref 18

Splash lubrication systems are the sim-plest, but they are limited to a pitch line veloc-ity of ~1000 m/min (~3000 ft/min). The gearsshould dip into the oil bath for about twice thetooth depth to provide adequate splash for pin-ions and bearings and to reduce losses due tochurning. The gear housing should have troughsto capture the oil flowing down the housingwalls, channeling it to the bearings.

The range of splash lubrication can beextended to ~1500 m/min (~5000 ft/min) byusing baffles and oil pans to reduce churning.However, at velocities >1000 m/min (>3000ft/min), providing auxiliary cooling with fansand improving heat transfer by adding fins to thehousing are usually necessary.

Pressure-Fed Systems. Above 1500 m/min(5000 ft/min), most gears are lubricated by apressure-fed system. For gearboxes withantifriction bearings, spraying the oil at the gearmesh only and relying on splash to lubricate thebearings is permissible up to a maximum pitchline velocity of 2100 m/min (7000 ft/min).Above this speed and for gear drives with jour-nal bearings, both the gears and bearings shouldbe pressure-fed.

The oil jets should be placed on the incomingside of the gear mesh for pitch line velocities≤2600 m/min (≤8000 ft/min). Above 2600m/min (8000 ft/min), more oil is needed forcooling than for lubricating, and the oil flow

removes heat best by being directed at the out-going side of the gear mesh where the oil jetscan strike the hot drive-side of the gear teeth.

For very high-speed gears (Ref 19) (>5300m/min, or 16,000 ft/min), there is a danger thatthe amount of oil carried to the incoming side ofthe gear mesh may be inadequate, and it is pru-dent to add a supplementary flow at the incom-ing side of the gear mesh. Generally, about two-thirds of the oil flow should be supplied to theoutgoing side of the mesh for cooling, and one-third of the flow directed at the incoming sidefor lubrication. The placement of the oil jets is acrucial factor when pitch line velocities are>6100 m/min (>20,000 ft/min). At speeds thishigh, experiments are required to find the opti-mum number and location for the oil jets.

In pressure-fed systems, the followingparameters must be considered to ensure ade-quate lubrication and cooling of the gear mesh:

• Quantity of flow• Jet size• Feed pressure• Number of jets

There are general guidelines, based on experi-ence and experimentation, for specifying theseparameters, but each application must be evalu-ated independently based on its particular oper-ating conditions and requirements.


c, hp/ (gal/min)

Flow conditions Applications

200 Copious General industrial400 Adequate Typical aviation800 Lean Lightweight, high-efficiency aviation

1000 Starved Only for unusual conditions

Table 5 Recommended values of constant cbased on oil flow and gear mesh specifications

An empirical equation used to calculate thequantity of oil flow, q, is:

(Eq 21)

where q is the oil flow rate (in gal/min), P is thetransmitted power (in hp), and c is taken fromTable 5.

For a typical industrial application transmit-ting 150 kW (200 hp), where weight is not crit-ical, the designer might choose a value of c =200 hp/(gal/min), resulting in a copious flow of4 L/min (1 gal/min). On the other hand, for ahigh-efficiency aviation application transmit-ting 150 kW (200 hp), where weight is critical,a value of c = 800 hp/(gal/min) might be chosen,resulting in a lean flow of 1 L/min (0.25gal/min). Some applications may require differ-ent flow rates than those given by Table 5. Forinstance, wide-face, high-speed gearing mayrequire a higher flow rate to ensure uniformcooling and full-face coverage.

The proper jet size, feed pressure, and num-ber of jets must be determined to maintain theproper flow rate, jet velocity, and full-face cov-erage.

Jet Size. The diameter of a jet can be calcu-lated for a given flow rate and pressure based onthe viscosity of the oil at the operating tempera-ture (Ref 24). There are practical limitations onjet size, and the minimum recommended size is0.8 mm (0.03 in.). If a jet smaller than this isused, contaminants in the oil may clog it. Typi-cal jet diameters range from 0.8 to 3.0 mm (0.03to 0.12 in.).

Feed Pressure. The feed pressure deter-mines the jet velocity, which in turn determinesthe amount of oil that penetrates the gear mesh.Typical feed pressures range from 20 to 100psig. Industrial application feed pressures aretypically 30 psig, and high-speed aerospaceapplications are typically 100 psig. In general,the higher the pressure, the greater the cooling(Ref 25), but the higher the pressure, the smallerthe jet diameter. Therefore, pressure is limited

q � P>c

by the minimum recommended jet diameter of0.8 mm (0.03 in.).

Jet Quantity. The number of jets should besufficient to provide complete lubrication cov-erage of the face width. More than one jet foreach gear mesh is advisable because of the pos-sibility of clogging. The upper limit on the num-ber of jets is determined by the flow rate and jetdiameter; too many jets for a given flow ratewill result in a jet diameter less than the mini-mum recommended.

Case History: Failure of a 24-Unit Speed-Increaser Gearbox

This case history demonstrates many of theprinciples of gear lubrication described in ear-lier sections of this chapter. Lubricant viscosity,EHD film thickness, contact temperature, anddesign considerations are addressed.

Background. In an industrial application,24 speed-increaser gearboxes were used totransmit 258 kW (346 hp) and increase speedfrom 55 to 375 rev/min. The gears were parallelshaft, single helical, carburized, and ground.The splash lubrication system used a mineral oilwithout antiscuff additives with ISO 100 vis-cosity. After about 250 h of operation, two gear-boxes failed by bending fatigue. The gear toothprofiles were so badly worn that determining theprimary failure mode was impossible. Threeother gearboxes with less service were selectedfor inspection. One had logged 15 h, and theother two had operated for 65 h each. Upon dis-assembly, no broken teeth were found, but allthree gearboxes had scuffed gear teeth. The pri-mary failure mode was scuffing, and the earlierbending fatigue failures were caused bydynamic loads generated by the worn gear teeth.Subsequent inspection of the remaining gear-boxes revealed that all had scuffing damage,which probably had occurred immediately uponstart-up because the loads were not reduced dur-ing run-in.

Analysis. Fortunately, a prototype gearboxhad been run at one-half load for about 50 h.When these gears were inspected, no signs ofdistress were seen on any of the gear teeth. Thetooth profiles were smooth with surface rough-ness, Rq, estimated to be 0.5 μm (20 μin.), andthe contact pattern indicated 100% face contact.This gearbox was reassembled and run underone-half load until its oil sump temperaturereached equilibrium at 95 °C (200 °F). For this


Fig. 9 Plot of contact temperature versus pinion roll angle forgear tooth geometry of scuffed gearset. Maximum Tc,

226 °C (439 °F); scuffing probability, 63%

Fig. 8 Plot of film thickness versus pinion roll angle for geartooth geometry of a scuffed gearset. Minimum specific

film thickness, lmin, 0.073; probability of wear, >95%

application, the ambient temperature was in therange of 10 to 50 °C (50 to 125 °F). The centerdistance of the gears was 405 mm (16 in.) andthe pitch line velocity was 120 m/min (400ft/min). Referring to AGMA 250.04 (Ref 21),the recommended viscosity for these conditionsis ISO 150 or ISO 220.

Using the empirical equation (Eq 18), the fol-lowing is obtained:

(Eq 22)

Hence, the empirical equation recommends aviscosity close to ISO 320. It is apparent that theviscosity that was originally supplied (ISO VG100) was too low.

The EHD film thickness was calculated witha special computer program (Ref 26). The gearbulk temperature was assumed to be 110 °C(230 °F), which is 17 °C (30 °F) hotter than themeasured oil sump temperature. The followingdata for the ISO VG 100 lubricant was obtainedfrom Fig. 4 and 5: m0 = 6.6 cP = 0.96 × 10–6

reyns and a = 1.02 × 10–4 in.2/lbf.Figure 8 shows a plot of the film thickness

versus position on the pinion tooth. The mini-mum film thickness occurs low on the piniontooth near the lowest point of single-tooth con-tact (LPSTC), where hmin is 0.053 mm (2.1 min.).The specific film thickness, based on Rq of 0.5mm (20 min.) for both profiles, is l = 0.073. Fig-ure 7 shows that the gears operate in the bound-ary lubrication regime. The program predictsthat the probability of wear is >95%.

The contact temperature was also calculatedwith the program. The scuffing temperature forthe ISO VG 100 lubricant was calculated withthe equation for nonantiscuff mineral oils:

n40 �7000

1400 2 0.5 � 350 cSt

(Eq 23)

Figure 9 shows a plot of the contact tempera-ture versus position on the pinion tooth. Themaximum contact temperature occurs high onthe pinion tooth near the highest point of single-tooth contact (HPSTC), where Tc is 226 °C (439°F). The program predicts that the probability ofscuffing is 63%. This is considered to be a highrisk of scuffing. The relatively high-temperaturepeak near the tip of the pinion tooth was causedby the geometry of the gears.

The designer selected a long-addendum toothfor the pinion. Long-addendum pinions performwell in speed reducers, where they increase theamount of recess action and decrease theamount of approach action of the gear mesh.Because recess action is much smoother thanapproach action, long-addendum pinions givespeed reducers smooth meshing characteristics.When operated as a speed increaser, however,the approach and recess portions of the gearmesh reverse, making a long-addendum pinionrough running and vulnerable to scuffing.

To explore the possibilities for reducing thescuffing risk, new gear tooth geometry was pro-posed with the pinion and gear addendadesigned to minimize the flash temperature rise.The new gearset, analyzed with the program,assumed the lubricant was a mineral oil withantiscuff additives, with a viscosity of ISO 220,and with the following properties: m0 = 10 cP =1.45 × 10–6 reyns, a = 1.09 × 10–4 in.2/lbf, and

(Eq 24)

Figure 10 shows that the film thicknessincreases to hmin of 0.068 mm (2.7 min.), and thespecific film thickness increases to l = 0.097.Figure 7 shows that the gears still operate in the

Ts � 245 � 59 ln 1220 2 � 563 °F

Ts � 146 � 59 ln 1100 2 � 418 °F


Fig. 11 Plot of contact temperature versus pinion roll anglefor gear tooth geometry that was optimized for max-

imum scuffing resistance. Maximum Tf, 150 °C (302 °F); scuffingprobability, <5%

Fig. 10 Plot of film thickness versus pinion roll angle for geartooth geometry that was optimized for maximum

scuffing resistance. lmin, 0.097; probability of wear, 94%

boundary lubrication regime; however, theprobability of wear is reduced to 94%. Figure 11shows that the optimized gear geometryreduced the maximum contact temperature to aTc of 150 °C (302 °F). The combination ofreduced contact temperature and the increasedscuffing resistance provided by the higher vis-cosity mineral oil with antiscuff additivesreduces the scuffing probability to <5%.

Summary. Typical of many gear failures,this case history shows that several factors con-tributed to the failures:

• The lubricant viscosity was too low• No antiscuff additives were used• A gearbox designed as a speed reducer was

used as a speed increaser• The gear teeth were not provided with a

coating or plating to ease running-in• The gears were not run-in properly under

reduced loads

Gear failures, as exemplified by this case his-tory, can be avoided if designers and operators

recognize that the lubricant is an importantcomponent of a gearbox and appreciate that thetribology of gearing requires the considerationand control of many interrelated factors.

ACKNOWLEDGMENT

This chapter was adapted from R. Errichello,Friction, Lubrication, and Wear of Gears, Fric-tion, Lubrication, and Wear Technology, Vol18, ASM Handbook, ASM International, 1992,p 535–545

REFERENCES

1. R. Errichello, The Lubrication of Gears,Lubrication Engineering, Jan–April, 1990

2. E.E. Shipley, Gear Failures, Mach. Des., 7Dec 1967, p 152–162

3. D.W. Dudley, Gear Wear, Wear ControlHandbook, American Society of Mechani-cal Engineers

4. P.M. Ku, Gear Failure Modes—Impor-tance of Lubrication and Mechanics, ASLETrans., Vol 19 (No. 3), 1975, p 239–249

5. D.J. Wulpi, Understanding How Compo-nents Fail, American Society for Metals,1985

6. L.E. Alban, Failures of Gears, FailureAnalysis and Prevention, Vol 11, 9th ed.,Metals Handbook, ASM International,1986, p 586–601

7. D. Godfrey, Recognition and Solution ofSome Common Wear Problems Related toLubrication and Hydraulic Fluids, Lubr.Eng., Feb 1987, p 111–114

8. W.E. Littman, The Mechanism of ContactFatigue, Interdisciplinary Approach to theLubrication of Concentrated Contacts, SP-237, National Aeronautics and SpaceAdministration, 1970, p 309–377

9. T. Ueno et al., “Surface Durability of Case-Carburized Gears—On a Phenomenon ofGrey Staining of Tooth Surface,” Paper No.80-C2/DET-27, American Society ofMechanical Engineers, 1980, p 1–8

10. H. Winter and T. Weiss, “Some FactorsInfluencing the Pitting, Micropitting(Frosted Areas) and Slow Speed Wear ofSurface-Hardened Gears,” Paper No. 80-C2/DET-89, American Society of Mechan-ical Engineers, 1980, p 1–7

11. E.E. Shipley, “Failure Analysis of Coarse-Pitch, Hardened, and Ground Gears,” Paper


No. P229.26, American Gear Manufactur-ers Association, 1982, p 1–24

12. S. Tanaka et al. “Appreciable Increases inSurface Durability of Gear Pairs with Mir-ror-Like Finish,” Paper No. 84-DET-223,American Society of Mechanical Engi-neers, 1984, p 1–8

13. A. Milburn, R. Errichello, and D. Godfrey,“Polishing Wear,” Paper No. 90 FTM 5,American Gear Manufacturers Associa-tion, 1990, p 1–13

14. J.H. Admas and D. Godfrey, Borate GearLubricant-EP Film Analysis and Perfor-mance, Lubr. Eng., Vol 37 (No. 1), Jan1981, p 16–21

15. H. Blok, “Les Temperatures de Surfacedans les Conditions de Graissage sons Pres-sion Extreme,” Second World PetroleumCongress (Paris), June 1937

16. H. Blok, The Postulate about the Constancyof Scoring Temperatures, InterdisciplinaryApproach to the Lubrication of Concen-trated Contacts, SP-237, National Aero-nautics and Space Administration, 1970, p153–248

17. D. Dowson, Elastohydrodynamics, PaperNo. 10, Proc. Inst. Mech. Eng., Vol 182,PT3A, 1967, p 151–167

18. “Fundamental Rating Factors and Calcula-tion Methods for Involute Spur and HelicalGear Teeth,” 2001-B88, American GearManufacturers Association, 1988

19. M. Akazawa, T. Tejima, and T. Narita,“Full Scale Test of High Speed, High Pow-ered Gear Unit—Helical Gears of 25,000PS at 200 m/s PLV,” Paper No. 80-C2/DET-4, American Society of Mechani-cal Engineers, 1980

20. R.J. Drago, “Comparative Load CapacityEvaluation of CBN-Finished Gears,” PaperNo. 88 FTM 8, American Gear Manufac-turers Association, Oct 1988

21. “AGMA Standard Specification—Lubrica-tion of Industrial Enclosed Gear Drives,”

No. 250.04, American Gear ManufacturersAssociation, Sept 1981

22. “Practice for High Speed Helical and Her-ringbone Gear Units,” No. 421.06, Ameri-can Gear Manufacturers Association, Jan1969

23. E.J. Wellauer and G.A. Holloway, Applica-tion of EHD Oil Film Theory to IndustrialGear Drives, J. Eng. Ind. (Trans. ASME),Vol 98, Series B (No. 2), May 1976, p626–634

24. R.J. Drago, Fundamentals of Gear Design,Butterworths, 1998

25. L. Akin and D. Townsend, “Study of Lubri-cant Jet Flow Phenomena in Spur Gears,”TMX-71572, National Aeronautics andSpace Administration, Oct 1974

26. SCORING+, computer program, GEAR-TECH Software, Inc., Copyright 1985–1992

SELECTED REFERENCES

• R.H. Boehringer, Grease, Friction, Lubri-cation, and Wear Technology, Vol 18, ASM Handbook, ASM International, 1992,p 123–131

• H.S. Cheng, Lubrication Regimes, Fric-tion, Lubrication, and Wear Technology,Vol 18, ASM Handbook, ASM Interna-tional, 1992, p 89–97

• R.S. Fein, Liquid Lubricants, Friction,Lubrication, and Wear Technology, Vol18, ASM Handbook, ASM International,1992, p 81–88

• S.Q.A. Rizvi, Lubricant Additives andTheir Functions, Friction, Lubrication, andWear Technology, Vol 18, ASM Handbook,ASM International, 1992, p 98–112

• H.E. Sliney, Solid Lubricants, Friction,Lubrication, and Wear Technology, Vol18, ASM Handbook, ASM International,1992, p 113–122

CHAPTER 3

Ferrous and Nonferrous Alloys

GEAR MATERIALS can be broadly classi-fied into two groups: nonmetallic and metallicmaterials. Nonmetallics are the plastics, boththermoplastic and thermosetting, used for gear-ing. These materials are described in Chapter 4,“Plastics.” Metallic gear materials can be fur-ther subdivided into ferrous, or iron-base alloys,and nonferrous alloys. The most commonlyused ferrous alloys are the wrought surface-hardening and through-hardening carbon andalloy steels. In fact, these steels are the mostwidely used of all gear materials and will be theemphasis of this chapter. Other ferrous alloysused for gears are cast irons, cast steels, powdermetallurgy (P/M) irons and steels, stainlesssteels, tool steels, and maraging steels.

Although a number of nonferrous alloys havebeen used for gears, by far the most commonlyemployed are copper-base alloys. Die cast alu-minum-, zinc-, and magnesium-base alloys arealso sometimes used. More recently titaniumalloy Ti-6Al-4V has been used in some special-ized applications.

Wrought Gear Steels

Wrought steel is the generic term applied tocarbon and alloy steels which are mechanicallyworked into form for specific applications. Thestandard wrought steel forms are round barstock, flat stock, and forgings. Forgings reducemachining time and are available in a widerange of sizes and grades.

In general, there are two types of wroughtgear steels: surface-hardening and through-hardening grades. The surface-hardened steelsare hardened to a relatively thin case depth andinclude carburizing, nitriding, and carbonitrid-ing steels. Surface-hardening steels includeplain carbon and alloy steels with carbon con-

tent generally not exceeding 0.25% C. Table 1lists compositions of surface-hardening steels.

Through-hardening steels may be compara-tively shallow hardening or deep hardening,depending on their chemical composition andmethod of hardening. Through-hardening steelsinclude plain carbon and alloy steels with car-bon content ranging from 0.30 to approximately0.55% C. Table 2 lists the compositions ofthrough-hardening gear steels. Table 3 lists themechanical properties of both surface- andthrough-hardening steels in various conditions.

The steels selected for gear applications mustsatisfy two basic sets of requirements that arenot always compatible—those involving fabri-cation and processing and those involving ser-vice. Fabrication and processing requirementsinclude machinability, forgeability, and re-sponse to heat treatment as it affects fabricationand processing. Service requirements are re-lated to the ability of the gear to perform satis-factorily under the conditions of loading forwhich it was designed and thus encompass allmechanical-property requirements, includingfatigue strength, response to heat treatment, andresistance to wear.

Because resistance to fatigue failure is partlydependent upon the cleanness of the steel andupon the nature of allowable inclusions, meltingpractice may also be a factor in steel selectionand may warrant selection of a steel producedby vacuum induction melting followed by vac-uum arc remelting (VIM/VAR) or by elec-troslag refining. The mill form from which asteel gear is machined is another factor that mayeffect its performance. Many heavy-duty steelgears are machined from forged blanks thathave been processed to provide favorable grainflow consistent with load pattern rather thanbeing machined from blanks cut from mill-rolled bar.




Table 1 Chemical compositions of carburizing steelsThe carburizing grades commonly used for gears are described in text.

Composition, %

Steel C Mn Ni Cr Mo Other

Carbon steels

1010 0.08–0.13 0.30–0.60 . . . . . . . . . (a), (b)1015 0.13–0.18 0.30–0.60 . . . . . . . . . (a), (b)1018 0.15–0.20 0.60–0.90 . . . . . . . . . (a), (b)1019 0.15–0.20 0.70–1.00 . . . . . . . . . (a), (b)1020 0.18–0.23 0.30–0.60 . . . . . . . . . (a), (b)1021 0.18–0.23 0.60–0.90 . . . . . . . . . (a), (b)1022 0.18–0.23 0.70–1.00 . . . . . . . . . (a), (b)1025 0.22–0.28 0.30–0.60 . . . . . . . . . (a), (b)1524 0.19–0.25 1.35–1.65 . . . . . . . . . (a), (b)1527 0.22–0.29 1.20–1.50 . . . . . . . . . (a), (b)

Resulfurized steels

1117 0.14–0.20 1.00–1.30 . . . . . . . . . 0.08–0.13 S1118 0.14–0.20 1.30–1.60 . . . . . . . . . 0.08–0.13 S

Alloy steels

3310 0.08–0.13 0.45–0.60 3.25–3.75 1.40–1.75 . . . (b), (c)4023 0.20–0.25 0.70–0.90 . . . . . . 0.20–0.30 (b), (c)4027 0.25–0.30 0.70–0.90 . . . . . . 0.20–0.30 (b), (c)4118 0.18–0.23 0.70–0.90 . . . 0.40–0.60 0.08–0.15 (b), (c)4320 0.17–0.22 0.45–0.65 1.65–2.00 0.40–0.60 0.20–0.30 (b), (c)4615 0.13–0.18 0.45–0.65 1.65–2.00 . . . 0.20–0.30 (b), (c)4620 0.17–0.22 0.45–0.65 1.65–2.00 . . . 0.20–0.30 (b), (c)4815 0.13–0.18 0.40–0.60 3.25–3.75 . . . 0.20–0.30 (b), (c)4820 0.18–0.23 0.50–0.70 3.25–3.75 . . . 0.20–0.30 (b), (c)5120 0.17–0.22 0.70–0.90 . . . 0.70–0.90 . . . (b), (c)5130 0.28–0.33 0.70–0.90 . . . 0.80–1.10 . . . (b), (c)8617 0.15–0.20 0.70–0.90 0.40–0.70 0.40–0.60 0.15–0.25 (b), (c)8620 0.18–0.23 0.70–0.90 0.40–0.70 0.40–0.60 0.15–0.25 (b), (c)8720 0.18–0.23 0.70–0.90 0.40–0.70 0.40–0.60 0.20–0.30 (b), (c)8822 0.20–0.25 0.75–1.00 0.40–0.70 0.40–0.60 0.30–0.40 (b), (c)9310 0.08–0.13 0.45–0.65 3.00–3.50 1.00–1.40 0.08–0.15 (b), (c)

Special alloys

CBS-600 0.16–0.22 0.40–0.70 . . . 1.25–1.65 0.90–1.10 0.90–1.25 SiCBS-1000M 0.10–0.16 0.40–0.60 2.75–3.25 0.90–1.20 4.00–5.00 0.40–0.60 Si

0.15–0.25 VPyrowear Alloy 53 0.10 0.35 2.00 1.00 3.25 1.00 Si, 2.00 Cu, 0.10 V

(a) 0.04 P max, 0.05 S max. (b) 0.15–0.35 Si. (c) 0.035 P max, 0.04 S max

Surface-Hardening Steels

General Properties. Carburizing or nitrid-ing grades of steel are usually specified wheremaximum wear resistance is required for bear-ing surfaces. Carburized case-hardened gearsare best suited for heavy-duty service, for exam-ple, transmission gears, and offer high resis-tance to wear, pitting, and fatigue. Surfacesmust be sufficiently hard to resist wear and ofsufficient depth to prevent case crushing. Arough rule for case depth is that it shall notexceed one-sixth of the base thickness of thetooth. Figure 1 shows the typical structure of acase-hardened gear steel.

A case-hardened gear provides maximum sur-face hardness and wear resistance and at the sametime provides interior toughness to resist shock.In general, case-hardened gears can withstandhigher loads than through-hardened gears, al-though the latter are quieter and less expensivebecause of the simpler heat treatment required(Ref 1).

Selection Factors. The following factorsmust be considered when selecting a case-hardened gear (Ref 1):

• High tooth pressures will crack a thin case.• Too soft a core will not provide proper back-

ing for a hard case.

Chapter 3: Ferrous and Nonferrous Alloys / 41

Table 2 Chemical compositions of through-hardening gear steelsComposition, %

Steel C Mn Ni Cr Mo Other

Carbon steels

1035 0.32–0.38 0.60–0.90 . . . . . . . . . (a)(b)1040 0.37–0.44 0.60–0.90 . . . . . . . . . (a)(b)1045 0.43–0.50 0.60–0.90 . . . . . . . . . (a)(b)1050

Free-cutting (resulfurized) carbon steels

1137 0.32–0.39 1.35–1.65 . . . . . . . . . 0.08–0.13 S1141 0.37–0.45 1.35–1.65 . . . . . . . . . 0.08–0.13 S1144 0.40–0.48 1.35–1.65 . . . . . . . . . 0.24–0.33 S

Alloy steels

1340 0.38–0.43 1.60–1.90 . . . . . . . . . (c)(d)3140 0.38–0.43 0.70–0.90 1.10–1.40 0.55–0.75 . . . (c)(d)4042 0.40–0.45 0.70–0.90 . . . . . . 0.20–0.40 (c)(d)

(c)(d)4130 0.28–0.33 0.40–0.60 . . . 0.80–1.10 0.15–0.254140 0.38–0.43 0.75–1.00 . . . 0.80–1.10 0.15–0.25 (c)(d)4142 0.40–0.45 0.75–1.00 . . . 0.80–1.10 0.15–0.25 (c)(d)4145 0.41–0.48 0.75–1.00 . . . 0.80–1.10 0.15–0.25 (c)(d)4150 0.48–0.53 0.75–1.00 . . . 0.80–1.10 0.15–0.25 (c)(d)4340 0.38–0.43 0.60–0.80 1.65–2.00 0.70–0.90 0.20–0.30 (c)(d)4350 0.48–0.53 0.60–0.80 1.65–2.00 0.70–0.90 0.20–0.30 (c)(d)5140 0.70–0.900.38–0.43 . . . 0.70–0.90 . . . (c)(d)6145 0.41–0.48 0.70–0.90 . . . 0.80–1.10 . . . (c)(d) 0.15 V min8640 0.38–0.43 0.75–1.00 0.40–0.70 0.40–0.60 0.15–0.25 (c)(d)8740 0.38–0.43 0.75–1.00 0.40–0.70 0.40–0.60 0.20–0.30 (c)(d)9840 0.38–0.43 0.70–0.90 0.85–1.15 0.70–0.90 0.08–0.15 (c)(d)

(a) 0.04 P max, 0.05 S max. (b) 0.10–0.60 Si. (c) 0.035 P max, 0.04 S max (d) 0.15–0.35 Si

• Compressive stresses in the case improvefatigue durability, and a high case hardnessincreases wear resistance.

• If the ratio of case depth to core thickness istoo small, excessive stresses in subsurfacelayers can produce poor fatigue life.

• Residual tensile stresses are highest withlow core hardness and increase with increas-ing case depth. These stresses can berelieved by tempering.

Grain size variations have an important effecton core properties. These variations are influ-enced by the type of steel and the method of heattreatment used subsequent to carburizing. Sec-tion thickness also influences core properties.

A tough tooth core may not be required inapplications where a gear will not be subjectedto impact loading. In these applications, coreproperties are relatively unimportant, providedthe core is sufficiently hard to support the case.Considering the case alone, it is important thatthe surface resist wear and fatigue bending,because bending stresses vary from a maximumat the surface to zero near the tooth center.

Carburizing Steels. Carburizing is a veryimportant commercial heat-treating operationthat is used to modify the surface chemistry ofcomponents manufactured from ferrous alloysby the processes of carbon absorption and diffu-sion. The process is carried out at a temperaturesufficient to render the steel austenitic (gener-ally between 850 and 950 °C, or 1560 and 1740°F), followed by quenching and tempering toform a high-carbon martensitic structure. Theincrease in carbon content of a carburized sur-face layer results in a substantial change in theproperties of the effected volume of material.For example, the carburized case will be harder,will be more resistant to abrasive wear, and willexhibit improved fatigue properties comparedwith the uneffected core. These variations inproperties are quite useful in applications wherea hard, wear-resistant surface is needed andwhere a softer, more ductile core is required toprevent catastrophic failure of the component.

Carburizing methods include:

• Gas carburizing• Vacuum carburizing


Table 3 Mechanical properties of selected gear steelsTensile strength Yield strength

Steel Condition MPa ksi MPa ksi

Carbon steel bar(a)

1015 Hot rolled 345 50 190 27.5 28 50 101Cold drawn 385 56 325 47 18 40 111

1018 Hot rolled 400 58 220 32 25 50 116Cold drawn 440 64 370 54 15 40 126





1045 Hot rolled 565 82 310 45 16 40 163Cold drawn 625 91 530 77 12 35 179Annealed, cold drawn 585 85 505 73 12 45 170Spheroidized annealed, cold drawn 650 94 500 72.5 10 40 192



Low-alloy steels(b)

4130 Normalized at 870 °C (1600 °F) 670 97 435 63 25.5 59.5 197Annealed at 865 °C (1585 °F) 560 81 460 67 21.5 59.6 217Water quenched from 855 °C (1575 °F)

and tempered at 540 °C (1000 °F)1040 151 979 142 18.1 63.9 302



4150 Normalized at 870 °C (1600 °F) 1160 168 731 106 11.7 30.8 321Annealed at 830 °C (1525 °F) 731 106 380 55 20.2 40.2 197Oil quenched from 830 °C (1525 °F)






8620 Normalized at 915 °C (1675 °F) 635 92 360 52 26.3 59.7 183Annealed at 870 °C (1600 °F) 540 78 385 56 31.3 62.1 149





9310 Normalized at 890 °C (1630 °F) 910 132 570 83 18.8 58.1 269 HRBAnnealed at 845 °C (1550 °F) 820 119 450 65 17.3 42.1 241 HRBAged sheet 6 mm (0.25 in.) 2169 315 2135 310 7.7 35 55.1 HRC

(a) All values are estimated minimum values; type 1100 series steels are rated on the basis of 0.10% max Si or coarse-grain melting practice; the mechanical proper-ties shown are expected minimums for the sizes ranging from 19 to 31.8 mm (0.75 to 1.25 in.). (b) Most data are for 25 mm (1 in.) diam bar.

Hardness, HB

Reduction in area, %

Elongation, in 50 mm, %

• Plasma carburizing• Salt bath carburizing• Pack carburizing

These methods introduce carbon by the use ofgas (atmospheric-gas, plasma, and vacuum car-

burizing), liquids (salt bath carburizing), orsolid compounds (pack carburizing). All ofthese methods have advantages and limitations,but gas carburizing is used most often for large-scale production because it can be accuratelycontrolled and involves a minimum of special


Fig. 1 Uniform case depth on a 40-tooth gear made from Fe-0.16C-0.6Mn-0.37Si-1.65Cr-3.65Ni steel that was pro-

duced by ion carburizing

handling. More detailed information on variouscarburizing methods can be found in Chapter 9,“Carburizing.”

The core carbon content of carburized gearsis usually within the range of 0.10 to 0.25%. Alower carbon content is usually used to obtainmaximum ductility, and a higher carbon contentis used to obtain maximum core strength. Somerepresentative SAE-AISI carburizing steelsused for gears include:

• Plain carbon steels: 1015, 1018, 1020, 1022,and 1025

• Free-machining steels: 1117 and 1118• Alloy steels: 4020, 4026, 4118, 4320, 4620,

4820, 5120, 8620, 8720, and 9310

Many other standard (SAE-AISI) and propri-etary carburizing steels are also available.

The nickel-bearing carburizing steels are usedchiefly where exceptional core toughness com-bined with the highest degree of wear resistanceand greatest surface compressive strength isrequired. These steels include the nickel-molyb-denum steels (4600 and 4800 series) and thenickel-chromium-molybdenum steels (4300,8600, 8700, and 9300 series). The carbon-molybdenum steels (4000 series) are used whereexceptional toughness and good resistance totemper embrittlement are required.

Another advantage of the more highlyalloyed steels is the ability of heavy sections toharden more completely. This greater harden-ability promotes better core strength properties

than can be achieved with shallow hardeningsteels quenched in the same size section.

Nitriding Steels. Nitriding is a surface-hardening heat treatment that introduces nitro-gen into the surface of steel at a temperaturerange of 500 to 550 °C (930 to 1020 °F) while itis in the ferritic condition. Thus, nitriding is sim-ilar to carburizing in that surface composition isaltered, but different in that nitrogen is addedinto ferrite instead of austenite. Because nitrid-ing does not involve heating into the austenitephase field and a subsequent quench to formmartensite, nitriding can be accomplished with aminimum of distortion and with excellentdimensional control. Process methods for nitrid-ing include gas, liquid (salt bath), and plasma(ion) nitriding. Details on these processes can befound in Chapter 10, “Nitriding.”

Nitriding steels can be used in many gearapplications where a hard, wear-resistant case,good fatigue strength, low notch sensitivity, andsome degree of corrosion resistance are desired.In addition, nitriding steels make it possible tosurface harden the teeth of large gears havingthin sections that might be impractical to car-burize and quench.

Nitrided gears are relatively free from wearup to the load at which surface failure occurs,but at this load they become badly crushed andpitted. Thus, nitrided gears are generally notsuitable for applications where overloads arelikely to be encountered.

Nitrided steels are generally medium-carbon(quenched-and-tempered) steels that containstrong nitride-forming elements such as alu-minum, chromium, vanadium, and molybde-num. The most significant hardening is achievedwith a class of alloy steels (Nitralloy steels asdescribed below) that contain about 1% Al.When these steels are nitrided, the aluminumforms AIN particles, which strain the ferrite lat-tice and create strengthening dislocations.

Table 4 lists chemical compositions of Nitral-loy gear steels. Nitralloy N, a nickel-bearing(3.5% Ni) nitriding steel, is a precipitation-hardening alloy that attains a core strength andhardness after nitriding that are considerably inexcess of its original properties. Both NitralloyN and Nitralloy 135M are outstanding for heavy-duty gears that are highly stressed. Little changein tensile strength of nitriding steels occurs if thetempering temperature used for treating the coreis at or above the nitriding temperature. How-ever, because of the increased hardness of thecase, the elongation, ductility, and impact


strength of both alloys are considerably reducedafter tempering, though not to the same extent;Nitralloy N develops a tougher and softer sur-face and a stronger core than Nitralloy 135M.

Any of the SAE-AISI steels that containnitride-forming elements, such as chromium,vanadium, or molybdenum, can also be nitrided.The steels most commonly nitrided are 4140,4340, 6140, and 8740. In some applications, the0.50% C grades are also used.

Through-Hardening Steels

By virtue of their higher carbon content,through-hardening steel gears possess greatercore strength than carburized gears. They arenot, however, as ductile or as resistant to surfacecompressive stresses and wear as case-hardenedgears. Hardness of gear surfaces may vary from300 to 575 HB. Through-hardened steels mayalso be effectively surface hardened by induc-tion heating or by flame hardening.

Typical of the relatively shallow-hardeningcarbon steel gear materials are SAE-AISI types1035, 1040, 1045, 1050, 1137, 1141, 1144, and1340. These steels are water-hardening, but notdeep-hardening types that are suitable for gearsrequiring only a moderate degree of strengthand impact resistance.

In general, the more highly alloyed through-hardening steels harden more completely whenquenched in heavy sections. This greater harden-ability provides greater strength than can beattained with shallow-hardening steels quenchedin the same size section.

Typical of the low-alloy, medium-to-deephardening gear materials are (in order of increas-ing hardenability): 4042, 5140, 8640, 3140,4140, 8740, 6145, 9840, and 4340. These steels,as well as many other alloy steels with the properhardenability characteristics and a carbon con-tent of 0.35 to 0.50%, are suitable for gearsrequiring medium-to-high wear resistance and

high load-carrying capacity. Other standard(SAE-AISI) and proprietary through-hardeningsteels are also available.

When selecting a through-hardening steel, itshould be considered that a higher carbon andalloy content is accompanied by greaterstrength and hardness (but lower ductility) ofthe surface and the core. Fully hardened andtempered medium-carbon alloy steels possessan excellent combination of strength and tough-ness at room temperature and at lower tempera-tures. However, toughness can be substantiallydecreased by temper embrittlement by slowcooling through the temperature range of 450 to540 °C (850 to 1000 °F), or by holding or tem-pering in this range. Because of their good hard-enability and immunity to temper brittleness,molybdenum steels have been widely used forgears requiring good toughness at room and lowtemperatures.

Gear Steel Requirements

Some of the more important requirements forgear steels are their:

• Processing characteristics (for example,hardenability and machinability)

• Response to heat treatment. This subject isaddressed in Chapters 8 through 12 whichcover through-hardening, carburizing, ni-triding, carbonitriding, and induction andflame hardening, respectively.

• Resistance to tooth bending fatigue—bothlow-cycle (≤105 cycles to failure) and high-cycle (>105 cycles to failure) fatigue. Be-cause carburized steels for high-performancegear applications are subjected to cyclicloading, this is one of the most importantproperties or measure of gear performance.The section on “Bending Fatigue Strength ofCarburized Steels” deals with this subject indetail.

Table 4 Nominal chemical compositions for aluminum-containing low-alloy steels commonly gas nitrided

Steel Composition, %

SAE AMS Nitralloy C Mn Si Cr Ni Mo Al Se

. . . . . . G 0.35 0.55 0.30 1.2 . . . 0.20 1.0 . . .7140 6470 135M 0.42 0.55 0.30 1.6 . . . 0.38 1.0 . . .. . . 6475 N 0.24 0.55 0.30 1.15 3.5 0.25 1.0 . . .. . . . . . EZ 0.35 0.80 0.30 1.25 . . . 0.20 1.0 0.20


• Resistance to surface-contact (pitting)fatigue. This subject is addressed in Chapter2, “Gear Tribology and Lubrication.”

• Resistance to rolling contact fatigue• Resistance to wear. This subject is briefly

discussed in this chapter, but more detailedinformation on adhesive wear, abrasivewear, and scuffing of gears can be found inChapter 2.

• Their hot hardness• Their bending strength and bend ductility• Their toughness, both impact toughness and

fracture toughness

Each of these will be described in subsequentsections.

Processing Characteristics of Gear Steels

Hardenability refers to the ability of a steelto be transformed partially or completely fromaustenite to martensite at a given depth whencooled under prescribed conditions. This defini-tion reflects the empirical nature of steel hard-enability, and, as discussed in Ref 2, many typesof experiments have been devised to measure ordescribe the hardenability of various kinds ofsteel.

Martensite is the microstructure usuallydesired in quenched carbon and low-alloy steels.The cooling rate in a quenched part must be fastenough so that a high percentage of martensite isproduced in critically stressed areas of the part.Higher percentages of martensite result in higherfatigue and impact properties after tempering.

Hardenability should not be confused withhardness as such or with maximum hardness.The maximum attainable hardness of any steeldepends solely on carbon content. Also, themaximum hardness values that can be obtainedwith small test specimens under the fastest cool-ing rates of water quenching are nearly alwayshigher than those developed under productionheat-treating conditions, because hardenabilitylimitations in quenching larger sizes can resultin less than 100% martensite formation.

Basically, the units of hardenability are thoseof cooling rate—for example, degrees per sec-ond. These cooling rates, as related to thecontinuous-cooling-transformation behavior ofthe steel, determine the hardness and micro-structural outcome of a quench. In practice,these cooling rates are often expressed as a dis-

tance, with other factors such as the thermalconductivity of steel and the rate of surface heatremoval being held constant. Therefore, theterms Jominy distance (J ) and ideal criticaldiameter (DI) derived from the Jominy end-quench test can be used.

The hardenability of steel is governed almostentirely by the chemical composition (carbonand alloy content) at the austenitizing tempera-ture and the austenite grain size at the momentof quenching. In some cases, the chemical com-position of the austenite may not be the same asthat determined by chemical analysis, becausesome carbide may be undissolved at the austen-itizing temperature. Such carbides would bereflected in the chemical analysis, but becausethe carbides are undissolved in the austenite,neither their carbon nor alloy content can con-tribute to hardenability. In addition, by nucleat-ing transformation products, undissolved car-bides can actively decrease hardenability. Thisis especially important in high-carbon (0.50 to1.10%) and alloy carburizing steels, which maycontain excess carbides at the austenitizing tem-perature. Consequently, such factors as austeni-tizing temperature, time at temperature, andprior microstructure are sometimes very impor-tant variables when determining the basic hard-enability of a specific steel composition. Certainingot casting and hot reduction practices mayalso develop localized or periodic inhomo-geneities within a given heat, further complicat-ing hardenability measurements. The effects ofall these variables are discussed in Ref 2.

Table 5 provides a qualitative rating of thehardenability of gear steels. Additional infor-mation on hardness and hardenability can befound in Chapter 9, “Carburizing.”

Machinability. The term machinability isused to indicate the ease or difficulty with whicha material can be machined to the size, shape, anddesired surface finish. The terms machinabilityindex and machinability rating are used as quali-tative and relative measures of the machinabilityof a steel under specified conditions. There are noclear-cut or unambiguous meanings for theseterms and no standard or universally acceptedmethod of measuring machinability. Histori-cally, machinability judgments have been basedon one or more of the following criteria:

• Tool life: Measured by the amount of mate-rial that can be removed by a standard cut-ting tool under standard cutting conditionsbefore tool performance becomes unaccept-able or tool wear reaches a specified amount


Table 5 Hardenability characteristics of commonly used gear steelsCommon alloy steel grades Common heat treat practice(a) Hardenability

Noncarburizing grades

1045 T-H, I-H, F-H Low hardenability4130 T-H Marginal hardenability4140 T-H, T-H&N, I-H, F-H Fair hardenability4145 T-H, T-H&N, I-H, F-H Medium hardenability8640 T-H, T-H&N, I-H, F-H Medium hardenability4340 T-H, T-H&N, I-H, F-H Good hardenability in heavy sections4150 I-H, F-H, T-H, T–H&N Quench crack sensitive

Good hardenability4142 I-H, F-H, T-H&N Used when 4140 exhibits

Marginal hardenability4350 T-H, I-H, F-H Quench crack sensitive, excellent

Hardenability in heavy sections

Carburizing grades

1020 C-H Very low hardenability4118 C-H Fair core hardenability4620 C-H Good case hardenability8620 C-H Fair core hardenability4320 C-H Good core hardenability8822 C-H Good core hardenability in heavy sections3310 C-H Excellent hardenability (in heavy sections) for all three grades4820 C-H9310 C-H

(a) C-H = Carburize harden, F-H = Flame harden, I-H = Induction harden, T-H = Through harden, T-H&N = Through harden then nitride. Source: American GearManufacturers Association

• Cutting speed: Measured by the maximumspeed at which a standard tool under stan-dard conditions can continue to provide sat-isfactory performance for a specified period

• Power consumption: Measured by the powerrequired to remove a unit volume of materialunder specified machining conditions

• Comparisons with a standard steel based onexperience in machine shops

• Quality of surface finish• Feeds resulting from a constant thrust force

Some of the test criteria are best suited to labo-ratory studies intended to elicit informationabout the effects of small changes in micro-structure, composition, or processing history onmachinability. Other types of tests are useful forstudying the effects of geometry changes or cut-ting tool composition.

Figure 2 is a plot of cutting speed for one-hour tool life versus the Brinell hardness of var-ious gear steels. This figure indicates a widerange correlation. For example, at a hardnessrange of 175 to 200 HB, the cutting speed forone-hour tool life varies from 23 to 43 m/min(75 to 140 surface feet per minute). The figureindicates decreased cutting speed for one-hourtool life as the hardness increases. In Table 6,the machinability of some of the more commongear steels is listed on the basis of good, fair,

and poor machinability. With good machinabil-ity as a base, a fair rating would add 20 to 30%to the machining cost, and a poor rating wouldadd 40 to 50%.

Bending Fatigue Strength of Carburized Steels

Bending fatigue of carburized steel compo-nents is a result of cyclic mechanical loading.The bending produces stresses, which are ten-sile at the surface, decrease with increasing dis-tance into the component, and at some pointbecome compressive. Such loading is a charac-teristic of the roots of gear teeth. Carburizingproduces a high-carbon, high-strength surfacelayer, or high-strength case, on a low-carbon,low-strength interior or core and is therefore, anideal approach to offset the high surface tensilestresses associated with bending. Thus when thedesign of a component maintains operatingstress gradients below the fatigue strength of thecase and core microstructures, excellent bend-ing fatigue resistance is established.

There are, however, many alloying and pro-cessing factors that produce various microstruc-tures, and therefore variable strength and frac-ture resistance, of the case regions of carburized


Fig. 2 Cutting speed for one-hour tool life versus Brinell hardness number for various through-hardened carbon and alloy steels

steels. When applied surface stresses exceed thesurface strength, surface fatigue crack initiationand eventual failure will develop. When the sur-face strength is adequate, depending on thesteepness of the applied stress gradients in rela-tionship to the case/core strength gradient, sub-surface fatigue cracking may develop.

Bending fatigue performance of carburizedsteels can vary significantly. One study reportedvalues of experimentally measured endurancelimits ranging from 200 to 1930 MPa (29 to 280ksi), with most values between 700 and 1050MPa (100 and 152 ksi) (Ref 3). As will bedescribed subsequently, this wide variation infatigue performance is a result of variations inspecimen design and testing, alloying, and pro-cessing interactions that produce large variationsin carburized microstructures and the response ofthe microstructures to cyclic loading.

Bending Fatigue Testing

Data Presentation and Analysis. Mostbending fatigue data for carburized steels are

presented as plots of maximum stress, S, versusthe number of cycles, N, to fracture for a speci-fied stress ratio (R), which is the ratio of mini-mum (or compressive) stress to maximum ten-sile stress (R = min-S/max-S). Figure 3 shows anexample of typical S-N plots for a series of car-burized alloy steels (Ref 4). The S-N curve con-sists of two parts: a straight section with nega-tive slope at low cycles and a horizontal sectionat high cycles. The horizontal line defines thefatigue limit or endurance limit, which is takento be the maximum applied stress below whicha material is assumed to be able to withstand aninfinite number of stress cycles without failure.Pragmatically, the endurance limit is taken asthe stress at which no failure occurs after a setnumber of cycles, typically on the order of 10million cycles. The low-cycle portion of the S-Nplot defines various fatigue strengths or thestresses to which the material can be subjectedfor a given number of cycles. The more cyclesat a given strength, the better the low-cyclefatigue resistance of a material.


Table 6 Machinability of commonly used gear materials. Refer also to the text describing this tableMaterial Remarks

Low-carbon carburizing steel grades(a)

1020 Good machinability, as rolled, as forged, or normalized.411846208620

Good machinability, as rolled, or as forged. However, normalized is preferred. Inadequate cooling duringnormalizing can result in gummy material, reduced tool life and poor surface finish. Quench and temper as aprior treatment can aid machinability. The economics of the pretreatments must be considered.

882233104320

Fair to good machinability if normalized and tempered, annealed or quenched and tempered. Normalizingwithout tempering results in reduced machinability.

48209310

Medium-carbon through-hardening steel grades(a)

1045 Good machinability if normalized.11411541413041404142

Good machinability if annealed, or normalized and tempered to approximately 255 HB or quenched andtempered to approximately 321 HB. Over 321 HB, machinability is fair. Above 363 HB, machinability ispoor. Inadequate (slack) quench with subsequent low tempering temperature may produce a part whichmeets the specified hardness, but produces a mixed microstructure which results in poor machinability.

41454150434043454350

Remarks for medium carbon alloy steel (above) apply. However, the higher carbon results in lowermachinability. Sulfur additions aid the machinability of these grades. 4340 machinability is good up to 363HB. The higher carbon level in 4145, 4150, 4345, and 4350 makes them more difficult to machine andshould be specified only for heavy sections. Inadequate (slack) quench can seriously affect machinability inthese steels.

Other gear materials

Gray Irons Gray cast irons have good machinability. Higher strength gray cast irons [above 345 MPa (50 ksi) tensilestrength] have reduced machinability.

Ductile Irons Annealed or normalized ductile cast iron has good machinability. The “as cast” (not heat treated) ductile ironhas fair machinability. Quenched and tempered ductile iron has good machinability up to 285 HB and fairmachinability up to 352 HB. Above 352 HB, machinability is poor.

Gear Bronzes and Brasses All gear bronzes and brass have good machinability. The very high strength heat treated bronzes [above 760MPa (110 ksi) tensile strength] have fair machinability.

Austenitic Stainless Steel All austenitic stainless steel grades only have fair machinability. Because of work hardening tendencies, feedsand speeds must be selected to minimize work hardening.

(a) Coarse grain steels are more machinable than fine grain. However, gear steels are generally used in the fine grain condition since mechanical properties are improved,and distortion during heat treatment is reduced. Increasingly cleaner steels are now also being specified for gearing. However, if sulfur content is low, less than 0.015%,machinability may decrease appreciably. Source: American Gear Manufacturers Association

Analysis of bending fatigue behavior of car-burized steels based on S-N curves represents astress-based approach to fatigue and assumesthat the carburized specimens deform nominallyonly in an elastic manner (Ref 5). This assump-tion is most valid at stresses up to the endurancelimit and is useful when machine componentsare designed for high-cycle fatigue. However, asmaximum applied stresses increase above theendurance limit, plastic strain becomes increas-ingly important during cyclic loading, andfatigue is more appropriately analyzed by astrain-based approach. In this approach, the totalstrain range is the sum of the applied elastic andplastic strains, and the strain amplitude is plottedas a function of the strain reversals required forfailure at the various levels of strain.

According to the strain-based approach, low-cycle fatigue behavior is determined by plastic

strains, while high-cycle fatigue behavior isdetermined by elastic strains. In particular, duc-tile materials with microstructures capable ofsustaining large amounts of plastic deformationhave better low-cycle fatigue resistance, whilehigh-strength materials with high elastic limitsand high yield strengths have better high-cyclefatigue resistance. Figure 4 shows the results ofstrain-based bending fatigue testing of uncarbur-ized and carburized 4027 steel (Ref 6). The moreductile, low-strength uncarburized specimensshow better fatigue resistance at low cycles thando the carburized specimens. The performanceis reversed at high cycles, where the carburizedspecimens with their high-strength surfacesshow better fatigue resistance, especially thosespecimens with the deeper cases.

Specimen Design. Many types of speci-mens have been used to evaluate bending


Fig. 3 Typical maximum stress (S ) vs. number of cycles (N ) bending fatigue plots for 6 carburized steels. R = –1. Source: Ref 4

fatigue in carburized steels. Rotating beam,unnotched four-point bend, notched four-pointbend, and cantilever beam specimens have allbeen used, and they have in common a maxi-mum applied surface tensile stress and decreas-ing tensile stress with increasing distance intothe specimen. Axial fatigue testing of carbur-ized specimens, which applies the maximumtensile stresses uniformly over the cross sectionof a specimen, invariably results in subsurfaceinitiation and propagation of fatigue cracks inthe core of carburized specimens, and thereforeit does not permit evaluation of the resistance ofcase microstructures to fatigue.

Brugger was the first to use cantilever bendspecimens to evaluate the fracture and fatigue ofcarburized steels (Ref 7). Figure 5 shows a can-tilever bend specimen that has evolved from the Brugger specimen. The radius between thechange in section simulates the geometry at theroot of gear teeth and results in maximumapplied surface stresses just where the cross sec-tion begins to increase, as shown in Fig. 6 (Ref8). An important feature of this specimen is the

rounding of the corners of the beam section. Ifthe corners are square, the carbon introducedinto the corner surfaces cannot readily diffuseinto the interior of the specimen. As a result, thecorner microstructures may have significantlyelevated levels of retained austenite and coarsecarbide structures—both microstructural fea-tures that influence bending fatigue resistance(Ref 8).

Mean Stress and Stress Ratio. The maxi-mum applied surface tensile stress is the testingparameter plotted in S-N curves that characterizebending fatigue. However, the applied stressranges between maximum and minimum valuesduring a fatigue cycle, and two other parameters,mean stress and stress ratio, are important for thecharacterization of fatigue. The mean stress isthe algebraic average of the maximum and mini-mum stresses in a cycle, and as discussed, thestress ratio, R, is the ratio of the minimum stressto the maximum stress in a cycle. Thus R valuesmay range from –1, for fully reversed loadingthat ranges between equal maximum tensile andcompressive stresses, to positive values where


Fig. 4 Strain amplitude vs. reversals to failure for uncarbur-ized (solid symbols) and carburized (open symbols)

4027 steel (0.80% Mn, 0.28% Si, 0.27% Mo). Source: Ref 6

Fig. 6 Location of maximum stress on the cantilever bendspecimen shown in Fig. 5 as determined by finite ele-

ment modeling

Fig. 5 Example of a cantilever specimen used to evaluatebending fatigue of carburized steels. Specimen edges

are rounded and maximum stress is applied at the locationshown in Fig. 6. Dimensions in millimeters

Fig. 7 Typical allowable-stress-range diagram. Source: Ref 9

especially effective for parts with sharp notches.In the absence of notches, carburizing is mostsuitable for parts subjected to fatigue loading atlow values of mean stress.

The testing of actual machine compo-nents is another important approach to thefatigue evaluation of carburized steels. Anexample of component testing is the bendingfatigue testing of single teeth in gears (Ref 11).Gears are fabricated, carburized, and mountedin a fixture so that one tooth at a time is sub-jected to cyclic loading. More recently, identi-cally carburized specimens of the same steelwere subjected to cantilever bend and singletooth bending fatigue testing (Ref 12). The

the stress is cycled between two tensile values(Ref 5). Much of the bend testing of cantileverspecimens described subsequently is performedwith R values of 0.1 in order to preserve detailsof the fracture surface.

Figure 7 shows a typical allowable-stress dia-gram that plots fatigue strength versus meanstress for a given material (Ref 9). The diagramshows that the most severe condition for fatigueis for fully reversed testing with R = –1.0. As themean stress increases, the fatigue strength interms of maximum applied stress increases, butthe allowable stress range decreases. Zurn andRazim (Ref 10) have examined the effect ofnotch severity and retained austenite on allow-able-stress/mean-stress diagrams of carburizedsteels, and they conclude that carburizing, rela-tive to the use of through-hardened steels, is


Fig. 8 Fatigue fracture in gas-carburized and modified 4320steel. (a) Overview of initiation, stable crack propaga-

tion, and unstable crack propagation. (b) Same area as shown in(a), but with extent of stable crack indicated by dashed line. (c)Higher magnification of intergranular initiation and transgranu-lar stable crack propagation areas. SEM Fractographs. Source:Ref 13

mechanisms of fatigue failure, based on fracturesurface examination, were found to be the same,but the single tooth testing showed higher levelsof fatigue resistance than did the cantilever test-ing, a result attributed to the higher surfacecompressive stresses that were measured in thegear tooth specimens. More detailed informa-tion on testing of gears can be found in Chapter15, “Mechanical Testing.”

Stages of Fatigue and Fracture

Bending fatigue fractures of carburized steelsconsist of well-defined stages of crack initiation,stable crack propagation, and unstable crackpropagation. The fracture sequence is stronglyinfluenced by the gradients in strength, micro-structure, and residual stress that develop in car-burized steels. Figure 8 shows a series of SEMfractographs that characterize the typical frac-ture sequence of a direct-quenched carburizedsteel. The cantilever bend specimen from whichthe fractographs of Fig. 8 were taken was a 4320steel carburized to a 1 mm (0.03937 in.) casedepth at 927 °C (1700 °F), quenched from 850°C (1560 °F) into oil at 65 °C (150 °F), and tem-pered at 150 °C (300 °F) for 1 h. The specimenwas tested in bending fatigue with an R value of0.1 (Ref 13). Figures 8(a) and (b) show a low-magnification overview of the initiation, stablepropagation, and unstable fracture surfaces, andFig. 8(c) shows the intergranular initiation andtransgranular stable crack propagation zones ofthe fracture at a higher magnification.

Intergranular cracking at prior-austenitegrain boundaries is an almost universal fracturemode in the high-carbon case of direct-quenched carburized steels (Ref 13). Not onlydo the fatigue cracks initiate by intergranularcracking, but also the unstable crack propagateslargely by intergranular fracture until it reachesthe lower-carbon portion of the case, where duc-tile fracture becomes the dominant fracturemode. In fact, sensitivity of the case microstruc-tures to intergranular fracture makes possiblethe quantitative characterization of the size andshape of the stable fatigue crack, as shown inFig. 8(b). The transition from the transgranularfracture of the stable crack to the largely inter-granular fracture of the unstable fracture is iden-tified by the dashed line.

A replica study of carburized specimens sub-jected to incrementally increasing stressesshowed that surface intergranular cracks initi-ated when the applied stresses exceeded theendurance limits (Ref 13). Thus, it appears that

in direct-quenched carburized specimens, inter-granular cracks are initiated as soon as theapplied surface bending stress reaches a levelsufficient to exceed the surface compressiveresidual stress and the cohesive strength of theprior-austenite grain boundary structures. Thesurface intergranular cracks are shallow, typi-cally approximately two to four austenitegrains, and are arrested, perhaps because of aplastic zone smaller than the grain size at the tip


Fig. 9 Hardness vs. distance from the surface of direct-cooledgas-carburized SAE 4320 steel. Superimposed on the

hardness profile is the range of critical depths (vertical dashedband) at which stable fatigue cracks became unstable in bendingfatigue of similarly processed steels. Source: Ref 13

Table 7 Fracture toughness results for carburized SAE 4320 bending fatigue specimens

Max stress, MPaCycles

to failureDepth, a,

mmWidth, c,

mm a/c MKIc, MPa ,

Eq 211m KIc, MPa ,

Eq 221m KIc, MPa ,

Eq 231m

1370 6,400 175 388 0.45 0.87 30 29 2216,900 170 355 0.48 0.86 29 28 2115,300 200 210 0.95 0.78 18 18 12

1285 17,400 230 300 0.77 0.81 22 22 1518,700 230 295 0.78 0.81 22 22 15

1235 34,100 210 300 0.70 0.81 22 22 151160 21,700 230 295 0.78 0.81 19 19 13

32,300 220 295 0.75 0.81 19 19 14

Equations used to determine the information in this table are defined in text. Source: Ref 13

of the sharp intergranular cracks, and the factthat strain-induced transformation of retainedaustenite in the plastic zone ahead of the crackintroduces compressive stresses (Ref 14, 15).The fatigue crack then propagates in a trans-granular mode, and when the stable crackreaches critical size, as defined by the fracturetoughness, unstable fracture occurs.

The initiation and stable crack zones of car-burized steels are quite small and are often diffi-cult to identify. Figure 9 based on the measure-ment of critical crack sizes in a number ofdirect-quenched carburized 4320 steels, showsthat the size of the unstable cracks ranges from0.170 to 0.230 mm (0.00669 to 0.00906 in.), andthat the cracks, therefore, become unstable wellwithin the high-carbon portion of the carburizedspecimens. The small critical crack sizes areconsistent with the low fracture toughness ofhigh-carbon steel low-temperature-tempered(LTT) microstructures susceptible to intergranu-lar fracture (Ref 16). When the critical crack

sizes and the stresses at which the cracks becomeunstable are used to calculate the fracture tough-ness of the case microstructures of carburizedsteels (Ref 13), the results show good agreementwith the range of fracture toughness, 15 to 25MPa , that has been measured from through-hardened specimens with high-carbon LTTmartensitic microstructures (Ref 16). Table 7shows the data used to calculate the various casefracture toughness values in gas-carburized4320 steel and the fracture toughness values cal-culated according to three different fracturetoughness equations (Ref 13):

(Eq 1)

(Eq 2)

and

(Eq 3)

where

with φ the aspect ratio of crack depth (a) andcrack length (c) such that:

The unstable crack that proceeds through thehigh- and medium-carbon martensitic portionsof the case may be arrested when the sensitivityto intergranular fracture decreases at a case car-

f2 � 1 � 1.464 a a

cb 1.65

Q � f2 � 0.212 a sa

sysb 2

KIC �Msa2ap

Q

KIC �

c1.2sa � 0.683 a 0s0xba d2ap

Q

KIC �1.2sa2ap

Q

1m


Fig. 10 Intergranular bending fatigue crack initiation at thesurface of a gas-carburized and direct-cooled SAE

8719 steel specimen. Source: Ref 20

Fig. 11 Intergranular fracture in case unstable crack propa-gation zone in gas-carburized and direct-cooled SAE

4320 steel

bon content between 0.5 and 0.6% (Ref 17). Thecontinued application of cyclic loading at thispoint then may cause a secondary stage of stablefatigue crack propagation, characterized bytransgranular fracture, resolvable fatigue stria-tions, and secondary cracking (Ref 12). Thisstage of low-cycle, high-strain fatigue is shortand gives way to ductile overload fracture of thecore.

Intergranular Fracture and Fatigue

Intergranular fracture at the prior-austenitegrain boundaries of high-carbon case micro-structures dominates bending fatigue crack ini-tiation and unstable crack propagation of direct-quenched carburized steels. The intergranularcracking may be associated with other micro-structural features, such as the surface oxidesgenerated by gas carburizing, but it generallyextends much deeper into a carburized case thanthe oxide layer. Several studies have docu-mented bending fatigue crack initiation by in-tergranular fracture even in the absence of sur-face oxidation, where, for example, the oxidizedsurface has been removed by chemical or elec-tropolishing (Ref 18) or no oxidation is presentbecause the specimens were vacuum or plasmacarburized (Ref 19).

Figure 10 shows an example of intergranularfatigue crack initiation in a direct-quenchedspecimen of gas-carburized type 8719 steel (Ref20). There is a shallow zone of surface oxida-tion, about 10 μm in depth, but the intergranularcracking extends much deeper into the speci-men. Figure 11 shows extensive intergranularcracking in the unstable crack propagation zonein the case of a direct-quenched, gas-carburized

4320 steel. Auger electron spectroscopy (Fig.12) shows that such intergranular fracture sur-faces have higher concentrations of phosphorusand carbon, in the form of cementite, than dotransgranular fracture surfaces removed fromprior-austenite grain boundaries (Ref 21, 22).Thus, the brittle intergranular fracture thatoccurs in stressed high-carbon case microstruc-tures of carburized steels is associated with thecombined presence of segregated phosphorusand cementite at prior-austenite grain bound-aries. These grain boundary structures are pres-ent in as-quenched specimens and do notrequire tempering for cementite formation, as istypical in the intergranular mode of temperedmartensite embrittlement in medium-carbonsteels (Ref 23). This embrittlement, termedquench embrittlement, is found in quenchedsteels with carbon contents as low as 0.6% (Ref24). There is evidence that phosphorus segrega-tion stimulates the formation of the grainboundary cementite (Ref 22).

The higher the phosphorus content of a car-burized steel, the lower its bending fatigue resis-tance and case fracture toughness. Figure 13shows S-N curves for a series of gas-carburizedand direct quenched modified 4320 steels withsystematic variations in phosphorus contentfrom 0.031 to 0.005% (Ref 22). Endurance lim-its and low-cycle fatigue resistance increasewith decreasing phosphorus content, but littledifference is noted between the performance ofthe 0.005 and 0.017% phosphorus specimens.All of the specimens, even those with the lowestphosphorus content, failed by intergranular ini-tiation of fatigue cracks.


Fig. 12 Auger electron spectra from case fracture surfaces of carburized 8620 steel. (a) From transgranular fracture surface. (b) Fromintergranular fracture surface. No phosphorus peak is detectable in the spectrum produced from the transgranular fracture,

and a small phosphorus peak, clearly shown by the 10× magnification, is produced from the intergranular fracture surface. These obser-vations are consistent with other investigations that show that phosphrous segregates to austenite grain boundaries during austenitizing.Source: Ref 21


Fig. 13 Effect of phosphorus content on the bending fatigueof direct-quenched, gas-carburized modified 4320

steel with 0.005, 0.017, and 0.031 wt% phosphorus, as marked.Source: Ref 22

The bending endurance limits of gas-carbur-ized specimens in which fatigue is initiated byintergranular fracture typically range between1050 and 1260 MPa (152 and 183 ksi) (Ref 25,26). This range is based on studies of cantileverbend specimens with good surface finish,rounded specimen corners, nominal amounts ofsurface oxidation, and loading at R = 0.1. Vari-ations within this range may be due to variationsin austenitic grain size, inclusion contents,retained austenite content, or residual stresses,as discussed subsequently. Nevertheless, thecommon mechanism of bending fatigue crackinitiation of direct-quenched specimens is inter-granular fracture at embrittled grain boundariesin a microstructure of LTT martensite andretained austenite.

Carburized steels with high nickel content donot appear to be as susceptible to intergranularcracking as steels with low nickel content (Ref27). Also, major changes in the case microstruc-tures of carburized steel, such as those producedby reheating, result in bending fatigue crack ini-tiation sites other than embrittled prior-austenitegrain boundaries. Microstructural conditionsthat produce fracture initiation other than byintergranular cracking are also described herein.

Inclusions and Fatigue

Inclusions—phases formed between metallicelements and nonmetallic elements such as sul-fur and oxygen—are an important microstruc-tural component of steels. Coarse or high densi-ties of inclusions initiate fracture and lower thetoughness of steels. As a result, modern steel-making practices, which incorporate improved

deoxidation, shrouding of liquid steel to preventreoxidation, vacuum degassing, argon blowing,and desulfurization, are designed to substan-tially increase the “cleanliness” of steels bylowering the number and/or modifying the mor-phology of inclusions.

In carburized steels, the very high strength ofthe carburized case makes the plastic zone aheadof surface discontinuities (such as machiningmarks), flaws, or cracks very small, and there-fore, in clean steels, distributed inclusions play asmaller role in fracture than, for example, uni-formly distributed and closely spaced grainboundary embrittling structures or surface ox-ides. In other words, the high stresses in the plas-tic process zone have a much higher probabilityof acting on grain boundaries or surface oxidesthan on widely spaced inclusions.

Although inclusions often play a secondaryrole in the fatigue of gas-carburized steels, espe-cially when there are other microstructuralcauses of fatigue crack initiation, they may beinvolved in the fatigue process in several ways.Inclusions in the carburized steel may eithercombine with other features that initiate fatiguecracks, or in the absence of such features, serveas the sole source of fatigue crack initiation.

An example of the first type of effect wasdemonstrated in a study that examined theeffects of systematic variations in sulfur contenton the bending fatigue resistance of a gas-carburized low alloy steel (Ref 20). Sulfur com-bines with manganese to form manganese sul-fide (MnS) inclusions in steel. The MnSparticles are plastic during hot rolling, and as aresult, are elongated in the rolling direction.This elongation imparts an anisotropy to themechanical properties of the steel, which makesthe effect of inclusions a function of the orienta-tion of the particles relative to the direction ofthe applied load.

S-N (stress vs. life) curves for specimens of agas-carburized SAE 8219-type steel with threelevels of sulfur are plotted in Fig. 14. Theendurance limit decreases with increasing sulfurcontent. A number of the specimens with thehigher sulfur contents showed runouts at 10 mil-lion cycles at stress levels higher than theendurance limits shown, but the specimens thatfailed at the lower stresses were used to establishthe endurance limits. In these specimens, elon-gated MnS inclusion particles that happened tobe close to the specimen surfaces were associ-ated with the fatigue fracture initiation. Fatiguefracture initiation of the direct-quenched, gas-


Fig. 15 Elongated manganese sulfide particles associatedwith bending fatigue crack initiation at the surface of

a gas-carburized SAE 8219-type steel. SEM photomicrograph.Source: Ref 20

Fig. 16 Endurance limits as a function of prior-austenitegrain size from various studies of bending fatigue of

gas-carburized 4320 steels. Source: Ref 28

Fig. 14 S-N curves determined by bending fatigue of a gas-carburized SAE 8219-type steel containing 1.40 Mn,

0.61 Cr, 0.30 Ni, 0.20 Mo, and three levels of sulfur. Source: Ref 20

carburized specimens was still dominated byintergranular fracture, but if sulfides were pres-ent at the highly stressed surfaces of the bendingfatigue specimens, they apparently provided anextra source of stress concentration and reducedfatigue performance.

An example of MnS particles associated withfatigue crack initiation in a carburized 8219-typesteel is shown in Fig. 15. Although fatigue resis-tance is lowered somewhat by the presence ofincreased densities of MnS particles, the de-crease may be outweighed by a gain in machin-ability associated with higher levels of sulfur.

Austenitic Grain Size and Fatigue

Effect of Fine Grain Size on Microstruc-tures and Properties. Prior-austenite grain

size of carburized steels correlates strongly withbending fatigue resistance. Generally, the finerthe prior-austenite grain size, the better thefatigue performance. For example, Fig. 16 showsa direct relationship of bending fatigue en-durance limit on prior-austenitic grain size, plot-ted as the inverse square root of the grain size, forseveral sets of carburized 4320 steels (Ref 28).

The refinement of austenite grain size hasseveral effects on the case microstructure of car-burized steels. A finer prior-austenite grain sizeproduces a finer martensitic microstructure onquenching, and therefore, raises the strength ofthe carburized case. Increases in strength arebeneficial to high-cycle fatigue resistance, asdiscussed previously in the section on bendingfatigue testing.

Another very important consequence of fineaustenitic grain size is the dilution of the grainboundary segregation of phosphorus. In fact,very fine austenitic grain sizes can eliminate thesensitivity of high-carbon case microstructuresto intergranular fracture. As a result, other mech-anisms of fatigue crack initiation replace inter-granular cracking, generally to the benefit offatigue performance. The high values of en-durance limits shown for the very fine grain spec-imens in Fig. 16 were associated with fatiguecrack nucleation at surface oxidation, not at em-brittled prior-austenite grain boundaries. Al-though, as discussed below, surface oxides formon austenite grain boundaries and fatigue cracksmay nucleate on the oxide-covered austeniteboundaries, fine-grain specimens show no inter-granular fracture below the oxidized surfacelayers.


Fig. 17 Prior-austenite grain size as a function of depth from the surface of gas-carburized 4320 specimens in the as-carburized,direct-quenched condition and reheated conditions. Source: Ref 28

Reheat Treatments to Achieve Fine GrainSize. The most effective way to produce veryfine grains in carburized steels is by slow coolingand reheating of carburized parts at temperaturesbelow the Acm where austenite and cementite arestable. The cementite particles effectively retardaustenite grain growth and reduce the carboncontent of the austenite. Specimens reheated toabove the Acm may show grain refinement,depending on the temperature of heating, butbecause all carbides are dissolved, grain sizerefinement is not as effective as in specimensheated below the Acm. Figure 17 shows aus-tenitic grain size as a function of distance fromthe carburized surface of gas-carburized 4320steel specimens in the direct-quenched conditionand after one and three reheating treatments (Ref28). The reheat treatments very effectivelyreduce the near-surface case grain size wherecarbon content is the highest, and therefore, thegreatest density of carbide particles is retainedduring intercritical reheating.

Intercritical-temperature reheat treatments ofcarburized steels produce very fine austeniticgrain sizes and high endurance limits. Typicallythe endurance limits are above 1400 MPa (203ksi) (Ref 28). However, the beneficial effects ofthe reheating on bending fatigue resistance arenot due to grain size refinement alone. Thereduced carbon content of the austenite whencarbides are retained raises Ms temperatures and

reduces the amount of retained austenite in theas-quenched case microstructures. Reduced lev-els of retained austenite raise the strength ofcase microstructures, and therefore, also maycontribute significantly to the improved high-cycle fatigue performance of fine-grain, inter-critically reheated carburized steels.

Surface Oxidation and Fatigue

The surface oxidation produced during gascarburizing may or may not significantly reducebending fatigue resistance. The most severeeffects of such oxidation are associated with areduction in near-surface case hardenability,which results from the removal of chromium,manganese, and silicon from solution in theaustenite by the oxide formation (Ref 29, 30).The reduced case hardenability can cause non-martensitic microstructures, such as ferrite, bai-nite, and pearlite, to form at the surface of thecarburized steel. Not only is the surface hard-ness reduced, but the residual surface stressesmay become less compressive or even tensile.

Figure 18 and 19 show the effects of surfaceoxidation with reduced hardenability on thebending fatigue and residual stresses of 8620 and4615 gas-carburized specimens (Ref 31). The4615 steel has higher hardenability by virtue ofhigher nickel and molybdenum contents and alower sensitivity to surface oxidation by virtueof reduced manganese and chromium contents


Fig. 18 S-N curves for direct-quenched gas-carburized 4615and 8620 steels, notched 4-point bend specimens.

Compositions of the steels are given in Table 1. Non-martensitictransformation products were present on the surfaces of the 8620steel specimens and absent on the 4615 steel specimens. Source:Ref 31

Fig. 19 Residual stress as a function of depth below the sur-face of the direct-quenched gas-carburized 4615

and 8620 steel specimens described in Fig. 18. E-Polish = elec-trolytic polish. Source: Ref 31

(Ref 31). As a result of the different chemistries,the 8620 steel formed pearlite in the near-surfaceregions of the case, while the microstructure ofthe 4615 steel, despite some oxidation, consistedonly of plate martensite and retained austenite atthe surface (Ref 31). These differences in micro-structures due to surface oxidation and reducedcase hardenability are consistent with the differ-ences in bending fatigue performance and resid-ual stresses shown between the two steels in Fig.18 and 19. This study illustrates the importanceof steel chemistry on controlling surface oxida-tion and the associated formation of nonmarten-sitic microstructures in gas-carburized steels.Another approach used to reduce surface oxideformation in steels with low hardenability is touse more severe quenching with higher coolingrates.

If the hardenability of a steel is sufficient toprevent the formation of nonmartensitic micro-structures for a given gas carburizing andquenching schedule, surface oxidation has amuch reduced effect on bending fatigue per-formance. In direct-quenched specimens, as dis-cussed previously and demonstrated in Fig. 10,intergranular fracture to depths much deeperthan the oxidized layers dominates fatigue crackinitiation. However, when the conditions forintergranular crack initiation are minimized, as,for example, by reheating or shot peening, thesurface oxide layers become a major location forbending fatigue crack initiation. Figure 20shows crack initiation in the oxidized zone of a

gas-carburized and reheated specimen of 4320steel. The initiation is confined to the oxidizedzone, and stable transgranular fatigue propaga-tion proceeds directly below the oxidized zonewith no evidence of intergranular fracture.

Retained Austenite and Fatigue

Retained austenite is one of the most impor-tant microstructural components in the case ofcarburized steels. The amounts of retainedaustenite vary widely, depending on carbon andalloy content, heat-treating conditions, and spe-cial processing steps such as shot peening andsubzero cooling. Generally, the higher the car-bon and alloy content, the lower the Ms temper-ature and the higher the retained austenite con-tent in the microstructure. The low-temperaturetempering applied to carburized steels, gener-ally performed at temperatures below 200 °C(400 °F), is not high enough to cause the re-tained austenite to transform, and therefore,retained austenite remains an important compo-nent of the microstructure. At higher temperingtemperatures, retained austenite transforms tocementite and ferrite with attendant decreases inhardness and strength as the martensitic micro-structure coarsens.

The role that retained austenite plays in thebending fatigue performance of carburizedsteels has been difficult to identify because ofthe variable loading conditions that may be ap-plied to carburized machine components andthe complicating effects of other factors, such as


Fig. 20 Bending fatigue crack initiation in gas-carburized and reheated 4320 steel. The dashed line corresponds to maximum depthof surface oxidation, and all fracture below dashed line is transgranular. Source: Ref 28

residual stresses, grain boundary embrittlingstructures, and surface oxidation. With respectto loading conditions, it appears that higheramounts of retained austenite are detrimental tohigh-cycle fatigue and reduce endurance limits(Ref 10, 14) while higher amounts of retainedaustenite are beneficial for low-cycle, high-strain fatigue (Ref 14, 32, 33).

Reduced retained austenite contents of LTTmartensite/austenite composite microstructuresincrease elastic limits and yield strengths (Ref34), and therefore, benefit stress-controlled,high-cycle fatigue. One of the approaches toreducing the retained austenite content in thecase microstructures of carburized steels, is toreheat carburized specimens to temperaturesbelow the Acm and quench. Invariably such re-heating and quenching significantly increasesbending fatigue endurance limits compared todirect-quenched specimens of identically car-burized specimens (Ref 28). The reheating notonly reduces retained austenite but also refinesthe austenitic grain size, refines the martensiticstructure, and reduces susceptibility to inter-granular fracture—all features that are known toimprove fatigue resistance. Therefore, im-proved high-cycle fatigue resistance of reheatedand quenched specimens is related to a combi-nation of microstructural changes, includinglow retained austenite contents.

The benefit of retained austenite to strain-controlled, low-cycle bending fatigue is relatedto the improved ductility and reduced strength

and hardness that retained austenite contributesto a composite LTT martensite/austenite casemicrostructure. In addition, retained austenite,at sufficiently high applied strains and stresses,undergoes deformation-induced transformationto martensite (Ref 35). The volume expansionassociated with the strain-induced formation ofmartensite creates compressive stresses (Ref21) that lead to reduced rates of fatigue crackgrowth, accounting for the enhanced low-cyclefatigue performance that is observed in carbur-ized steels with high amounts of retainedaustenite in the case (Ref 33).

Subzero Cooling and Fatigue

Cooling carburized steel below room temper-ature is a processing approach sometimes usedto reduce the retained austenite content in thecase regions of carburized steels. The transfor-mation of austenite to martensite is driven bytemperature changes, and the low Ms tempera-tures of high-carbon case regions of carburizedalloy steels limit the temperature range betweenMs and room temperature over which martensiteforms. Therefore, the temperature range formartensite formation and the reduction of re-tained austenite is extended by cooling belowroom temperature. The cooling treatments arevariously referred to as subzero cooling, refrig-eration treatments, or deep cooling.

In addition to the effects of retained austeniteon bending fatigue, as discussed, any deforma-tion-induced transformation of retained austen-


Fig. 21 S-N curves of vacuum-carburized 8620 and EX 24(0.89% Mn, 0.24% Mo, 0.55% Cr) steels. The lower

curves were obtained from specimens subzero cooled to –196°C, and the upper curves were obtained from specimens not sub-jected to subzero cooling. Source: Ref 38

ite during cyclic loading in service, because ofthe volume expansion that accompanies thetransformation of austenite to martensite, maychange the dimensions of a carburized compo-nent. Therefore, subzero cooling is one ap-proach to reduce retained austenite in parts thatrequire high precision and stable dimensionsthroughout their service life. However, severalstudies show that subzero cooling lowers thebending fatigue resistance of carburized steels.Nevertheless, high-quality, high-performanceaircraft and helicopter gears are routinely sub-jected to subzero cooling without apparent detri-mental effects (Ref 36). For example, a com-monly used carburizing steel for aircraft gears is 9310, which contains about 3 wt% Ni (seeTable 1). The high nickel content lowers the Mstemperature and increases the amount of aus-tenite at room temperature. The austenite con-tent can be reduced by subzero cooling, probablywith adverse effects on localized residual stress.However, the latter adverse effect of subzerocooling may be offset by fine austenite grainsize, and high nickel content may improve thefracture toughness and fatigue resistance of car-burized steels (Ref 37) to a level where fatigueresistance is not adversely affected by subzerocooling.

In the low-alloy steels commonly used for car-burizing, subzero cooling used to reduce re-tained austenite may reduce the bending fatigueresistance of carburized components. If refriger-ation treatments are applied, parts should betempered both before and after. Figure 21 showsan example of the detrimental effects of subzerocooling on the bending fatigue resistance of car-burized specimens. The data were produced inan experimental study of vacuum-carburizedspecimens of 8620 and EX 24 steel that weredeep cooled to –196 °C (–321 °F) in liquid nitro-gen (Ref 38). The overall fatigue performance inthis study was complicated by high retainedaustenite contents and coarse carbide particles atsquare specimen corners, but the detrimentaleffect of subzero cooling on bending fatigue per-formance is clearly demonstrated in Fig. 21.

The detrimental effect of subzero cooling onthe bending fatigue of carburized specimens hasbeen related to changes in residual stress by sev-eral investigations (Ref 39–41). The overall sur-face residual stresses become increasingly com-pressive, as measured from the martensite in thecase and as expected from the constraint of theexpansion that accompanies the transformationof austenite to martensite as temperature is

decreased. However, the residual stresses in theaustenite phase are measured to be tensile, espe-cially at the surface of the carburized specimens.These tensile stresses would then be expected tolower the surface tensile stresses applied in bend-ing to initiate fatigue cracks. Microcrack forma-tion within martensite plates and at plate/austen-ite interfaces may be enhanced by the localizedresidual stresses induced by subzero cooling(Ref 41), but they could be minimized by main-taining a fine prior-austenite grain size andapplying reheating treatments (Ref 42, 43).

Residual Stresses, Shot Peening, and Fatigue

Compressive residual stresses are formed inthe case microstructures of carburized steels asa result of transformation and temperature gra-dients induced by quenching (Ref 44, 45). Themagnitude and distribution of the residualstresses, therefore, are complex functions of thetemperature gradients induced by quenching(Ref 46), which in turn are dependent on speci-men size and geometry, the hardenability of thesteel, the carbon gradient, and the case depth.The residual stresses as a function of case depthare routinely measured by x-ray diffraction, andconsiderable effort has been applied to model-ing residual stress profiles in carburized steelsas a function of cooling and hardenability (Ref47, 48).

Figure 22 shows the range and pattern of com-pressive residual stresses typically formed in thecase regions of direct-cooled carburized steels(Ref 49). The compressive residual stresses off-set the adverse effects of factors such as quenchembrittlement and intergranular fracture to


Fig. 22 Ranges and patterns of residual stresses as a functionof depth for 70 carburized steels. Source: Ref 49

Fig. 23 Effect of a shot peening parameter (Almen intensityas described in text) on the low-cycle fatigue of a

carburized helical gear made from 4023 steel. Source: Ref 51

which high-carbon microstructures are suscepti-ble (Ref 24), and they increase the fracture andfatigue resistance of direct-quenched parts tolevels that provide good engineering perfor-mance. As discussed earlier, case residualstresses in carburized steels are adversely modi-fied by subzero cooling, and they are positivelymodified (made locally more compressive) bythe strain-induced transformation of austenite tomartensite. Tempering lowers residual compres-sive stresses because of dimensional changesthat accompany the recovery and coarsening ofthe martensitic microstructure during tempering(Ref 50).

The fatigue lives of carburized steel gears canbe significantly improved by shot peening,which is a method of cold working in whichcompressive stresses are induced in the exposedsurface layers of metallic parts by the impinge-ment of a stream of shot. The shot, which maybe composed of cast steel, cast iron, or glassbeads, is directed at the metal surface at highvelocity under controlled conditions. Details onthe process can be found in the article “ShotPeening” in Volume 5 of the ASM Handbook.

The effect of shot peening process parame-ters on fatigue life of carburized helical gearshas been investigated (Ref 51). Low-cycle gear-tooth bending fatigue lives were evaluated as afunction of Almen intensity parameter. Almenintensity is an indirect method of monitoring theaggregate amount of energy transfer or residualcompressive stresses imparted to the workpiece.The method uses a strip of SAE-AISI 1070spring steel in the 44 to 50 HRC range. The stripis mounted to an Almen test block and exposedto the blast in identical fashion as the criticalarea of the workpiece, with the same parame-ters. After peening, the Almen strip is removedfrom the block and the amount of maximum

deviation from flat is measured by an Almengage. This measurement is called arc height.Details of the design and use of Almen gagesand test strips are given in SAE standards J442,“Test Strip, Holder and Gage for Shot Peening,”and J443, “Procedure for Using Shot PeeningTest Strip.” Additional information on the shotpeening process can also be found in Chapter 9,“Carburizing.” Refer to the section “Shot Peen-ing of Carburized and Hardened Gears” and inparticular Fig. 62 in Chapter 9 which illustratesthe shot peening test setup.

Figure 23 shows the data obtained from thefatigue life versus Almen intensity study on car-burized 4023 steel. The gears were peened tothree Almen intensity “A” levels (0.305, 0.457,and 0.609 mm, or 0.012, 0.018, and 0.024 in.)using steel shot in the size of S280, and to oneAlmen intensity “C” level of 0.008 in. with S280shot. As Fig. 23 clearly shows, the mean fatiguelife of unpeened gears was about 9800 cycleswhile optimized shot peening procedures (24AAlmen intensity) resulted in a mean fatigue lifeexceeding 33,000 cycles. The improved fatigue


Vacuum carbon deoxidationPrecipitation deoxidationPrecipitation deoxidation, plus shrouding

Original bottom pourRecent bottom pourVacuum-arc remelted

0.0001

100

10

1

1000

0.001 0.01 1 100.1

Tool length of inclusion stringers, mm/cm3

Fatig

ue li

fe (

mill

ions

of r

evol

utio

ns)

1980Present

Fig. 24 Cleanness and rolling contact fatigue life improvements in carburized steels as steelmaking practices have changed. Source:Ref 57

life for 24A peened gears was attributed to thehighest compressive residual stress incurred.

Other Properties of Interest for Carburized Steels

Although much of the recent research on prop-erties of carburized steels has centered aroundbending fatigue (see previous section), there areother properties that effect the service life of car-burized components. As will be described forth-with, these mechanical properties are stronglyinfluenced by core and case microstructure, casedepth, residual stresses, and alloy chemistry.

Rolling Contact Fatigue

Rolling contact fatigue is a surface-pitting-type failure commonly found in gears (seeChapter 13, “Gear Failure Modes and Analy-sis,” for details). Rolling contact fatigue differsfrom classic structural fatigue (bending or tor-sional) in that it results from contact or Hertzianstress state. This localized stress state resultswhen curved surfaces are in contact under a nor-mal load. Generally, one surface moves over theother in a rolling motion. The contact geometryand the motion of the rolling elements producesan alternating subsurface shear stress. Subsur-face plastic strain builds up with increasingcycles until a crack is generated. The crack thenpropagates until a pit is formed. Once surfacepitting has initiated, the bearing becomes noisyand rough running. If allowed to continue, frac-

ture of the rolling element and catastrophic fail-ure occurs. Fractured races can result fromfatigue spalling and high hoop stresses.

Extreme cases of spalling are associated withcase crushing or cracking initiated at the case-core interface. If sliding is coupled with contactloading, surface pits develop. Very high contactloads cause microstructural changes withinhigh-carbon martensite that are revealed by var-ious types of etching (Ref 52–54). Generallyretained austenite is regarded as a microstruc-tural constituent that is beneficial for rolling-contact fatigue resistance (Ref 55, 56).

One of most effective means for improvingthe rolling contact fatigue life of carburizedsteels is by utilizing clean steel technology. Sec-ondary metallurgical techniques in ladle refin-ing and teeming practice have become the keyelements in improved steelmaking practices.Important developments include degassing anddeoxidation practices, improved temperaturecontrol, inert gas shrouding, improved refracto-ries, and the use of bottom-poured or signifi-cantly improved tundish systems, and largecross-section continuous casters. Figure 24demonstrates the improvements in rolling con-tact fatigue life of carburized steels as steelmak-ing practices have improved.

Wear Resistance (Ref 58)

Another important property afforded by thecarburizing process is wear resistance resultingfrom the high hardness of the case. As with bend-


Fig. 25 Hot hardness of three carburized steels. The dashedline corresponds to a surface hardness of 58 HRC.

Compositions for SAE 9310 and CBS 1000M are listed in Table1. The nominal composition for steel D is 0.12% C, 0.5% Mn,1.1% Si, 1.0% Cr, 2.0% Ni, 2.3% Mo, and 1.2% V. Source: Ref59

ing fatigue, there are a number of microstruc-ture/property relationships that must be consid-ered for wear-resistant applications.

Microstructural Features. The indepen-dent variables available for controlling the mi-crostructure/properties of carburized cases arethose that define the carburizing alloy (composi-tion, cleanliness) and those that define thecarburizing process (time/temperature/carbon-potential carburizing history, time/temperaturequenching history, time/temperature temperinghistory). These tools provide a considerabledegree of control over these microstructuralfeatures:

• Martensitea. Carbon content of source austeniteb. Plate size (austenite grain size)c. Strengthd. Secondary hardening

• Primary carbidesa. Sizeb. Volume fraction

• Retained austenitea. Volume fractionb. Carbon content

• Nonmetallic inclusionsand these global features:

• Case depth• Residual stress distribution

which determine the tribological properties ofthe case. The combination of properties that isbest for each application must then be decided.

The necessary case depth and case hardnesscan be estimated from a Hertzian stress calcula-tion, but other microstructural objectives can bespecified only qualitatively. For many applica-tions, the following “rules of thumb” apply:

• Sufficient case depth and case hardness mustbe provided to prevent indentation or casecrushing under the anticipated contact loads.For gears loaded in “line contact,” a mini-mum case hardness of 58 HRC frequently isspecified. When high contact loads are ac-companied by sliding, the near-surface hard-ness (to a depth of about 50 μm, or 2 mils)may have to be raised to prevent shearing ofsurface layers.

• The retained austenite content should be ashigh as possible, consistent with the require-ments of the previous rule. The retained aus-tenite content should be controlled by adjust-

ing the case carbon content, not by subzeroquenching after carburizing or by temperingat temperatures above 200 °C (390 °F).

• The tempering temperature chosen shouldbe as low as possible, but above the surfacetemperatures anticipated in finishing opera-tions and in service.

• The content of nonmetallic inclusionsshould be no higher than that needed foreconomical machining.

• Coarse primary carbides can be helpful inresisting abrasive wear. Fine primary car-bides can permit more retained austenite atthe same hardness level. Experiments shouldbe conducted to verify any benefits presumedto be associated with primary carbides.

Hot Hardness

Retention of hardness at elevated tempera-tures (hot hardness) is vitally important in appli-cations where high local temperature conditionscan be encountered. Examples include helicop-ter gears, speed reduction gear sets, and turbinegearing. Figure 25 provides hot hardness datafor several carburized steels. It is evident fromthese data that higher alloy content is needed toassure sufficient hardness at temperatures above315 °C (600 °F) encountered in severe service.

Bending Strength and Bend Ductility

In service, carburized and hardened steels aresubjected to bending loads and must be able to


Fig. 26 Bend ductility transition curves for carburized and hardened steels. Nominal alloy contents of the steels are listed withinthe diagram. Source: Ref 59

resist design loads and overloads without frac-ture. A variety of laboratory tests have been per-formed to define the resistance of carburizedand hardened steels to failure under bendingloads, and to provide information on the contri-bution of alloys in resisting failure.

Bend ductility of several carburized andhardened steels over a range of test tempera-tures from room temperature to –195 °C (–320°F) is given in Fig. 26. A comparison of the datafor carburized SAE 4817 steel with those forSAE 4027 (both with about the same amount ofretained austenite) shows that the steel alloyedwith a substantial amount of nickel exhibitedmuch greater ductility.

Razim (Ref 60) has observed that the staticbend test is useful in evaluating the ability of acarburized and hardened surface zone to sustainplastic deformation without cracking. A suit-able measurement can be the initial crackstrength. His summary of such tests indicatesthat with low surface carbon contents of about0.6% C, the initial crack strength increases withincreasing core strength; while with high sur-face carbon contents (about 1.2% C), the initialcrack strength becomes less dependent on corestrength, but drops to a considerably lower levelthan the crack strength exhibited by the steelswith 0.6% C at the surface.

Toughness

Toughness in carburized steels can be mea-sured in a variety of ways. In recent years,

attempts have been made to simulate serviceloads, single- as well as multiple-load applica-tions, different rates of load application, and toinclude realistic details in the test specimensuch as changes in notch severity or the use of apart such as a gear tooth as the specimen. Re-sults of one such test, the impact fracture test,will be described in this section. Additional testresults are reviewed in Ref 4.

Impact Fracture Strength. The specimenshown in Fig. 27 was used by Cameron and oth-ers (Ref 61) for single-blow impact tests as wellas fatigue tests. This simulated gear specimenwas loaded in a standard pendulum type testingmachine, with the specimen held in a verticalposition, similar to an Izod impact test. Aninstrumented tup permitted recording the energyabsorbed by the specimen as a function of timeduring the test. For carburized-and-hardenedsteels, the investigators found that alloy contentand core carbon content significantly influencedresistance to fracture under impact bending con-ditions. In Fig. 28 the chromium-molybdenumsteels exhibited higher fracture strengths thanthe manganese-chromium steels, but the nickel-chromium-molybdenum steel, PS55, not onlyexhibited much higher fracture strength, butfracture strength did not decrease with increas-ing carbon content.

In another study by Smith and Diesburg (Ref62), an attempt was made to define in moredetail the effect of alloy interactions on fracturestrength using the simulated gear-tooth speci-men shown in Fig. 27. Figure 29 summarizes


Fig. 27 Test specimen used by Cameron for fatigue, bend, and impact fracture tests. Typical results are shown in Fig. 28 and 29.Source: Ref 61

Fig. 28 Effect of core carbon content and alloy content on impact fracture strength of a series of steels, carburized at 925 °C (1700°F), cooled to 840 °C (1550 °F), oil quenched, and tempered at 150 °C (340 °F). Source: Ref 61


Fig. 29 Impact fracture strength of carburized steels contain-ing various combinations of molybdenum and

nickel. Open data points are for vacuum-melted heats; solid datapoints are for air-melted heats. Compositions were those of stan-dard steels to which molybdenum was added in varyingamounts, as indicated in the accompanying table. Source: Ref 62

the effect of molybdenum and nickel on fracturestrength for several different groups of steels,each modified by adding molybdenum. Eachgroup of steels was carburized to have similarcase depths and surface carbon contents, thenthe steel specimens were cooled from the car-burizing temperature to 845 °C (1550 °F),quenched in oil at 65 °C (150 °F), and then tem-pered at least 1 h at 170 °C (340 °F). It is evidentthat nickel in amounts greater than 0.5% is veryeffective in increasing fracture strength, espe-cially when molybdenum content is greater than 0.25%. The investigators also comparedvacuum-melted steels with air-melted steels and obtained higher fracture strengths with thevacuum-melted steels.

Fracture Toughness Data. Work by Dies-burg (Ref 63) included a study of fracturetoughness of several steels carburized to pro-duce case depths (at 0.5% C) between 0.75 and1.00 mm (0.030 and 0.040 in.) thick. Resultsshown in Fig. 30 indicate that the plane-strainfracture toughness (KIc) values for the highernickel steels SAE PS55, PS32, 9310, and 4820are quite similar, much higher than the valuesobserved for the lower nickel SAE 8620 steel at

all depths below the surface. Close to the car-burized surface, only small differences could beobserved among the steels tested.

Improved Elevated-TemperaturePerformance (Ref 58)

Several secondary hardening carburizingalloys have been developed for applications thatrequire resistance to elevated temperatures,such as helicopter gearing. (See the “Specialalloys” listed in Table 1.) These alloys make useof the precipitation of copper and/or M2C andMC carbides to provide resistance to softeningfor temperatures up to 550 °C (1020 °F).Because they contain substantial amounts ofmolybdenum and vanadium, these alloys re-semble low-carbon versions of tool steels. Someof the alloys are difficult to carburize because ofhigh silicon and chromium contents; preoxida-tion prior to carburizing is necessary to permitcarbon penetration. Secondary hardening alloyscould also be useful in ambient-temperatureapplications in which lubrication is marginal,because the heat generated by intermittentmetal-to-metal contact would not readily softenthe underlying metal.

One of the “Special Alloys” listed in Table 1 isPyrowear 53 (UNS K71040) which is used forhelicopter transmission drive gears. The highercopper content increases core impact strength,while the increased molybdenum provides im-proved elevated-temperature properties. The re-duced chromium levels enhance carburizability,while the vanadium maintains a fine grain size.

When compared to conventional grades, e.g.,SAE-AISI 9310, Pyrowear Alloy 53 exhibitssuperior temper resistance and high case hothardness while maintaining high core impactstrength and fracture toughness (126 to 132MPa , or 115 to 120 ). Table 8 listscore mechanical properties for this proprietarycarburizing grade.

Other Ferrous Alloys for Gears

In addition to wrought steels, the followingiron-base alloys are also used for gears:

• Cast carbon and alloy steels• Gray and ductile cast irons• P/M irons and steels• Stainless steels

1in.1m


Fig. 30 Fracture toughness in carburized steels as a function of distance below the surface. The SAE PS55, 9310, and 8620 steelswere commercial heats; the SAE PS32 and 4820 steels were laboratory heats. The PS32 and 4820 steels were quenched

directly after carburizing at 925 °C (1700 °F) into 170 °C (340 °F) oil; other steels were cooled from 925 °C to 840 °C (1700 to 1550 °F)before quenching into 65 °C (150 °F) oil. Data are also shown for 9310 steel that was refrigerated after quenching and before tempering.Source: Ref 63

Table 8 Core mechanical properties of Pyrowear Alloy 53Test temperature Yield strength Ultimate tensile strength Charpy V-notch impact

–54 –65 1103 160 1331 193 18 63 53–56 39–41Room temperature 965 140 1172 170 16 66.5 118–129 87–95100 212 . . . . . . . . . . . . . . . . . . 140–163 103–120177 350 896 130 1207 175 12 46 155–157 114–116

Source: Carpenter Technology Corporation

°C °F MPa ksi MPa ksiElongation in 4D, %

Reduction of area, % ft · lbfJ

• Tool steels• Maraging steels

Each will be discussed in subsequent sections.

Cast Steels

Steel castings are produced by pouringmolten steel of the desired composition into amold of the desired configuration and allowingthe steel to solidify. The mold material may besilica, zircon, chromite sand, olivine sand,graphite, metal, or ceramic. The choice of moldmaterial depends on the size, intricacy, dimen-sional accuracy of the casting, and cost. Whilethe producible size, surface finish, and dimen-sional accuracy of castings vary widely with thetype of mold, the properties of the cast steel arenot affected significantly.

Steel castings can be made from any of themany types of carbon and alloy steel produced inwrought form. Those castings produced in anyof the various types of molds and wrought steelof equivalent chemical composition respondsimilarly to heat treatment, have the same weld-ability, and have similar physical and mechani-cal properties. However, cast steels do notexhibit the effects of directionality on mechani-cal properties that are typical of wrought steels.This nondirectional characteristic of cast steelmechanical properties may be advantageouswhen service conditions involve multidirec-tional loading.

The cast steels used for gears are generallymodifications of standard SAE-AISI designa-tions. Common through-hardening cast steelsinclude 1045, 4135, 4140, 8630, 8640, and4340. Carburizing grades are usually 1020,


Fig. 31 Gear rack segment made from cast ASTM A 148Grade 120-95 alloy steel

Table 9 Properties of cast carbon and low-alloy steelsYield strength

MPa ksi MPaHardness,

HB MPa

Carbon steels

60 A 434 63 241 35 54 30 131 207 30 0.4865 N 469 68 262 38 48 28 131 207 30 0.4470 N 517 75 290 42 45 27 143 241 35 0.4780 NT 565 82 331 48 40 23 163 255 37 0.4585 NT 621 90 379 55 38 20 179 269 39 0.43100 QT 724 105 517 75 41 19 212 310 45 0.47

Alloy steels(b)

65 NT 469 68 262 38 55 32 137 221 32 0.4770 NT 510 74 303 44 50 28 143 241 35 0.4780 NT 593 86 372 54 46 24 170 269 39 0.4590 NT 655 95 441 64 44 20 192 290 42 0.44105 NT 758 110 627 91 48 21 217 365 53 0.48120 QT 883 128 772 112 38 16 262 427 62 0.48150 QT 1089 158 979 142 30 13 311 510 74 0.47175 QT 1234 179 1103 160 25 11 352 579 84 0.47200 QT 1413 205 1172 170 21 8 401 607 88 0.43

(a) Class of steel based on tensile strength, in ksi. A = Annealed, N = Normalized, NT = Normalized and tempered, QT = Quenched and tempered. (b) Below 8% totalalloy content. Source: Ref 64

Enduranceratioksi

Endurance limitElongation,

%Reduction in

area %ksiClass(a) and

heat treatment

Tensile strength

8620, and 4320 types. The compositions ofsome cast steels are selected by the steel pro-ducer in order to achieve the specified proper-ties. For example, the ASTM A 148 Grade 120-95 alloy steel rack segment shown in Fig. 31must have a minimum tensile strength of 827MPa (120 ksi) and a minimum yield strength of655 MPa (95 ksi). Table 9 lists mechanicalproperties for various heat treated cast steels.

Cast Irons

The term “cast iron,” like the term “steel,”identifies a large family of ferrous alloys. Castirons primarily are alloys of iron that containmore than 2% C and from 1 to 3% Si. Wide vari-ations in properties can be achieved by varyingthe balance between carbon and silicon, by al-

loying with various metallic or nonmetallic ele-ments, and by varying melting, casting, and heattreating practices. Two types of cast irons areused for gears: gray cast irons and ductile castirons.

Gray iron refers to a broad class of ferrouscasting alloys normally characterized by amicrostructure of flake graphite in a ferrousmatrix (Fig. 32). Gray irons are in essence iron-carbon-silicon alloys that usually contain 2.5 to4% C, 1 to 3% Si, and additions of manganese,depending on the desired microstructure (as lowas 0.1% Mn in ferritic gray irons and as high as1.2% Mn in pearlitics). Sulfur and phosphorusare also present in small amounts as residualimpurities.

Gray cast irons used for gears are classified inASTM specification A 48 by their tensilestrengths in ksi. As shown in Table 10, theyrange from class 20 (minimum tensile strengthof 138 MPa or 20 ksi) to class 60 (minimum ten-sile strength of 414 MPa or 60 ksi). Generally, itcan be assumed that the following properties ofgray cast irons increase with increasing tensilestrength from classes 20 to 60:

• All strengths, including strength at elevatedtemperature

• Ability to be machined to a fine finish• Modulus of elasticity• Wear resistance

On the other hand, the following propertiesdecrease with increasing tensile strength, so that


Fig. 32 Flake graphite in a pearlitic matrix in a class 30 as-cast gray iron

Table 10 Minimum hardness and tensilestrength requirements for gray cast irons

Tensile strength

MPa ksi

20 155 140 2030 180 205 3035 205 240 3540 220 275 4050 250 345 5060 285 415 60

Source: ASTM A 48

Brinell hardnessASTM class number

low-strength irons often perform better thanhigh-strength irons when these properties areimportant:

• Machinability• Resistance to thermal shock• Damping capacity• Ability to be cast in thin sections

Gray cast iron has long been used as a gearmaterial (Ref 65). Cast iron is low in cost and itcan be cast easily into any desired shape for therim, web, and hub of a gear. Cast iron machineseasily.

Cast iron gears generally show good resis-tance to wear and are often less sensitive tolubrication inadequacies than are steel gears.Cast iron has good dampening qualities.

Cast-iron gear teeth have about three-quartersof the surface load-carrying capacity of steel

gears of the same pitch diameter and face width.Their bending strength capacity is about one-third that of steel gears of the same normaldiametral pitch. By making cast-iron gearssomewhat coarser in pitch for the same pitchdiameter, it is possible to design cast-iron gearsets about the same size as steel gear sets for agiven application.

Gray cast iron has low impact strength andshould not be used where severe shock loadsoccur.

Ductile cast iron, also known as nodulariron or spheroidal-graphite (SG) cast iron, iscast iron in which the graphite is present as tinyspheres (nodules) (see Fig. 33). In ductile iron,eutectic graphite separates from the molten ironduring solidification in a manner similar to thatin which eutectic graphite separates in gray castiron. However, because of additives introducedin the molten iron before casting, the graphitegrows as spheres, rather than as flakes of any of

Fig. 33 Spheroidal graphite in an unetched ductile ironmatrix shown at 75× (a) and in the etched (picral)

condition shown at 300× (b). Etching reveals that the matrix con-sists of ferritic envelopes around the graphite nodules (bull’s-eyestructure) surrounded by a pearlitic matrix.


Table 11 Minimum mechanical property requirements for ductile cast ironsTensile strength Yield strength

MPa ksi MPa ksi

60-40-18 Annealed ferritic 170 max. 415 60 275 40 18.065-45-12 As-cast or annealed ferritic-pearlitic 156–217 450 65 310 45 12.080-55-06 Normalized ferritic-pearlitic 187–255 550 80 380 55 6.0100-70-03 Quench and tempered pearlitic 241–302 690 100 485 70 3.0120-90-02 Quench and tempered martensitic Range specified 830 120 620 90 2.0

Source: ASTM A 536

Elongation in 50 mm(2 in.), % min

ASTM gradedesignation

Recommended heat treatment and microstructure

Brinell hardness range

the forms characteristic of gray iron. Cast ironcontaining spheroidal graphite is much strongerand has higher elongation than gray iron. Theflakes in gray cast iron act as stress risers andmake the impact strength and fatigue strengthlow. The nodules in ductile iron exhibit less of astress-riser effect. Ductile iron has good impactstrength and enough ductility to have elonga-tions in the range of 2 to 15%, depending on theclass. The fatigue strength of ductile iron canapproach that of steel of equal hardness.

Most of the specifications for standard gradesof ductile iron used for gears are based on prop-erties. That is, strength and/or hardness is spec-ified for each grade of ductile iron, and compo-sition is either loosely specified or madesubordinate to mechanical properties. As shownin Table 11, the ASTM system for designatingthe grade of ductile iron incorporates the num-bers indicating tensile strength in ksi, yieldstrength in ksi, and elongation in percent. Forexample, grade 80-55-06 has a tensile strengthof 522 MPa or 80 ksi, a yield strength of 379MPa or 55 ksi, and an elongation of 6%.

Ductile iron may be used as-cast or it may beheat treated to a wide range of strength and hard-ness levels. Common heat treatments includeannealing, normalizing and tempering, quench-ing and tempering, and austempering (see dis-cussion below). Figure 34 compares the strengthand ductility of as-cast ductile iron with heat-treated ductile irons. The hardness levels in duc-tile irons can range from less than 160 HB tospecified ranges greater than 300 HB.

If ductile iron is austenitized and quenched ina salt bath or a hot oil transformation bath at atemperature of 320 to 550 °C (610 to 1020 °F)and held at this temperature, it transforms to astructure containing mainly bainite with a minorproportion of austenite (Fig. 35). Irons that aretransformed in this manner are called austem-pered ductile irons. Austempering generates arange of structures, depending on the time oftransformation and the temperature of the trans-

formation bath. The properties are characterizedby very high strength, some ductility and tough-ness, and often an ability to work harden, whichgives appreciably higher wear resistance thanthat of other ductile irons. As shown in Fig. 34and Table 12, austempered ductile irons exhibitin excess of 5% elongation at tensile strengthsexceeding 1000 MPa (145 ksi).

Most applications for austempered ductileiron gears are in transportation equipment: auto-mobiles, trucks, and railroad and military vehi-cles. The same improved performance and costsavings are expected to make these materialsattractive in equipment for other industries,such as mining, earthmoving, agriculture, con-struction, and machine tools.

P/M Irons and Steels

Both pressed-and-sintered and powderforged iron-base gears are produced for a vari-ety of applications. Most P/M gears are madefrom iron-copper steels or iron-nickel steels.These steels can also undergo surface hardeningtreatments such as carburizing and carbonitrid-ing. More detailed information on P/M materi-als for gears can be found in Chapter 7, “Pow-der Metallurgy.”

Sintered Steels. The copper-bearing steelsin the as-sintered condition have a tensilestrength range of 170 to 570 MPa (25 to 82 ksi),an elongation of 2.0% or less, and an apparenthardness of 11 to 80 HRB. Heat-treated sinteredcopper steels have a tensile strength range of450 to 720 MPa (65 to 105 ksi), an elongationless than 0.5%, and an apparent hardness of 58to 60 HRC. The nickel steels in the as-sinteredcondition have a tensile strength range of 170 to620 MPa (25 to 90 ksi), an elongation of 10% orless (average values are about 4%), and appar-ent hardness of 55 to 88 HRB. Heat-treated sin-tered nickel steels have a tensile strength rangeof 590 to 1340 MPa (85 to 195 ksi), and anelongation of less than 0.5%.


Fig. 34 Strength and ductility ranges of as-cast and heat-treated ductile irons

Fig. 35 Austempered ductile iron structure consisting ofspheroidal graphite in a matrix of bainitic ferritic

plates (dark) and interplate austenitic (white)

Powder forged nickel steels for gears areproduced from 4600-series powders. The ten-sile strength for quenched-and-tempered pow-der forged 4600 materials can exceed 1500 MPa(220 ksi). Powder forged steels have densitiesapproaching those of wrought steels.

Stainless Steels

Stainless steels are iron-base alloys that con-tain a minimum of approximately 11% Cr, the

amount needed to prevent the formation of rustin unpolluted atmospheres (hence the designa-tion stainless). Few stainless steels contain morethan 30% Cr or less than 50% Fe. They achievetheir stainless characteristics through the forma-tion of an invisible and adherent chromium-richoxide surface film. Unfortunately, the thin oxidelayer on stainless steels is hard and brittle andbreaks up easily under sliding loads, exposingthe bare metal and thus promoting wear. Never-theless, stainless steels gears are used in someapplications where corrosion resistance is criti-cal, for example, food processing machinery.Austenitic (types 303, 304, and 316), marten-sitic (type 440C), and precipitation-hardening(17-4PH and 17-7PH) stainless steels have beenused as gear materials. Type 304 (18Cr-8Ni),which is one of the most widely used stainlesssteels, is used for gears in juice extractors andfishing reels.

Tool Steels

Tool steels are normally used for machiningand metal forming operations. The two types oftool steels that are occasionally used for gearsare high-speed tool steels and hot-work toolsteels. More detailed information on these mate-rials can be found in the ASM Specialty Hand-book: Tool Materials.

High-speed tool steels are so named pri-marily because of their ability to machine mate-rials at high cutting speeds. They are complexiron-base alloys of carbon, chromium, vana-dium, molybdenum, or tungsten, or combina-tions thereof, and in some cases substantialamounts of cobalt. The carbon and alloy con-tents are balanced at levels to give high attain-able hardening response, high wear resistance,high resistance to the softening effect of heat,and good toughness.

Hot-work tool steels (group H steels) havebeen developed to withstand the combinationsof heat, pressure, and abrasion associated withvarious metalworking operations such aspunching, shearing, and other forming methods.Group H tool steels usually have medium car-bon contents (0.35 to 0.45%) and chromium,tungsten, molybdenum, and vanadium contentsof 6 to 25%.

Maraging Steels

Maraging steels are a special class of high-strength steels that differ from conventionalsteels in that they are hardened by a metallurgi-


Table 12 ASTM standard A 897-90 and A 897M-90 mechanical property requirements of austempered ductile iron

Tensile (min) Yield (min)

Grade MPa ksi MPa ksi J ft · lbf

125-80-10 . . . 125 . . . 80 10 . . . 75 269–321850-550-10 850 . . . 550 . . . 10 100 . . . 269–321150-100-7 . . . 150 . . . 100 7 . . . 60 302–3631050-700-7 1050 . . . 700 . . . 7 80 . . . 302–363175-125-4 . . . 175 . . . 125 4 . . . 45 341–4441200-850-4 1200 . . . 850 . . . 4 60 . . . 341–444200-155-1 . . . 200 . . . 155 1 . . . 25 388–4771400-1100-1 1400 . . . 1100 . . . 1 35 . . . 388–477230-185 . . . 230 . . . 185 (b) . . . (b) 444–5551600-1300 1600 . . . 1300 . . . (b) (b) . . . 444–555

(a) Unnotched Charpy bars tested at 72 ± 7 °F (22 ± 4 °C). The values in the table are a minimum for the average of the highest three test values of four tested samples.(b) Elongation and impact requirements are not specified. Although grades 200-155-1, 1400-1100-1, 230-185, and 1600-1300 are primarily used for gear and wear resis-tance applications, grades 200-155-1 and 1400-1100-1 have applications where some sacrifice in wear resistance is acceptable in order to provide a limited amount ofductility and toughness. (c) Hardness is not mandatory and is shown for information only.

Hardness, HB(c)

Impact(a)

Elongation, %

cal reaction that does not involve carbon.Instead, these steels are strengthened by the pre-cipitation of intermetallic compounds at tem-peratures of about 480 °C (900 °F). The termmaraging is derived from martensite age hard-ening of a low-carbon, iron-nickel lath marten-site matrix. Commercial maraging steels aredesigned to provide specific levels of yieldstrength from 1030 to 2420 MPa (150 to 350ksi) with some having yield strengths as high as3450 MPa (500 ksi). These steels typically havevery high nickel, cobalt, and molybdenum con-tents and very low carbon contents. The use ofmaraging steels for gears is discussed in Chap-ter 8, “Through Hardening” (refer to the casehistory that describes the design and manufac-ture of a gear rack).

Nonferrous Alloys

Copper-base alloys account for much of thenonferrous gear materials used. Die cast alu-minum-, zinc-, and magnesium-base alloys forgears are also produced but these materials havelargely been replaced by plastics for low-loadapplications.

Bronzes

A family of four bronzes are widely used forpower transmission gearing. Most of these areused in worm gears and are mated against steelgears. The four gear bronzes are:

• Tin bronzes• Manganese bronzes

• Aluminum bronzes• Silicon bronzes

Tin bronzes, also referred to as phosphorbronzes, are copper-tin or copper-tin-lead(leaded tin bronzes) that are deoxidized withphosphorus. These alloys are tough and havegood corrosion resistance. They possess excel-lent wear resistance which permits their use ingears and worm wheels for severe wear applica-tions. The most commonly used alloy in thisgroup is C90700, or gear bronze, which con-tains 89% Cu and 11% Sn. Nominal composi-tions and properties of tin bronzes and leaded tinbronzes are listed in Table 13. Composition andmechanical property requirements for tinbronzes used for gears are covered in ASTMstandard B 427.

Manganese Bronzes. This is the namegiven to a family of high-strength brass alloys(brasses are alloys which contain zinc as the prin-cipal alloying element). They are characterizedby high strength and hardness and they are thetoughest materials in the bronze family. Theyachieve mechanical properties through alloyingwithout heat treatment. These bronzes have thesame strength and ductility as annealed caststeels. Table 13 lists compositions and propertiesfor cast manganese bronzes. Table 14 lists thecomposition and properties of a wrought man-ganese bronze containing 36.5% Zn. Cast andwrought manganese bronzes have good wearresistance but do not possess the same degree ofcorrosion resistance, wearability, or bearingquality as the tin bronzes or aluminum bronzes.

Aluminum bronzes are similar to the man-ganese bronzes in toughness, but are lighter in


Table 13 Compositions and properties of cast gear bronzesTypical mechanical properties, as cast (heat treated)

Tensile strength Yield strength Brinell hardness

MPa ksi MPa ksi 500 kg 3000 kg

Manganese bronzes

C86100 67Cu, 21Zn, 3Fe, 5Al, 4Mn

655 95 345 50 20 . . . 180 30 C, I, P, S

C86200 64Cu, 26Zn, 3Fe, 4Al, 3Mn

655 95 331 48 20 . . . 180 30 C, T, D, I, P, S

C86300 63Cu, 25Zn, 3Fe, 6Al, 3Mn

793 115 572 83 15 . . . 225 8 C, T, I, P, S

C86400 59Cu, 1Pb, 40Zn 448 65 172 25 20 90 105 65 C, D, M, P, S

C86500 58Cu, 0.5Sn, 39.5Zn,1Fe, 1Al

490 71 193 28 30 100 130 26 C, T, I, P, S

Silicon bronzes

C87400 83Cu, 14Zn, 3Si 379 55 165 24 30 70 100 50 C, D, I, M, P, S

C87500 82Cu, 14Zn, 4Si 462 67 207 30 21 115 134 50 C, D, I, M, P, S

Tin bronzesC90700 89Cu, 11Sn 303

(379)44

(55)152

(207)22

(30)20

(16)80

(102). . .

. . . .20 C, T, I, M, S

C91600 88Cu, 10.5Sn, 1.5Ni 303 (414)

44 (60)

152 (221)

22 (32)

16 (16)

85 (106)

. . .

. . .20 C, T, M, S

C91700 86.5Cu, 12Sn, 1.5Ni 303 (414)

44 (60)

152 (221)

22 (32)

16 (16)

85 (106)

. . .

. . .20 C, T, I, M, S

Leaded tin bronzes

C92500 87Cu, 11Sn, 1Pb, 1Ni

303 44 138 20 20 80 . . . 30 C, T, M, S

C92700 88Cu, 10Sn, 2Pb 290 42 145 21 20 77 . . . 45 C, T, S

C92900 84Cu, 10Sn, 2.5Pb,3.5Ni

324 (324)

47 (47)

179 (179)

26 (26)

20 (20)

80 (80)

. . .

. . .40 C, T, M, S

Aluminum bronzes

C95200 88Cu, 3Fe, 9Al 552 80 186 27 35 . . . 125 50 C, T, M, P, S

C95300 89Cu, 1Fe, 10Al 517 (586)

75 (85)

186 (290)

27 (42)

25 (15)

. . .

. . .140

(174)55 C, T, M, P, S

C95400 85Cu, 4Fe, 11Al 586 (724)

85 (105)

241 (372)

35 (54)

18 (8)

. . .

. . .170

(195)60 C, T, M, P

C95500 81Cu, 4Ni, 4Fe, 11Al

689 (827)

100 (120)

303 (469)

44 (68)

12 (10)

. . .

. . .192

(230)50 C, T, M, P, S

(a) Free-cutting brass = 100. (b) C, centrifugal; T, continuous; D, die; I, investment; M, permanent mold; P, plaster; S, sand

UNS designation

Nominal composition, %

Casting types(b)

Machinabilityrating(a)

Elongation in 50 mm (2 in.), %

Table 14 Compositions and properties of wrought gear bronzes

Tensile strength Yield strength

MPa ksi MPa ksi

C62300 87 Cu, 3 Fe, 10 Al 620 90 310 45 25 180 HB (1000 kgf)C62400 86 Cu, 3 Fe, 11 Al 655 95 345 50 12 200 HB (3000 kgf)C63000 82 Cu, 3 Fe, 10 Al, 5 Ni 620 90 310 45 17 100 HRBC64200 91.2 Cu, 7 Al 640 93 415 60 26 90 HRBC67300 60.5 Cu, 36.5 Zn, 1.2 Al,

2.8 Mn, 1 Si485 70 275 40 25 70 HRB

Note: Typical mechanical properties vary with form, temper, and section size considerations

UNS designation Nominal composition, %Hardness HB

and HRBElongation in 50 mm

(2 in.), % min

weight and attain higher mechanical propertiesthrough heat treatment (refer to Table 13). Asthe strength of aluminum bronzes is increased,their ductility decreases. Bearing characteristicsof aluminum bronzes are better than manganesebronzes but inferior to tin bronzes. Aluminumbronzes are available in both cast and wrought(Table 14) forms.

Silicon bronzes, also referred to as siliconbrasses, are commonly used in lightly loadedgearing for electrical applications because oftheir low cost and nonmagnetic properties. Asshown in Table 13, these alloys contain 14% Znwith silicon additions of 3 to 4%.

Other copper-base alloys used for gear-ing include yellow brass, an alloy containing


nominally 65% Cu and 35% Zn, and copperalloys produced by P/M processing (refer toTable 3 in Chapter 7, “Powder Metallurgy”).

Other Nonferrous Alloys

The following alloys are also used for gears:

• High-strength wrought aluminum alloyssuch as 2024 (Al-4.4Cu-1.5Mg-0.6Mn),6061 (Al-1.0Mg-0.6Si-0.30Cu-0.20Cr), and7075 (Al-5.6Zn-2.5Mg-1.6Cu-0.23Cr)

• Die cast aluminum-silicon alloys such as360.0 and A360 (Al-9.5Si-0.5Mg), 383.0(Al-10.5Si-2.5Cu),384.0 (Al-11.2Si-3.8Cu),and 413.0 (Al-12Si)

• Die cast zinc-aluminum alloys such as ZA-8(Zn-8Al-1Cu-0.02Mg), ZA-12 (Zn-11Al-1Cu-0.025Mg), and ZA-27 (Zn-27Al-2Cu-0.015Mg)

• Die cast magnesium-aluminum alloys suchas AZ91A and AZ91B (Mg-9Al) andAM60A and AM60B (Mg-6Al)

Properties of these die cast alloys can be foundin Properties and Selection: Nonferrous Alloysand Special-Purpose Materials, Vol 2, of theASM Handbook.

Because of their high strength-to-weight ratio,titanium alloys, such as Ti-6Al-4V, have alsobeen used for gears. The poor tribological prop-erties of titanium alloys, however, limits theiruse to low-load applications. Wear-resistantcoatings produced by ion implantation or diffu-sion treatments (oxidizing and nitriding) canincrease the wear resistance of titanium alloys.

ACKNOWLEDGMENTS

Portions of this chapter were adapted from:

• Gas Carburizing, Surface Hardening ofSteels: Understanding the Basics, J.R.Davis, Ed., ASM International, 2002, p 17–89

• Steels for Gears, ASM Specialty Handbook:Carbon and Alloy Steels, J.R. Davis, Ed.,ASM International, 1996, p 591–598

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CHAPTER 4

Plastics

PLASTIC GEARS are continuing to displacemetal gears in applications ranging from auto-motive components to office automation equip-ment. In the past, plastic gears were not consid-ered to be able to transmit power, were limited asto top operating speed, and were not consideredable to transmit motion to a high degree of accu-racy. However, improved materials with higherload capacities, advances in mold design andmolding technology, and the development of re-liable engineering data have led to the successfuland increasing use of plastics for both motion-carrying gears and power transmission gears.

General Characteristics of Plastic Gears (Ref 1)

Advantages. Among the characteristics re-sponsible for the large increase in plastic gearusage, the following are the most significant:

• Relative low cost (particularly for high-volume injection molded gears)

• Ease and speed of manufacture• Wide range of configurations and complex

shapes possible• Elimination of machining and finishing

operations• Capability of fabrication with metal inserts

and integral designs• Lower density (light weight and low inertia)• Ability to dampen moderate shock and

impact• Ability to operate with minimal or no lubri-

cation• Low coefficient of friction• Smooth, quiet operation• Lower critical tolerances than with metal

gears, due in part to their greater resilience• Resistance to corrosion

Limitations. There are also limitations ofplastic gears relative to metal gears. Theseinclude:

• Maximum load-carrying capacity lowerthan metal gears

• Reduced ability to operate at elevated tem-perature. Operation is generally limited toless than 120 °C (250 °F). Cold temperatureapplications are also limited.

• Ambient temperature and temperatures attooth contact surface must be limited

• Plastic gears cannot be molded to the sameaccuracy as high-precision machined/fin-ished metal gears

• Plastic gears are subject to greater dimen-sional instabilities due to their greater coef-ficient of thermal expansion and moistureabsorption

• Initial high mold costs in developing correcttooth form and dimensions

• Can be negatively affected by certain chem-icals and even some lubricants

• Improper molding tools and process canproduce residual internal stresses at thetooth roots resulting in overstressing and/ordistortion with aging

• Cost of plastics are based on petrochemicalpricing and thus are more volatile in com-parison to metals

Classification of Plastics for Gear Applications

One very important classification scheme forplastics is based on their response to heat. Thereare two types of response possible, leading tothe classification of plastics as thermoplastics orthermosets.




Fig. 1 Typical stress-strain curve for an engineering metal.Note high degree of linearity below the proportional

limit.

Thermoplastics are materials that repeat-edly soften, or melt, when heated, and harden,or freeze, when cooled (Ref 2). Heating permitsthe intertwined molecular chains to slide rela-tive to each other. At some higher temperature,the sliding is free enough for the materials tobehave as a liquid and may be used to fill molds.The temperature at which this degree of soften-ing occurs varies with the type and grade ofplastic. Cooling restores the intermolecularbonds and the material behaves as a solid. How-ever, these solid materials, to a varying degree,retain some aspects of a liquid in the form ofviscoelastic behavior (see the section “Metalsversus Plastics” in this chapter). Thermoplasticshave greater toughness, or resistance to impactloads, than do thermosetting plastics. However,their upper temperature limit is only about 120 °C (250 °F). Above this temperature, ther-moplastics lose about 50% of their rated room-temperature strength.

Thermosets are plastics that undergo chem-ical change during processing to become per-manently infusible (Ref 2). If excessive heat isapplied to a thermoset material after the chemi-cal change has taken place, the plastic is de-graded rather than melted. Before the process-ing, the molecular structure of the thermosetplastic is similar to that of a thermoplastic mate-rial. Heating permits the relative sliding of themolecules, the material takes on the propertiesof a liquid and can be used to fill molds. How-ever, while still subjected to heat in the mold ina curing process, the intertwined moleculesdevelop cross-links to form an irreversible net-work which prevents further relative sliding.

The resulting solid plastic behaves muchmore like an elastic material similar to metals.The viscoelastic behavior is much reduced fromthat of most thermoplastics. At the same time,these thermoset materials tend to be much lessresistant to impact loading, and tend to be usedonly with some reinforcing medium in evenmoderate impact applications. On the otherhand, thermosets tend to maintain their strengthproperties at much higher temperatures thanmost thermoplastics. Very little degradation ofmechanical properties occurs at temperatures upto 230 °C (450 °F).

Metals versus Plastics

Designing with plastics is often a more com-plex task than designing with metals. Engineer-

ing plastics, which are viscoelastic, do not re-spond to mechanical stress in the linear, elasticmanner for which most designers have devel-oped an intuitive feel. In many applications, en-gineering plastics exhibit a more complex prop-erty mix than do metals. Because engineeringplastics, as a family, are much younger than en-gineering metals, their database is not yet com-plete. In addition, their rapid evolution makesthe material selection process more difficult.

A typical stress-strain curve for an engineer-ing metal is shown in Fig. 1. The salient featuresof metal behavior are that the slope of the stress-strain curve is a constant up to the proportionallimit and is known as the elastic modulus, andthat the elastic modulus remains a constant overa wide range of strain rates and temperatures. Alarge number of design equations have beenderived for use in the design of structural mem-bers such as beams, plates, and columns. All ofthese equations use the elastic modulus as a fun-damental measure of the response of the mate-rial to stress.

However, if the designer attempts to use theseequations for plastics part design using a modu-lus value taken from a plastics property specifi-cations sheet, serious design errors will be madein many cases. The implicit assumption behindthe design equations is that the material behavesin a linear, elastic manner. As already noted,this assumption is not true for plastics.

Chapter 4: Plastics / 79

Fig. 2 Typical stress-strain curve for an engineering plastic.Note that there is no true proportional limit.

When comparing the mechanical behavior of metals to that of plastics, as shown in Fig. 1and 2, it can be seen that plastic, unlike metal,has no true proportional limit and that its stress-strain curve is not linear. Furthermore, theshape of the plastic stress-strain curve is greatlyaffected by the rate at which stress is applied,and stress-strain behavior is greatly affected bytemperature.

Clearly, the mechanical response of plastic ismore complex than that of metal. Because aplastic behaves in a manner that seems to com-bine elastic-solid and highly viscous liquidbehaviors, it is said to be viscoelastic.

Plastic Gear Materials

This section will briefly review some of thecommonly used plastic materials for gear appli-cations (many more plastic formulations areanticipated for gears in the future). These mate-rials can be used in the unmodified condition ormodified with various additives to produce awide variety of gear configurations includingspur, worm, face, helical, bevel, internal, andelliptical gears, gear racks, and microgears (forcomputer memory devices). Selection of a ma-terial depends not only on its properties, but alsoon the manufacturing methods used, part shapeand size, molding or machining characteristics,shrinkage rates, moisture absorption, and pro-cessing variables. Material suppliers and/or

processors should always be consulted whenchoosing a plastic for a gear application.

AdditivesA wide variety of organic and inorganic

materials are added to plastics either to reducecosts or property improvement. Some of theseproperties are (Ref 2):

• Strength• Modulus (rigidity)• Impact resistance• Wear resistance• Thermal conductivity• Flame retardance• Dimensional control• Color• Heat stability• Noise reduction• Oxidative stability• Ultraviolet stability• Lubricity• Processability

Fillers are added to reduce costs, improvedimensional control (stability) during the mold-ing operation, enhance conductivity, and im-prove heat resistance. Common mineral fillersinclude mica, talc, carbon powder, and glassbeads. The amount of filler added can rangefrom 5 to 40%. Organic fillers (<1%) are alsosometimes used as a processing aide. Limita-tions of adding fillers include reduced impactresistance and increased tool wear.

Reinforcements are usually thought of asan added material whose purpose is to alter oneor more of the mechanical properties of thebasic material. Glass fibers (added in the rangeof 5 to >40%) are often used to alter both long-and short-term mechanical properties of thebasic material resin. Heat and wear resistanceare also improved. Limitations of adding glassfibers include increased distortion during mold-ing, increased wear of the mating gear material,and increased tool wear.

Carbon fibers in the percentage range of 10 to>40% are added to enhance heat resistance,electrical properties, and wear resistance. Limi-tations of adding carbon fibers include highercosts, increased distortion during molding, andincreased tool wear.

Kevlar (aramid) fibers in the percentagerange of 5 to 20% are added to increase heatresistance, strength, and wear resistance and to reduce friction. The primary limitation of


adding Kevlar fibers is the added cost. Somedistortion may also occur during molding.

Lubricants. The following lubricants areadded to plastics for the primary purpose ofreducing friction and wear:

Lubricant Typical percentage range added

Polytetrafluoroethylene 1–20%(PTFE, or Teflon)

Silicone 1–4%Graphite 5–10%Molybdenum disulfide (MoS2) 2–5%

The primary limitation of adding PTFE is addedcost. Graphite additions can reduce strength andimpact resistance. There are no significant lim-iting factors for adding MoS2.

Impact modifiers are additives that im-prove the impact strength or toughness of plas-tics with minimal impairment of other proper-ties. They can be added in such large percentages(>50%) that they become a component in ablended material rather than an additive. To beeffective, the added phase must be more impactresistant and have a lower modulus than the par-ent phase. Commonly used impact modifiers in-clude acrylonitrile-butadiene-styrene (ABS),methacrylate-butadiene-styrene (MBS), acryl-ics, chlorinated polyethylene (CPE), and ethyl-ene vinyl acetate (EVA).

Thermoplastic Gear MaterialsMost of the plastics used for gear applications

are thermoplastics. The two most commonlyused thermoplastic formulations are the poly-amides (nylons) and the acetals. These materialshave been used in gears for more than 50 years inhundreds of diverse products including:

• Windshield wipers• Automobile window lifts• Automobile seat controls• Speedometers• Rotary pumps• Appliances• Electric garage door openers• Small power tools• Clocks• Copy machines• Laser printers

Nylons. This is a family of thermoplasticresins that were the first plastics used for gearapplications. The most common grades used areNylon 6, 6/6, and 6/12. These materials, whichcome in unmodified, toughened, and reinforced

conditions, exhibit outstanding toughness andwear resistance, low coefficient of friction, andexcellent electrical properties and chemicalresistance. Properties of Nylons 6 and 6/6 arelisted in Tables 1 (0.2% moisture content) and 2(50% relative humidity). Some nylons arehygroscopic (absorb moisture) and this has anegative effect on their strengths (see Fig. 3 andcompare Tables 1 and 2). In addition, the dimen-sional stability of these resins is poorer thanother engineering plastics. Nylon gears can bemanufactured by either machining or molding.

Acetal polymers have a lower water absorp-tion rate than nylon and, therefore, are more sta-ble after molding or machining. The acetals,which come in unmodified, toughened, rein-forced, and internally lubricated conditions, arestrong, have good resistance to creep andfatigue, have a low coefficient of friction, andare resistant to abrasion and chemicals. Proper-ties of various acetal resins are listed in Table 3.The effect of temperature on the stress-straincurve for an unmodified acetal grade is shown inFig. 4. The effect of internal lubricants on thesliding wear resistance of acetal resins is shownin Fig. 5. As this figure indicates, the PTFE-lubricated grades exhibited far greater wearresistance than the unmodified grades.

Other thermoplastics used for gearsinclude:

• Polycarbonates are generally reinforcedwith glass fibers and lubricated with PTFE.Noted for their low-shrinkage characteris-tics, they are manufactured by either mold-ing or machining.

• Polyesters are unmodified or reinforced withglass fibers. Applications for these moldedresins are similar to the nylons and acetals.Polyesters can also be blended with elas-tomers for extra tough gears subject toextreme shock or when mesh noise reduc-tion is required.

• Polyurethanes are unmodified, reinforced,or internally lubricated. These molded resinsare noted for their flexibility, ability toabsorb shock, and deaden sound.

• Polyphenyline sulfides are generally rein-forced with glass fibers (up to 40%) with orwithout internal lubricants. These resinshave higher elevated temperature strengththan most other thermoplastics.

• Liquid crystal polymer resins contain min-eral fillers or are reinforced with glass fibers.They are used for extremely thin or small


Table 1 Property values for Nylons 6 and 6/6Dry, as-molded, approximately 0.2% moisture content

Nylon 6 Toughened

Property

Molding and extrusion

compound

Glass fiber reinforced,

30–35%Molding

compound


30–33% Unreinforced

Glass fiberreinforced,

33%

Tensile strength at break, MPa (ksi)

. . . 165 (24) 94.5 (13.7) 193 (28) 50 (7.0) 140 (20.3)

Elongation at break, % 30–100 2.2–3.6 15–60 2.5–34 125 4–6Tensile yield strength,

MPa (ksi)80.7 (11.7) . . . 55 (8.00) 170 (25) . . . . . .

Compressive strength, rupture or yield, MPa (ksi)

90–110 (13–16) 131–165 (19–24)

86.2–103(12.5–15.0)(a)

165–276 (24–40)

. . . 103 (15)

Flexural strength, rupture, or yield, MPa (ksi)

108 (15.7) 240 (35) 114–117 (16.5–17.0)

283 (41) 59 (8.5) 206 (29.9)

Tensile modulus, GPa (106 psi)

2.6 (0.38) 8.62–10.0 (1.25–1.45)

1.59–3.79(0.23–0.55)

9.0 (1.3) . . . . . .

Flexural modulus at 23 °C (73 °F), GPa (106 psi)

2.7 (0.39) 9.65 (1.40) 2.8–3.1 (0.41–0.45)

8.96–10.0(1.30–1.45)

1.65 (0.240) 7.58 (1.10)

Izod impact, 3.2 mm (1/8 in.)thick specimen, notched, J/m (ft · lbf/in.)

32–53 (0.6–1.0) 117–181 (2.2–3.4)

29–53 (0.55–1.0)

85–240 (1.6–4.5)

907 (17.0) 240 (4.5)

Rockwell hardness R119 M93–96 R120 R101–119 R100 R107

Thermal

Coefficient of linear thermal expansion, 10–6/K

80–83 16–80 80 15–54 . . . . . .

Deflection temperature under flexural load, °C (°F)

At 1.82 MPa (0.264 ksi) 68–85 (155–185) 200–215 (392–420)

75–88 (167–190)

120–250(252–490)

65 (150) 245 (470)

At 0.46 MPa (0.066 ksi) 185–190 (365–375)

215–220 (420–430)

230–246 (450–474)

125–260(260–500)

. . . 260 (495)

Thermal conductivity, W/m · K (Btu · in./h · ft2 · °F)

0.243 (1.69) 0.243–0.472 (1.69–3.27)

0.243 (1.69) 0.211–0.483(1.46–3.35)

. . . . . .

Physical

Specify gravity 1.12–1.14 1.35–1.42 1.13–1.15 1.15–1.40 1.08 1.34Water absorption, 3.2 mm

(1/8 in.) thick specimen, 24 h, %

1.3–1.9 0.90–1.2 1.0–2.8 0.7–1.1 1.0 0.7

Saturation, % 8.5–10.0 6.4–7.0 8.5 5.5–6.5 . . . . . .

Electrical

Dielectric strength, 3.2 mm (1/8 in.) thick specimen, short time, MV/m (V/mil)

0.0157 (400) 15.7–17.7 (400–450)

0.0236 (600) 14.2–19.7(360–500)

. . . . . .

(a) Yield

Nylon 6/6

Mechanical

gears and exhibit both high-temperature re-sistance and chemical resistance and excel-lent dimensional stability.

Thermoset Gear MaterialsOnly a small number of thermoset plastics

have been used for gears to any substantialdegree. The properties of thermoplastics gener-ally make them more suitable for gears. The dif-ferent type of processing required for some ther-mosets also limits their use.

Polyimides, which are available commer-cially either as thermoplastic or thermosetresins, are used for high-temperature gear appli-cations. Finish machined thermoset polyimidegrades are unmodified or internally lubricated.Thermoplastic polyimide gears can be manufac-tured by either injection molding or machining.The thermoplastic grades are available in un-modified, glass reinforced (up to 65% glassfibers), toughened, and lubricated forms. Lubri-cants for thermoplastic polyimides include


Table 2 Property values for Nylons 6 and 6/6Conditioned to 50% relative humidity

Nylon 6

Property

Molding and extrusion

compound


30–35%Molding

compound


30–33%

Tensile strength at break, MPa (ksi)

. . . 110 (16) 75 (11) 152 (22)

Elongation at break, % 300 . . . 150–300 5–7Tensile yield strength,

MPa (ksi)51 (7.4) . . . 45 (6.5) . . .

Flexural strength, rupture or yield, MPa (ksi)

40 (5.8) 145 (21.0) 42 (6.1) 170 (25)

Tensile modulus, GPa (106 psi)

0.690 (0.100) 5.52 (0.800) 3.45 (0.500)

Compressive modulus, GPa (106 psi)

1.70 (0.250) . . . . . . . . .

Flexural modulus at 23 °C (73 °F), GPa (106 psi)

0.965 (0.140) 5.52–6.55 (0.800–0.950) 1.28 (0.185) 5.52 (0.800)

Izod impact, 3.2 mm (1/8 in.) thick specimen, notched,J/m (ft · lbf/in.)

160 (3.0) 197–292 (3.7–5.5) 45–112 (0.85–2.1) 138–159 (2.6–3.0)

Rockwell hardness . . . M78 . . . . . .

Nylon 6/6

graphite (15 to 40%), PTFE (10%) plus graphite(15%), and MoS2 (up to 15%).

Phenolics are injection molded resins com-pounded with various mineral and glass fillers,glass fibers, and lubricants such as PTFE andgraphite. Phenolics are used in applications re-quiring dimensional stability improved heatresistance.

Laminated Phenolic. Composite, or lami-nated thermosets, consist of a fibrous sheet mate-rial (paper, cotton fabric, nylon fabric, or glassfabric) that is impregnated or coated with a liq-uid phenolic resin binder and consolidated underhigh pressure and temperatures. By stacking andconsolidating the unidirectional laminations (orplies) at different angles, the cut gear blanks/teeth will have equal strength in all directions.

Plastic Gear Manufacture

Plastic gears are manufactured by eithermachining or injection molding. Machining ofplastic gears is performed by most of the sameprocesses used in the machining of metal gears(see Chapter 5, “Machining, Grinding, and Fin-ishing”). Machining may be selected over mold-ing as the plastic gear manufacturing process forseveral reasons:

• The quantities may be too small to justifythe tooling cost for molding

• The required accuracy or some special de-sign feature (such as a very thick section)may be too difficult for molding

• The desired plastic material may not besuited to precision molding

Plastic materials to be machined into gears areavailable in a variety of forms, the most commonof which are nonreinforced extruded circularrods or tubes. These rods are extruded by stockshape suppliers in diameters up to 200 mm (8 in.). Some of the properties of the material inextruded stock form can vary between the outersurface (or skin), which has formed throughmore rapid cooling, than the inner material (orcore). Machining invariably leaves the gear teethmade from the core material, which generallyhas different strength, wear resistance, andchemical resistance. In addition, machining mayexpose voids in the stock. This is particularlytrue for fibrous materials, such as glass or carbonfiber, or hard granular materials, when used asadditives in molded gears. These additives maybe removed from the surface during machiningto leave openings or surface roughness.

Injection MoldingInjection molding refers to a variety of

processes that generally involve forcing orinjecting a fluid plastic material into a closedmold. The process has been used to produce


Fig. 3 Effect of temperature and moisture content of anunmodified nylon. Source: Ref 1

Table 3 Mechanical properties of various Delrin acetal resinsDelrin is a registered trademark of DuPont Engineering Polymers

Product description

Unmodified, general purpose

Enhanced crystallinity Toughened

Properties 100P 500P 900P 511P 100ST 500T 525GR 520MP 510MP

Tensile strength at yield MPa (ksi) ASTM D638

67 (9.7)

68 (9.9)

69 (10.0)

72 (10.4)

45 (6.5)

53 (7.7)

151(a) (21.9)(a)

54 (7.8)

61 (8.9)

Elongation at yield, % ASTM D638

23 15 11 11 35 15 NA(b) 12 10

Elongation at break, % ASTM D638

80 40 25 33 >150 75 3 14 13

Flexural modulus MPa (ksi)ASTM D790

2790 (410)

3100 (450)

3240 (470)

3300 (480)

1130 (160)

2250 (330)

8000 (1160)

3100 (450)

3160 (460)

Izod impact, notched J/m (ft-lb/in.) ASTM D256

120 (2.3)

75 (1.4)

69 (1.3)

73 (1.4)

NB 128 (2.4)

96 (1.8)

32 (0.6)

27 (0.5)

Izod impact, unnotched J/m (ft-lb/in.) ASTM D256

NB(c) NB(c) 1630 (30.6)

NB(c) NB(c) NB(c) 1100 (20.6)

720 (13.5)

950 (17.8)

(a) Values are tensile strength at break since these materials do not yield. (b) Not applicable. (c) No break occurred. Material code: Delrin 100P, 500P, and 900P are unmodified acetals with high, medium, and low viscosities, respectively; Delrin 511P is a medium viscosity acetal; Delrin 100ST and 500ST have high and me-dium viscosities, respectively; Delrin 525GR is a medium viscosity, 25% glass-reinforced acetal; and Delrin 520MP and 510MP contain 20% and 10% PTFE,respectively.

Lubricated

PTFEGlass

reinforced

plastic gears since the 1950s. American GearManufacturers Association (AGMA) qualitylevels ranging from 6 to 8 can be obtained (Ref4). The process is particularly well suited forhigh-volume, automated production of thermo-plastic gears. The development of manufactur-

ing of injection molded gears requires the jointefforts of the gear design engineer, the moldproducer, the molder, and the material supplier.

Injection-molding compounds are ther-moplastic or thermosetting materials and theircomposites that are specifically formulated for

Fig. 4 Effect of temperature on the stress-strain behavior of anunmodified acetal. Source: Ref 2


Fig. 5 Effect of internal lubricants on the sliding wear (acetal against steel) of 27 tooth, 2.12 module (12 pitch), involute thermo-plastic spur gears. Initial contact stress = 42 MPa 9 (6 ksi). Pitchline velocity = 5.6 m/s (18.4 ft/s). Solid lines show median of

measured wear range. Dotted lines are extrapolated data. Source: Dupont Engineering Polymers

injection process conditions is well understood.Where this understanding is absent, reinforce-ments may be broken, and polymers may beeither degraded or prematurely cured.

Injection Molding Machines. Althoughthere are many variations in thermoplastic in-jection molding machines, the reciprocating-screw machine has become the most commontype, and the following description of its opera-tion illustrates the basic principles of all types.The functions performed by the machineinclude heating the plastic until it is able to flowreadily under pressure, pressurizing this melt toinject it into a closed mold, holding the moldclosed both during the injection and while thematerial is solidifying in the mold, and openingthe mold to allow removal of the solid part.

As depicted in Fig. 6, the main components ofthe machine are the hopper, heated extruder bar-rel, reciprocating screw, nozzle, and moldclamp. The hopper feeds the unmelted thermo-plastic, usually in pellet form, into the barrel.The hopper is often equipped with a desiccant-type drying system to remove moisture degra-

the injection-molding process. This processrequires materials capable of being fed into amolding machine, transported to accumulatepressure, injected through channels, and madeto flow into a small opening in the mold. Theprocess may cause major changes in both thephysical and chemical properties of the moldingcompound. Because of their resistance to flow,neither high-molecular-weight resins nor longreinforcing fibers, or flakes, can be effectivelymanipulated through the molding process. Con-sequently, parts produced from molding com-pounds represent a compromise between opti-mal physical properties and the essential abilityto flow under pressure. This compromise is off-set by the ability to produce three-dimensionalproducts with holes, ribs, and bosses, oftenwithout secondary operations or direct labor.

While the flow process has the potential tophysically change the molding compound, thesechanges are not always negative. Improvedhomogeneity, better reinforcement wetting, andhigher physical properties may be achieved ifthe response of the molding compound to the


Fig. 6 The injection end of a reciprocating-screw injection molding machine

dation. A magnet is placed in the hopper throatto remove any iron that has accidentally enteredthe feedstock.

In the heated extruder barrel, which containsthe reciprocating screw, the thermoplastic isgradually melted by a combination of shearheating (caused by the mechanical working ofthe material as it is conveyed down the barrel)and heat conduction from the barrel. The ther-moplastic is gradually conveyed by the rotatingscrew from the rear of the barrel to the front.The barrel is usually heated by band-type elec-trical resistance heaters fitted around its periph-ery. Because the amount of heat required varieswith position along the barrel, the band heatersare controlled in several zones along the barrel.Some barrels are equipped about halfway downwith a vent to remove gases from the meltingfeedstock. A vacuum is usually applied to thevent, and a specially designed screw is requiredto depressurize the melt in the region of the ventto keep it from extruding through the vent.

The reciprocating screw usually has three suc-cessive zones, each with specific functions: The feed zone of relatively deep screw flightsconveys the unmelted plastic from the hopperthroat into the heated barrel, where it begins tomelt; the compression zone of decreasing flightdepth, and thus volume, provides gas removaland melt densification, along with a material

mixing action for better material and tempera-ture uniformity; and the metering zone, gener-ally of constant, shallow-flight depth, providesthe final shear heating and mixing of the melt.After the melt passes through the metering sec-tion and a check valve at the end of the screw, itjoins the melt pool in front of the screw. As thevolume of melt in front of the screw increases, itforces the screw to the rear of the barrel againstan adjustable “back pressure.” This back pres-sure is applied hydraulically to the back end ofthe screw. Increasing the pressure increases theamount of mechanical working of the feedstock.Screw rotation and feedstock melting continueuntil a sufficient amount of melt is available infront of the screw to fill the mold. At this stage,the screw rotation is stopped, and the machine isready for injection. The stages in the operation ofa reciprocating screw are shown in Fig. 7.

The melted thermoplastic is injected into themold through the nozzle, under high pressure(typically 70 to 205 MPa, or 10 to 30 ksi,depending on the mold-filling resistance). Injec-tion occurs as the screw is hydraulically forcedforward in the barrel. The hydraulic cylinder islocated at the rear of the screw and barrel. Acheck valve at the tip of the screw keeps themelt from flowing back along the screw as thescrew is pushed forward. In contemporarymachines, the injection rate (determined by the


Fig. 8 Two-plate injection mold

forward velocity of the screw) and injectionpressure are closely controlled throughout themold-filling stage.

The mold clamp, which holds the halves ofthe mold closed against the injection pressure ofthe melt, opens the mold to allow part removalafter the thermoplastic has solidified. During thecooling and solidification period, the screwbegins to rotate and melt new material for thenext shot.

The clamping system consists of a fixedplaten and a movable platen, each of which hashalf of the mold attached. The fixed platen(shown in Fig. 6) has a hole in its center to allowthe injection cylinder nozzle to be placed in con-tact with the sprue bushing of the mold. A mov-able platen is moved along tie bars by eitherhydraulic or mechanical means, or a combina-tion of both. The amount of clamping force themachine can apply, rated in tons, generallydetermines the size of the part that the machinecan process. It is this clamping force that over-comes the injection pressure of the melt in themold and keeps the mold halves together. The

clamping force, or “tonnage,” required is deter-mined by the amount of injection pressurerequired to fill the mold and the projected areaof the part (that is, the area perpendicular to theaxis of the machine). If the machine has inade-quate clamping force, the two halves of the toolwill begin to separate during injection, causingthe melt to squirt out, or “flash,” at the moldparting line, potentially causing an incompletemold-fill, or “short shot.”

Contemporary molding machines have twoor more closing speeds: a high-speed closing,requiring only a low force, followed by a slow-speed closing stage, which generates the highclamping force to close the mold firmly (stretch-ing the tie bars) prior to injection. The clampusually opens slowly at first, followed by a rapidtraverse. These high-speed motions reduce thetime of the overall process cycle.

Injection Mold Design. Injection molds, intheir simplest form, consist of two halves, oftencalled the core and cavity (Fig. 8). A hole orsprue bushing conducts the melt from the injec-tion nozzle through the sprue and through a gateinto the mold cavity.

Gates and Runners. Commonly, more thanone gate is used to deliver material into the mold,and each gate is fed by a “runner” channel lead-ing from the sprue to the gate. After the mold is

Fig. 7 Stages in the operation of a reciprocating-screw injec-tion molding machine


Fig. 9 Hot runner injection mold

filled and the melt has solidified, the material inthe sprue and runners also solidifies and must beremoved with the part before the next shot. Thesprue and runner material are usually regroundin a granulator machine and fed back, along withvirgin material, into the injection cylinder forreuse. To reduce the amount of material thatmust be recycled, some molds are equipped witha hot runner manifold (Fig. 9), which keeps thematerial in the sprue and runners molten tobecome a part of the next shot.

With larger and more complex parts, it iscommon to use more than one gate for injectingmaterial into the mold. The configuration of therunners and gates determines the way the moldis filled. This can change the amount of injec-tion pressure required, the location and condi-tion of “knit” lines, the orientation of materialflow (which can affect mechanical properties),and the ability to vent air from the mold. Knitlines are surfaces along which the flow frontsmeet and are generally weaker. Nonuniformmold filling, caused by poor gate locations, canresult in overpacking the mold in the regionswhich fill first, causing residual stresses andpossible warp-age in the part. Computer pro-grams are now available to assist in mold designand the layout of runners and gates for effectivemold filling at minimum pressure.

Mold Cooling. With thermoplastic injec-tion molding, a method of cooling is usually

incorporated into the mold to speed the solidifi-cation of the plastic. This usually consists ofholes bored in each half of the mold throughwhich a heat-exchange fluid, usually water, cancirculate. The mold temperature is usually con-trolled above room temperature. The optimalmold temperature depends on the type of plasticbeing molded, but typical mold temperatures forthe more common thermoplastics vary from 40to 120 °C (100 to 250 °F).

Material Shrinkage. All thermoplastic so-lidification is accompanied by a volumetricshrinkage. For crystalline plastics, the shrinkageis associated with crystallization. For amor-phous plastics, the shrinkage is generally lessand is associated with the glass transition. Inboth cases, the amount of shrinkage depends onvarious processing parameters, including themold temperature and rate of cooling of the melt.This shrinkage can continue for a period of timeafter the part is removed from the mold. It isimportant that the shrinkage be repeatable, so themold can be appropriately sized. For partsrequiring tight dimensional control or optimalmechanical properties, uniform cooling is essen-tial. If the part does not solidify uniformly in themold, residual stresses will occur as a result ofdifferential shrinkage. Computer programs areavailable to assist in the optimal layout of cool-ing channels for uniform part cooling.

Part Removal. The mold is usually designedsuch that the part remains on the moving half ofthe mold when it is opened. Ejector pins are thenactuated to separate the part from the mold.These ejector, or knockout, pins are activatedeither as a direct result of the moving platen(mechanical knockouts), or hydraulically.

The geometry of the mold must be such thatthe part can be readily removed after the materialhas solidified, sometimes by means of a mechan-ical part remover. This requires careful part de-sign and selection of the “parting surface” acrosswhich the two halves of the mold separate. Nei-ther half of the mold can have undercuts or “dielocks” that would trap the part or keep it frombeing ejected. If the part cannot be designedwithout undercuts, then moving cores, slides, orlifters must be incorporated to eliminate thetrapped condition when the mold is opened.

Mold Venting. Air must be removed as themold fills with plastic. This is usually accom-plished by grinding channels, or vents, into theparting line of the mold. These vents must benarrow enough to keep molten plastic fromescaping, while allowing air to escape. They


should be located adjacent to the last region ofthe mold to fill. Sometimes undersized ejectorpins are also used to assist in venting the mold.Insufficient venting can result in an incom-pletely filled mold, or in cosmetic defects calleddiesel burns, which are caused by the heating ofthe air as it is compressed.

Mold Materials. For high-volume gearproduction applications, the mold cavity and core are usually machined from special mold-making steels. Steel is chosen for its wear resis-tance and durability.

ACKNOWLEDGMENT

A portion of this chapter was adapted fromInjection Molding, Engineered Materials

Handbook Desk Edition, ASM International,1995, p 299–307

REFERENCES

1. C.E. Adams, Plastics Gearing: Selectionand Application, Marcel Dekker, 1986

2. Materials for Plastic Gears, AGMA 920-A01, American Gear Manufacturers Asso-ciation, 2001

3. M.I. Kohan, Polyamides (PA), EngineeringPlastics, Vol 2, Engineered MaterialsHandbook, ASM International, 1988, p 124–127

4. D.P. Townsend, Ed., Dudley’s Gear Hand-book, Second Edition, McGraw Hill, Inc.1991, p 17.2

CHAPTER 5

Machining, Grinding, and Finishing

METAL REMOVAL processes for gearmanufacture can be grouped into two generalcategories:

• Rough machining (or gear cutting) opera-tions such as milling, hobbing, and shapingwhich cut the tooth spaces into preparedgear blanks leaving the desired teeth

• Finishing (or high-precision machining)operations such as shaving, grinding, hon-ing, and lapping which improve the accu-racy and surface finish of previously pre-pared gear teeth

Gear Cutting. The methods of gear cuttingcan be divided broadly into form cutting andgenerating processes. The tooth profile in theformer is obtained by using a form cutting tool.This may be a multiple-point cutter used in amilling machine or a broaching machine, or asingle-point tool for use in a shaper. A variationof the form cutter method is based on transfer-ring the profile from a templet. This method isused in the shaperlike cutting of large toothforms and in cutting bevel gear teeth on a bevelgear planer. In all these processes, the work-piece is held stationary until a tooth is finished;the piece is then indexed for successive teeth.

In the generating process, the tooth profile isobtained by a tool that simulates one or moreteeth of an imaginary generating gear. A relativerolling motion of the tool with the workpiecegenerates the tooth surface. This method is usedin the hobbing, shaping, and milling processesfor manufacturing spur and helical gears and inthe face milling and face hobbing of bevel gears.

A wide variety of machines are used to cutgear teeth. As shown in Fig. 1, there are fourmore or less distinct ways to cut material from agear blank so as to leave a toothed wheel aftercutting. First, the cutting tool can be threadedand gashed. If so, it is a hob, and the method of

cutting is called hobbing. Second, when the cut-ting tool is shaped like a pinion or a section of arack, it will be used in a cutting method calledshaping. Third, in the milling process, the cut-ting tool is a toothed disk with a gear tooth con-tour ground into the sides of the teeth. The fourthgeneral method uses a tool (or a series of tools)that wraps around the gear and cuts all teeth atthe same time. Methods of this type are termedbroaching, punching, or shear cutting.

Finishing. As listed earlier, there are severalmethods available for the improving the qualityof gears following the standard rough machin-ing operation. Gear shaving is a chip formingfinishing operation that removes small amountsof metal from the working surfaces of gearteeth. Its purpose is to correct errors in index,helix angle, tooth profile, and eccentricity.Shaving is carried out prior to gear heat treat-

Fig. 1 Outline of methods of producing gear teeth




Fig. 2 Relation of cutter and workpiece when milling teeth ina spur gear

Fig. 3 Progressive action of broach teeth in cutting teeth of aninternal spur gear

ment. Grinding is a technique of finish machin-ing utilizing a rotating abrasive wheel. Grindingis an effective means of finishing heat-treatedhigh-hardness steels (40 HRC and above). Gearhoning is a particularly effective method ofremoving nicks and burrs from the active pro-files of the teeth after heat treatment. Lapping isa low-speed low-pressure abrading operationused to refine the tooth surface and to reducenoise levels in gear sets. The mating gear andpinion are run together under a controlled lightload while a mixture of abrasive compound andsuitable vehicle are pumped onto the pair. Aswith grinding and honing, lapping is also car-ried out after gear heat treatment.

Machining Processes for Gears

Simple gear tooth configurations can be pro-duced by basic processes such as milling,broaching, and form tooling. Complex geartooth configurations require more sophisticatedprocesses designed especially for the manufac-ture of gears.

Processes for Gears Other Than Bevel Gears

The methods used to cut the teeth of gearsother than bevel gears are milling, broaching,shear cutting, hobbing, shaping, and rack cut-ting. In any method, a fixture must hold the gearblank in correct relation to the cutter, and thesetup must be rigid.

Milling produces gear teeth by means of aform cutter. The usual practice is to mill onetooth space at a time. After each space is milled,the gear blank is indexed to the next cuttingposition.

Peripheral milling can be used for the rough-ing of teeth in spur and helical gears. Figure 2shows teeth in a spur gear being cut by periph-eral milling with a form cutter. End milling canalso be used for cutting teeth in spur or helicalgears and is often used for cutting coarse-pitchteeth in herringbone gears.

In practice, gear milling is usually confined toone-of-a-kind replacement gears, small-lot pro-duction, the roughing and finishing of coarse-pitch gears, and the finish milling of gears hav-ing special tooth forms. Although high-qualitygears can be produced by milling, the accuracyof tooth spacing on older gear milling machineswas limited by the inherent accuracy of the

indexing mechanism. Most indexing techniquesused on modern gear milling machines incorpo-rate numerical control or computer numericalcontrol, and the accuracy can rival that of hob-bing machines.

Broaching. Both external and internal gearteeth, spur or helical, can be broached, but con-ventional broaching is usually confined to cut-ting teeth in internal gears. Figure 3 shows pro-gressive broach steps in cutting an internal spurgear. The form of the space between broachedgear teeth corresponds to the form of the broachteeth. The cutting action of any single broachtooth is similar to that of a single form tool.Each cross section of the broach has as many

Chapter 5: Machining, Grinding, and Finishing / 91

Fig. 4 Progressive action in shear cutting teeth of an externalspur gear. Shear cutting operation proceeds from

roughing (a) to intermediate (b) to finishing (c) operations.

teeth as there are tooth spaces on the gear. Thediameter of each section increases progressivelyto the major diameter that completes the toothform on the workpiece. Broaching is fast andaccurate, but the cost of tooling is high. There-fore, broaching of gear teeth is best suited tolarge production runs.

Shear cutting is a high-production methodfor producing teeth in external spur gears. Theprocess is not applicable to helical gears. Inshear cutting, as in broaching, all tooth spacesare cut simultaneously and progressively (Fig.4). Cutting speeds in shear cutting are similar tothose for broaching the same work metal.Machines are available for cutting gears up to508 mm (20 in.) in diameter, with face width upto 152 mm (6 in.).

The shear cutting head is mounted in a fixedposition, and the gear blanks are pushed throughthe head. Cutting tools are fed radially into thehead, a predetermined amount for each stroke,until the required depth of tooth space isreached. In shear cutting, some space is requiredfor over-travel, although most workpieces withintegral shoulders or flanges (such as clustergears) do have enough clearance between sec-tions to allow shear cutting to be used. There-fore, this process is best suited to large produc-tion runs.

Hobbing is a practical method for cuttingteeth in spur gears, helical gears, worms, wormgears, and many special forms. Conventionalhobbing machines are not applicable to cuttingbevel and internal gears. Tooling costs for hob-bing are lower than those for broaching or shearcutting. Therefore, hobbing is used in low-quantity production or even for a few pieces. Onthe other hand, hobbing is a fast and accuratemethod (compared to milling, for example) andis therefore suitable for medium and high pro-duction quantities.

Hobbing is a generating process in whichboth the cutting tool and the workpiece revolvein a constant relation as the hob is being fedacross the face width of the gear blank. The hobis a fluted worm with form-relieved teeth thatcut into the gear blank in succession, each in aslightly different position. Instead of beingformed in one profile cut, as in milling, the gearteeth are generated progressively by a series ofcuts (Fig. 5). The hobbing of a spur gear isshown in Fig. 6.

Fig. 5 Schematic of hobbing action. Gear tooth is generatedprogressively by hob teeth. Fig. 6 Hobbing of a spur gear


Fig. 7 Relation of cutter and workpiece in shaping gear teeth

Fig. 8 Relation of cutter and workpiece in generating a wormby shaping

Gear shaping is the most versatile of allgear cutting processes. Although shaping ismost commonly used for cutting teeth in spurand helical gears, this process is also applicableto cutting herringbone teeth, internal gear teeth(or splines), chain sprockets, ratchets, ellipticalgears, face gears, worm gears, and racks. Shap-ing cannot be used to cut teeth in bevel gears.Because tooling costs are relatively low, shap-ing is practical for any quantity of production.Workpiece design often prevents the use ofmilling cutters or hobs (notably, for clustergears), and shaping is the most practical methodfor cutting the teeth.

Gear shaping is a generating process that usesa toothed disk cutter mounted on a spindle thatmoves in axial strokes as it rotates. The work-piece is carried on a second spindle. The work-piece spindle is synchronized with the cutterspindle and rotates as the tool cuts while it isbeing fed gradually into the work. The actionbetween a shaping cutter and a gear blank isillustrated in Fig. 7. Shaping applied to the cut-ting of a worm (Fig. 8) involves no axial strokeof the cutter spindle.

Rack cutting is done with a cutter in theform of a rack with straight teeth (usually threeto five). This cutter reciprocates parallel to thegear axis when cutting spur gears and parallel tothe helix angle when cutting helical gears. Metalis removed by a shaper-like stroke similar to thecutting action in gear shaping. In addition to thereciprocating action of the rack cutter, there issynchronized rotation of the gear blank witheach stroke of the cutter, with a correspondingadvance of the cutter as in the meshing of a gearand rack. By these combined actions, the trueinvolute curve of the gear tooth is developed.Several gear cutting machines use this principle.Rack cutters are less expensive than hobs. Rackcutting is especially adapted to the cutting oflarge gears or gears of coarse pitch or both.Gears with diametral pitch as coarse as ⅜ arecommonly cut by the rack method.

Processes for Bevel Gears

The machining of bevel gears is treated as aseparate subject because most bevel gears arecut in special machines with special cutters.However, the action of these cutters bears aclose resemblance to one or more of the basicprocesses—milling, broaching, or shaping.Both generating and nongenerating processesare discussed below.

Milling is not widely used for cutting bevelgears, because of the accuracy limits of index-ing devices and because the operation is timeconsuming (as many as five cuts around the gearmay be required for completing one gear).Straight bevel gears are sometimes roughed bymilling and then finished by another method.This two-operation procedure is more commonwhen the availability of special gear cuttingmachines is limited.

Template machining is a low-production,nongenerating method used to cut the tooth pro-files of large bevel gears using a bevel gearplaner (Fig. 9). Because the setup can be madewith a minimum of tooling, template machiningis useful when a wide variety of coarse-pitchgears are required. Template machining uses asimple, single-point cutting tool guided by atemplate several times as large as the gear toothto be cut. Under these conditions, high accuracyin tooth forms is possible.

The necessary equipment is unique. Thesetup utilizes two templates; one for each side ofthe gear tooth. In theory, a pair of templateswould be required for each gear ratio, but inpractice a pair is designed for a small range of


Fig. 9 Cutting teeth in a large straight bevel gear by templatemachining in a bevel gear planer

Fig. 10 Relative positions of cutter and workpiece in For-mate single-cycle cutting

ratios. A set of 25 pairs of templates encom-passes all 90° shaft angle ratios from 1:1 to 8:1for either 14½ or 20° pressure angles. This sys-tem of templates is based on the use of equal-addendum tooth proportions for all ratios. Thetooth bearing localization is produced by aslight motion of the tool arm as the cutting toolmoves along the tooth. The length and positionof the cut can be controlled by the machineoperator.

To produce a finished gear, five or six cuttingoperations are required. The first is a roughingoperation, made by feeding a slotting tool or acorrugated V-tool to full depth. If the first cut ismade with a slotting tool, a second cut isrequired with a V-tool or a corrugated V-tool.Cuts are made with the template follower rest-ing on a straight guide. After roughing, the tem-plates are set up, and the teeth are finished bymaking two cuts on each side. Slotting tools arespecified by point width and depth of cut; corru-gated roughing tools, by point width, depth ofcut, and pressure angle; finishing tools, by pointwidth only. To set up a straight bevel gearplaner for template machining, the operatorneed know only the tooth proportions of thegear to be cut, plus the template list and theindex gear list furnished with the machine.

Formate cutting and Helixform cut-ting are nongenerating methods for cutting spi-ral bevel and hypoid gears. Nongeneratingmethods can be used for cutting the gear mem-ber of spiral bevel and hypoid pairs when thegear-to-pinion ratio is 2.5:1 or greater. The twoprincipal methods are Formate cutting andHelixform cutting.

Formate cutting is applicable to both theroughing and single-cycle finishing of gearswith pitch diameters up to 2540 mm (100 in.).

Roughing and finishing are sometimes bothdone by one cutter in the same machine. Moreoften, for greater efficiency, roughing and fin-ishing operations are done in differentmachines.

The Formate method can be used with thetwo-cut roughing and finishing method, inwhich the gear is roughed to depth and then sin-gle-cycle finished, or with a one-cut roughingand finishing method known as completing. Inthe completing method, the cutter is plunged toapproximately 0.25 mm (0.010 in.) of wholedepth, the cutting speed is doubled, and the cut-ter is fed to whole depth, taking a light chip.This final portion of the cycle removes the built-up edge on the cutter and produces an accept-able surface finish. The completing method isused for both face milling and face hobbing.

In the Formate single-cycle finishing method,one tooth space is finish cut in one revolution ofthe cutter. Stock removal is accomplished bycutting blades mounted in a circular cutter thatresembles a face milling cutter. Each blade inthe cutter is slightly longer and wider than thepreceding blade; thus, the cutting action is, ineffect, that of a circular broach. A gap betweenthe first and last cutting blades permits indexingof the workpiece as each tooth space is com-pleted. The relative positions of cutter and gearduring Formate single-cycle cutting are illus-trated in Fig. 10.

Helixform cutting, another nongeneratingmethod of cutting spiral bevel and hypoid gears,is generally similar to Formate cutting. How-ever, there is one significant difference in themethod and in the finishing operation for thegear member.


One turn of the Helixform cutter finishes bothsides of a tooth space. The cutter has both rota-tional and reciprocating motion, and this combi-nation makes the path of the cutter-blade tipstangent to the root plane of the gear. Because thecutting edge is a straight line, the surface cut bya Helixform gear cutter is a true helical surface.The principal advantage of Helixform cuttingcompared to Formate cutting is that the gearproduced by Helixform is conjugate to the mat-ing pinion, and the resulting contact pattern haslittle or no bias.

The Cyclex method is also a nongenerat-ing method, and the result is the same as that forthe Formate method. The Cyclex method wasdeveloped for the rough and finish cutting ofgears in one operation and is particularly suit-able when production quantities are not greatenough to warrant separate Formate roughingand finishing machines for the gear member.Cyclex machines of the generator type can cut awide range of gear sizes and can be used for cut-ting both gears and pinions.

In the Cyclex method, the gear is roughed andfinished in one chucking from the solid blank.The finishing blades of the cutter are set belowthe roughing blades and do not contact the workduring the roughing cycle. Several revolutions of the cutter may be necessary for roughing, thenumber required depending on the pitch of thegear. In the final revolution, after the last rough-ing blade has passed through the cut, the work israpidly advanced, permitting the finishing bladesto make contact and finish the tooth space to size.After the finishing blades have passed throughthe cut, the work is rapidly withdrawn andindexed, and the cycle is repeated until all teethare completed.

Face mill cutting machines are used to fin-ish cut teeth in spiral bevel, Zerol, and hypoidgears. Machines and cutters are available for cut-ting gears ranging from small instrument gearsup to about 2540 mm (100 in.) in diameter.

The three types of face mill cutters are identi-fied by the design of their cutting blades: inte-gral, segmental, and inserted. All of these can beused for both roughing and finishing. Solid orintegral-blade cutters are made from a singlepiece of tool steel and are usually less than 152mm (6 in.) in diameter. They are used for fine-pitch gears. Segmental cutters are made up ofsections, each having two or more blades. Thesegments are bolted to the cutter head aroundthe periphery. Inserted-blade cutters are of twotypes. The first type has blades that are bolted to

the slotted head. This cutter usually has parallelsfor changing diameter, and adjusting wedges fortruing individual blades. The blades are sharp-ened in a radial or near-radial plane. The secondtype of inserted-blade cutter has blades that areclamped in the slot. The blades are sharpened bytopping the blades down and repositioning themin the head.

For finishing, the three types of cutters can befurnished with all outside blades, all insideblades, or alternate outside and inside blades.Roughing cutters and completing cutters canhave either alternate inside and outside blades orhave end-cutting or bottom-cutting blades alter-nately spaced with inside and outside blades.

There are four basic cutting methods: com-pleting, single-side, fixed-setting, and single-setting. In each case, the rotating cutting edgesof a face mill cutter represent the imaginary gearsurface.

The completing method is the generation ofthe part by a circular face mill or face hob cutterwith alternate inside and outside blades that cutthe tooth surfaces on both sides of a tooth spaceat the same time. With this method, each mem-ber is finished in one operation.

In the single-side method, the part is fin-ished by a circular face mill cutter with alternateinside and outside blades that cut the tooth sur-face on each side of a tooth space in separateoperations with independent machine settings.

In the fixed-setting method, the part is fin-ished by two circular face mill cutters: one withinside blades only for cutting the convex side ofthe tooth, and the other with outside blades onlyfor cutting the concave side. The two sides ofthe tooth are produced separately in two entirelydifferent machine setups. For large productionruns, a pair of machines is used. One machine isfor cutting one side of the tooth, and the other isfor the other side of the tooth.

The single-setting method is a variation ofthe completing method and is used when theavailable cutters have point widths too small forcompleting cutting. Both sides are cut with thesame machine settings, and the blank is rotatedon its axis to remove the amount of stock neces-sary to produce the correct tooth thickness. Afterthe first cut, only one side of the cutter is cuttingin the tooth slot. Figure 11 illustrates the actionof a face mill when generating pinion teeth bythe fixed-setting method (inside blades).

Face hob cutting is similar to face millingexcept that the indexing is superimposed on thegenerating cycle. Cutters are arranged with


Fig. 11 Face mill cutter shown in position to generate a pin-ion by the fixed-setting method

Fig. 12 Schematic of the face hob cutting method

blade groupings. As each blade group passesthrough the cut, the work is being indexed onepitch (Fig. 12). Gears cut by this method aregenerally completed in one operation. Most facehob cutters are of the inserted-blade type. Inte-gral and segmental systems are available.

Interlocking cutters, known also as com-pleting generators, generate the teeth on straightbevel gears or pinions from a solid blank in oneoperation.

In this method, two interlocking disk-typecutters rotate on axes inclined to the face of themounting cradle, and both cut in the same toothspace (Fig. 13). The cutting edges present a con-cave cutting surface that removes more metal atthe ends of the teeth, giving localized tooth con-tact. The gear blank is held in a work spindlethat rotates in timed relation with the cradle onwhich the cutters are mounted. A feed-camcycle begins with the workhead and blank mov-ing into position for rough cutting, without gen-erating roll, and cutting proceeds until the cut isjust short of full depth. After a rough generatingroll, the work is fed in to full depth, and a fastup-roll finish generates the tooth sides. At thetop of the roll, the work backs out, and the cra-dle and work spindle roll down again into


Fig. 13 Relation of interlocking cutters (completing genera-tors) with the bevel gear being cut Fig. 14 Revacycle cutter in position to cut a bevel gear

roughing position. During this short down-roll,the blank is indexed.

Revacycle is a generating process used forcutting straight bevel gears up to about 255 mm(10 in.) pitch diameter in large production runs.This is the fastest method for producing straightbevel gears of commercial quality. Initial tool-ing cost is greater for the Revacycle processthan for other processes for cutting straightbevel gears, but the high production rate resultsin the lowest cost for mass production.

Most gears produced by the Revacyclemethod are completed in one operation, usingcutters 406, 457, 533, or 635 mm (16, 18, 21, or25 in.) in diameter that rotate in a horizontalplane at a uniform speed (Fig. 14). The cutterblades, which extend radially outward from thecutter head, have concave edges that produceconvex profiles on the gear teeth. During cut-ting, the work-piece is held motionless whilethe cutter is moved by means of a cam in astraight line across the face of the gear and par-allel to its root line. This motion produces astraight tooth bottom while the desired toothshape is being produced by the combined effectof the motion of the cutter and the shapes of thecutter blades. The cutter is actually a circularbroach in that each successive cutting tooth islarger than the one that precedes it along the cir-cumference of the cutter. The cutter makes onlyone revolution per tooth space.

Feed is obtained by making cutter blades pro-gressively longer, rather than by moving the

entire cutter into the work. The completing cut-ter contains three kinds of blades: roughing,semifinishing, and finishing. One revolution ofthe cutter completes each tooth space, and thework is indexed in the gap between the last fin-ishing blade and the first roughing blade. For thesmall amount of Revacycle work that is too deepto be completed in one cut, separate roughingand finishing operations are used. Under theseconditions, separate cutters and setups are re-quired for each operation. The cutters and ma-chine cycles are similar to those for completingcutters, except that the roughing cutters have nosemifinishing or finishing blades. A second cut-ter has only semifinishing and finishing blades.

Two-tool generators are used for cuttingstraight bevel gears by means of two reciprocat-ing tools that cut on opposite sides of a tooth(Fig. 15). Tooling cost is low for two-tool gen-erators, but production rates are lower thanthose for other straight bevel generators, such asinterlocking cutters and Revacycle machines.Two-tool generators are usually used when:

• The gears are beyond the practical size range(larger than about 254 mm, or 10 in., pitchdiameter) of other types of generators

• Gears have integral hubs or flanges that proj-ect above the root line, thus preventing theuse of other generators

• A small production quantity or a variety ofgear sizes cannot be accommodated by othertypes of machines used for cutting straightbevel gears

Two-tool generators are used for both roughand finish cutting. When warranted by produc-


Fig. 15 Angle of straight bevel gear tooth and sections oftools used for two-tool generating

Fig. 16 Provision for crowning gear teeth by means ofadjustable guides in two-tool generators Fig. 17 Components of a planing generator

tion quantities, roughing is done in separatemachines, which are the same as the generatorsexcept that the machines used only for roughinghave no generating roll. For small productionquantities, both roughing and finishing cuts aremade in the generators, the roughing cut beingmade without generating roll.

To make the machine setup for producing agear that will operate at right angles to its mat-ing gear, the operator must have the gear speci-fications and one calculated machine settingcalled the tooth angle (Fig. 15). The remainingsetup data are taken from tables furnished withthe machine. When the shaft angle of the twogears is not a right angle, the ratio of roll, as wellas the data required for checking the roll, mustbe calculated.

Most two-tool generators can producestraight bevel gears with teeth crowned length-wise to localize tooth contact. Crowned teethare produced by means of two angularlyadjustable guides on the back of each slide. Theguides ride on a pair of fixed rollers (Fig. 16).When the guides are in line with each other, thetool stroke is a straight line, and when they areout of line, the tool is stroked along a curvedpath. The amount of curvature is controlled bysetting the two guides. A table with eachmachine lists the guide settings for making thetooth contact approximately one-half the facewidth. The machine settings can be varied toshorten or lengthen the tooth contact.

Planing generators are unique because theycan cut both straight-tooth and curved-toothbevel gears. However, the use of planing gener-ators is ordinarily restricted to cutting gearsabout 889 mm (35 in.) in diameter or larger or todiametral pitch coarser than 1½. Standardmachines can generate straight, Zerol, and spiralbevel gears. Special heads can be added to stan-dard machines to permit the cutting of hypoidgears.

Tools have straight cutting edges and aremounted on a reciprocating slide that is carriedon the face of the cradle and connected to a rotat-ing crank by a connecting rod (Fig. 17). Toothprofiles are made by rolling the work with thegenerating gear. The lengthwise shape of theteeth is formed by a combination of threemotions:

• Stroke of the tool• Continuous, uniform rotation of the work


• An angular oscillation of the work producedby the eccentric shown in Fig. 17

The eccentric motion modifies the effect that thefirst two motions have on the shape of the teeth.The eccentric is timed for the correct toothrelief.

The spiral angle of the teeth is controlled bythe angular offset of the tool slide from theangle of the cradle axis. Continuous rotation ofthe work is principally for indexing. In effect,the tool makes a cut on all teeth in succession inone generating position, and then the cradle andthe work roll together a slight distance beforeanother cut is taken on all teeth in the new gen-erating position. Actually, however, rolling iscontinuous and occurs gradually until all teethare completely generated in the last pass aroundthe gear.

Several passes are required to complete a gear,the number depending on tooth depth and shape.Flat gear blanks are usually roughed without aroll, first using a corrugated tool and then using asingle cut with a V-roughing tool. This is fol-lowed by at least two side-cutting operations oneach side of the tooth, including generating cutswith roll. A similar sequence is used for cuttingpinions except that roughing is done with roll.

Tools for use in planing generators are simpleand inexpensive. Corrugated tools are furnishedwith a 14½° pressure angle, regardless of thepressure angle of the gear being cut, but pointwidth and depth of cut must be specified whenthe tools are ordered. The operator must knowthe specifications for the gear being cut. A tableof settings for specific requirements is suppliedwith the machine.

Selection of Machining Process

Each gear cutting process discussed in thepreceding sections has a field of application towhich it is best adapted. These fields overlap,however, so that many gears can be producedsatisfactorily by two or more processes. In suchcases, the availability of equipment often deter-mines which machining process will be used.

The type of gear being machined (spur, heli-cal, bevel, or other) is usually the major factor inthe selection of machining process, although oneor more of the following factors usually must beconsidered in the final choice of the method:

• Size of the gear• Configuration of integral sections (flanges or

other)

• Quantity requirements• Accuracy requirements• Gear-to-pinion ratio• Cost

The following sections consider the type of gearas the major variable and discuss the machiningmethods best suited to specific conditions.

Machining of Spur Gears

Milling, shear cutting, hobbing, and shapingare the methods most commonly used for cut-ting teeth in spur gears.

Form milling, with the cutter ground to thedesired shape of the tooth space (Fig. 2), is asimple means of cutting teeth in spur gears.Tooling cost is low, and the process requiresonly a conventional milling machine, a formcutter, and an indexing mechanism. Except forlow-quality production, milling is seldom usedfor cutting spur gears. The main disadvantage inthe form milling of spur gears is the lack ofaccuracy in tooth spacing, which depends on theaccuracy of the indexing mechanism. In addi-tion, form milling is much slower than shearcutting or hobbing.

One milling cutter is not universal for all num-bers of teeth, as are hobs and shaper cutters. Toproduce theoretically correct gear teeth, thetooth form of the cutter must be designed for theexact number of teeth. However, if a smalldeparture in tooth form is acceptable, cuttershave been standardized for a range of teeth, theform being correct for the lowest number of teethin that particular range. Thus, all teeth within therange are provided with sufficient tip relief. Thesame form is produced in all tooth spaces withinthat range. For reasonably accurate gear cutting,eight standard involute gear cutters are requiredto cut all sizes of gears of a given pitch:

Cutter No. Gear tooth range

1 135 to rack2 55–1343 35–544 26–345 21–256 17–207 14–168 12–13

If a more accurate tooth form is desired forgears near the higher part of the ranges, sevenhalf-number cutters can be obtained. A No. 1½cutter, for example, will cut gears with 80 to 134teeth; a No. 2½ cutter, 42 to 54 teeth; and a No.3½ cutter, 30 to 34 teeth. For still greater accu-


racy, cutters of the proper shape for an exactnumber of teeth can be furnished by most toolmanufacturers on short notice.

The tooth form of a single cutter is centeredwith the gear axis so that a symmetrical toothspace is produced. By the use of gang cutters,portions of adjacent tooth spaces can be roughmachined simultaneously. Normally, a rough-ing and a finishing cutter are ganged, the finish-ing cutter being centered with the gear axis.Gang cutters and multiple-tooth cutters are spe-cially designed for the specific application.

Shear cutting is faster and more accuratethan milling for cutting teeth of almost anyinvolute modification in spur gears. Total cut-ting time is often less than 1 min for gears up toabout 152 mm (6 in.) in diameter. However,tooling cost is high, and shear cutting is there-fore practical only for large-scale production.

Hobbing is the process most widely usedfor cutting teeth in spur gears, usually for one ormore of the following reasons:

• High accuracy in a wide range of gear sizes• Flexibility in quantity production• Low cost• Adaptability to work metals having higher-

than-normal hardness

The shape of the workpiece sometimes limitsthe use of hobbing—for example, if the teeth tobe cut are close to another portion of the work-piece having a diameter larger than the rootdiameter of the gear. The axial distance betweenthe two sections must be large enough to allowfor hob overtravel at the end of the cut. Thisover-travel is about one-half the hob diameter.The clearance required between the gear beingcut and any flange or other projecting portion ofthe workpiece is, therefore, about one-half thehob diameter plus additional clearance to allowfor the hob thread angle.

In many cases, it is necessary to cut teeth onheat-treated gear blanks to avoid the difficultiescaused by distortion in heat treating. Hobbing isespecially suitable for cutting gear teeth in hard-ened steel (sometimes as hard as 48 HRC). Al-though hob wear increases rapidly as workpiecehardness increases, normal practice should pro-duce an acceptable number of parts per hobsharpening. Success in hobbing gears at highhardness depends greatly on maintaining mini-mum backlash in the machine and on rigidmounting of both the hob and the workpiece.

The ability to cut teeth in two or more identi-cal spur gears in one setup can also justify use ofthe hobbing method. Inexpensive fixturing is

often utilized for cutting two or more gears atone time when the ratio of face width to pitchdiameter is small.

Shaping can produce high accuracy in cut-ting spur gears because shaping is a generatingprocess. Although seldom as fast as hobbing,shaping is used for a wide range of productionquantities. Many types of gears can be producedto requirements by either shaping or hobbing,and the availability of equipment determineswhich of the two processes is used. However, ifthe workpiece configuration cannot be hobbed,shaping is often the only practical method.

Cutting of teeth in cluster gears that mustmeet close tolerances is sometimes a problembecause the method used must frequently berestricted to shaping and shaving. The samequality requirements cannot be met by shapingand shaving as by hobbing and grinding. Whentolerances for cluster gears are closer than canbe met by shaping and shaving, a corrective pro-cedure sometimes must be employed. A clustergear can be hobbed to greater precision by sep-arating it into a two-piece assembly that isrigidly attached using threaded fasteners.

Machining of Helical Gears

Milling, hobbing, shaping, and rack cuttingare methods most used for producing teeth inhelical gears. Rack cutting is most often usedfor large gears. Identical machining methods areapplicable to conventional helical and crossed-axes helical gears.

Milling is used less than any other methodbecause of the difficulty in obtaining accuracyand productivity. However, for some low pro-duction requirements, milling is the most satis-factory method because the tooling cost is low.In low-volume production, milling is some-times used for roughing only, and the gear is fin-ished by hobbing or shaping.

The milling of helical gears usually requirescutters specially designed for the specific gear. Inmilling helical teeth, the cutter travels along thehelix angle of the gear. At this setting, the cutteraxis of rotation is in the normal plane through thecenter of the gear tooth space. Under these condi-tions, only one point on the finished profile is pro-duced in this normal plane. All the others are pro-duced in different planes. Therefore, the form ofthe cutter teeth is not reproduced in the gear. Inaddition to the setting angle, the diameter of thecutter affects the gear tooth form and must beconsidered in designing the cutter.

Hobbing is extensively used for generatingthe teeth of helical gears for any production vol-


ume. With the exception mentioned below, pro-cedures for hobbing helical gears are the same asthose for spur gears: When hobbing spur gearswith a single-thread hob, the blank rotates onetooth space for each rotation of the hob, the rota-tion being synchronized by means of changegears. When hobbing helical gears, the rotationof the work is retarded or advanced, through theaction of the machine differential, in relation tothe rotation of the hob, and the feed is also held indefinite relation to the work and the hob. Thedecision to advance or retard the workpiece rota-tion depends mainly on whether the hob is aright-hand or left-hand type or whether the helixangle is of right-hand or left-hand configuration.The amount by which the workpiece is retardedor advanced depends on the helix angle. Inmedium-to-high production, it is common to usefixtures that allow hobbing of two or more iden-tical gears in one loading of the machine.

Gears with integral shanks can usually behobbed without difficulty. The shanks can assistin fixturing and handling for loading and unload-ing. When warranted by high-volume produc-tion, hobbing can be done in automatic machinesutilizing automatic unloading and loading.

Although hob life decreases as workpiecehardness increases, helical gears of hardness ashigh as 48 HRC are sometimes hobbed. Whenhardnesses of 48 HRC or lower can be tolerated,the sequence of rough hobbing, heat treating,and finish hobbing is likely to cost less thangrinding after heat treatment.

Shaping is a practical process for generat-ing teeth of helical gears having helix angles upto 45°. The only difference between shapinghelical gears and spur gears is that the machinesused for cutting helical gears must impart addi-tional rotary motion to the cutter spindle as itreciprocates. The amount of rotation per strokeis controlled by a helix guide. The lead of theguide must be the same as the lead of the cutter.

Workpiece configuration is often the mainfactor in the selection of shaping as a process forcutting helical gears. For example, rotary cut-ters such as hobs cannot be used when the teethbeing cut are too close to the flange.

Machining of Herringbone Gears

Milling, hobbing, and shaping are the meth-ods most often used for cutting herringbonegears. Selection of method depends largely onwhether the gear is designed with a gap betweenthe two helixes or whether the herringbone iscontinuous.

Rotary cutters such as form milling cuttersand hobs can be used to cut herringbone teethonly when there is a gap wide enough to permitcutter runout between the right-hand and left-hand helixes. Hobbing machines have beenbuilt that can cut herringbone teeth in gears upto 5590 mm (220 in.) in diameter.

End milling can also be used for machiningteeth in herringbone gears, regardless of whetherthe gears have center slots. The end mills for cut-ting herringbone gears are used in special ma-chines. Many large-diameter herringbone gearsare cut by end milling.

Shaping is also a suitable method for cuttingteeth on herringbone gears; those designed with acenter slot as well as the continuous herringbonecan be shaped. The type of shaper used for cuttingherringbone gears is similar in principle to thetype used for helical gears, except that for her-ringbone gears two cutters, one for each helix, areoperated simultaneously. Both cutters recipro-cate, one cutting in one direction to the center ofthe gear blank and the other cutting to the samepoint from the opposite direction when themotion is reversed. The cutters not only recipro-cate, but also rotate. Both the gear blank and thecutters turn slowly, thus generating the teeth thesame way as in a conventional shaper.

Machining of Internal Gears

Broaching, shear cutting, and shaping are themethods most frequently used for cutting inter-nal parts. Milling is seldom used, except forsome very large gears.

The broaching of internal spur gear teeth isrestricted to workpieces having configurationsthat permit the broach to pass completelythrough the piece. The action of a broach in cut-ting internal gear teeth is shown in Fig. 3. Thebroaching of gear teeth, which is similar to othertypes of broaching, is discussed in the section“Broaching” in this chapter. Broaching is anextremely fast and accurate means of machininginternal gear teeth, but tooling cost is high;therefore, broaching is practical only for high-volume production.

Shear cutting is applicable to internal gearteeth. The principle involved is essentially thesame as that illustrated in Fig. 4 for cuttingexternal spur gears, except that the cutting edgesand direction of radial feed are reversed. Unlikebroaching, shear cutting is not restricted to partswhere the tool must pass completely through thepiece. Shear cutting can be used with no morethan a 3.2 mm (⅛ in.) relief groove between the


Fig. 18 Mating of worm gear (worm wheel) and worm in adouble-enveloping worm gear set

end of the cut and a shoulder. Because toolingcost is high for shear cutting, the process is prac-tical only for high-volume production.

Shaping is applicable to cutting internalgear teeth. Tooling cost is lower than that forbroaching and shear cutting; therefore, shapingis applicable to low-volume production. Shap-ing is less restricted to specific configurationsthan broaching is, because gear teeth can be cutto within 3.2 mm (⅛ in.) of a shoulder; however,for adequate chip clearance and to avoid thedanger of striking the shoulder, it is better tohave ample clearance. Shaping is often the onlypractical method for cutting teeth in large inter-nal gears because the cost of large broaches orshear cutting tools is prohibitive.

Machining of Worms

Several types of worms are used for powertransmission, among them the double-envelop-ing type (Fig. 18), also known as the hour-glassworm because of its shape. Milling, hobbing,and shaping are used to machine the varioustypes of worms.

Milling. For double-thread worms of lowlead angle and commercial accuracy, a duplexcutter can be used. Each milling cutter is spe-cially designed for cutting a specific worm.Another technique for machining worms uti-lizes the multiple-thread cutter. The cutter is setwith its axis parallel to the work axis and is fedto depth. The work then makes one revolutionfor completion. The infeed can be made auto-matic, and because no indexing is required, thismethod is adaptable to volume production.

Hobbing produces the highest-grade wormat the lowest machining cost, but hobbing canbe used only when production quantities arelarge enough to justify the tooling cost. Becauseof the large helix angle at which most worm

hobs operate, the teeth at the entering end arechamfered to reduce the cutting load. Hobs forcutting worms are made to the same tolerancestandards as those for cutting spur gears. Whenit is necessary to increase the hob diameter toprovide more flutes, the tolerances are increasedproportionately. The number of flutes in a wormhob is increased to improve surface finish,because the greater the number of flutes, thesmaller the feed marks.

Shaping. Worms can also be generated by ashaper-cutter. In this technique, a helical gearcutter is used in a special machine similar to ahobber. Both the work and the cutter rotate, andthe cutter is rolled axially along the worm, pro-viding true generating action (Fig. 8).

Machining of Racks

Milling and shaping are used to cut teeth inspur and helical racks.

Milling can be used to produce teeth in bothspur and helical racks. The milling cutter musthave the exact tooth space form. Racks can becut in any standard milling machine; require-ments are essentially the same as those for aconventional milling operation, and the rack tobe cut must be rigidly clamped. Either manualor automatic, indexing mechanisms are avail-able for milling all sizes of racks in high-volumeproduction.

The shaping of spur and helical racksinvolves the rolling action of the operating pitchcircle of the generating shaper-cutter along thecorresponding pitch line of the rack. In cuttingracks on a gear shaper, the machine is equippedwith a special fixture to hold the work. Severalarrangements are used for imparting a trans-verse indexing movement to the member carry-ing the rack. One method employs a face gearsecured on the work spindle that meshes with apinion. The latter, by means of change gears,drives a lead screw, which operates the slidecarrying the rack. Another method is to attach apinion to the work spindle, which meshes with amaster rack attached directly to the slide carry-ing the rack being cut. The first method is nec-essary when high ratios are involved in thedrive; the second method needs only the regularwork change gears.

Machining of Bevel Gears

Face mill cutting, face hob cutting, Formatecutting, Helixform cutting, the Cyclex method,interlocking cutters, Revacycle, two-tool gener-


ators, planing generators, and template machin-ing are used to cut teeth in straight and spiralbevel gears. The fundamentals of these processesare discussed in the section “Processes for BevelGears” in this chapter. Choice of method de-pends mainly on the type of gear being cut(straight or spiral bevel), size, configuration, ac-curacy requirements, and production quantities.

Template machining and planing in a geargenerator are more often used for cutting teethin gears larger than 813 mm (32 in.) outsidediameter.

Straight Bevel Gears. The two-tool gener-ator is widely used for cutting straight bevelgears and is especially well adapted to the cut-ting of gears in a wide range of sizes (up toabout 889 mm, or 35 in., outside diameter) inlow-to-medium production quantities becausetool cost is low. Two-tool generating is alsoadaptable to the cutting of gears that have pro-truding portions (such as front hubs) that pre-clude the use of some processes.

Interlocking cutters provide a means of com-pleting straight bevel gears in one operation.The interlocking-cutter method is faster thantwo-tool generating, but more costly. Gearswithout front hubs and less than 406 mm (16 in.)in outside diameter are best adapted to machin-ing with interlocking cutters.

The Revacycle process is the fastest methodfor cutting straight bevel gears. Gear teeth areoften completed at the rate of 1.8 s per tooth.This method was primarily designed for cuttinggears having up to 254 mm (10 in.) pitch diam-eter at 4:1 ratio with the pinion and having amaximum face width of 29 mm (1⅛ in.). In theRevacycle method, the cutter must have anuninterrupted path; therefore, the process can-not cut gears that have front hubs. Because ofthe high tooling cost, Revacycle cutting is eco-nomical only for high-volume production.

Cost Versus Quantity (Straight BevelGears). The two-tool generator, because it hasthe lowest tooling cost, is the most economicalmethod for producing up to approximately 150pairs of gears, at which point the two-tool gen-erator and interlocking-cutter methods areequivalent. For large production runs, the two-tool generating method becomes prohibitivelyexpensive. The Revacycle and interlocking-cutter methods are equivalent in cost at about1200 pairs of gears, beyond which the Revacy-cle method is cheaper.

Spiral Bevel Gears. Spiral, Zerol, andhypoid bevel gears are cut in the same type of

equipment and by the same general procedures.(Hypoid gears are by far the most numerous,being used in quantities exceeding those of spi-ral and Zerol gears combined.) Pinions are gen-erally cut by some type of generator. Gears mayor may not be cut in generators. When the gear-to-pinion ratio is greater than about 2.5:1, it iscommon practice to cut the gears without gen-erating roll. Therefore, the Formate completing,Formate single-cycle, Helixform, and Cyclexmethods are extensively used for cutting spiralbevel gears having a ratio of 2.5:1 or greater.

Nongenerated gears are less expensive thantheir generated counterparts, although there is asmaller difference in cost between the variousmethods for cutting spiral bevel gears (of lessthan 813 mm, or 32 in., in outside diameter)than between the various methods for cuttingstraight bevel gears.

Machining of Large Gears

There is no one dimension that defines a largeor a small gear. As various sizes are reached,some methods of manufacture become imprac-tical, and other methods must be used.

Herringbone Gears. The same conditionspreviously discussed in the section “Machiningof Herringbone Gears” in this chapter also applyto the machining of large herringbone gearcomponents.

Spur and Helical Gears. Milling, hobbing,and rack cutting are the methods most com-monly used for cutting large spur and helicalgears.

Milling is the least expensive and the leastaccurate of these three methods; therefore, theaccuracy required in the gear will determinewhether or not milling can be used.

Hobbing is more costly than milling, butproduces more accurate gears. Hobs are avail-able for cutting gears well over 2540 mm (100in.) in outside diameter, provided the diametralpitch is finer than 1. Because of the size of thehob required and the limitations of hobbingmachines, it is difficult to hob gears of 1 diame-tral pitch and coarser.

Once it has been decided that hobbing will beused, it must be determined whether a groundhob will be required or whether an ungroundhob will provide the required degree of accu-racy. The two types vary greatly in cost. How-ever, if a ground hob is selected, extreme caremust be used in resharpening; if this is not done,the original accuracy will not be maintained,and errors may occur in the gear tooth form.


Fig. 19 Rack-type cutter generating the teeth of a spur gearFig. 20 Shaving of gears. (a) Work gear in mesh with shaving

cutter. (b) Serrated gear-shaving cutter

Rack Cutting. For machining large gearsthat have large teeth (coarser than 1 diametralpitch), rack cutting (Fig. 19) is usually the mostpractical method. Rack cutting may be lessexpensive than hobbing, even when teeth arefiner than 1 diametral pitch.

Bevel Gears. Face milling and face hob-bing, two-tool generating, and planing generat-ing are the methods most commonly used forcutting large straight and spiral bevel gears.

Large face mill generators that can cut gearsup to 2540 mm (100 in.) in outside diameter arethe fastest and most accurate machines for cut-ting large bevel gears.

Two-tool generators offer a practical meansfor cutting straight bevel gears having diametersup to about 889 mm (35 in.), face widths up to152 mm (6 in.), and teeth as coarse as 1 diame-tral pitch. Tooling cost for the two-tool generat-ing method is also low.

Planing generators can be used for cuttingstraight bevel gears, but they are most widelyused for cutting spiral bevel gears ranging from889 to 1830 mm (35 to 72 in.) in outside diam-eter, with up to 254 mm (10 in.) face width andteeth as coarse as ¾ diametral pitch.

Shaving of Spur and Helical Gears

Gear shaving is a finishing operation thatremoves small amounts of metal from the flanksof gear teeth. It is not intended to salvage gearsthat have been carelessly cut, although it cancorrect small errors in tooth spacing, helixangle, tooth profile, and concentricity. Shavingimproves the finish on tooth surfaces and caneliminate tooth-end load concentration, reducegear noise, and increase load-carrying capacity.Shaving has been successfully used in finishinggears of diametral pitches from 180 to 2. Stan-dard machines and cutters are available forshaving gears that range in size from 6.4 to 5590mm (¼ to 220 in.) pitch diameter.

Leaving excessive stock for shaving willimpair the final quality of the shaved gear. For

maximum accuracy in the shaved gear and max-imum cutter life, a minimum of stock should beallowed for removal by shaving; the amountdepends largely on pitch. As little as 0.008 to0.025 mm (0.0003 to 0.001 in.) of stock shouldbe left on gears having diametral pitch as fine as48; 0.08 to 0.13 mm (0.003 to 0.005 in.) isallowable for gears having diametral pitch of 2.

Operating Principles. The shaving opera-tion is done with cutter and gear at crossed axes;helical cutters are used for spur gears, and viceversa. The action between gear and cutter is acombination of rolling and sliding. Vertical ser-rations in the cutter teeth take fine cuts from theprofiles of the gear teeth.

During operation, the tip of the shaving cuttermust not contact the root fillet, or uncontrolled,inaccurate involute profiles will result. Forgears to be shaved, protuberance-type hobs thatprovide a small undercut at the flank of the toothmay be preferred. This type of hob avoids theinitial tip loading of the shaving cutter.

Shaving Cutters. A typical rotary gear-shaving cutter is shown in Fig. 20(b). This cutteris serrated on the profile to form the cuttingedges. The depth of the serrations governs totalcutter life in terms of the number of sharpeningspermitted. A shaving cutter is sharpened byregrinding the tooth profiles, thus reducing thetooth thickness. This causes a reduction in oper-ating center distance for the same backlash andin turn changes the operating pressure angle.These changes are compensated for by a changein addendum after resharpening. Tolerance is animportant consideration in original purchase and


resharpening. Shaving cutters are manufacturedto standardized tolerances, not unlike those ofmaster gears. For example, cumulative toothspacing error can be held to 0.008 mm (0.0003in.) and profile to 0.00064 mm (0.000025 in.).Because the engineering and facilities necessaryto produce such accuracy are not available in most gear manufacturing plants, cutters areordinarily returned to a tool manufacturer for resharpening.

Shaving Methods. Shaving is done by twobasic methods: rack and rotary.

In rack shaving, the rack is reciprocatedunder the gear, and infeed takes place at the endof each stroke. Because racks longer than 508mm (20 in.) are impractical, 152 mm (6 in.) isthe maximum diameter of gear that can beshaved by the rack method.

Rotary Shaving. The several applications ofrotary shaving include underpass, modifiedunderpass, transverse, axial traverse, and angu-lar traverse. Crown shaving can be incorporatedin all of these modifications.

In rotary shaving, the cutter has the approxi-mate form of a gear (Fig. 20). The size of gearthat can be shaved is limited by the machinerather than by the cutter. Rotary shaving can beany of three types: underpass, modified under-pass, and transverse.

Underpass shaving is used on cluster gears orgears with shoulders. To avoid interference withthe adjacent gear or shoulder, the cross-axesangle is usually 4 to 6°. The face of the tool mustbe wider than the face of the shaved gear.Because underpass shaving is a one-cycle,short-stroke process, it is the fastest method ofshaving. Disadvantages include relatively shorttool life and light stock removal, thus requiringprecise size control of the preshaved gear.

Modified underpass shaving is the mostwidely used method because it is a rapid one-cycle process. Tool cost is moderate because thecutter need be no wider than the gear and maybe narrower. The high cross-axes angle of 30 to60° promotes rapid stock removal and smoothersurface finish.

Transverse shaving is the slowest shavingmethod because multiple passes are required. Itis a method of handling gears much wider thanthe cutter; therefore, cutter cost is moderate forgears with wide faces.

Crown shaving is used to relieve load con-centration at the ends of gear teeth caused by themisalignment of axes in operation. Crowning isa modification of the tooth profile in both the

radial and axial planes. In the axial traversemethod of shaping, crowning is done by rockingthe worktable as it is reciprocated. In the higher-production angular traverse method, the cutteris modified to provide crowning. The amount ofcrown varies, but usually 0.0003 to 0.0005mm/mm (0.0003 to 0.0005 in./in.) of face widthis sufficient.

Speed and Feed. Although cutting speedsare always high, the optimum speed of rotationfor gear shaving varies considerably with workmetal hardness and composition. Speeds andfeeds for several steels and hardness ranges aregiven in Table 1.

Cutter Material and Construction

High-speed tool steel is used almost exclu-sively as the material for cutting edges of gearcutting tools. The steels most widely used arethe general-purpose grades such as M2 or M7.Grade M3 (higher in carbon and vanadium thangeneral-purpose grades) is also used in manygear cutting applications and is often preferredto M2 and M7 for cutting quenched and tem-pered alloy steels. The more highly alloyedgrades of high-speed tool steel such as T15 orM30 are recommended only for conditionswhere greater red hardness is necessary. Suchconditions include hard work metal, inadequatesupply of cutting fluid, or high cutting speeds.Cutters are made from these highly alloyedgrades only when the general-purpose grades(or M3) have proved inadequate.

Carbide cutters are used to hand finish gearscut by the face mill and face hob methods whensmall quantities of high-quality parts areneeded. For most applications, carbide cuttersare not economical. However, one applicationin which they are a cost-effective tool is theTangear generator method.

Tangear Generator. Single-point cementedcarbide cutting tools are rotated in oppositedirections on the peripheries of two cutter headswith horizontal and parallel axes on the Tangeargenerator as shown in Fig. 21. The workpiece,with its axis vertical, is rotated as it is fed hori-zontally (typically a short distance of 8 mm, or5 ⁄16 in.) between the cutter heads. The motionsare synchronized so that the cutters act asthough in mesh with the gear and progressivelygenerate the teeth and form cut the root fillets.The teeth are rough cut as the gear moves to thecutters and are finish cut on the back stroke. The


Table 1 Feeds and speeds for the shaving of carbon and low-alloy steel gears with high-speed steel tools

Gear tooth size

Feed per revolution of gear(a)

Cutter pitch line speed

High-speed steel tool material

Material Hardness, HB Condition Module Diametral pitch mm in. m/min sfm ISO AISI

Wrought free-machining carbon steels

Low-carbonresulfurized

100–150 Hot rolled orannealed

25–65–3

1–45–10

0.30.2

0.0120.008

185 610 S4, S2 M2, M7

1116 1119 2–1.5 11–19 0.12 0.0051117 1211 1 and finer 20 and finer 0.07 0.0031118 1212 25–6 1–4 0.3 0.012

5–3 5–10 0.2 0.0082–1.5 11–19 0.12 0.005

1 and finer 20 and finer 0.07 0.003Medium-carbon

resulfurized175–225 Hot rolled,

normalized, 25–6

5–31–45–10

0.30.2

0.0120.008

150 500 S4, S2 M2, M7

1132 1144 2–1.5 11–19 0.12 0.0051137 1145 1 and finer 20 and finer 0.07 0.0031139 1146 25–6 1–4 0.3 0.0121140 1151 tempered 5–3 5–10 0.2 0.0081141 2–1.5 11–19 0.12 0.005

1 and finer 20 and finer 0.07 0.003Low-carbon leaded12L1312L1412L15

100–150 Hot rolled,normalized,annealed, orcold drawn

25–65–3

2–1.51 and finer

1–45–10

11–1920 and finer

0.30.20.120.07

0.0120.0080.0050.003

215 700 S4, S2 M2, M7


25–65–32–1.5

1 and finer

1–45–10

11–1920 and finer

0.30.20.120.07

0.0120.0080.0050.003

185 600 S4, S2 M2, M7

Wrought carbon steels

Low carbon1005 10151006 10161008 1017


25–65–32–1.5

1 and finer

1–45–10

11–1920 and finer

0.30.20.120.07

0.0120.0080.0050.003

160 525 S4, S2 M2, M7

1009 1018 1029 25–6 1–4 0.3 0.0121010 1019 1513 5–3 5–10 0.2 0.0081011 1020 1518 2–1.5 11–19 0.12 0.0051012 1021 1522 1 and finer 20 and finer 0.07 0.0031013 1022Medium carbon1030 1044 15261033 1045 15271035 1046 1536

Hot rolled,normalized,annealed, orcold drawn

25–65–32–1.5

1 and finer

1–45–10

11–1920 and finer

0.30.20.120.07

0.0120.0080.0050.003

135 450 S4, S2 M2, M7

1037 1049 1541 325–375 Quenched and 25–6 1–41038 1050 1547 tempered 5–3 5–10 0.2 0.0081039 1053 1548 2–1.5 11–191040 1055 1551 1 and finer 20 and finer1042 1524 15521043 1525

125–175

205

Quenched and cold drawnannealed, or

0.0120.3

Annealed or 225–275

102310251026

(continued)

Wrought free-machining alloy steels

Medium-carbon resulfurized

4140 4145Se4140Se 4147Te


25–65–32–1.5

1 and finer

1–45–10

11–1920 and finer

0.30.20.120.07

0.0120.0080.0050.003

150 500 S4, S2 M2, M7

4142Te 4150tempered 5–3 5–10 0.2 0.008

2–1.5 11–19 0.12 0.0051 and finer 20 and finer 0.07 0.003

325–375 84 275 S4, S2 M2, M7

cold drawn

0.0050.003 0.07

0.12

325–375 Quenched and 25–6 1–4 0.3 0.012 76 250 S5 M3

150–200 Cold drawn 675 S4, S2 M2, M7

115 375 S4, S2 M2, M7

84 275 S5 M3

(a) Feed recommendations apply to conventional (axial-transverse) gear shaving. Feeds should be increased 100% for gears shaved by the diagonal (angular-transverse)method. Source: Metcut Research Associates Inc.


Medium- andhigh-carbonleaded

41L30 41L50


25–65–3

2–1.51 and finer

1–45–1011–19

20 and finer

0.30.20.120.07

0.0120.0080.0050.003

160 525 S4, S2 M2, M7

41L40 43L40 86L40 25–6 1–4 0.3 0.01241L45 51L32 5–3 5–10 0.2 0.00841L47 52L100 2–1.5 11–19 0.12 0.005

1 and finer 20 and finer 0.07 0.003

Wrought alloy steels

Low carbon4012 46214023 4718

125–175 Hot rolled,annealed, orcold drawn

25–65–3

2–1.5

1–45–1011–19

0.30.20.12

0.0120.0080.005

145 475 S4, S2 M2, M7

4024 4720 8617 1 and finer 20 and finer411843204419

481548174820

862086228822

325–375 Normalized or quenchedand tempered

25–65–3

2–1.5

1–45–1011–19

0.30.20.12

0.0120.0080.005

76 250 S5 M3

4422 5015 9310 1 and finer 20 and finer4615 5115 94B154617 5120 94B174620Medium carbon1330 44271335 4626

Hot rolled,annealed, orcold drawn

25–65–3

2–1.5

1–45–1011–19

0.30.20.12

0.0120.0080.005

120 400 S4, S2 M2, M7

1340 50B40 8625 1 and finer 20 and finer134540274028

50B44504650B46

862786308637

325–375 Normalized orquenched andtempered

25–65–3

2–1.5

1–45–1011–19

0.30.20.12

0.0120.0080.005

69 225 S5 M3

4032 50B50 8640 1 and finer 20 and finer4037 5060 86424042 50B60 86454047 5130 86B454130 5132 86504135 5135 86554137 5140 86604140 5145 87404142 5147 87424145 5150 92544147 5155 92554150 5160 92604161 51B60 94B304340

(a) Feed recommendations apply to conventional (axial-transverse) gear shaving. Feeds should be increased 100% for gears shaved by the diagonal (angular-transverse)method. Source: Metcut Research Associates Inc.

Table 1 (continued)

86L20

175–225

0.0030.07

0.0030.07

0.0030.07

0.0030.07

61188115

615081B45

325–375 Quenched and tempered

84 275 S5 M3

Material ConditionHardness, HB Module Diametral pitch mm in. m/min sfm ISO AISI

Gear tooth size

Feed per revolution of gear(a)

Cutter pitch line speed


relationship set between workpiece and cutterhead velocities determines the helix angle.

Conventional and crowned helical gears canbe cut with diameters from 19 to 102 mm (¾ to4 in.), face widths up to 25 mm (1 in.), and helixangles from 10 to 40°. Gears can be generated atthe rate of about 600 per hour, six to ten times asfast as hobbing. The time required for changingcutting tools is about 30 min, but this needs tobe done only every 30 to 50 h. Although fast, theprocess is applicable only for the large-quantityproduction of a limited variety of gears.

Construction. Most reciprocating toolssuch as those used in gear shaping and planing

operations are made of solid high-speed toolsteel. Rotary cutters (hobs and milling cutters)for spur and helical gears can be either solid orinserted blade. Economy is the governing factor;the two methods of construction are equally sat-isfactory in terms of producing acceptable gears.Cutters less than about 75 mm (3 in.) in diameterare invariably solid. As cutters increase in size,the practice of using high-speed tool steel cuttingedges (blades) as inserts in alloy steel bodies isusually more economical. Inserts are normallyheld by mechanical fasteners.

Rotary cutters (face mill, rotary broach, andother) for bevel gears are usually designed to


Fig. 21 Schematic of operation of the Tangear gear cutter Fig. 22 Method of operation of a G-Trac gear generator

use inserts. In rotary cutters, feed rate is a directfunction of the number of cutting faces. There-fore, it is desirable to have as many cuttingedges as possible to increase the amount ofmetal removed during each revolution. How-ever, tooth strength and chip clearance must beconsidered when selecting the number of blades(cutting edges). Despite the limitations imposedby chip clearance and tooth strength, gear cut-ters are often redesigned for greater efficiency.

The G-Trac gear generator is a specialmachine that uses large numbers of single-pointhigh-speed tool steel cutting tools carried on anendless chain of tool blocks. One model formoderate quantities of gears has a single row ofcutting tools (Fig. 22). As these are sped aroundthe track, the work is fed into the cutters androlled as though in mesh with a single tooth sim-ulated by the cutters. Thus, one tooth space isgenerated. The work is then withdrawn, indexedto the next tooth space, fed in again, and so on,around the gear.

Another G-Trac model for large quantitieshas a number of rows of teeth (typically 14)around the chain of blocks. The work is fed intothe cutters and revolved continuously as thoughin mesh with a simulated rack, until all toothspaces are finished. On both models, spur andhelical gears (up to 45° helix angle) as large as356 mm (14 in.) in diameter can be cut andcrowned and can be stacked to a height of 190mm (7½ in.) times the cosine of the helix angle.

G-Trac generator cutter life is 6 to 175 timesas long as that for hobs. Special machines areavailable for sharpening the cutters, and the cut-ters can also be sharpened all at one time in aspecial fixture on a standard surface grinder. AG-Trac machine has a 19 kW (25 hp) motor. Itis six to ten times faster than hobbing, but themachine is expensive.

Speed and Feed

In addition to the type of gear being machinedand the method of cutting, other factors thatinfluence the choice of cutting speed are workmetal composition and hardness, diametral pitchof the work gear, rigidity of the setup, toleranceand finish requirements, and cutting fluid used.

Hobbing Speed. Nominal speeds and feedsfor gear hobbing that take into account severalof the above variables are listed in Table 2. Ascarbon content, alloy content, and hardness ofthe steel workpiece increase, recommended cut-ter speed decreases; for any given work metal,

Table 2 Feeds and speeds for the hobbing of carbon and low-alloy steel gears with high-speed steel toolsFor hobbing class 9 (per AGMA 390.03) or better gears, it may be necessary to reduce speeds and feeds by 50% and/or take twocuts. To meet finish requirements, it may be necessary to try both conventional and climb cutting.

Gear tooth size Feed per revolutionof workpiece(a) Hob speed


Material Condition ModuleDiametral

pitchNumber of cuts mm in. m/min sfm ISO AISI


Low-carbon resulfurized

100–150 Hot rolled orannealed

25–1312–2.5

1–23–10

21

1.501.50

0.0600.060

6770

220230

S4, S2

1116 2–1.5 11–19 1 1.50 0.060 731117 1–0.5 20–48 1 1.25 0.050 761118 0.5 and finer 48 and finer 1 0.75 0.030 851119 Cold drawn 25–13 1–2 2 1.50 0.060 701211 12–2.5 3–10 1 1.50 0.060 73 2401212 2–1.5 11–19 1 1.50 0.060 81

1–0.5 20–48 1 1.25 0.050 840.5 and finer 48 and finer 1 0.75 0.030 90

Medium-carbonresulfurized

1132 11441137 1145


25–1312–2.5

2–1.51–0.5

1–23–10

11–1920–48

2111

1.501.501.501.25

0.0600.0600.0600.050

52555860

170180190200

S4, S2

1139 1146 0.5 and finer 48 and finer 1 0.75 0.030 671140 1151 Quenched and 25–13 1–2 2 1.50 0.060 21

12–2.5 3–10 1 1.50 0.060 27 902–1.5 11–19 1 1.50 0.060 341–0.5 20–48 1 1.25 0.050 37

0.5 and finer 48 and finer 1 0.75 0.030 40Low-carbon

leaded12L1312L14


25–1312–2.5

2–1.51–0.5

1–23–10

11–1920–48

2111

1.651.651.501.25

0.0650.0650.0600.050

78819095

255265295305

S4, S2

12L15 0.5 and finer 48 and finer 1 0.75 0.030 105200–250 Hot rolled,

normalized,annealed, orcold drawn

25–1312–2.5

2–1.51–0.5

1–23–10

11–1920–48

2111

1.501.501.501.25

0.0600.0600.0600.050

50586973

165190225240

S4, S2 M2, M7

0.5 and finer 48 and finer 1 0.75 0.030 84


Low carbon1005 10161006 10171008 1018

102610291513


25–1312–2.5

2–1.51–0.5

1–23–10

11–1920–48

2111

1.801.801.501.25

0.0700.0700.0600.050

62758185

205245265280

S4, S2

1009 1019 1518 0.5 and finer 48 and finer 1 0.75 0.030 8810101011

10201021

1522 225–275 Annealed orcold drawn

25–1312–2.5

1–23–10

21

1.501.50

0.0600.060

3749

120160

S4, S2 M2, M7

1012 1022 2–1.5 11–19 1 1.50 0.060 561013 1023 1–0.5 20–48 1 1.25 0.050 591015 1025 0.5 and finer 48 and finer 1 0.75 0.030 60Medium

carbon1030 10441033 1045

15261527


25–1312–2.5

2–1.51–0.5

1–23–10

11–1920–48

2111

1.801.801.501.25

0.0700.0700.0600.050

50535660

165175185200

S4, S2

1035 1046 1536 0.5 and finer 48 and finer 1 0.75 0.030 6410371038

10491050

15411547

Quenched andtempered

25–1312–2.5

1–23–10

21

1.151.15

0.0450.045

2124

1039 1053 1548 2–1.5 11–19 1 0.65 0.025 301040 1055 1551 1–0.5 20–48 1 0.65 0.025 321042 1524 1552 0.5 and finer 48 and finer 1 0.65 0.025 371043 1525


Medium-carbonresulfurized

41404140Se


25–1312–2.5

2–1.51–0.5

1–23–10

11–1920–48

2111

1.501.501.501.25

0.0600.0600.0600.050

44475055

145155165180

S4, S2

4142Te 0.5 and finer 48 and finer 1 0.75 0.030 604145Se4147Te

Quenched andtempered

25–1312–2.5

1–23–10

21

1.151.15

0.0450.045

2023

4150 2–1.5 11–19 1 0.65 0.0251–0.5 20–48 1 0.65 0.025

0.5 and finer 48 and finer 1 0.65 0.025

Hardness, HB

M2, M7

230280250240

M2, M7

265275300

150–200

22070 S5, S11 M3, M42

tempered1141110120130

M2, M7

340

M2, M7

275

290

185195200

M2, M7

210M3, M42S5, S1170

80325–375

100105120

M2, M7

200M3, M42S5, S1165

75325–375

95291003013541

S4, S2 M2, M7

(continued)

325–375

(a) Feeds are based on the largest standard recommended hob diameter. When using a smaller hob diameter, the feed must be reduced proportionally. Source: MetcutResearch Associates Inc.


Medium- and high-carbon leaded41L30 43L4041L40 51L32


25–1312–2.5

2–1.51–0.5

1–23–10

11–1920–48

2111

1.501.501.501.25

0.0600.0600.0600.050

52555860

170180190200

S4, S2 M2, M7

41L45 52L100 0.5 and finer 48 and finer 1 0.75 0.030 67 22041L47 86L20 25–13 1–2 2 1.15 0.045 21 7041L50 86L4 tempered 12–2.5 3–10 1 1.15 0.045 27 90

2–1.5 11–19 1 1.15 0.045 34 1101–0.5 20–48 1 1.15 0.045 37 120

0.5 and finer 48 and finer 1 0.75 0.030 40 130

Wrought alloy steelsLow carbon4012 46214023 4718


25–1312–2.5

2–1.5

1–23–10

11–19

211

1.501.501.50

0.0600.0600.060

495255

160170180

S4, S2 M2, M7

4024 4720 8617 20–48 1 1.25 0.050 58 1904118 4815 8620 48 and finer 1 0.75 0.030 64 210432044194422

481748205015

862288229310

275–325 Normalized orquenched andtempered

25–1312–2.5

2–1.5

1–23–10

11–19

211

1.151.151.15

0.0450.0450.045

273034

90100110

S4, S2 M2, M7

Medium carbon1330 4427 81B451335 4626 8625


25–1312–2.5

2–1.5

1–23–10

11–19

211

1.501.501.25

0.0600.0600.060

384144

125135145

S4, S2 M2, M7

1340 50B40 8627 20–48 1 1.25 0.050 49 1601345 50B44 8630 48 and finer 1 0.75 0.030 55 180402740284032

504650B4650B50

863786408642

Normalized orquenched andtempered

25–1312–2.5

2–1.5

1–23–10

11–19

211

1.151.150.65

0.0450.0450.025

182023

606575

S5, S11 M3, M42

4037 5060 8645 20–48 1 0.65 0.025 24 804042 50B60 86B45 48 and finer 1 0.65 0.025 29 954047 5130 86504130 5132 86554135 5135 86604137 5140 87404140 5145 87424142 5147 92544145 5150 92554147 5155 92604150 5160 94B304161 51B604340 6150

(a) Feeds are based on the largest standard recommended hob diameter. When using a smaller hob diameter, the feed must be reduced proportionally. Source: MetcutResearch Associates Inc.

46154617

51155120

94B15

462094B17

125–175

175–225

325–375

325–375 Quenched and S5, S11 M3, M42

61188115

1–0.50.5 and finer

1–0.5 20–48 1 1.15 0.045 37 1200.5 and finer 48 and finer 1 0.75 0.030 40 130



Table 2 (continued)

Material ConditionHardness,

HB ModuleDiametral

pitchNumber of cuts mm in. m/min sfm ISO AISI

High-speed steel tool materialHob speed

Feed per revolutionof workpiece(a)

Gear tooth size

cutting speed increases as diametral pitchbecomes finer. For the numerical values givenin Table 2. it is assumed that an additive-typecutting fluid will be used. Low cutting speedsprolong tool life and eliminate the difficultiesinvolved in changing tools and matching cuts.

Shaping speed is influenced by variablessimilar to those that affect hobbing speeds, withthe exception of diametral pitch. Nominal speedsand feeds for gear shaping under a variety of con-ditions are given in Table 3. Cutter speed varieswith the composition and hardness of the workmetal but not with diametral pitch. The speedslisted in Table 3 are generally conservative.

Speeds for Interlocking and Face MillCutters. Nominal speeds for cutting straight

and spiral bevel gears with two common typesof cutters are given in Table 4. As in shaping,speed is not varied with diametral pitch whenother conditions are the same. For both theinterlocking cutters and the face mill cutters,speeds are increased for finishing when rough-ing and finishing are done separately. Thespeeds used for cutting straight and spiral bevelgears with rotating cutters are close to thosesuggested in Table 4. When straight bevel gearsare being cut with reciprocating cutters, muchlower speeds are required.

Feeds. Nominal feeds for the hobbing ofsteel gears are included in Table 2. Values aregiven in millimeters per revolution (inches perrevolution) of the gear being hobbed and are


Table 3 Feeds and speeds for the shaping of carbon and low-alloy steel gears with high-speed steel tools

Rotary feed per cutterstroke (102 mm,

or 4 in., pitch diameter cutter)(a)

MaterialHardness,

HBNumberof cuts(a)

Diametralpitch

Wrought free-machining carbon steelsLow-carbon resulfurized 100–150 Hot rolled 4 25–6 1–4 0.55 0.022 26 85 S4, S21116 1119 or annealed 2 5.5–2.5 5–10 0.40 0.0161117 1211 2 2–1.5 11–19 0.28 0.0111118 1212 2 1–0.5 20–48 0.20 0.008

150–200 Cold drawn 4 25–6 1–4 0.55 0.022 27 90 S4, S2 M2, M72 5.5–2.5 5–10 0.40 0.0162 2–1.5 11–19 0.28 0.0112 1–0.5 20–48 0.20 0.008

Medium-carbon 175–225 Hot rolled, 4 25–6 1–4 0.55 0.022 24 80 S4, S2resulfurized normalized,1132 1144 annealed, or 2 2–1.5 11–19 0.28 0.0111137 1145 cold drawn 1–0.5 20–48 0.20 0.0081139 1146 4 25–6 1–4 0.30 0.0121140 1151 tempered 2 5.5–2.5 5–10 0.25 0.0101141 2 2–1.5 11–19 0.20 0.008

2 1–0.5 20–48 0.20 0.008Low-carbon leaded 100–150 Hot rolled, 4 25–6 1–4 0.55 0.022 38 125 S4, S212L13 normalized, 2 5.5–2.5 5–10 0.40 0.01612L14 annealed, or 2 2–1.5 11–19 0.28 0.01112L15 cold drawn 2 1–0.5 20–48 0.20 0.008

200–250 Hot rolled, 4 25–6 1–4 0.55 0.022 27 90 S4, S2 M2, M72 5.5–2.5 5–10 0.40 0.0162 2–1.5 11–19 0.28 0.0112 1–0.5 20–48 0.20 0.008


Low carbon 85–125 Hot rolled, 4 25–6 1–4 0.45 0.018 27 90 S4, S2 M2, M71005 1015 1023 2 5.5–2.5 5–10 0.30 0.0121006 1016 1025 2 2–1.5 11–19 0.25 0.0101008 1017 1026 1–0.5 20–48 0.20 0.0081009 1018 1029 225–275 Annealed or 4 25–6 1–4 0.40 0.016 18 60 S4, S2 M2, M71010 1019 1513 5.5–2.5 5–10 0.30 0.0121011 1020 1518 2–1.5 11–19 0.25 0.0101012 1021 1522 1–0.5 20–48 0.20 0.0081013 1022Medium carbon 125–175 Hot rolled, 4 25–6 1–4 0.45 0.018 23 75 S4, S21030 1044 1526 2 5.5–2.5 5–10 0.30 0.0121033 1045 1527 2 2 –1.5 11–19 0.25 0.0101035 1046 1536 2 1–0.5 20–48 0.20 0.0081037 1049 1541 325–375 Quenched and 4 25–6 1–4 0.30 0.012 12 40 S5, S11 M3, M421038 1050 1547 2 5.5–2.5 5–10 0.25 0.0101039 1053 1548 2 2–1.5 11–19 0.20 0.0081040 1055 1551 2 1–0.5 20–48 0.20 0.0081042 1524 15521043 1525


Medium-carbon resulfurized

150–200 Hot rolled, normalized,

42

25–65.5–2.5

1–45–10

0.550.45

0.0220.018

24 80

4140 4145Se 2 2–1.5 11–19 0.28 0.0114140Se 4147Te 2 1–0.5 20–48 0.20 0.0084142Te 4150 4 25–6 1–4 0.30 0.012

2 5.5–2.5 5–10 0.25 0.0102 2–1.5 11–19 0.20 0.0082 1–0.5 20–48 0.20 0.008

Medium- and high-carbonleaded

150–200 Hot rolled,normalized,

42

25–65.5–2.5

1–45–10

0.550.40

0.0220.016

24 80

41L30 41L50 52L100 2 2–1.5 11–19 0.28 0.01141L40 43L40 86L20 2 1–0.5 20–48 0.20 0.00841L45 51L32 86L40 4 25–6 1–4 0.30 0.01241L47 tempered 2 5.5–2.5 5–10 0.25 0.010

2 2–1.5 11–19 0.20 0.0082 1–0.5 20–48 0.20 0.008

Condition Module mm in.m/

min sfm ISO AISI

Gear tooth size High-speed steel tool material

Cutter speed

M2, M7

M2, M7

M2, M7

2 5.5–2.5 5–10 0.40 0.016

2

cold drawnannealed, ornormalized,


cold drawn 2

2

22

M2, M7


tempered

M2, M7S4, S2

Quenched and cold drawnannealed, or

M2, M7S4, S2

tempered

cold drawnannealed, or

(continued)

325–375 Quenched and 12 40 S5, S11 M3, M42

325–375 11 35 S5, S11 M3, M42

325–375 Quenched and 11 35 S5, S11 M3, M42

(a) For cutting gears of class 9 (AGMA 390.03) or better, the rotary feed should be reduced, and the number of cuts should be increased. Source: Metcut Research Asso-ciates Inc.


Low carbon 125–175 Hot rolled, 4 25–6 1–4 0.45 0.018 21 70 S4, S2 M2, M74012 4621 6118 annealed, or 2 5.5–2.5 5–10 0.30 0.0124023 4718 8115 cold drawn 2 2–1.5 11–19 0.25 0.0104024 4720 8617 2 1–0.5 20–48 0.20 0.0084118 4815 8620 325–375 Normalized 4 25–6 1–4 0.30 0.012 12 40 S5, S11 M3, M424320 4817 8622 or quenched 2 5.5–2.5 5–10 0.25 0.0104419 4820 8822 and tempered 2 2–1.5 11–19 0.20 0.0084422 5015 9310 2 1–0.5 20–48 0.20 0.0084615 5115 94B154617 5120 94B174620Medium carbon 175–225 Hot rolled, 4 25–6 1–4 0.45 0.018 18 60 S4, S21330 4427 81B45 annealed, or 2 5.5–2.5 5–10 0.30 0.0121335 4626 8625 cold drawn 2 2–1.5 11–19 0.25 0.0101340 50B40 8627 2 1–0.5 20–48 0.20 0.0081345 50B44 8630 325–375 Normalized 4 25–6 1–4 0.30 0.012 11 35 S5, S11 M3, M424027 5046 8637 or quenched 2 5.5–2.5 5–10 0.25 0.0104028 50B46 8640 and tempered 2 2–1.5 11–19 0.20 0.0084032 50B50 8642 2 1–0.5 20–48 0.20 0.0084037 5060 86454042 50B60 86B454047 5130 86504130 5132 86554135 5135 86604137 5140 87404140 5145 87424142 5147 92544145 5150 92554147 5155 96204150 5160 94B304161 51B604340 6150

(a) For cutting gears of class 9 (AGMA 390.03) or better, the rotary feed should be reduced, and the number of cuts should be increased. Source: Metcut Research Asso-ciates Inc.

Wrought alloy steels

M2, M7

Table 3 (continued)

MaterialHardness,

HB ConditionNumberof cuts(a) Module

Diametralpitch mm

m/minin. sfm ISO AISI


Cutter speed

Rotary feed per cut-ter stroke (102 mm,

or 4 in., pitch diameter cutter)(a)

Gear tooth size

based on the assumption that the gears will beground after hobbing. Hobbing feeds should bedecreased when gears are to be finished by shav-ing. As indicated in Table 2, hobbing feeds aresensitive to differences in diametral pitch, butfeeds are not ordinarily changed for differencesin the composition or hardness of the gear steelwhen diametral pitch is the same, except for thecoarser-pitch heat-treated gears.

Nominal feeds for cutting gears by shapingare given in Table 3. These values are based onthe assumption that the gears will be finished bygrinding; a reduction in speed is recommendedwhen gears are to be finished by shaving. Feedsfor shaping vary with diametral pitch and varycomparatively little with work metal composi-tion and hardness. Conditions for a specificoperation may require feeds higher or lowerthan those given in Table 3.

Feeds for cutting straight and spiral bevelgears by rotary cutters are suggested in Table 4.The optimum feed is greatly influenced by

diametral pitch; work metal composition andhardness have a minor influence. The same ratesof feed are commonly used for both roughing andfinishing, although the cutting edges of the teethare altered for finishing, as indicated in Table 4.

Cutting Fluids

Cutting fluids are recommended for all gearcutting, although for some applications (notablythe cutting of large gears) the use of a cuttingfluid is impractical. The three cutting fluidsmost commonly used for gear cutting are:

• Mineral oil (without additives) having a vis-cosity of 140 to 220 SUS at 40 °C (100 °F)

• Cutting oil, sulfurized or chlorinated (orboth), usually diluted with mineral oil to aviscosity of 180 to 220 SUS at 40 °C (100 °F)

• Motor oil (SAE 20 grade), either detergentor nondetergent type


Cutting speed(a)

Roughing FinishingHigh-speed steel

tool material

Material Hardness, HB Condition m/min sfm m/min sfm ISO AISI


Low-carbon resulfurized 100–150 Hot rolled or annealed 38 125 76 250 S4, S21116 150–2001117 1119 1212Medium-carbon resulfurized 175–225 Hot rolled, normalized, 26 85 53 175 S4, S21132 1140 1145 annealed, or cold drawn1137 1141 1146 325–375 Quenched and tempered 15 50 30 100 S5 M31139 1144 1151Low-carbon leaded 100–150 Hot rolled, normalized, 44 145 88 290 S4, S212L13 annealed, or cold drawn12L14 Hot rolled, normalized,

annealed, or cold drawn 34 110 69 225 S4, S2 M2, M7

Wrought carbon steelsLow carbon 85–125 Hot rolled, normalized, 27 90 58 190 S4, S2 M2, M71005 1015 1023 annealed, or cold drawn1006 1016 1025 Annealed or cold drawn1008 1017 10261009 1018 10291010 1019 15131011 1020 15181012 1021 15221013 1022Medium carbon 125–175 Hot rolled, normalized, 26 85 53 175 S4, S2 M2, M71030 1044 1526 annealed, or cold drawn1033 1045 1527 Quenched and tempered1035 1046 15361037 1049 15411038 1050 15471039 1053 15481040 1055 15511042 1524 15521043 1525

Wrought free-machining alloy steelsMedium-carbon resulfurized 150–200 Hot rolled, normalized, 26 85 53 175 S4, S24140 4142Te 4147Te annealed, or cold drawn4140Se 4145Se 4150 Quenched and temperedMedium- and high-carbon leaded 150–200 Hot rolled, normalized, 26 85 53 175 S4, S241L30 41L50 52L100 annealed, or cold drawn41L40 43L40 86L2041L45 51L32 325–375 Quenched and tempered 14 45 27 90 S5 M341L47

Wrought alloy steelsLow carbon 125–175 Hot rolled, annealed, 26 85 53 175 S4, S2 M2, M74012 4621 6118 or cold drawn4023 4718 81154024 4720 8617 quenched and tempered4118 4815 86204320 4817 86224419 4820 88224422 5015 93104615 5115 94B154617 5120 94B174620Medium carbon 175–225 Hot rolled, annealed, 20 65 41 135 S4, S2 M2, M71330 4047 4161 or cold drawn1335 4130 4340 325–375 Normalized or 15 50 30 100 S5 M31340 4135 4427 quenched and tempered1345 4137 46264027 4140 50B404028 4142 50B444032 4145 50464037 4147 50B464042 4150 50B50

Table 4 Gear cutting speeds for the rough and finish cutting of carbon and low-alloy steel straightand spiral bevel gears with high-speed steel tools

M2, M7

M2, M7Cold drawn12111118

M2, M7

200–250

M2, M7

325–375 14 45 29 95 S5 M3M2, M7

12L15

86L40

(continued)

325–375 15 50 30 100 S5 M3

43 140 84 275 S4, S2 M2, M7

225–275 21 70 44 145 S4, S2 M2, M7

325–375 Normalized or 15 50 30 100 S5 M3

(a) Cutting speed recommendations are for use with alternate-tooth milling cutters or gear generators. For planer-type generators, use the recommended cutting speedsin Table 3. Source: Metcut Research Associates Inc.


50B60 6150 86505130 81B45 86555132 8625 86605135 8627 87405140 8630 87425145 8637 92545147 8640 92555150 8642 92605155 8645 94B305160

(a) Cutting speed recommendations are for use with alternate-tooth milling cutters or gear generators. For planer-type generators, use the recommended cutting speedsin Table 3. Source: Metcut Research Associates Inc.

5060 51B60 86B45Medium carbon 175–225 Hot rolled, annealed,

or cold drawn325–375 Normalized or

quenched and tempered

20 65 41 135 S4, S2 M2, M7

15 50 30 100 S5 M3

Water-soluble oils, which are widely used inmany metal cutting operations, are used to alesser extent for gear cutting because the oils re-ferred to above are more effective for producingthe surface finishes desired on gear teeth and forprolonged cutter life. Nevertheless, soluble oilsare sometimes used in gear cutting. One notableapplication for soluble oil (20 parts water to 1part oil) is the finish broaching of fine-pitchgears.

The relative advantages and disadvantages ofthe three oils mentioned above are matters ofopinion among different plants producing steelgears. Most data in speed and feed tables arebased on the use of cutting oils with additives(the second of the cutting fluids listed above).However, in some plants, mineral oils (includingmotor oils) are used when records have provedthat the use of these oils resulted in longer cutterlife than when prepared cutting oils were used.

In some plants, additive cutting oils are usedfor roughing operations and mineral oils for fin-ishing when the operations are done separatelyin different machines. An adequate supply (aflood) of fluid under slight pressure (about 35kPa, or 5 psi) at the cutting area is extremelyimportant—usually more important than thecomposition of the oil.

Comparison of Steels for Gear Cutting

End use is the main factor in the selection ofsteel for a specific gear. However, two or moresteels will often serve equally well. Under theseconditions, the cost of the steel and the cost ofprocessing it are significant factors in making a

final selection, and in all selections both thesefactors must be considered. When the cost ofmachining standard steels is compared with the cost of free-machining counterparts, the useof a free-machining grade will almost alwaysresult in lower machining costs. However, whenchanging from one standard grade of a givensteel to its free-machining counter-part, the ad-ditional cost of the free-machining grade mustbe considered in the cost comparison. Whenchanges in steel composition that result in lowermachining costs require changes in the methodof heat treating, the cost of heat treating mustalso be considered.

A change in microstructure, independent ofsteel composition, also has a significant effect ontool life or surface finish or both. Altering theheat treatment can produce a more machinablemicrostructure that results in increased cutterlife.

Computer Numerical Control (CNC)Milling and Hobbing Machines

In practice, gear milling is usually confined toreplacement gears or to the small-lot produc-tion, roughing, and finishing of coarse-pitchgears. The milling of low-production, specialtooth forms is also done. Milling is often used asthe first operation prior to finish hobbing orshaping, especially in large diametral pitchspur, helical, and straight bevel gears. The gearis then finished to final size by another methodselected by the manufacturer.

Special high-power (56 to 75 kW, or 75 to100 hp) CNC machines, called gashers (Fig.

Cutting speed(a)

Roughing FinishingHigh-speed steel

tool material

Material Hardness, HB Condition m/min sfm m/min sfm ISO AISI

Table 4 (continued)


Fig. 23 Four types of gashers. (a) Duo-axis. (b) Helical machine. (c) Rack machine. (d) Slitting head

23), are used for the roughing of gears from 6 to ⅝ diametral pitch. These machines employstrong, rigid machine components and areextremely powerful. They operate at peak effi-ciency with large inserted carbide cutters. Theability to remove large amounts of metal at sub-stantial feed rates makes this process quite eco-nomical for coarse pitches. The gears can be fin-ished on the same machines with high-speedtool steel formed cutters. The accuracy of indexon these machines is more than adequate to pro-duce tooth spacing requirements.

The advent of the CNC-controlled indexmechanism of the gasher allows the manufac-ture of large, coarse-pitch sprockets for rollerchains of all sizes. The face capacity of thesemachines permits the stacking of many platesprockets at one time with good quality and reli-able production.

The power of these machines and their abilityfor two-axis interpolation make coarse-toothstraight bevel gears a natural application. Thetime savings can be significant; two-tool genera-tors can be used to finish the gashed bevel blank.

Computer numerical control gear hobbingmachines are available in 305, 508, 914, 1220,and 1625 mm (12, 20, 36, 48, and 64 in.) capac-ities. Figure 24 shows a CNC machine hobbinga gear.

Grinding of Gears

Gear teeth can be produced entirely by grind-ing, entirely by cutting, or by first cutting andthen grinding to the required dimensions. Usu-ally, gear grinding removes only several hun-dredths of a millimeter of metal from precut


Fig. 24 CNC gear hobbing machine producing a gear

gears to make accurate teeth for critical applica-tions. Teeth made entirely by grinding are usu-ally only those of fine pitch, for which the totalamount of metal removed is small. The grindingof fine-pitch gear teeth from uncut blanks maybe less costly than the two-step procedure ifthere is not much metal to be removed.

The two basic methods for the grinding ofgear teeth are form grinding (nongenerating)and generation grinding. Many varieties ofmachines have been built specifically to grindgears and pinions.

Advantages and Disadvantages. A gear isground when it is so hard that it cannot be fin-ished by other methods or when the requiredaccuracy is greater than can be obtained byother methods. If the hardness of the gear doesnot exceed 40 HRC and if its size is within thecapacity of the machine, shaving will produceteeth of an accuracy close to that produced bygrinding. Gears made of steel harder than 40HRC are finished by grinding when dimen-sional accuracy is required or when correctionbeyond that feasible by honing is required.

The major disadvantage of grinding gears isthe cost. It is usually more expensive to grindgears than to cut them because material isremoved in small increments in grinding.Ground gears are usually subjected to moreinspection than cut gears. Magnetic particle

inspection of the finished teeth detects finecracks, and macroetching with dilute nitic aciddetects grinding burn. Both inspection proce-dures are advised in gear grinding.

A carbide network in carburized steels, or thepresence of sufficient retained austenite or ofhydrogen in any hardened steel, can increase thesusceptibility of the steel to grinding cracks.Therefore, it is necessary to keep these condi-tions under control. Reducing the heat gener-ated in grinding (by decreasing the rate of stockremoval or by the use of a grinding fluid) canhelp to eliminate cracking and burning of theground surface.

Stock Allowance. When workpieces areprepared for grinding by cutting, the leastamount of stock possible should be left to beremoved by grinding. This stock should beevenly distributed to reduce the wheel dressingsand operating adjustments needed to maintainwheel contour when using conventional (alu-minum oxide or silicon carbide) dressablewheels. With cubic boron nitride (CBN) wheels,where stock is removed in one pass, evenly dis-tributed stock results in more uniform grindingpressure.

In general, it is not practical to remove morethan 0.15 mm (0.006 in.) of stock from eachface of the teeth of spur gears up to 178 mm (7in.) in diameter or 0.20 mm (0.008 in.) fromgears between 178 and 254 mm (7 and 10 in.) indiameter. These amounts of stock can usually beremoved in three to five passes with conven-tional dressable wheels or in one pass with CBNwheels. However, the number of passes de-pends on number of teeth, pressure angle, andrequired finish. Sometimes nine or ten passesare needed with conventional wheels.

The recommended stock allowance for grind-ing straight bevel teeth is 0.08 mm (0.003 in.) atthe root of the tooth and 0.08 to 0.13 mm (0.003to 0.005 in.) on the face of each tooth. Grindingtime depends on the amount of stock to be re-moved. For example, removing 0.076 to 0.089mm (0.0030 to 0.0035 in.) of stock from a gearof 4 diametral pitch and 32 teeth takes 30 s pertooth; a gear of 10 diametral pitch and 32 teethtakes about 20 s per tooth. Figure 25, whichshows the cross sections of gear teeth of variousdiametral pitches, can be used to gage the rela-tive sizes of the 4 and 10 diametral pitch gears.

Grinding stock allowance per tooth side forspiral bevel and hypoid gears should be 0.10 to0.13 mm (0.004 to 0.005 in.) for gears coarserthan 10 diametral pitch and 0.08 to 0.10 mm


Fig. 25 Gear teeth of various diametral pitch

(0.003 to 0.004 in.) for gears of 10 to 20 diame-tral pitch. Stock allowance at the root of thetooth should be about 0.08 mm (0.003 in.) forgears up to 20 diametral pitch.

Multiple-Piece Loads. Because gear grind-ing is an expensive operation, it is important tocontrol the amount of metal to be removed bygrinding, to reduce runout and spacing errors,and to try to grind multiple-piece loads. Multi-ple-start hobs can cause enough spacing error tomake extra grinding passes necessary. There-fore, when a hobbed gear is to be ground, it isbetter to use a single-thread hob. The multiple-start hob will not save enough to pay for theextra grinding passes. Single-thread hobs areavailable with nonground class-C tooth forms.

Wheel Specifications. Aluminum oxidewheels are preferred for the grinding of teeth in

through-hardened and case-hardened steel gears.For nitrided gears, silicon carbide wheels aresometimes used. Grit size, which dependsmainly on the type of grinding and the pitch of thegear, ranges from 46 to 100, although somewhatfiner grits can be used for form grinding. A gritsize of 60 is generally recommended for diame-tral pitch in the range of 1 to 10; 80 for the rangeof 8 to 12; and 100 for gears of pitch finer than 14.With crush-formed wheels, grit sizes as small as400 are used in grinding gears of diametral pitchas fine as 200. For grade (hardness), a range of Hto M is generally recommended.

Vitrified bond wheels are used because oftheir rigidity and ability to be diamond dressedwith a minimum of diamond wear. Wheel rigid-ity is particularly important for dish-shapedwheels of the large sizes used in generationgrinding. Resinoid bond cup wheels are satis-factory for generating bevel gear teeth.

Vitrified bond wheels are used for forming.They are generally crush trued. The vitrifiedbond is friable and is rigid enough to support theforce of crush truing without deflection.

Steel-core wheels plated with CBN are com-monly used because their open grain textureallows for slow traverse across the tooth surfaceand rapid stock removal without burning. Sur-faces are generally finished in one pass. Becauseof the hardness of the material, several thousandparts can be ground before wheel contours needto be replated. More detailed information ongrinding wheel specifications and factors inselection can be found in Ref 1 and 2.

Speed. Most gears ground with conven-tional wheels are ground with wheel surfacespeeds of 1700 to 2000 m/min (5500 to 6500sfm). When very small amounts of stock arebeing removed, speeds higher than 2000 m/min(6500 sfm) can be used. When grinding gearswith cup-shaped or dish-shaped wheels, slowerspeeds (140 m/min, or 450 sfm, or less) arecommon. Wheel speeds up to 3000 m/min(10,000 sfm) are used with CBN wheels.

Infeed. When using conventional wheels,pitch of the gear being ground is the main factorinfluencing optimum infeed. For example, inthe plunge grinding of case-hardened or hard-ened-and-tempered steels (50 to 62 HRC), aninfeed of 0.038 mm/pass (0.0015 in./pass) isrecommended for gears having diametralpitches of 1 to 4. Infeed is reduced to 0.030mm/pass (0.0012 in./pass) for pitches of 5 to 8and to 0.013 mm/pass (0.005 in./pass) forpitches finer than 8. With CBN wheels, 0.13 to


Fig. 26 Setup for grinding a thin-web gear. Damper platesprevent excessive vibration. Dimensions in figure

given in inches

0.25 mm (0.005 to 0.010 in.) of stock isremoved in one pass.

Correcting for Distortion in Heat Treating

Most steel gears are heat treated. Becausesome diametral change occurs during heat treat-ment, gear teeth are cut prior to heat treating andground to finish dimensions after heat treating.The magnitude of the dimensional changedepends on the type of heat treatment and theshape of the part. Distortion is greatest when theentire part is heated and quenched. Inductionhardening and flame hardening cause smallchanges because only the tooth area of the partis heated and quenched.

Usually, nitrided gears do not need to beground to correct for distortion. When gears areproperly nitrided, dimensional change is sosmall that any correction required can beaccomplished by honing or lapping.

When the entire gear is heat treated, dimen-sional change is less in gears of nearly uniformcross section than in those of intricate design orlarge variation in cross section. For example,short, stubby pinions are least likely to lose accu-racy because of unequal cooling rates duringquenching, while thin-web gears with heavy-section teeth or heavy rims change the most.

The use of a heat-treating procedure thatallows maximum dimensional control, such asplacing the heated part in a fixture for quench-ing, helps reduce the amount of grinding andsometimes has eliminated the need for grinding.However, some dimensional changes occur dur-ing heat treatment regardless of special tech-niques. The following example is typical of agear that required grinding even though it hadbeen quenched in a die to control distortion.

Example 1: Grinding Die-QuenchedGears. The gear teeth for the part illustrated inFig. 26 were cut by hobbing, after which theywere carburized and quenched in a die to mini-mize distortion. However, this practice did notprevent distortion beyond tolerance, and light-ening holes caused a scalloping of the pitch lineby approximately 0.10 mm (0.004 in.) totalindicator reading. Therefore, grinding was nec-essary. No grinding burns or cracks could beaccepted.

Conditions of the grinding operation aregiven in the table with Fig. 26. Damper platesprevented excessive vibration of the gear duringgrinding, thus reducing the likelihood of bothburns and cracks.

Form Grinding

Usually, form grinding consists of passing aformed wheel through a tooth space to grind toroot depth the left side of one tooth and the rightside of the next tooth at the same time (see mod-ifications in Fig. 27). When straight teeth areground, as in spur gears, the workpiece is heldin a fixed radial position during a pass. For hel-ical gears, however, the workpiece must be


Fig. 27 Relations of wheel and workpiece in the form grind-ing of spur gears (top views). (a) Single-ribbed grind-

ing wheel. (b) Multiribbed grinding wheel. (c) Two single-ribbedwheels, also known as a straddle wheel

rotated so that the helix will be followed as thewheel passes through the tooth space. A lead barhaving the same lead as the helix controls rota-tion during grinding.

When the wheel pass through a tooth space iscompleted, the workpiece is indexed to the nextposition, and the procedure is repeated. Theindexing mechanism usually consists of anindex plate with the same number of spaces atthe workpiece. Control of tooth spacing errorsdepends primarily on the accuracy of this plate.

Spur gears are ground with a single straightwheel with a periphery that has been formed toproduce the space between teeth (Fig. 27a), a sin-gle wheel with several ribs that grind more thanone tooth space during each wheel pass (Fig.27b), or two single-ribbed wheels (Fig. 27c).Helical gears are ground with a formed, singlestraight wheel. Bevel gears are form ground witha cup-shaped wheel. Form grinding can also beused to finish grind precut threads of worms.

Wheels for form grinding are usually less than152 mm (6 in.) in diameter; wheel thicknessdepends on the size of the teeth to be ground.Wheels of larger diameter can be used, but thesmaller wheels are more common because theyneed less clearance in finishing a gear that is closeto a larger gear or to a shoulder. In addition,smaller wheels are better for grinding internalgears.

Standard gear grinding machines are avail-able for form grinding spur gears ranging froma minimum root diameter of 19 mm (¾ in.) to anoutside diameter of 914 mm (36 in.). Specialmachines have been built to grind spur gears 2.4m (8 ft) in diameter. Machines are available thatare capable of form grinding external helicalgears up to 457 mm (18 in.) in diameter.

Generation Grinding

There are four methods of generating gearteeth by grinding. Each method is identified bythe type of wheel used: straight, cup-shaped,dish-shaped, and rack-tooth worm wheels.

Straight Wheels. In this method, a straightwheel beveled on both sides reciprocates acrossthe periphery of the workpiece as the workpiecerolls under it in a direction perpendicular to itsreciprocating motion. The reciprocating actionof the wheel is similar to that of a reciprocatinggear cutter. This grinding method can be used togenerate the teeth of spur gears.

Cup-Shaped Wheels. In this method, thegear tooth is rolled against a cup-shaped wheel,the sides of which are beveled to an angle equalto the pressure angle required on the teeth. Dur-ing grinding, the wheel moves in a straight linealong the length of the tooth. The sides of thewheel simultaneously grind adjacent sides oftwo teeth. A number of mechanical methods areused to control the generating motion and theindexing of the workpiece. Electronic controlsare used on newer machines.

Teeth can be generated by grinding with acup-shaped wheel on spur and helical gears upto 457 mm (18 in.) in pitch diameter. However,when helical gears are being ground, the gener-ating motion must match the pitch in the planeof rotation of the gear to be ground. With thisgrinding method, it is impractical to generate tipand root reliefs.

Dish-Shaped Wheels. This method usestwo dish-shaped grinding wheels, which may beinclined 15 or 20° or may be parallel in a verti-cal position (0°), as shown in Table 5.

The generating motion is sometimes con-trolled by steel bands that are fastened to a pitchblock of the same diameter as the pitch circle ofthe workpiece minus the thickness of the rollingbands. The shape of the tip and root of the teethcan be modified by using a cam to change thenormal generating motion.

Usually an index plate similar to that used inform grinding indexes the workpiece if a pitchblock is used. Large machines use worm gear-ing for indexing. Gears are ground dry, andmachines incorporate a device depending on afeeler diamond to compensate for wheel wear.Machines are available for grinding spur andhelical gears ranging from 25 to 3610 mm (1 to142 in.) in diameter, with diametral pitch 2 to 17by this method.

When the wheels are in the 15 or 20° position,as in illustration (a) in Table 5 their active faces


Table 5 Grinding of gears with dish-shaped wheels in the 0° positionDetails for seven different spur and helical gears that had been carburized and hardened.

Parameter Gear details

Diametral pitch 10 5 4 3 5 3 2.75Module 2.5 5 6 8 5 8 9.5Number of teeth 23 44 80 80 120 100 379Face width, mm 55.9 61.0 119 119 300 180 419

(in.) (2.2) (2.4) (4.7) (4.7) (11.8) (7.1) (16.5)Tip diameter, mm 71.1 234 503 653 630 828 3350

(in.) (2.8) (9.2) (19.8) (25.7) (24.8) (32.6) (132)Pressure angle,

degree15 20 20 20 20 15 15

Helix angle, degree 26 20 10 10 15 0 7Grinding allowance

per flank, mm0.15

(0.006)0.18

(0.007)0.20

(0.008)0.23

(0.009)0.18

(0.007)0.23

(0.009)0.25

(0.010)(in.)

rotate in planes forming an acute angle. In thisposition, the wheels simulate the tooth flanks ofa rack that the workpiece engages during therolling-generating motion (Fig. 28). The incli-nation of the grinding wheels to the vertical inthe pitch plane generally equals the pressureangle of the gear to be ground (usually 15 or20°). Under these conditions, the generating cir-cle coincides with the pitch circle of the gear.This method produced a criss-cross pattern ofgrooves (lay of surface roughness) and has beenwidely used because machine settings are sim-ple and the desired pressure angle is accuratelyand simply set by adjusting the inclinationangles of the wheels.

The 15 or 20° wheel position is not suitablefor making longitudinal modifications. Al-though the two simultaneous points of contactbetween the grinding wheels and the respectivetooth flanks move along the tooth-form invo-lutes during each transverse rolling-generatingmotion, the locations of these points relative toeach other change constantly.

For helical gears, this differential positionapplies not only along the involutes but also tothe position in the longitudinal tooth direction.Therefore, it would be impractical to try to coor-dinate modification impulses of the grindingwheel and the generating or feed motion tomake longitudinal modifications.

In a newer method, the angle between the twowheels is 0°, as shown in illustration (b) inTable 5. The active surfaces of the wheels areparallel and face each other. Because the grind-ing pressure angle is 0° and corresponds to thepressure angle on the base circle, the generatingmotion is obtained by rolling on the base circle.

The advantages of grinding gears in the 0°position over the 15 or 20° position are:

• Greater production without sacrifice inquality

• Ability to grind more exacting flank profilesand to make longitudinal modifications

The main disadvantage is the lack of uniformtransition between the flank and the tooth root,which is objectionable in some gearing applica-tions.

Rack-Tooth Worm Wheels. The wheelused in this method of generating gear teeth iscrush trued into the shape of a conventionalrack-tooth worm or a CBN-plated rack-toothworm. Grinding a gear by this method is illus-trated in Fig. 29.

The workpiece is mounted vertically on anarbor or in a fixture that fits between the centersof the machine. For grinding helical gears, theworkholding slide of the machine is set at anangle equal to the helix angle required on thegear. The workpiece is rotated by a motor that issynchronized with the wheel motor.

The gear can be ground with a small portionof the length of the grinding worm wheel. Gen-eration takes place as a result of rotating theworm wheel and gear in mesh as the wheel istraversed axially across the gear face.

A soft, conventional aluminum oxide or sili-con carbide wheel is used to prevent burning thehardened teeth, but this results in greater wheelbreakdown and loss of correct tooth profile. Tocontinue using a fresh, unbroken part of thewheel, the work is fed in a direction parallel tothe axis of the worm using the setup shown inFig. 30.


Fig. 30 Setup used to grind an aircraft pinion by the wormwheel method

for each pitch and pressure angle required. Indiamond dressing, two diamonds are needed todress both sides of the thread at the same time.Gear tooth design can be easily modified by lap-ping the tip of the dressing diamond.

Burning the hardened steel is much less of aproblem when using CBN-plated wheels be-cause of the open texture of the wheel surface.The hardness of the CBN material and the stiff-ness of the steel core allow for several thousandpieces to be ground before the worm needsreplating and returning. Modifications of thegear tooth design are manufactured into the corebefore it is plated.

Spur gears and helical gears up to 508 mm (20in.) in diameter can be ground in machines usinga threaded wheel. Although fine-pitch gears canbe ground from a solid gear blank, gear teeth withdiametral pitch of 24 or coarser should be cutprior to grinding.

The advantages of gear grinding with athreaded wheel are accuracy, speed, and ease ofincorporating changes in tooth design. Machinesare also available that crown the gear teeth duringgrinding. Because mechanical grinders are com-plicated and sensitive, a considerable amount ofoperator skill is required. However, with elec-tronic CNC machines, crowning is a standardfeature. Gear grinding with a threaded wheel issix to thirty times as fast as the other methods dis-cussed in this section.

Grinding of Bevel Gears

When accuracy is required, grinding is themost economical method for finishing teeth ascoarse as 1.5 diametral pitch on straight bevel,spiral bevel, and hypoid gears. With good grind-ing practice, bevel and hypoid gears can be fin-ished with a tooth-to-tooth spacing accurate

Fig. 28 Schematic of dish-shaped wheels simulating themotion of a rack. The gear being machined rolls and

moves. Wheels may or may not be reciprocated.

Fig. 29 Generation grinding with a rack-tooth worm wheel

Success in gear grinding with a conventionalgrinding worm wheel depends greatly on care-ful dressing of the wheel to the required contourand on synchronization of the workpiece rota-tion with the rotation of the worm wheel. Spe-cial diamond wheel dressers are required. Theaccuracy of the diamond and of the dressingoperation determine to a great extent the qualityof the gear teeth produced.

Wheels are about 50 mm (2 in.) wide, and theycan be rough formed by crushing and can be fin-ished to the proper pressure angle by diamonddressing. Some machines use wheels that havebeen finish dressed by crushing only. Because aconsiderable amount of time is required to crushtrue a new wheel, it is advisable to stock wheels


Fig. 31 Waguri grinding method for nongenerated spiralbevel and hypoid gears

within 0.005 mm (0.0002 in.), eccentricity withbore or shaft within 0.0064 mm (0.00025 in.), aslittle backlash as 0.025 to 0.051 mm (0.001 to0.002 in.), and a surface finish of 0.38 to 0.76μm (15 to 30 μin.). In general, any bevel orhypoid gear that is cut with a circular cutter canbe ground with a wheel of similar shape andgrinding action, except nongenerated gears thatare cut with a face mill.

Nongenerated (Formed) Gears. The gearteeth are ground by two methods. The firstmethod involves a cup-shaped wheel that simul-taneously grinds the facing sides and root ofadjacent teeth. There is no generating motion,and the wheel produces a curved tooth whosesides have a straight profile. Three or four revo-lutions of the workpiece are required for thecomplete finish grinding of a bevel gear usingconventional dressable wheels. A predeter-mined amount of stock is removed with eachrevolution of the workpiece. With CBN-platedwheels, the entire finishing stock is removed inone revolution of the workpiece. The grindingwheel makes line contact with the tooth beingground. This method is applicable for finishinghypoid and spiral gears and for special spiralgears that have a 0° mean spiral angle.

The second method is called the Wagurimethod. The grinding wheel is circular and hasan average point width of 0.25 to 0.50 mm(0.010 to 0.020 in.) less than the slot width ofthe workpiece. The wheel axis follows a circu-lar path with a diameter equal to the differencebetween its point width and its slot width. Thus,the desired surfaces are ground with line contact(Fig. 31). Conventional dressable wheels can be

used with several revolutions of the workpiece,or CBN-plated wheels with one revolution ofthe workpiece.

An A-46-J-V wheel is the conventionalwheel commonly used to grind gears rangingfrom 2 to 10 diametral pitch. Wheel speedranges from 1200 to 1400 m/min (3800 to 4500sfm). The wheel is dressed automatically at pre-determined intervals between grinds.

Cubic boron nitride-plated wheels cover thesame range of diametral pitch. Wheel speedsrange from 1400 to 2000 m/min (4500 to 6500sfm).

Generated Gears. Spiral bevel and hypoidgears are ground with a cup-shaped wheel. Theconventional grinding wheel is dressed to pro-duce a smooth blend of flank and root profile.The core of the CBN wheel is machined to pro-duce a smooth blend of the flank and tooth pro-file. The curved profile of the tooth is generatedby relative rolling motion between the grindingwheel and the workpiece.

Vitrified bond and resinoid bond aluminumoxide cup-shaped wheels are the conventionalwheels used for spiral bevel and hypoid gears.Typical wheel classifications are A-60-J-V andA-60-M-B. Wheel speed ranges from 1200 to1400 m/min (3800 to 4500 sfm). Cubic boronnitride-plated wheels are also used.

Generating gear teeth with a cup-shapedwheel produces spiral bevel gears with highlyaccurate tooth spacing, concentricity, and pro-file shape. The following is an example of a typ-ical application of this grinding method.

Example 2: Grinding Spiral Bevel GearsWith a Cup-Shaped Wheel. The spiral bevelgear illustrated in Fig. 32 was carburized, hard-ened, and tempered before being ground by thegeneration method with a cup-shaped wheel. Anautomatic wet-type 3.7 kW (5 hp) machinedesigned for grinding spiral bevel, Zerol, andhypoid gears was used for this application.Additional manufacturing information is givenin the table with Fig. 32.

Grinding Fluids

The use of a grinding fluid is generally rec-ommended for the grinding of steel gears. Agrinding fluid prolongs wheel life betweendressings, flushes away chips, and improvesgear tooth finish. Flooding the work surfaceminimizes the possibility of burning the sur-faces of gear teeth. The complete absence ofgrinding burn is essential for high-quality gears.Virtually all the grinding fluids mentioned in the


section “Cutting Fluids” in this chapter havebeen used successfully for the grinding of gears.

In many critical gear-grinding applications,mineral-base sulfochlorinated or sulfurized oilsare used. Plain soluble-oil emulsions haveproved satisfactory for many gear grinding appli-cations. Chemical solutions have also been satis-factory.

Surface Finish

Grinding produces a finish unlike that pro-duced by any other process. Whether this finish

is more desirable than some other finish de-pends on the service requirements of the gear. Insome applications, a gear with a ground finishoperates more quietly, even though grinding hasnot improved the dimensional accuracy of theproduct. The effect of a ground finish, in com-parison with other finishes, on the lubrication ofgears has not been precisely evaluated.

The surface finish of ground gears usuallyranges from 0.38 to 0.80 μm (15 to 32 μin.).Under conditions of unusually good control, asurface finish of 0.25 μm (10 μin.) or better canbe produced. Surface finish sometimes becomesthe major consideration in determining whethera gear will be ground. Grinding can have thedual purpose of correcting dimensional changefrom heat treating and of producing a fine sur-face finish.

Honing of Gears

Honing is a low-velocity abrading processthat uses bonded abrasive sticks to remove stockfrom metallic and nonmetallic surfaces. As oneof the last operations performed on the surfaceof a part, honing generates functional character-istics specified for a surface, such as geometricaccuracy, dimensional accuracy, and surfacefeatures (roughness, lay pattern, and integrity).It also reduces or corrects geometric errorsresulting from previous operations.

The most common application of honing ison internal cylindrical surfaces (Fig. 33a). How-ever, honing is also used to generate functionalcharacteristics on external cylindrical surfaces,flat surfaces, truncated spherical surfaces, andtoroidal surfaces (both internal and external). Acharacteristic common to all these shapes is thatthey can be generated by a simple combinationof motions.

Gear-tooth honing is designed to improvegeometric accuracy and surface conditions of ahardened gear. The teeth of hardened gears arehoned to remove nicks and burrs, to improvefinish, and to make minor corrections in toothshape. Gear teeth are honed on high-speedmachines specially designed for the process(Fig. 34). The honing tool is like a gear drivingthe workpiece at high speed (up to 30 m/min, or100 sfm) while oscillating so that the teeth slideaxially against the workpiece.

Spur gears and internal or external helicalgears ranging in diametral pitch from 24 to 2.5,in outside diameter from 19 to 673 mm (¾ to

Fig. 32 Grinding of a spiral bevel gear. Dimensions in figuregiven in inches


Fig. 33 (a) Schematic representation of honing. (b)Schematic representation of superfinishing

Fig. 34 Honing of helical gear teeth

26½ in.), and up to 75 mm (3 in.) in face widthhave been honed on these machines. Finishes of0.75 μm (30 μin.) are easily achieved, and fin-ishes of 0.075 to 0.10 μm (3 to 4 μin.) are pos-sible. Both taper and crown honing can be done.

Tools used in honing gear teeth are of twotypes, a helical gear shape tool made of abrasiveimpregnated plastic, and a metal helical gearwith a bonded abrasive coating that is renew-able. The plastic tool, which is discarded at theend of its useful life, is widely used. The metaltool is used mainly for applications in whichplastic tools would be likely to break; also, it isused primarily for fine-pitch gears.

Plastic tools are supplied with abrasives of60-grit to 500-grit size. Size of abrasive, gearpitch, and desired finish are usually related as:

Finish

Grift size Gear pitch μm μin.

60 ≤16 0.75–0.89 30–35100 16–20 0.63–0.75 25–30180 >20 0.38–0.50 15–20280 >20 0.25–0.30 10–12500 >20 0.075–0.10 3–4

Honing tools do not load up, and a plastic hon-ing tool can wear until its teeth break. Stockremoval of 0.025 to 0.050 mm (0.001 to 0.002in.) measured over pins is the recommendedmaximum.

Methods. The two methods used to honegear teeth are the zero-backlash method and theconstant-pressure method. In the zero-backlashmethod, which is used for gears made to com-mercial tolerances, the tool head is locked sothat the distance between the center of the workgear and the center of the honing tool is fixedthroughout the honing cycle. In the constant-pressure method, which is used for gears pro-duced to dimensions outside commercial toler-ance ranges, the tool and the work gear are keptin pressure-controlled tight mesh.

Applicability. The use of honing for remov-ing nicks and burrs from hardened gears canresult in a considerable cost saving in compari-son to the usual method. In the usual method,the gears are tested against master specimens onsound test machines. Nicks indicated aresearched for and removed using a hand grinder.The gear is then retested to make certain thenick has been removed. When honing is used,all of these various tests and procedures can beeliminated.

Some shape correction can be achieved in theremoval of 0.050 mm (0.002 in.) of stock byhoning. A helical gear 127 mm (5 in.) in diame-ter may show lead correction of 0.010 mm(0.0004 in.), involute profile correction of0.0075 mm (0.0003 in.), and eccentricity cor-rection of 0.010 mm (0.0004 in.).

The advisability of using honing for sal-vaging hardened gears hinges on cost consider-ations. As the error in tooth shape increases,honing time increases and tool life decreases.On the other hand, if the gears represent a largeinvestment in production time and material,honing may be the most economical method.

Because honing is not designed for heavystock removal or tooth correction, it cannot be


Fig. 35 Setup for the lapping of hypoid gears

substituted for grinding or shaving of gears.Rotary shaving usually leaves gear teeth smoothwithin 0.25 to 1.00 μm (10 to 40 μin.).

Microhoning is a low-velocity abradingprocess very similar to honing. However, unlikeconventional honing, microhoning focuses pri-marily on the improvement of surface finish andmuch less on correction of geometric errors(Fig. 33b). As a result, the pressures and ampli-tude of oscillation applied during microhoningare extremely small. This process is also re-ferred to as microsurfacing, microstoning, andsuperfinishing.

Lapping of Gears

Lapping is the process of finishing work mate-rials by applying a loose abrasive slurry betweena work material and a closely fitting surface,called a lapping plate. When loose abrasive isused to machine the work material, it may slide,roll, become embedded, or do all three, depend-ing on the shape of the abrasive grain and thecomposition of the backup surface.

Gear lapping corrects the minute errors ininvolute profile, helix angle, tooth spacing, andconcentricity created in the forming or cuttingor in the heat treatment of the gears. The lappingcan be done by running a set of gears in mesh orby running one gear with a gear-shaped masterlapping tool.

Gear lapping is most often applied to sets ofhardened gears that are required to run silentlyin service. Gear lapping is strictly a matingprocess and is not intended for stock removal.Two gears that have been matched by lappingshould be operated as a set, and they should bereplaced as a set, rather than singly.

Gears are lapped in special machines, whichcan be arranged for manual, semiautomatic, orautomatic operation. In semiautomatic opera-tion, loading and unloading are manual; in auto-matic operation, loading and unloading are doneautomatically in accordance with a programmedcycle.

Angular, spur, and helical gears can be lapped,but the process is mainly applied to spiral bevelgears and hypoid gears. A typical setup used forlapping hypoid gears is shown in Fig. 35. Gearsof up to 915 mm (36 in.) pitch diameter can belapped in semiautomatic or automatic operation.Manual lapping, in special equipment, is em-ployed for gears of approximately 2540 mm (100

in.) pitch diameter down to the smallest gear thatcan be manufactured. Production lappingmachines can be adjusted to lap gears with shaftangles of 0 to 180°.

Lapping Media. Optimum grit size varieswith different types and sizes of gears. A 280-grit abrasive is used for spiral bevel gears; afiner abrasive (about 400-grit) is more suitablefor hypoid gears because the sliding action isgreater. As a rule, coarser grit is used for gearshaving a coarse pitch, and finer grits are used forgears having a fine pitch. When compound isbrushed on, as in manual operation, a paste-typevehicle is used. However, in semiautomatic orautomatic lapping, the abrasive should be mixedwith a thin oil (such as mineral seal oil) so thatit can be pumped to the workpieces (Fig. 35).

Processing Techniques. It is important toroll all mating gears together before lapping todetect nicks and burrs, which can be removedby a small portable hand grinder before thegears are lapped. This preliminary rolling alsoinspects tooth contact, which should be in thesame location for each set of gears and is espe-cially important in automatic lapping.

During the lapping operation, the pinion(smaller gear) is used as the driver, and thelarger gear is the driven member. The drivenspindle is also used for applying the necessarytooth-contact load by adjusting to a slight drag.


Fig. 36 Surface roughness values produced by common manufacturing/production methods. The ranges shown are typical of theprocesses listed. Higher or lower values can be obtained under special conditions. Source: Ref 3

Running cycles as short as 15 s at about 76m/min (250 sfm) can frequently produce de-sired results. However, longer time cycles maybe necessary, depending on initial gear-toothfinish and service requirements.

Low noise level is the criterion of successfulgear lapping. Because gear lapping is strictly amating process and no stock removal is in-tended, measurements are not made as in mostother lapping processes. Minor corrections intooth bearing shape and position can be ob-tained, however. Lapping does improve the fin-ish of gear teeth, but improved finish is seldomthe purpose of gear lapping.

Superfinishing

Superfinishing processes are those that canachieve a surface roughness average (Ra) of≤0.10 μm (4 μin.) (Ref 3). As shown in Fig. 36,superfinishing can be achieved under carefullycontrolled conditions by grinding, honing/microhoning, lapping, polishing /electropolish-ing, or combinations of finishing processes (forexample, grinding, honing, and lapping). In thepast, such processing was rarely carried out ongears because of the time and expense involved.Recently, however, there have been a number ofstudies that show that the reduction of surfaceroughness improves the lubricating condition of


Fig. 37 Weibull plot of surface fatigue test results for both carburized and ground and carburized, ground, and superfinished gears.Source: Ref 4

gears and offers the possibility of increasing theirsurface fatigue lives (Ref 4).

In order to quantify the effect of surfaceroughness on fatigue life, a series of tests werecarried out on two sets of 28-tooth, 8-pitch gearsmade from consumable-electrode vacuum-melted (aerospace quality) AISI 9310 steel (Ref4). Both sets of gears were case carburized andground. One set of gears was superfinished byplacing them in a vibrating bath consisting ofwater, detergent, abrasive powder, and smallpieces of zinc for several hours (details of thesuperfinishing treatment can be found in Ref 5).Upon removal from the bath the gears hadhighly polished, mirrorlike surfaces. Thesuperfinishing treatment removed about 2 to 3 μm (79 to 118 μin.) of material from the toothsurfaces. The effects of the superfinishing on thequality of the gear tooth surfaces were deter-mined from metrology, profilometry, and inter-ferometric microscope inspections. The su-perfinishing reduced the roughness average byabout a factor of 5. The mean Ra value beforesuperfinishing was 0.380 μm (15.0 μin.). Aftersuperfinishing the mean Ra value was loweredto 0.070 μm (2.8 μin.). The gears were thenfatigue tested at a Hertzian contact stress of 1.71GPa (248 ksi) for 300 million cycles or untilsurface failure occurred on any one tooth. Asshown in Fig. 37, the lives of the superfinished

gears were about four times longer than those ofthe conventionally ground gears.

ACKNOWLEDGMENTS

This chapter was adapted from:• T.J. Krenzer and J.W. Coniglio, Gear Man-

ufacture, Machining, Vol 16, Metals Hand-book, ASM International, 1989, p 330–355

• Honing, Machining, Vol 16, Metals Hand-book, ASM International, 1989, p 472–491

• P. Lynah, Lapping, Machining, Vol 16,Metals Handbook, ASM International,1989, p 492–505

REFERENCES

1. W.N. Ault, Grinding Equipment andProcesses, Machining, Vol 16, MetalsHandbook, ASM International, 1989, p430–452

2. K. Subramanian, Superabrasives, Machin-ing, Vol 16, Metals Handbook, ASM Inter-national, 1989, p 453–471

3. M. Field, J.F. Kahles, and W.P. Koster,Surface Finish and Surface Integrity,Machining, Vol 16, Metals Handbook, 9thed., ASM International, 1989, p 19–36

4. T.L. Krantz, M.P. Alanou, H.P. Evans, andR.W. Snidle, Surface Fatigue Lives ofCase-Carburized Gears With an ImprovedSurface Finish, J. Tribology (Trans.ASME), October 2001, Vol 123, p709–716

5. R.W. Snidle, H.P. Evans, M.P. Alanou,The Effect of Superfinishing on Gear ToothProfile, Report AD-327916, June 1997,available from the Defense TechnicalInformation Center (DTIC), the NationalTechnical Information Service (NTIS), or

the NASA Scientific and Technical Infor-mation Center (http://www.grc.nasa.gov)

SELECTED REFERENCES

• Dudley’s Gear Handbook: The Design,Manufacture, and Application of Gears,2nd ed., D.P. Townsend, Ed., McGraw-HillInc., 1991

• D.W. Dudley, Handbook of Practical GearDesign, McGraw-Hill Book Company,1984


CHAPTER 6

Casting, Forming, and Forging

GEAR MANUFACTURE depends on ma-chinery available, design specifications orrequirements, cost of production, and type ofmaterial from which the gear is to be made.There are many methods for manufacturinggears including:

• Metal removal processes (hobbing, shaping,milling, shaving, grinding, honing, and lap-ping) as discussed in Chapter 5

• Various casting processes for both produc-tion of gear blanks and near-net shape gears

• Stamping and fine blanking• Cold drawing and extrusion• Powder metallurgy (P/M) processing as dis-

cussed in Chapter 7• Injection molding (applicable to plastic gear

materials as discussed in Chapter 4)• Gear rolling• Forging for production of gear blanks and

precision-forged near- and net-shape gears

Most of the processes listed are suited to gearsfor low wear requirements, low power transmis-sion, and relatively low accuracy of transmittedmotion (Ref 1). When the application involveshigher values of one or more of these character-istics, forged or cut/machined gears are used.Table 1 lists the tolerances in terms of AmericanGear Manufacturers Association (AGMA)quality numbers for various gear manufacturingprocesses (Ref 2).

Casting

Although the casting process is used mostoften to make blanks for gears which will havecut teeth (Fig. 1 and 2), there are several varia-tions of the casting process that are used tomake toothed gears with little or no machining.

Table 1 Recommended tolerances in terms of AGMA quality numbers for various gearmanufacturing processes

Highest quality number

Process Normal With extra care

Sand mold casting 1 3Plaster mold casting 3 5Permanent mold casting 3 5Investment casting 4 6Die casting 5 8Injection and compression molding 4 8Powder metallurgy 6 9Stamping 6 9Extrusion 4 6Cold drawing 6 9Milling 6 9Hobbing 8 13Shaping 8 13Broaching 7 12Grinding 10 15Shaving 9 14Honing 10 15Lapping 10 15

Source: Ref 2

For example, cast tooth internal gears (Fig. 3)are produced in several sizes up to 1633 kg(3600 lb). They are heat treated to strength lev-els of 689 MPa (100 ksi) and machining is notrequired on these gears. In circumstances wheremachining is necessary, the machining expenseis reduced by casting close to final shape.

Another example of a cast tooth gear is thepinion gear produced from cast high-manganese(Hadfield) steel for an electric mining shovelshown in Fig. 4. It was not necessary to machinethe gear teeth.

Specific Casting Processes. Most castingprocesses have been used to produce gearblanks or cast tooth gears including sand cast-ing, shell molding, permanent mold casting,centrifugal casting, investment casting, and die




Fig. 2 Large machined cast steel gear. Source: Ref 3

Fig. 1 Cast steel gear blank. Weight: 478 kg (1053 lb).Source: Ref 3

casting. Cut gears have also been produced fromcontinuously cast bars. Some of the commonlyemployed processes will be briefly reviewedbelow. More detailed information on theseprocesses can be found in Casting, Volume 15of the ASM Handbook.

Sand casting is used primarily to producegear blanks. In recent times there has been onlyvery limited use of gears with teeth made bysand casting (Ref 4). In some instances gears forfarm machinery, stokers, and some hand-oper-ated devices have used cast teeth. The draft onthe pattern and the distortion on cooling make itdifficult to obtain much accuracy in cast iron orcast steel gear teeth. Table 1 shows that sandcast gears have the lowest AGMA quality levelsof the major gear manufacturing methods.

The shell molding process is particularlysuited to castings for which:

• The greater dimensional accuracy attainablewith shell molding (as compared with con-ventional green sand molding) can reduce

Chapter 6: Casting, Forming, and Forging / 131

Fig. 3 Cast tooth internal gears. Weights up to 1633 kg (3600lb). Source: Ref 3

the amount of machining required for com-pletion of the part

• As-cast dimensions may not be critical, butsmooth surfaces (smoother than can beobtained by sand casting) are the primaryobjective. An example of a cast tooth bevelgear with an excellent surface finish pro-duced by shell molding is shown in Fig. 5.

The investment casting process has also hadlimited use in gear manufacture. Its most appar-ent value lies in the making of accurate gear teeth

out of materials which are so hard that teeth can-not be readily produced by machining (Ref 4).The process can be used with a variety of steels,bronzes, and aluminum alloys. With machinablematerials, the process is still useful if the gear isintegral with some complicated shape that isvery difficult to produce by machining.

Large quantities of small, low-cost gears aremade by the cold chamber die casting process(die cast gears are usually under 150 mm (6 in.) indiameter and from 10 to 48 diametral pitch, DP).Complicated gear shapes which would be quitecostly to machine can be made quickly and at lowcost by the die casting process. The main disad-vantage of the process is that the low-meltingpoint metals suitable for die casting—aluminum,zinc, and copper—do not have high enough hard-ness for high load-carrying capacity.

Many different types of gears can be die cast,such as spur, helical worm, clusters, and bevelgears. Applications for these types of gearsinclude toys, washing machines, small appli-ances, hand tools, cameras, business machines,and similar equipment.

Forming

Stamping and Fine Blanking. Stamping isa metalworking technique that has been com-pared to using a cookie cutter. In this process, asheet of metal is placed between the top and bot-tom portions of a die; the upper die is pressedinto the lower section and “removes” or cuts thegear from the sheet. This is a low-cost, veryefficient method for producing lightweightgears for no-load to medium-duty applications.Stamping is restricted by the thickness of the

Fig. 4 Cast tooth pinion gear for an electric mining shovel.Weight: 212 kg (468 lb). Source: Ref 3

Fig. 5 Cast tooth bevel gear produced by the shell moldingprocess to obtain excellent surfaces and close toler-

ances. Source: Ref 3


Table 2 Recommended stock thicknesses forstamped gears

Thickness

Pitch range mm in.

20–36 0.51–1.98 0.020–0.07838–60 0.38–1.57 0.015–0.06262–72 0.25–1.02 0.010–0.04074–90 0.25–0.89 0.010–0.03592–120 0.25–0.64 0.010–0.025

Source: Ref 6

workpiece and is used primarily for spur gearsand other thin, flat forms (Ref 5). Stamped gearsrange in size from 20 through 120 DP and 0.25to 3 mm (0.010 to 0.125 in.) thick (Ref 6). Asthe pitch becomes finer, the materials specifica-tion must become thinner. Table 2 shows rec-ommended stock thicknesses for various pitchesthat are commonly used and require no specialcare in die maintenance. As shown in Table 1,tolerances for stamped gears are good andAGMA quality class 9 can be achieved withextra care.

A wide range of materials can be processed bystamping, including all the low and medium car-bon steels, brasses, and some aluminum alloys.Nonmetallic materials can also be stamped.Gears manufactured by this process are used intoys, clock and timer mechanisms, watches,small appliances such as mixers, blenders, toast-ers, and can openers, as well as larger appliancessuch as washers and dryers.

Fine blanking (also known as fine-edgeblanking) is actually more akin to cold extrusionthan to a cutting operation such as stamping.The process takes metal from a sheet like stamp-ing but differs from it in that it uses two dies andforms the workpiece by pressing it into thedesired shape. The metal is extruded into the diecavities to form the desired shape. Also unlikestamping, fine blanking offers the designer alimited three-dimensional capability and canthus be used to create bevels, multiple gear sets,and other complex forms (Ref 5). Fine blankedgears can be found in a wide range of applica-tions including the automotive, appliance, officeequipment, hydraulic, and medical equipmentindustries.

Cold Drawing and Extrusion (Ref 6). Thisprocess requires the least tool expenditure formass production of spur gear toothed gear ele-ments and is extremely versatile in that almostany tooth form that can be desired can be pro-

duced. As the name implies, a bar is pulled(drawn) or pushed (extruded) through a series ofseveral dies, the last having the final shape ofthe desired tooth form. As the material is runthrough these dies it is actually squeezed intothe shape of the die. Since the material is dis-placed by pressure, the outside surface is workhardened and quite smooth.

The bars that are “blanks” for this process areusually 3 to 3.7 m (10 to 12 ft) in length. Afterpassing through the dies, they are known as pin-ion rods, and often are put into screw machinesthat finish the individual gears. Experience hasshown that it is more economical to slice a seg-ment off an extruded bar than to cut an individ-ual gear. In some cases it would be impossibleto produce the desired shape of pinion in anyother way. Pinion rods from 16 to 100 DP canbe obtained, but as the pitch becomes finer, itbecomes more difficult to obtain the close toler-ances that are sometimes desired on fine-pitchpinions. Any material that has good drawingproperties, such as high-carbon steels, brass,bronze, aluminum, and stainless steel, may beused for the drawn pinion rod.

Gears and pinions manufactured by this pro-cess have a large variety of applications and havebeen used on watches, electric clocks, spring-wound clocks, typewriters, carburetors, magne-tos, small motors, switch apparatus, taximeters,cameras, slot machines, all types of mechanicaltoys, and many other parts for machinery of allkinds.

Gear Rolling (Ref 1). Spur and helicalgears, like splines, are roll formed. Millions ofhigh-quality gears are produced annually by thisprocess; many of the gears in automobile trans-missions are made this way. As indicated in Fig.6, the process is basically the same as that bywhich screw threads are roll formed, except thatin most cases the teeth cannot be formed in asingle rotation of the forming rolls; the rolls aregradually fed inward during several revolutions.

Because of the metal flow that occurs, the toplands of roll-formed teeth are not smooth andperfect in shape; a depressed line between twoslight protrusions can often be seen. However,because the top land plays no part in gear toothaction, if there is sufficient clearance in the mat-ing gear, this causes no difficulty. Where de-sired, a light turning cut is used to provide asmooth top land and correct addendum diameter.

Rolling produces gears 50 times as fast asgear cutting and with surfaces as smooth as 0.10μm (4 μin.). Not only does rolling usually need


Fig. 6 Method for forming gear teeth and splines by coldforming. Source: Ref 1

Fig. 7 Gear blank that was closed-die forged in four hammerblows from pancaked stock (not shown), and then

trimmed and pierced in one press stroke. Dimensions are givenin inches.

no finish operation, but rolling refines the mi-crostructure of the workpiece.

Production setup usually takes only a set ofrolling dies and the proper fixture to equip therolling machine. By either the infeed (plunge)method or the throughfeed method, the rollingdies drive the workpiece between them, formingthe teeth by pressure.

Limits. Spur gears can be rolled if they have18 teeth or more. Fewer teeth cause the work toroll poorly. Helical gears can be rolled withfewer teeth if the helix angle is great enough.

It is usually impractical to roll teeth withpressure angle less than 20°. Lower angles havewide flats at root and crest that need more pres-sure in rolling. Lower angles also hinder metalflow. Although 0.13 mm (0.005 in.) radius fil-lets can be rolled, 0.25 mm (0.010 in.) is a bet-ter minimum. For greater accuracy, gear blanksare ground before rolling. Chamfers should be30° or less.

Steels for gear rolling should not have morethan 0.13% S and preferably no lead. Blanksshould not be harder than 28 HRC.

Forging

Forging has long been used in the manufac-ture of gears. This is particularly true for theproduction of gear blanks which would subse-quently be cut/machined into the final desiredconfiguration. Gear blanks have been produced

by open-die forging, closed-die forging (Fig. 7),and hot upset forging. During the past thirty-five years there has been considerable researchand development aimed at producing near-netor net-shape gears by precision forging. Todayprecision forged gears requiring little or no fin-ish machining are commonly used in the auto-motive, truck, off-highway, aerospace, railroad,agriculture, and material handling industries, aswell as the energy and mining fields.

High-Energy Rate ForgingOne of the first forging processes for manu-

facturing near- or net-shape gears was the high-energy rate forging process which is a closed-die hot or cold forging process in which thework metal is deformed at unusually high veloc-ities. Ideally, the final configuration of the forg-ing is developed in one blow, or at most, a fewblows. Velocity of the ram, rather than its mass,generates the major forging force.

It is possible to produce gears with a con-toured grain flow that follows the configurationof the teeth using high-energy-rate forging. Inthe case of spur gears, this is achieved by pan-caking to cause lateral flow of the metal in a diecontaining the desired tooth configuration at itsperiphery. Contoured grain increases the load-bearing capacity without increasing the toothsize. In addition, the process minimizes themachining required to produce the finishedgear. Although spur gears are the easiest toforge, helical and spiral-bevel gears can also be


Fig. 8 Near-net shape cluster gear made by high-energy rateforging. Dimensions are given in inches.

Fig. 9 Near-net shape automotive flywheel made by high-energy rate forging. Dimensions are given in inches.

forged if their configurations permit ejection ofthe gear from the die cavity. Gears have beenforged from low-alloy steel, brass, aluminumalloys, stainless steel, titanium, and some of theheat-resistant alloys.

Gears with a DP of 5 to 20 are commonlyforged with little or no machining allowance.The die life decreases significantly when forg-ing finer-pitch gears.

The forging of 5 DP gears with an involutetolerance of 0.013 mm (0.0005 in.) and totalcomposite error of 0.08 mm (0.003 in.) has beenreported. These gears were forged with a tooth-to-tooth spacing deviation of about 0.025 mm(0.001 in.) and a total accumulated deviation of0.089 mm (0.0035 in.). Over-the-pins dimen-sions were held to ±0.05 mm (0.002 in.) onthese gears, and the total composite error wasabout 0.20 mm (0.008 in.).

Holding gear dimensions to extremely closetolerances may eliminate finish machining, butthe savings may be exceeded by higher die mak-ing/maintenance costs. Consequently, mostforged gears have an allowance for machining.

A surface finish of 0.5 to 1.5 μm (20 to 60μin.) on gear teeth is practical. However, evenwith a 0.5 μm (20 μin.) finish, local imperfec-tions can increase the average to 1.5 μm (60μin.) or greater. Therefore, it would be difficultto maintain a good surface finish on gear teethwithout grinding.

Typical Gear Forgings. The 4.5 kg (10 lb)gear shown in Fig. 8 was forged from 8620 steelbillet 75 mm (3 in.) in diameter by 124 mm (4.9in.) in length. An energy level of 353,000 J(260,000 ft · lbf) was needed to forge the gear inone blow at 1230 °C (2250 °F). The web on thegear was forged to final thickness; the teeth

were forged with 0.51 mm (0.020 in.) of stockfor finish machining.

The die inserts originally used to forge thisgear were made of H11 or H13 tool steel. Thissteel typically softened after producing 20 gearsbecause of its temperature rising above the 565°C (1050 °F) tempering temperature of H13steel. The use of Alloy 718 (UNS N07718) wasfound to improve the die insert life.

The automotive flywheel shown in Fig. 9,272.49 mm (10.728 in.) in diameter over theteeth and weighing 11 kg (24 lb), was forgedfrom a machined blank cast from class 40 grayiron (generally considered unforgeable). Themachined preform, a section of which is shownin Fig. 9, was heated to 955 °C (1750 °F) andforged at an energy level of 271,000 J (200,000ft · lbf). This part had the smallest tolerancespecification. The diameter over the teeth andthe thickness of the body had a tolerance of+0.00 mm, –0.18 mm (+0.000 in., –0.007 in.).The largest tolerance on the part was ±1.02 mm(±0.040 in.) on the diameter of a recess. Toler-ances on the other recesses were ±0.18 mm(±0.007 in.) and +0.48 mm, –0.00 mm (+0.019in., –0.000 in.). This gear was forged to the fin-ished dimensions.

Various gears with teeth as an integral parthave been forged. These have ranged in outsidediameter from 64 to 267 mm (2.5 to 10.5 in.)and in weight from 0.54 to 11 kg (1.2 to 24 lb).Most have been made with 0.13 to 0.51 mm(0.005 to 0.020 in.) of stock on the flank of eachtooth for finish hobbing and grinding. Gearsforged with integral teeth normally have longer


Fig. 11 Fatigue data for (a) cut gears and (b) near-net shapeforged gears. Source: Ref 8

fatigue and wear life than those made from aconventionally forged blank on which the teethare hobbed, shaped, or milled.

Precision ForgingThe term “precision forging” does not spec-

ify a distinct forging process but rather de-scribes a philosophical approach to forging. Thegoal of this approach is to produce a net shape,or at least a near-net shape, in the as-forged con-dition.

The term net indicates that no subsequentmachining or finishing of a forged surface isrequired. Thus, a net shape forging requires nofurther work on any of the forged surfaces,although secondary operations may be requiredto produce minor holes, threads, and other suchdetails. A near-net shape forging can be eitherone in which some but not all of the surfaces arenet or one in which the surfaces require onlyminimal machining or finishing. Precision forg-ing is sometimes described as close-toleranceforging to emphasize the goal of achieving,solely through the hot forging operation, thedimensional and surface finish tolerancesrequired in the finished part.

In recent years, computer-aided design andmanufacturing (CAD/CAM) techniques havebeen applied to various forging processes (Ref7). This computerized approach is applicable toprecision hot forging of spiral bevel, spur, andhelical gears in conventional presses in that itallows the die designer to examine the effects ofvarious process variables (loads, stresses, andtemperature) on the die design.

Precision hot-forged gears have the sameadvantages over cut gears as other molded gears(cast, P/M processed, injection molded) in thatthere is little or no material lost (Fig. 10). This isa cost savings from the standpoint of both thecost of the material itself and, more importantly,the cost of machining. In addition, precisionforged gears also have the advantage over cutgears of increased load-carrying capacity. Thisadded strength in the form of increased fatiguestrength is due to the difference in grain flow be-tween gears cut from bar stock and forged gears.The grain flow in cut gears is determined by thehot rolled orientation of the bar stock and has norelationship to gear tooth contour. On forgedspecimens, the grain flow follows the tooth con-tour in every gear tooth. Figure 11 compares the fatigue properties of cut and forged gears(Ref 8).

Fig. 10 Material/weight savings using the near-net shapeforging process. The large spur gear weighs 25 kg (55

lb) as a blank (left side). As a forged tooth gear (right side) with 1 mm (0.04 in.) of stock allowance on the tooth profile for finishmachining, it weighs 17 kg (37 lb). Source: Presrite Corporation

Near-Net Shape Quality Gears. The ma-jority of forged gears produced today are near-net shape configurations. Gear teeth are forgedwith an envelope of material (stock allowance)around the tooth profile. This envelope is subse-


Fig. 12 Examples of near-net shape forged gears. (a) Spiral bevel gear with a 0.5 mm (0.02 in.) stock allowance developed for useon gears with a DP less than 7. (b) Coarse-pitch (less than 5 DP) spur gear with a stock allowance of 1 to 2 mm (0.04 to

0.80 in.). Source: Presrite Corporation

quently removed by the forging house or the cus-tomer purchasing the forged gears.

The manufacturing process begins with steelbar stock, usually turned and polished toimprove the surface, and cut to the exact weight.The exact weight is critical because the amountof steel must completely fill the die to producethe complete gear profile. Prior to forging, bil-lets are heated between 925 and 1230 °C (1700and 2250 °F) in an electrical induction furnacethat is controlled by an optical pyrometer to ±14°C (25 °F).

In a single stroke, standard mechanical forg-ing presses, ranging from 14,235 to 53,375 kN(1600 to 6000 tonf), form near-net shape gearswith the complete allowable stock allowance.The purpose of this first operation, which formsa “pancake,” is to break the scale off of the billetand size the outside diameter to just under thesize of the root diameter in the gear die. Next, anoperator positions the billet into the finish die.After forging, a hydraulic knockout systemimmediately extracts the gear from the finish die.

After the raw forged gear is hydraulicallyejected from the die, it is placed in a trimmingnest where the hole is punched. It is then allowedto cool to ambient temperature, which usuallytakes up to 24 h. Once cooled, it is ready for fin-ish machining.

Near-net shape gears can be produced usingany carburizing or induction hardening steel infive basic configurations: spiral bevel, helical,straight bevel, spur gears with a 1 mm (0.04 in.)stock allowance, and spur gears with a 0.1 to 0.3mm (0.004 to 0.012 in.) stock allowance. Thenear-net shape gears can be produced in diame-ters up to 425 mm (17 in.) with stock allowancesranging from 0.1 to 1.5 mm (0.004 to 0.06 in.).The specifications for various gear configura-tions include:

• Spiral bevel gears can be produced up to 425mm (17 in.) in diameter, with 0.5 mm (0.02in.) minimum stock per flank. A maximumspiral angle of 35° and a pitch range of lessthan 7 DP can be achieved.

• Straight bevel gears have configurations/properties similar to spiral bevel gears

• Helical gears can be produced up to 250 mm(10 in.) in diameter and up to 40 kg (90 lb)in weight, with a 0.5 mm (0.02 in.) mini-mum stock per flank. A maximum helixangle of 25° and a pitch range of 4 to 12 DPcan be achieved.

• Spur gears with a 1 mm (0.04 in.) stockallowance can be produced up to 400 mm(16 in.) in diameter and up to 135 kg (300 lb)in weight, with a 1 mm (0.04 in.) minimum


stock allowance per flank. A pitch range ofless than 5 DP can be achieved. This type ofgear requires a finish process of hobbing,hobbing and shaving, or hobbing and grind-ing, or skiving.

• Spur gears with a 0.1 to 0.3 mm (0.004 to0.012 in.) stock allowance can be producedup to 250 mm (10 in.) in diameter and up to150 mm (6 in.) maximum face width, with a0.1 to 0.3 mm (0.004 to 0.012 in.) stockallowance per flank. A pitch range of 4 to 12DP can be achieved. This type of gear re-quires a finish process of grinding or skiv-ing. A net root is possible.

Figure 12 shows examples of precisionforged near-net shape gears.

REFERENCES

1. T.T. Krenzer and J.W. Coniglio, GearManufacture, Machining, Vol 16, ASMHandbook, ASM International, 1989, p 330–355

2. J.G. Bralla, Handbook of Product Designfor Manufacturing, Vol 16, McGraw-HillBook Company, 1986, p 355

3. M. Blair and T.L. Stevens, Ed., Steel Cast-ings Handbook, Sixth Edition, SteelFounders’ Society and ASM International,1995, p 2–34

4. D.W. Dudley, Gear-Manufacturing Meth-ods, Handbook of Practical Gear Design,McGraw-Hill Book Company, p 5.86

5. C. Cooper, Alternative Gear Manufactur-ing, Gear Technol., July/Aug 1998, p 9–16

6. D.P. Townsend, Ed., Gears Made by Dies,Dudley’s Gear Handbook: The Design,Manufacture, and Application of Gears,Second Edition, McGraw Hill Book Com-pany, 1992, p 17.1–17.21

7. D.J. Kuhlmann and P.S. Raghupathi, Man-ufacturing of Forged and Extruded Gears,Gear Technol., July/Aug 1990, p 36–45

8. T. Russell and L. Danis, Precision FlowForged Gears, Gear Manufacture and Per-formance, American Society for Metals,1974, p 229–239

CHAPTER 7

Powder Metallurgy

POWDER METALLURGY (P/M) is a flexi-ble metalworking process for the production ofgears. The P/M process is capable of producingclose tolerance gears with strengths to 1240 MPa(180 ksi) at economical prices in higher volumequantities. Spur, helical, bevel, face, spur-helical, and helical-helical gears are produced byP/M techniques. The process is particularlyattractive when the gear contains depressions,through holes, varying levels, or projections.

The first application of P/M gears was for oilpumps in 1937/1938 (Ref 1). Gear pumps con-stitute a common type of application. Depend-ing on application stress levels, different mate-rials and density levels are used. For example,iron-carbon or iron-carbon-copper materialswith densities of 6.0 to 6.8 g/cm3 are used ingear pumps for low-pressure applications suchas engine lubrication and automatic transmis-sions. For higher stress applications up to 20MPa (3 ksi), alloy steels at the minimum densityof 7.1 g/cm3 are used. Powder metallurgy mate-rial requirements for gear pump applications atvarious stress levels are given in Table 1.

With the considerable progress in P/M tech-nology over the years, the quality and applica-tion of P/M gears has increased. Progress in

production, compaction, and sintering hasresulted in new techniques such as infiltration,powder forging, surface rolling, and several fin-ishing treatments. These developments haveenabled the P/M parts to compete successfullywith wrought metal counterparts.

Figure 1 summarizes the various P/M manu-facturing methods used in gear production. Theconventional process consisting of compaction(pressing) and sintering is the most commonlyemployed method for producing gears. Selec-tion of a process method depends on factorssuch as dimensional accuracy. The AmericanGear Manufacturers Association (AGMA)quality classes 5 to 7 can be obtained throughconventional press-and-sinter operations. WhenAGMA quality levels above 7 are required, sec-ondary operations such as coining, burnishing,and grinding typically are employed. See thesection “Gear Tolerances” in this chapter foradditional information.

Performance of any P/M part is influencedprimarily by density. Theoretical density ofsteel is around 7.85 g/cm3, and Table 2 summa-rizes density levels obtained from various P/Mprocesses for steel. All of these P/M methodsare employed for gear manufacture, including

Table 1 Material requirements for P/M pump gear applications

Application Designation(a) Density, g/cm3

Output pressure less than 0.69 MPa (100 psi) and light service FC-0208 type; as-sintered 5.8–6.2Output pressure less than 6.9 MPa (1000 psi) but subject to high vibration and

heavy service; hardened by heat treatingFC-0208 or FN-0106 6.4–6.8

Medium high pressure 6.9–8.6 MPa (1000–1250 psi) for short intervals; hardenedby heat treating

FC-0208 type 6.2–6.5

General-purpose hydraulic pumps up to 10.3 MPa (1500 psi) continuous service FN-0106 type; heat treated 6.8–7.1General-purpose hydraulic pumps up to 17.2 MPa (2500 psi) continuous service AISI 4630 type; heat treated 7.2–7.6

(a) FC-0208 is a copper infiltrated steel. FN-0106 is a nickel steel. Source: Ref 1

Material




Fig. 1 P/M gear production process. CIP, cold isostatic pressing; HIP, hot isostatic pressing

Table 2 Density range for P/M steel consolidation methodsP/M method Density range, g/cm3 Notes

Pressed-and-sintered steel 6.9–7.1 Conventional powder metallurgyDouble processing (press, presinter, restrike, full sinter,

heat treat)7.2–7.4 Restrike (or repress) tooling has tolerances closer to

finish dimensions than the tooling for the first strikeWarm compaction (single pressed) 7.2–7.5 Specially formulated powders to obtain higher green

strength at lower compaction pressureWarm compaction (double pressed) 7.4–7.7 . . .Cold densification (press, sinter, cold form, heat treat) 7.6–7.8 Cold forming improves fatigue and wear resistancePowder forging (press, sinter, forge, heat treat) 7.6–7.8+ Limited to spur, bevel, and face gears although trials with

helical gears have been done (Ref 2)Powder injection molding 7.8+ . . .Copper infiltrated steel Near full density Copper infiltration also improves machinabilityRoll densification 7.6–7.8 Increases localized densification for wear and fatigue

resistance

various surface treatment such as carbonitrid-ing, shot peening, and steam oxide treatments(Ref 2).

A wide variety of base metals are available inpowder form, such as brass, bronze, iron, low-alloy steels, and stainless steel. The selection isgoverned by required mechanical properties,physical properties, service conditions, and cost.Table 3 lists commonly used P/M materials andbroad applications of standard grades. Cus-tomized mixing and blending of elemental pow-

ders also provides a variety of possibilities for thedevelopment of alloy compositions formulatedfor specific mechanical and physical properties.

Capabilities and Limitations

Powder metal gears are used in various appli-cations for appliances, office machines, ma-chinery, machine tools, and automotive prod-ucts. The P/M process offers various advantages

Chapter 7: Powder Metallurgy / 141

Table 3 Commonly used metal powder gradesMPIF designation Chemistry Applications

F-0000 Pure Fe Low strength at highdensity, soft magneticproperties

F-0005 Fe + 0.5% C Moderate strength,medium-carbon steel

FC-0208 Fe + 2% Cu + 0.8% C Higher-strengthstructural components

FN-0205 Fe + 2% Ni + 0.5% C High strength (heattreated), good impactresistance

FX-2008 Fe + 20% Cu + 0.8% C Copper-infiltrated steel,high strength,machinable

SS-316L 316 stainless steel Good toughness,corrosion resistance

SS-410 410 stainless steel Good hardenability,abrasion resistance

CZ-2002 Brass Good toughness,elongation, corrosionresistance

CT-1000 Bronze Structural and bearingapplications

CNZ-1818 Nickel silver Decorative, tough,ductile, corrosionresistance

MPIF: Metal Powder Industries Federation

over traditional gear manufacturing for variousapplications.

In traditional methods, gears are manufac-tured from blanks obtained by machining ofcastings, forgings, and rolled bar stock. Theseblanks are machined by various methods suchas milling, hobbing, and shaping. For precisionand high-speed applications, the gear teeth arefinished by secondary operations such as shav-ing and grinding. Gear production by thesemethods has the following disadvantages:

• Processing times are long, particularly withdifficult-to-machine alloys.

• Material utilization is very low.• Machined gear teeth have an unfavorable

grain flow pattern with flow lines intersect-ing the gear tooth profile.

In comparison to the traditional gear manu-facture process, the P/M process offers severaladvantages, particularly the elimination of ma-chining and scrap losses for the manufacture ofvarious gear types such as helical, bevel (bothstraight and spiral), rack, face, internal andexternal spur gears, and also compound gears.Internal configurations (splines, keys, keyways)also can be formed simultaneously with the gear

profile during P/M manufacture, eliminatingsubsequent machining operations. Thus, P/Mgear manufacturing allows efficient utilizationof materials for moderate- to high-volume pro-duction. The minimum quantity required tomake the P/M process economically competi-tive with machining depends on the size andcomplexity of the part and its accuracy andother property requirements. While P/M pro-cessing is best suited and most widely knownfor high-volume production quantities, there arenumerous applications where small quantities (athousand parts) can still offer cost benefits overtraditional manufacturing methods.

General process advantages of P/M gearmanufacture include:

• Economy in mass production• Repeatability and uniformity of part features

and dimensions• Production of multilevel gears• Close control of density or, conversely,

porosity to suit a particular application• Reduction or elimination of secondary oper-

ations• Improved surface finishes on gear teeth by

reducing or eliminating the machiningmarks (or “scoring”) that can be imparted byconventional methods

• Self-lubricating ability from impregnationof oils and lubricants

• Noise reduction from the sound dampeningqualities of the pore structure of a P/M com-ponent, high surface finish and tooth formconsistency also can have an effect on over-all reduction of noise in comparison to cutgear sets of comparable quality

• Weight reduction by incorporating weightsaving or lightening holes (or similarshapes) in the initial tool design

Limitations of the P/M process for gearmanufacturing include (Ref 2):

• Not economical in low- and medium-quan-tity production

• Not normally suitable for production of worngears, herringbone gears, and helical gearswith helix angle exceeding 35° because ofvarious pressing and tooling considerations

• In view of the press capacities required forcompaction, the sizes of gears are limited

• The gear thickness or face width is restrictedby the requirement that the depth of the diecavity and the stroke of the press must be atleast 2 to 2½ times the gear thickness


Fig. 2 Examples of powder metallurgy gear forms. Courtesy of Carbon City Products

Gear Forms

The size of P/M gears range from as small asa few millimeters to more than 300 mm in diam-eter. For all practical purposes the face width ofP/M gears is limited to less than 75 mm (3 in.).The commonly used compaction presses haveinsufficient press stroke to consolidate the pow-der to greater than this length (face width).

The following types of gears can be producedby the P/M process:

• Spur gears• Bevel gears• Face gears• Hypoid gears• Helical gears of helix angle not exceeding

35°

Combination gears or multiple gears in whichtwo or more gear forms are combined into onecomponent are a specialty of the P/M process.

Some examples of P/M gear design are shownin Fig. 2 to 5. True involute forms (Fig. 3a) thatare expensive to make by other methods can beeasily made by the P/M process. The P/M process

also is particularly advantageous for gear designsthat have irregular curves, radial projections,keyways, or recesses, because these features areeasily obtainable without requiring secondarymachining operations. Full tooth face width forcompound gears and sufficient fillet radii at theroot diameter for tip clearance can be attainedwithout allowances for cutter clearance.

Spur gears are the most common type ofP/M gear in use today. The P/M process is capa-ble of producing spur gears of many tooth formsand modifications. If an electrodischarge ma-chining (EDM) electrode can be ground or cut,the mating form can be duplicated in P/M dies.

Compared to wrought metal gears, the facewidth or thickness of a spur gear is restricted inpowder metallurgy in order that the density andmechanical properties are maintained fairly uni-form throughout the section. Fine pitch (module<0.75 mm) spur gear teeth present powder fill-ing problems, which are more serious if the facewidth is large.

Helical gears are also commonly made bythe P/M process. However, in contrast to metal-cutting processes, the helix angle of P/M gears


Fig. 3 Features produced in powder metallurgy gears. (a) True involute forms. (b) Gear teeth straight up to a flange in P/M gear.Source: Ref 3

is limited to approximately 35°. As with spurgears, many tooth forms and modifications arepossible.

Helical gears have not been produced bypowder forging, but recent production testshave been performed on a unique toolingmethod for powder forging of helical gears. Oneproduction trial involved the powder forging ofa helical gear with a 31° helix angle and a nor-mal pressure angle of 15° for an automotivetransmission part (Ref 4). Experimental worklater carried out by the German Research Soci-ety showed the superiority of the finished prod-uct in terms of toughness, tooth root fatigue, andcontact fatigue (Ref 5). During powder forgingof a helical gear, the die is the only helical partof the tool.

Bevel and face gears are readily made bythe P/M process, but differ somewhat from spurand helical gears in mechanical property flexi-bility. Due to the nature of the compactionprocess, sections such as face gear teeth cannotbe made to high densities without resorting tocopper infiltration or repressing. Most bevel andface gear forms can be made providing they arenot undercut, but the maximum mechanicalproperties attainable will be somewhat less thanthose that can be achieved for spur and helicalgears.

All face tooth forms must be such that thegreen compact does not lock into the punch. Forthis reason undercut gear forms cannot be pro-duced. Under the action of the punch, the crownarea of face gear teeth also normally receivesless compaction than the root zone. This resultsin an undesirable density variation, which canbe offset by copper infiltration or repressing.

Another method to offset density variations isby putting a nonfunctional gear form with its

teeth in the offset position so that a tooth gapcomes below a tooth crown; this allows fullpunch pressure to be exerted on the toothcrowns of the functional gear, enabling a betterdensity distribution (Ref 3).

Combination Gears. Powder metallurgygear manufacture allows the production of com-bination gears or multilevel (two-to-four level)gears resulting in a single part with two or moregear forms. All the gear forms can be positionedclose to one another, thus making the part verycompact. This helps in saving space and han-dling and assembly costs. Combination gearscan be produced by either of the two methods:

• Compacting the part in the combined form• Compacting separately, assembling them in

green state and sintering

Gear Tolerances

Tolerances of P/M gears are determined bythe compaction tooling, compaction process,sintering process, and the P/M alloy. Toothform and dimensions remain relatively stablethroughout the process. The density variation inthe compact should not exceed 0.2 g/cm3, other-wise, dimensional control will be difficult dur-ing sintering.

Powder metallurgy gears are produced typi-cally in AGMA 5 to 7 quality levels. HigherAGMA classification is possible, depending onthe size of the compacted gear and the additionalsecondary operations. Higher AGMA classifica-tion increases the cost of manufacturing due tothe secondary (machining) or restrike operationsthat are added to meet the tighter tolerances. Ingeneral, traditional press-and-sinter operations


Table 4 Minimum tolerance capabilities forspur and helical P/M gears

Tooth-to-tooth compositetolerance

AGMA class 6

Total composite tolerance AGMA class 6Test radius 0.05 mm + 0.002 × diameterOver-pin measurement 0.10 mm + 0.002 × diameterLead error 0.001 mm/mmPerpendicularity—face to bore 0.05 mm + 0.001 × diameterParallelism 0.025 mm + 0.001 × diameterOutside diameter 0.10 mm + 0.002 × diameterProfile tolerance 0.008 mm

Tolerances with single press and sinter without secondary operations. Source:Ref 3

Table 5 Minimum tolerance capabilities forbevel P/M gears

Tooth-to-tooth compositetolerance

AGMA class 6

Total composite tolerance AGMA class 6Outside diameter 0.10 mm + 0.002 × diameterPerpendicularity—face to bore 0.05 mm + 0.001 × diameter

Tolerances with single press and sinter without secondary operations. Source:Ref 3

Fig. 4 Keyways and integral keys. Source: Ref 3

Fig. 5 Weight reducing holes on P/M gear. Source: Ref 3

are economical for achieving AGMA qualitylevels 5 to 7. It is not advisable to produce higherquality levels through only compaction and sin-tering, as closer tolerances and tool wear willimpact costs. Where higher accuracy is required,secondary operations such as sizing, shaving,burnishing, and grinding are required. Sizing(repressing) is the most common methodbecause it improves mechanical propertiesthrough cold working.

Because dimensional variation is a functionof part geometry, material, density, and subse-quent thermal operations, dimensional toler-ances may vary by application.

Powder metallurgy gear tolerances are deter-mined by the compaction tooling, compactionprocess, sintering techniques, and the alloy. Thetolerances can be divided into functional toler-ances that directly affect gear function and non-functional elements that pertain to portions ofthe gear that are more properly termed generalmachine design considerations. Nonfunctionalelements include such items as hub designdimensions, fastening designs such as keyways,set screw holes, inside diameters for press fits,and other special body configurations.

Functional gear tolerances are controlled bythe compaction tooling, the processing meth-

ods, and gear material. Because most P/M gearsare pressed in carbide dies, the tooth form anddimensions remain relatively stable and con-stant throughout the process. Concentricity ofthe gear outside diameter and pitch diameter tothe bore are also controlled by the tooling. If thepressing core rod or punches are eccentric to thedie, the parts will be eccentric. Once the part ispressed, the material characteristics and sinter-ing process determine the dimensional tolerancecapability of the outside diameter, pitch diame-ter, test radius, and bore diameter.

Because of the number of variables within theP/M process it is not possible to state absolutedimensional tolerance capabilities. Howeverminimum tolerances that one should expect forferrous-base P/M gears without secondary oper-ations are listed in Table 4 for spur and helicalgears and in Table 5 for bevel gears. Typical tol-erances for single press and sinter are listed inTable 6.

Gear Design and Tooling

Properly designed gears and compactiontooling are the key factors in the economicalproduction of P/M gears with consistent quality.


Fig. 6 Compaction tooling for compound gear. Source: Ref 6

Table 6 Typical tolerances of single pressedand sintered gearsSee Tables 4 and 5 for specific gear forms.

Feature mm in.

Length ±0.125 ±0.005Flatness on end 0.05 0.002Concentricity ±0.075 ±0.003(a)Inside diameter ±0.050 ±0.002(a)Profile tolerance ±0.0075 ±0.0003Tooth-to-tooth error ±0.025 ±0.001Circular tooth error ±0.05 ±0.002Parallelism on ends ±0.04 ±0.0015Lead error ±0.025 ±0.001Total composite error ±0.08 ±0.0032(b)Outside diameter tolerance

with pitch diameter up to:25 mm (1 in.) 0.075 0.003(c)50 mm (2 in.) 0.1 0.004(c)75 mm (3 in.) 0.125 0.005(c)100 mm (4 in.) 0.15 0.006(c)

(a) Tolerance depends on feature size. (b) Tolerance depends on gear sizeand number of levels. (c) Total tolerance on outside diameter and meas-urement over wires

Tolerance (without secondary operations)

Blended metal powder is usually compacted atroom temperature, at pressures between 275 to690 MPa (40 to 100 ksi) of projected surfacearea. The tooling for a single-level gear includesa die, an upper punch, and a lower punch. If theparticular component to be formed requires abore or other inside-diameter configuration, acore rod is also part of the tooling. Multilevelcompound gears or other complex structuralparts may have two or more upper and/or lowerpunches (Fig. 6).

To form the gear, the die is filled with powderat a ratio of approximately two times the partsthickness; for example, a spur gear that has athickness of 19 mm (0.75 in.) will be compactedto form a column of 38 mm (1.50 in.) thick.During the compaction cycle of the more com-monly used type of press, the upper punchenters the die while the lower punch, which inthe fill position seals off the bottom of the die,remains stationary. As the upper punch travelsdownward, the compressive forces cause the dieassembly to move downward in relationship tothe lower punch, resulting in the same effect asif the lower punch were moving upward duringthe compaction stroke. The rate of movementand pressure of the upper punch and the motionof the die are relatively equal to ensure uniformdensity within the compacted preform. After

completion of the compaction cycle, the upperpunch retracts from the die, and the lower punchinitiates an upward motion, ejecting the preformfrom the dies.

The shape of the compacted preform is deter-mined by the shape of the tooling and the axialmotion of the compaction press. Two main fac-tors influence part design: the flow behavior andcharacteristics of the metal powders and themovement of the tools within the pressingcycle. Metal powders do not flow hydraulically,and the allowance for friction between the pow-der particles themselves and with the movingtool members must be factored in the final P/Mpart design. The pressing action from both topand bottom largely governs the shape, length,and dimensional details of the preform. Theclearance tolerance of the moving tool mem-bers, relative to the inside diameter or bore, con-tributes to a larger degree of eccentricity thanwith machined gears. Details, or features thatincrease the number of tool members compoundthe eccentricity. Concentricity can be improvedwith the addition of secondary operations, suchas grinding the bore in relationship to the pitchdiameter.

The compacted preform is sintered typicallyat temperatures of approximately 1120 °C(2050 °F) to obtain tensile properties around125 to 620 MPa (18 to 90 ksi), depending on thematerial composition. The addition of heattreatment can increase ultimate tensile proper-ties of a compacted-and-sintered steel compo-nent to 1240 MPa (180 ksi).


Fig. 7 Hub feature. Source: Ref 6

Fig. 8 Preferred design for section thickness changes. Source:Ref 6

Design GuidelinesDesign guidelines for P/M gears include the

following considerations:

• Ejection from the die• Die filling during compaction• Clearance• Thickness changes• Right-angle intersections• Edge detail

Ejection from the Die. Some features mustbe eliminated from the final part (or addedthrough secondary machining operations) whenthey inhibit ejection of the preform from the die.For example, undercuts, reverse angles, detailsat right angles to the direction of pressing (e.g.,holes, grooves), threads, diamond knurls andreentrant angles would interfere with smoothejection.

Die Filling During Compaction. Gear de-sign should allow for the movement of the metalpowders throughout the tool members duringthe compaction cycle. Metal powders do notflow hydraulically. Therefore, extremely thin-walled sections, very narrow grooves, and deepcounter-bores should be avoided because themetal powders may not completely fill thesedetails within the tool members.

Tool life can be improved by avoiding nar-row deep grooves, very sharp edges, completespherical profiles, and knife-thin tool thick-nesses. Often design simplification of these fea-tures allows for a more robust or “practical” setof compaction tools without adding machiningoperations.

Clearance. Hubs or bosses for gears,sprockets, or cams can be readily produced, butthe designs should ensure the maximum permis-sible material between the outside diameter ofthe hub and the root diameter of gear or sprocketfeatures (Fig. 7) (Ref 6). Another considerationfor gear design is to maintain sufficient clear-ance between the inside diameter and the rootdiameter, which can range from 0.9 mm (0.035in.) on small pinions to 7.5 mm (0.30 in.) formore demanding applications. Design consider-ation should be given to maximize the clearancebetween the gear root diameter and compoundgears, pinions, or features (i.e., cams, etc.) thatare incorporated parallel to the gear teeth.

Thickness Changes. The configuration ofthe gear should limit major changes in sectionthickness (Fig. 8) for compound gear geome-tries such as gear-pinion and spur-face combi-

nations, which are well within the capability ofthe P/M process. Uniform density and highstrength is best achieved by limiting the numberof section thickness changes (levels) that aredesigned into the preform. The number of levelsa part may have is determined by the specifictype of compaction press and/or the design ofthe compaction tooling.

Right-Angle Intersections. The configura-tion of the gear should minimize right-angleintersections. Radii should be incorporated atright-angle intersection of section thicknesschanges. These radii improve the integrity of thepreform. Gear engagement should be designedto occur above the radius. Often raised surfacefeatures can be added to the compacted preformto assist in this engagement.

Edge Detail. The configuration of the gearshould incorporate edge detail (i.e., chamfers ontop and bottom of the gear teeth and on outsideand inside diameters) (Fig. 9). This edge detailof chamfer has two main purposes. First, itincreases the density of the teeth. Higher toothdensity results in improved mechanical proper-ties, particularly strength. It also reduces theadverse effects of burrs. The chamfer detail willin most cases keep the burr within the overall


Fig. 9 Edge radii design features. Source: Ref 6Fig. 10 Schematic of gear damage mechanisms. Source:

Ref 15

thickness (width) of the gear. These burrs are aresult of the fit clearance of the tool membersand, if necessary, can be removed by a vibratoryfinishing (tumbling) operation.

Gear Performance

In general terms, gear teeth loading is akin tonormal loading of two parallel cylinders with acombined sliding and rolling. In rolling contact,two elements roll in contact with each otherwithout slippage. Both elements rotate at thesame velocity. Gear teeth have sliding contactover most of their surfaces, with rolling contactoccurring only at the pitch line. The amount ofsliding varies with the distance from the pitchline. When the rolling and sliding are in thesame direction, less damage occurs than withnegative slide (Ref 7).

Gears can be damaged by several mecha-nisms such as bending fatigue or by surfacefatigue mechanisms such as pitting or spalling.The origin of pitting occurs where the combina-tion of pressure and negative sliding are thehighest. On spur gears, this is usually at the low-est point of single-tooth contact on the deden-dum of the drive gear (Ref 8).

As with any other material the choice of aP/M alloy is governed by the magnitude andnature of the transmitted load, the speed, the life

requirements, the environment, the type oflubrication, and the gear and assembly preci-sion. Allowable loads on contact surfaces ofgears are limited by the occurrence of pitting, inmost cases, provided they are not run at veryhigh speeds to cause scoring (Fig. 10). Even atlight loads, gear teeth experience relatively highconcentrated stresses because contact areas arevery small. In general, Hertz equations are usedto design for contact stresses, and these equa-tions consider compressive loads on stationarycontact surfaces.

Spalling damage of wrought and P/M alloyshas similar appearance but different crack prop-agation mechanisms. In wrought alloys, most ofthe time is spent in the crack initiation phase(under high-cycle conditions) with relativelyquick crack propagation once the crack is bigenough. In P/M alloys, the porosity blunts crackgrowth to the surface. Until the crack can prop-agate to the surface, a band of subsurface crack-ing continues. The depth of the band is probablyrelated to the depth of the maximum shearstress.

Selecting Gear MaterialsRequired strength is the first factor when

selecting a gear material. In spite of the approx-imations involved, one can generally arrive atthe correct material by using the methods out-lined in the AGMA standards for rating thestrength of spur, helical, and straight bevel gearteeth (Ref 9–11). A good approximation ofcompressive load carrying ability can be foundby using the methods outlined in the AGMAstandards for surface durability of spur, helical,and bevel gear teeth (Ref 12–14). In addition,the allowable contact stress Sac, the elastic mod-ulus, and Poisson’s ratio of the P/M materialmust be determined.


Allowable Contact Stress. Tensile strength,elastic modulus, and Poisson’s ratio for most fer-rous P/M materials is given in MPIF standard 35.In the absence of data for allowable contactstress of ferrous P/M materials, an approxima-tion of Sac is 70 MPa (10 ksi) below the ultimatetensile strength (Sac = UTS = 10 ksi).

Allowable bending stress (Sab) for a P/Mmaterial can be approximated in the absence ofdata at 0.3 of the ultimate tensile strength of fer-rous-base P/M materials (Sab = 0.3 UTS). Theonly caution one should be aware of is that ten-sile data may be typical properties. The designershould consult the supplier or specifications forminimum property data.

Impact and Fatigue Strength. Most P/Mgears are limited in performance by their impactand fatigue strength as opposed to their com-pressive yield strength and surface durability.Surface treatments such as shot peening, mate-rial cleanliness, and other factors influence con-tact fatigue. Detailed information on P/M gearfatigue testing and evaluation is discussed fur-ther in Ref 15 and 16. Additional information onfatigue is also contained in Chapter 13, “GearFailure Modes and Analysis” and Chapter 14,“Fatigue and Life Prediction.”

Quality Control and Inspection

Inspection is one of the most important stagesin gear production. Inspection and testing isdone on dimensional specifications, mechanicalproperties, and surface durability (hardness).The information required to describe a gear forthe P/M process and subsequent inspectionmethods are essentially the same as for amachine-cut gear. The part drawing shouldinclude:

• Number of teeth• Diametral pitch (normal diametral pitch for

a helical gear)• Pressure angle (normal pressure angle for a

helical gear)• Tooth form for spur, helical, and straight

bevel gears• Helix angle and rotation (right or left hand)

for a helical gear• Pitch, face, root, and back angles for straight

bevel gears

To assist in the qualification (i.e., inspection)the drawing should also include:

• Outside diameter (as a reference dimensionfor straight bevel gears)

• Root diameter• Pitch apex to back face• Total composite tolerance• Tooth-to-tooth tolerance (not appropriate

for straight bevel gears)• Test radius

Measurement over wires (MOW) and mea-surement between wires (MBW) (for internalgears) are convenient measurable criteria thatshould also be included as drawing specifica-tions. Master gear information (specificationand/or data) should be included on the drawing.Tip radius detail for spur gears is also necessary.It is advisable that right-angle (rolling) fixturesbe developed to check mesh and backlash.Often several ID (inside diameter) pins arerequired to confirm mesh, after/during criticalprocessing operations (minimally, compaction,sintering, and heat treatment). Typically, theseinspection fixtures are specified and purchase atthe time the tooling is manufactured.

Gear drawing specifications are outlined inANSI/AGMA 6008-A98, “Specifications forPowder Metallurgy Gears.” This standard de-fines the minimum detailed information to beincluded in the P/M gear specifications submit-ted by the gear purchaser to the gear producer.In addition to gear drawing specifications, thisinformation also covers gear tooth geometrydata and gear material specifications.

In production, it is common practice to checkthe face width, outside diameter, over-pin meas-urement, total composite error, tooth-to-tootherror, perpendicularity of face-to-bore, paral-lelism, and inside diameter of the gears. Alsothe tooth strength and macroscopic hardness areusually checked. The sampling plan and fre-quency of measurement varies and depends onthe criticality of the application.

Gear inspection terms include:

• Runout (radial): the total variation of theradial distance of the gear teeth from thecenter or bore

• Runout (axial): the total variation of gearteeth along its axis, measured from a refer-ence plane perpendicular to its axis. Alsoreferred to as “wobble” or face runout

• Lead: the axial advance of a gear tooth inone revolution (360°)

• Lead variation: the condition in a gearwhere some teeth vary in lead, plus or minusfrom the average lead


Fig. 11 Spur gear tooth strength test. Source: Ref 17

• Total composite error: the total variation ofthe center distance in one complete revolu-tion

• Tooth-to-tooth variation: the variation of thecenter distance in a section of its circumfer-ence (the section of the circumference is anangle of 360°/N where N is the number ofgear teeth)

Mechanical Testing. Mechanical proper-ties are also measured, and in many cases benchlife and impact tests or field tests are made tocheck the gear functionality. Because tensilestrength of a gear cannot be measured directly, itis appropriate to establish a minimum toothbreakage strength that can be used as a produc-tion acceptance criteria from either sample gearsmade from a die or gears cut from a P/M slug.

One quick and accurate means of measuringtooth strength of a spur gear is shown in Fig. 11.By mounting the gear between fixed supportsand applying a vertical load, one can measure atooth breakage strength. By testing a number ofgears that perform successfully in the particularapplication, it is possible to calculate statisticallimits for the tooth breakage strength that can beused as a future material strength acceptance.Helical and bevel gears are usually evaluated intorque-type tests and the same type of statisticalanalysis applied. The use of statistics is particu-larly expedient in gear strength testing becauseproper sampling allows process control to a nor-mal statistical distribution (i.e., a ± 3σ) mini-

mum acceptance criteria ensures 99.85% confi-dence of adequate strength.

Surface durability is a specified and mea-sured minimum Rockwell hardness because thismacroscopic hardness relates to the compres-sive yield strength of the materials. The mini-mum Rockwell hardness depends on the mate-rial and can be established either from samplesor from the supplier’s historical information.

In cases where scoring may be a problem, inparticular with heat treated gears, it is appropri-ate to specify and measure a microscopic hard-ness. This is accomplished with a diamondindenter, and the microscopic or individual par-ticle hardness of the material is measured. Theparticle hardness specification is generallydetermined from historical data for the pro-ducer’s material.

In contrast to most metals, P/M materialshave both a macro- and microhardness as aresult of porosity within the structure. Becausethe P/M structure consists of individual hardparticles bonded together with interdispersedvoids, the conventional Rockwell indention reg-isters a composite hardness. Because slidingand surface contact involves microscopic con-tact (individual asperities) the particle or micro-hardness of the P/M material influences thescore resistance of the P/M material more sothan the macro Rockwell hardness. As a gener-ality, when a P/M gear is run against a wroughtgear, the P/M particle hardness should be noharder than the hardness of the wrought gear toprevent wear of the mating gear.

Examples of P/M Gears

Powder metallurgy gears are used in a widevariety of application areas including businessmachines, appliances, farm, lawn, and gardenequipment, automobiles, trucks, and militaryvehicles. The examples that follow illustrate the versatility of the P/M process for gear manu-facture.

Example 1: Drive Gear for MailhandlingMachine. A flat-belt drive gear weighing 490 g(17.3 oz), which is compacted to a density of 7.45 g/cm3, is shown in Fig. 12. This type of gearis used in high-speed mailhandling and insertingmachines. This part, consisting of electrolyticiron preblended with 0.35% C, replaced a two-piece gear assembly made of American Iron andSteel Institute (AISI) 1030 steel, thus resulting ina total cost savings of 66%.


Fig. 12 Iron-carbon P/M drive gear. (Left) Finished ma-chined, hardened, ground part. The hub diameter is

machined oversized (+0.254 mm, or +0.010 in.) to allow forfinal grinding. (Right) P/M blank as-pressed

Fig. 13 P/M transfer gear made of high-strength low-alloysteel. (a) Original P/M processing technique, which

required machining of flange section. (b) Modified P/M tech-nique, which required no additional machining

The powder was first compacted on a 5340kN (600 ton) press to a density of 6.8 to 6.9g/cm3 at a compaction pressure of 414 MPa (30tsi). It was then presintered and repressed to adensity of 7.45 g/cm3 at 965 MPa (70 tsi). Afterrepressing, the part was sintered at 1120 °C(2050 °F) for 30 min.

As shown in Fig. 12, considerable machining(turning) of the hub was required to generate thefinal shape. In use, this gear rotates and a mag-netic clutch rides on the machined hub. Whenthe operator trips the cycle control on themachine, the clutch closes around the small hubdiameter, and the load is transferred to the P/Mgear. Pressing of a large hub ensures a uniformdensity in the cross-sectional area, but requiresadditional machining of the P/M blank.

After machining, the hub area is carboni-trided to a case depth of 0.127 mm (0.005 in.).Case hardness is 700 DPH (minimum), whilecore hardness is 550 DPH. To maintain a 0.025mm (0.001 in.) diameter tolerance between thehub and the magnetic clutch, the hub diameter isground to final dimensions. Typical propertiesfor this P/M part are:

Tensile strength, MPa (ksi) 414–586 (60–85)Yield strength, MPa (ksi) 365–414 (53–60)Elongation, % 1–2Transverse-rupture strength, MPa (ksi) 930 (135)

Example 2: Transfer Gears for PostageMeter Counting Applications. The high-precision, high-strength gears shown in Fig. 13are made of 4600 alloy powder prealloyed with0.25% Mn, 1.7 to 1.9% Ni, and 0.5 to 0.6% Mo

and subsequently preblended with 0.75% Cuand 0.35 to 0.45% C. These gears are used inpostage meters for counting applications.

The powder was compacted in a floating diepress system to a density of 6.85 to 7.0 g/cm3.Sintering was conducted in an endothermicatmosphere at 1120 °C (2050 °F). After sinter-ing, the parts were carbonitrided to provide acase hardness of 700 DPH for a 0.127 mm(0.005 in.) case depth and a core hardness of400 DPH. After case hardening, the parts weredeburred and oil impregnated.

The original method for manufacturing thesegears consisted of a two-piece copper-brazed andgear-hobbed assembly of AISI 1030 steel. Thelarger (bottom) gear was first turned as a diskwith a center hole. Gear teeth were then hobbed.

The smaller (top) gear was also turned andgear hobbed. The two parts were then press fit-ted and copper brazed. At this point, inspectionwas required to reject and scrap any gears thatshifted during brazing, thus losing the criticaltooth-to-tooth relationship required between thesmall-diameter gear and the large-diametergear. The rejection rate due to assembly errorsran as high as 50%.

Figure 13(a) shows the single-piece transfergear manufactured using P/M techniques. Theflange section was made thick enough so thatthe hub section could be machined as a second-ary operation. The normal timing of the floatingdie press mechanism forced powder to transferfrom the small gear teeth into the flange section,thus resulting in low density in the small (top)gear teeth. Consequently, tooling was modifiedto produce the gear configurations shown in Fig.13(b), which required no machining of the gear


Fig. 14 Eccentric gear for a washing machine made of ironalloy powder containing 2% copper and 0.5%

graphite. Center hole inside diameter: approximately 19 mm(0.76 in.); eccentric outside diameter: approximately 57 mm(2.28 in.); total thickness: approximately 28.50 mm (1.14 in.);eccentric thickness: approximately 15.90 mm (0.63 in.); pitchdiameter: approximately 115 mm (4.59 in.)

teeth located on the hub section. Typical fin-ished P/M properties are:

Ultimate tensile strength 586–793 MPa (85–115 ksi)Yield strength 552–655 MPa (80–95 ksi)Elongation <1%Transverse-rupture strength 1172–1379 MPa (170–200 ksi)

Example 3: Eccentric Gear. Figure 14shows an eccentric gear for a washing machinethat is made of a blend of 2% copper, 0.5%graphite, and the balance iron, which is com-pacted, sintered, sized, and machined. An inter-mediate level of graphite was chosen to producean as-sintered part that could be sized readily toensure an accurate gear tooth profile. Lower car-bon content also improves machinability. Den-sity of this part is 6.5 g/cm3.

This gear is made from atomized powder toobtain optimum compressibility. Because thisgear is a two-level part, green strength is criticalto eliminate cracking at juncture. Press motionand tool design also are critical in preventinghub cracking.

Sintering is done in an endothermic atmo-sphere for 30 min at 1105 °C (2025 °F). Dewpoint is monitored to prevent carburization ofthe surface layers so as not to affect sizing ormachining. After sintering, the part is deburred

in a steel medium to facilitate sizing. Prior tosizing, the part is dipped in soluble sizing wax,which also acts as a long-term storage and rustprotection medium.

Sizing enhances the tooth form and pitchdiameter tolerances. After sizing, the centerhole is bored for concentricity, and the outsideof the hub is machined to correct any ovality.This part replaced a class 30 gray iron castingthat was machined from a rough blank.

Example 4: Fourth Reduction Gears. Lawnand garden tractors require gears that can with-stand extremely high wear and heavy loading.For example, the fourth reduction gear shown inFig. 15 is a drive gear in a six-speed transmis-sion. A crush load of 4000 kg (8800 lb) per toothis specified. High tooth density is required of theP/M part. To provide this feature, repressing thepart to a density of 7.3 to 7.5 g/cm3 would seemto be the solution. However, the part is too largeto be compacted on a 4.45 MN (500 ton) press.To overcome this limitation, the part is com-pacted to three densities: 6.4 to 6.6 g/cm3 in thehub, 6.6 to 6.8 g/cm3 in the inner flange, and 6.9to 7.0 g/cm3 in the tooth area.

After presintering, the gear is repressed onlyin the tooth area to a density of 7.3 to 7.5 g/cm3.Carbon content is kept low to improve com-pressibility during repressing, after which theteeth are carburized.

Fig. 15 Fourth reduction gear

MPIF material FN-0205Carbon, % 0.5Nickel, % 2Molybdenum, % 0.5Density, g/cm3

Tooth 7.3–7.5Inner flange 6.6–6.8Hub 6.4–6.6

Tooth apparent hardness, HRC 50–56Tooth crush strength, kN (ton) 40 (4.5)Finished weight, kg (lb) 1.042 (2.300)


Fig. 17 Powder forged internal ring gear used in automatictransmission for trucks of up to 22,700 kg (50,000 lb)

gross vehicle weight. Courtesy of Precision Forged ProductsDivision, Borg Warner Corp.

Fig. 16 Comparison of material used for a conventionally forged reverse idler gear (top) and the equivalent powder forged part (bot-tom). Material yield in conventional forging is 31%; that for powder forging is 86%. 1 lb = 453.6 g.

Example 5: Powder Forged Internal RingGear. Powder forging is a process in which un-sintered, presintered, or sintered powder metalpreforms are hot formed in confined dies. Oneof the main economic benefits of powder forg-ing is the reduced amount of machiningrequired, as illustrated in Fig. 16.

The powder forged internal ring gear shownin Fig. 17 is used in automatic transmissions fortrucks with a maximum gross vehicle weight of22,700 kg (50,000 lb). The gear transmits 1355N · m (1000 ft · lbf) of torque through the gearand spline teeth.

Originally, the gear was produced by forgingan AISI 5140M tubing blank. The convention-ally forged blank required rough machining,gear tooth shaping, spline machining, core heattreating, carburizing, and deburring. The onlysecondary operations required on the powderforged part are surface grinding, hard turning,shot blasting, and vibratory tumbling.

The powder forged 4618 ring gear is pro-duced to a minimum density of 7.82 g/cm3. Thepart is selectively carburized using a proprietaryprocess and quench hardened. Minimum sur-face hardness is 57 HRC (2070 MPa, or 300 ksi,ultimate tensile strength), while the core hard-

ness is 25 HRC (825 MPa, or 120 ksi, ultimatetensile strength). The internal gear teeth are pro-duced to AGMA Class 7 tolerances.


ACKNOWLEDGMENTS

This chapter was adapted from:

• G.T. Shturtz, Powder Metallurgy Gears,Powder Metal Technologies and Applica-tions, Vol 7, ASM Handbook, ASM Interna-tional, 1998, p 1058–1064

• Appendix 3: Examples of Powder Metal-lurgy Parts, Powder Metal Technologies andApplications, Vol 7, ASM Handbook, ASMInternational, 1998, p 1101–1108

• W.B. James, M.J. McDermott, and R.A.Powell, Powder Forged Steel, Powder MetalTechnologies and Applications, Vol 7, ASMHandbook, ASM International, 1998, p803–827

REFERENCES

1. P.W. Lee, Press and Sintered Parts andTheir Applications, Powder MetallurgyApplications Advantages and Limitations,Erhard Klar, Ed., American Society forMetals, 1983, p 82

2. S.D.K. Saheb and K. Gopinath, PowderMetallurgy Gears—A Brief Review, Pow-der Metall. Sci. Technol., Vol 1 (No. 4),July 1990, p 43–66

3. S.D.K. Saheb and K. Gopinath, Tooling forPowder Metallurgy Gears, Powder Metall.Sci. Technol., Vol 2 (No. 3), April 1991, p25–42

4. Met. Powder Rep., Vol 43, 1988, p 5365. W. Konig, G. Rober, K. Vossen, and M.

Stromgren, Powder Forging of HelicalGears for Car Manual Gear Boxes—Concept and Properties, Met. Powder Rep.,Vol 45 (No. 4), 1990, p 269–273

6. Powder Metallurgy Design Manual, MetalPowder Industries Federation, 1994, p 193

7. G. Parrish and G.S. Harper, ProductionGas Carburizing, Pergamon, 1985, p 20

8. Gear Design Manufacturing and Inspec-tion Manual, SAE No. 841083, Society ofAutomotive Engineers, 1990, p 46

9. “AGMA Standard for Rating the Strengthof Spur Gear Teeth,” AGMA 220.02,American Gear Manufacturers’ Associa-tion, 1966

10. “AGMA Standard for Rating the Strengthof Helical and Herringbone Gear Teeth,”AGMA 221.02, American Gear Manufac-turers’ Association, 1965

11. “AGMA Standard for Rating the Strengthof Straight Bevel and Zero Bevel GearTeeth, AGMA 222.02, American GearManufacturers’ Association, 1964

12. “AGMA Standard for Surface Durability ofSpur Gear Teeth,” AGMA 210.02, Ameri-can Gear Manufacturers’ Association, 1965

13. “AGMA Standard for Surface Durability ofHelical and Herringbone Gear Teeth,”AGMA 211.02, American Gear Manufac-turers’ Association, 1969

14. “AGMA Standard for Surface DurabilityFormulas for Straight Bevel and Zero BevelGear Teeth,” AGMA 212.02, AmericanGear Manufacturers’ Association, 1964

15. T. Prucher and H. Sanderow, SurfaceFatigue of P/M Alloys, Characterization,Testing, and Quality Control, Vol 2,Advances in Powder Metallurgy and Par-ticulate Materials, Metal Powder Indus-tries Federation, 1994, p 99–111

16. R. Gnanamoorthy and K. Gopinath, Sur-face Durability Studies on As-SinteredLow Alloy Steel Gears, Advances in Pow-der Metallurgy and Particulate Materi-als—1992, Vol 6, Metal Powder IndustriesFederation, 1992, p 237–250

17. W. Smith, Ferrous Based Powder Metal-lurgy Gears, Gear Manufacture and Per-formance, American Society for Metals,1974, p 257–269

SELECTED REFERENCES

• AGMA & MPIF Develop Standards, Infor-mation Sheet for Powder Metal Gears, GearTechnol., J. Gear Manuf., Sept/Oct 1996

• R. Moderow, Gear Inspection and Measure-ment, Gear Technol., J. Gear Manuf.,July/Aug 1992

• MPIF Standard 35, Material Standards forP/M Structural Parts, Metal Powder Indus-tries Federation, 1997

• Powder Metallurgy Design Manual, 2nded., Metal Powder Industries Federation,1995

• Powder Metallurgy Design Solutions, MetalPowder Industries Federation, 1993

• H. Sanderow, Powder Metal Gear Designand Inspection, Gear Technol., J. GearManuf., Sept/Oct 1996

• G. Shturtz, The Beginner’s Guide to PowderMetal Gears, Gear Technol., J. GearManuf., Sept/Oct 1995

CHAPTER 8

Through Hardening

THE THROUGH-HARDENING PROCESSis generally used for gears that do not requirehigh surface hardness. Typical gear tooth hard-ness following through hardening ranges from32 to 48 HRC. Most steels used for through-hardened gears have medium carbon content(0.3 to 0.6%) and a relatively low alloy content(up to 3%). The purpose of alloying is toincrease hardenability. The higher the harden-ability, the deeper is the through hardening ofgear teeth. Since strength increases directlywith hardness, high hardenability is essentialfor through hardening steels. High hardenabil-ity, again, has some adverse effect on materialductility and impact resistance. The other draw-back of through-hardened gears is lower allow-able contact stresses than those of surface-hard-ened gears. This tends to increase the size ofthrough-hardened gears for the same torquecapacity compared with those with hardenedsurfaces.

In through hardening, gears are first heated toa required temperature and then cooled either inthe furnace or quenched in air, gas, or liquid.The process may be used before or after the gearteeth are cut. If applied before cutting the teeth,the hardness usually is governed and limited bythe most feasible machining process. Sincethese gear teeth are cut after heat treatment, nofurther finishing operation is needed. On theother hand, gears that are designed for hardnessabove the machining limit are first cut to semi-finish dimensions and then through hardened. Incase of some minor heat treat distortion, a fin-ishing operation such as lapping or grinding isvery often used to improve the quality of thesegears—American Gear Manufacturers Associa-tion (AGMA) class 10 and above. For quality upto class 9, gears are finished cut at least oneAGMA class above the requirement prior toheat treatment.

Four different methods of heat treatment areprimarily used for through-hardened gears. In ascending order of achievable hardness, these methods are annealing, normalizing andannealing, normalizing and tempering, andquenching and tempering. Sometimes, hard-nesses of through-hardened gears are specifiedand measured in other scales besides Rockwell,such as Vickers and Brinell. Table 1 shows anapproximate relationship among the variouscommonly used hardness scales.

Through-Hardening Processes

Annealing refers to any heating and coolingoperation that is usually applied to induce soft-ening. There are two types of annealing—fulland process. In full annealing, the steel is heatedusually to approximately 38 °C (100 °F) abovethe upper critical temperature and held for thedesired length of time, followed by very slowcooling in the furnace. The purposes of fullannealing are to:

• Soften the steel and improve ductility andmachinability

• Relieve internal stresses caused by previoustreatment and improve dimensional stability

• Refine the grain structure

In process annealing, the steel is heated to atemperature below or close to the lower criticaltemperature followed by the desired rate ofcooling. The purpose here is to soften the steelpartially and to release the internal stresses. Inthis treatment, grain refinement by phase trans-formation is not accomplished as it is in fullannealing. Process annealing uses temperaturesbetween 550 and 650 °C (1020 and 1200 °F).

Gears with hardness up to 34 HRC are fullyannealed by heating to 800 to 900 °C (1475 to




Table 1 Approximate relation between various hardness-test scales

Brinell(a) C A 30-N 15-N B 30-T 15-T Vickers pyramid Tukon (Knoop)

. . . 70 86.5 86.0 94.0 . . . . . . . . . 1076 . . .

. . . 65 84.0 82.0 92.0 . . . . . . . . . 820 840

. . . 63 83.0 80.0 91.5 . . . . . . . . . 763 790614 60 81.0 77.5 90.0 . . . . . . . . . 695 725587 58 80.0 75.5 89.3 . . . . . . . . . 655 680547 55 78.5 73.0 88.0 . . . . . . . . . 598 620522 54 77.5 71.0 87.0 . . . . . . . . . 562 580484 50 76.0 68.5 85.5 . . . . . . . . . 513 530460 48 74.5 66.5 84.5 . . . . . . . . . 485 500426 45 73.0 64.0 83.0 . . . . . . . . . 446 460393 52 71.5 61.5 81.5 . . . . . . . . . 413 425352 38 69.5 57.5 79.5 . . . . . . . . . 373 390301 33 67.0 53.0 76.5 . . . . . . . . . 323 355250 24 62.5 45.0 71.5 . . . . . . . . . 257 . . .230 20 60.5 41.5 69.5 . . . . . . . . . 236 . . .200 . . . . . . . . . . . . 93 78.0 91.0 210 . . .180 . . . . . . . . . . . . 89 75.5 89.5 189 . . .150 . . . . . . . . . . . . 80 70.0 86.5 158 . . .100 . . . . . . . . . . . . 56 54.0 79.0 105 . . .80 . . . . . . . . . . . . 47 47.7 75.7 . . . . . .70 . . . . . . . . . . . . 34 38.5 71.5 . . . . . .

(a) Load, 3000 kgf; diam, 10 mm (0.4 in.)

Rockwell

Table 2 Typical Brinell hardness ranges of gears after through hardening

Material

Annealed; normalized

and annealedNormalized

and tempered

Maximum Brinellhardness, quench

and tempered Material

Annealed; normalized

and annealedNormalized

and tempered

Maximum Brinellhardness, quench

and tempered

4130 155–200 170–215 350 4145 195–240 285–330 4508630 155–200 170–215 350 4150 195–240 285–330 4504140 185–230 260–300 425 4340 210–255 300–340 4804142 185–230 260–300 425 HP 9-4-30 200–240 (a) 5208640 185–230 260–300 425 Maraging steel 200–240 (a) 485

(a) Process generally is not used with these types of materials.

Brinell hardness (HB) Brinell hardness (HB)

1650 °F) and then furnace cooled to a pre-scribed temperature, generally below 315 °C(600 °F). Typical hardnesses obtained after fullannealing gears of different materials are shownin Table 2.

Normalizing and Annealing. In general,the term normalizing refers to the heating of steelto approximately 38 °C (100 °F) above the up-per critical temperature, followed by cooling in still air. The normalizing and annealing process is used, either singularly or in a combination, as a grain structure homogenizing for alloy steel gears. The process also is used to reducemetallurgical nonuniformity such as segregatedalloy microstructures from previous mechanicalworking. A hypoeutectoid steel consisting of astructure of ferrite and coarse pearlite may bemade easier to machine if the ferrite and cemen-tite are more finely distributed. A very soft steelhas a tendency to tear in machining; therefore,

some increase in hardening obtained by normal-izing leads to a more brittle chip and thus im-proves machinability. Some through-hardenedgears may just require hardness obtained withnormalizing and annealing.

Normalizing and Tempering. Normaliz-ing consists of heating gears to 870 to 980 °C(1600 to 1800 °F) and then furnace cooling instill or circulated air. This process results inhigher hardness than annealing, with hardnessbeing a function of the grade of steel and geartooth size. However, normalizing does not in-crease hardness significantly more than anneal-ing does, regardless of tooth size for plain carbonsteels containing up to 0.4% carbon (but it defi-nitely helps to ensure homogeneous microstruc-ture of steels). After normalizing, alloy steelgears are tempered at 540 to 680 °C (1000 to1250 °F) for uniform hardness and dimensionalstability.

Chapter 8: Through Hardening / 157

Quench and Temper. The quench and tem-per process involves heating the gears to formaustenite at 800 to 900 °C (1475 to 1650 °F), fol-lowed by quenching in a suitable media such asoil. The rapid cooling causes the gears to becomeharder and stronger by the formation of marten-site. Hardened gears then are tempered at a tem-perature, generally below 690 °C (1275 °F), toachieve the desired mechanical properties.

Tempering lowers both the hardness andstrength of quenched steels but improves materi-als properties such as ductility, toughness, andimpact resistance. The tempering temperaturemust be carefully selected based on the specifiedhardness range, the quenched hardness of thepart, and the material. Normally, the optimumtempering temperature is the highest tempera-ture possible while maintaining the specifiedhardness range. It is to be remembered that hard-ness after tempering varies inversely with thetempering temperature used. After tempering,parts usually are air cooled at room temperature.

Some steels can become brittle and unsuit-able for service if tempered in the temperaturerange of 430 to 650 °C (800 to 1200 °F). Thisphenomenon is called temper brittleness andgenerally is considered to be caused by segrega-tion of alloying elements or precipitation ofcompounds at ferrite and austenite grain bound-aries. If the gear materials under considerationmust be tempered in this range, investigation todetermine their susceptibility to temper brittle-ness is needed. Molybdenum content of 0.25 to0.50% has been shown to eliminate temper brit-tleness in most steels. (Note: Temper brittlenessshould not be confused with the temperingembrittlement phenomenon that sometimes re-sults from tempering at a lower temperaturerange, such as 260 to 320 °C, or 500 to 600 °F.)

The major factors of the quench and temperprocess that influence hardness and materialstrength are:

• Material chemistry and hardenability• Quench severity• Section size• Time at temper temperature

Of the four commonly used through-harden-ing processes, the quench and temper method isthe most commonly used. This is particularlytrue when:

• The hardness and mechanical propertiesrequired for a given application cannot beachieved by any of the other three processes.

• It is necessary to develop mechanical prop-erties (core properties) in gears that will notbe altered by any subsequent heat treatmentsuch as nitriding or induction hardening.

Typical hardness ranges achieved for differentmaterials after through hardening by differentprocesses are listed in Table 2.

Through-Hardened Gear Design

After finalizing a design, a gear designerneeds to specify the following information on athrough-hardened gear drawing. This informa-tion will help to minimize confusion for allinvolved with gear manufacturing and materialprocurement:

• Grade of steel with Aerospace MaterialSpecification (AMS), if applicable

• AMS specification for material cleanliness,if required

• Hardnesses on tooth surface and at the core• AGMA gear quality level

Each hardness callout should have at least a rangeof 4 points in HRC scale or 40 points in Brinellhardness (HB). Also, specify a tempering tem-perature range on the drawing. This allows gearmanufacturing engineers to select a particulartempering temperature for a specified hardness.

Hardness Measurement

The hardness of through-hardened gears gen-erally is measured either on the gear tooth endface or rim section. This is the hardness that isused for gear rating purposes. Sometimes,achieving specified hardness on the tooth endface may not necessarily assure the desired hard-ness at the roots of teeth because of the grade ofsteel, tooth size, and heat treat practice. If geartooth root hardness is critical to a design, then itshould be specified and measured on a sample(coupon) processed with the gears. However,needless increase of material cost by selecting ahigher grade of steel should be avoided.

Distortion of Through-Hardened Gears

All steel gears experience distortion during a heat treat process. It is a physical phenome-non and cannot be eliminated from any heat treat operation, although distortion of through-


Table 3 Distortion ratings of through-hardened gears

MaterialAMS

specificationAMS

quality Hardness (HRC)Distortion

rating

AISI 4340 6414 2300 48/50 Good(a)Maraging 250 6520 2300 49/52 Predictable and good(a)Maraging 300 6521/6514 2300 52/56 Predictable and good(a)AISI 4140 6382 2300 48/50 Good(a)

(a) Within one AGMA class of gear quality.

hardened gears is not as severe as in otherprocesses such as carburizing and nitriding.Still, through-hardened gears, particularlyquench and tempered class, experience enoughdistortion that will eventually lower the qualitylevel of gears after heat treatment. This necessi-tates a finishing operation for higher quality. Ingeneral, some materials expand after a through-hardening operation while others contract. Thisrequires a suitable stock allowance to be pro-vided on teeth for finish machining before heattreatment of gears that are likely to distort. Theallowance needs to include expansion or con-traction of material and also distortion of toothgeometry. For materials with predictable anduniform distortion, gears could be cut to includethe distortion so that no finishing operation isrequired, possibly up to AGMA class 10 geartooth quality. The majority of steels listed inTable 2 expand during the through-hardeningprocess, whereas a few materials, such as marag-ing steel, are found to contract. The amount ofexpansion or contraction depends on alloy con-tent, quality of steel, and configuration of gears.In this regard, knowledge of distortion charac-teristics is helpful in optimizing the manufactur-ing process of gears. When gears are made froma material without any previous heat treat distor-tion data, an experimental investigation is bene-ficial to establish the distortion characteristics ofthe material. With such data, cost-effective man-ufacturing methods can be established. Aninvestigation of this nature carried out by anaerospace company to determine the heat treatdistortion characteristics of a through-hardenedgear rack for an aerospace application is dis-cussed at the end of this chapter. Table 3 shows acomparative distortion rating of some preferredthrough-hardening materials for gears.

Applications

Of the four different through-hardeningprocesses described, those gears hardened byquenching and tempering have some limited use

in power transmission applications. The otherthree processes are only employed to eitherimprove machinability or to enhance homoge-neous grain structure of the gear steel. Use ofthrough-hardened gears is limited because of thelow surface hardness that results in low gear pit-ting life and low power density gearbox com-pared with the one made with case-hardenedgears. Also, for similar torque capacity, through-hardened gears are larger with higher pitch linevelocity. This increases dynamic problems sub-stantially in a gearbox. However, in a bendingstrength limited design, through-hardened gearssometimes are successfully used, particularly forlarge gears (over 508 mm, or 20 in., outer diam-eter) that normally exhibit high distortion if acase hardening process is used. An example forsuch an application is the internal ring gear of anepicyclic gearbox. These gears are usually de-signed with hardness in the range of 32 to 34 HRC that can be finish cut after hardening,thus eliminating costly finishing operations.Through-hardened gears also are found to be ef-fective in applications susceptible to gear scuff-ing. It is claimed that profile conformance ofthrough-hardened gears, because of their lowsurface hardness, reduces sliding friction andthereby helps to increase scuffing resistance.

Overall, through-hardened gears are used ingearboxes that require large gears that cannot beeconomically case hardened, such as large ma-rine propulsion gears and railway power trans-mission gears.

Case History: Design and Manufacture of a Rack

As explained in the section “Distortion ofThrough-Hardened Gears,” all steel gears dis-tort after any type of heat treat process. Carbur-izing imparts the highest distortion, whilethrough hardening imparts the least distortion.Even then, distorted gears require a finishingoperation for higher tooth quality. Sometimes,


Fig. 1 Rack dimensions (given in inches) for preliminary tests. DP, diametral pitch; PA, pressure angle

Table 4 Chemical compositions of steels considered for racksMaterial C Mn Si P S Ni Cr Mo V Co W Cu

Quench-hardening steels

AISI 4340 . . . 0.60/0.80 0.20/0.35 . . . . . . 1.65/2.00 0.70/0.90 0.20/0.30 . . . . . . . . . . . .HP 9-4-30 0.30 0.20 0.01 0.005 0.0007 7.50 1.00 1.00 0.08 4.0H-11 0.35 . . . . . . . . . . . . . . . 5.00 2.50 0.40 . . . . . . . . .300M 0.42 0.68 1.61 0.005 0.006 1.77 0.85 0.40 0.09 . . . . . . . . .

Precipitation-hardening steels

17-4 PH . . . . . . . . . . . . . . . 4.00 16.50 . . . . . . . . . . . . 4.0013-8 Mo . . . . . . . . . . . . . . . 8.00 12.80 2.30 . . . . . . . . . . . .

Age-hardening steels

Maraging C-250

0.026 0.10 0.11 . . . . . . 18.5 . . . 4.30 . . . 7.0 . . . . . .

for through-hardened gears, the knowledge ofdistortion characteristics may be included in thedesign of gear cutting tools such that gears afterheat treatment meet the desired quality. Such acase history is presented here.

The project was to develop a low-cost, high-bending strength (minimum of 250 ksi, or1720 MPa, ultimate tensile strength) corrosion-resistant rack. For this application, the qualityrequired was rack teeth of AGMA class 9. Tominimize manufacturing cost, it was decidednot to consider any post-heat-treat finishingoperation. To meet these criteria, selection of aproper material and a process was vital, forwhich the following investigation was carried

out. The dimensions and configuration of therack are shown in Fig. 1.

Material SelectionTable 4 lists the chemical compositions of

various materials considered in this case his-tory. The positive and negative attributes ofeach and the associated heat treat process con-sidered before rack material selection aredescribed subsequently.

Option 1: Use of Quench-HardeningSteels. The following steels were considered:

• AISI 4340• 300M


• HP 9-4-30• H-11

An excellent survey was made from publishedliterature to determine the various properties ofeach, with the following results and conclusion:

Results. High heat treat distortion:

• Grinding of rack is necessary after heattreatment to attain the required accuracy ofteeth

• High cost of material• Poor corrosion resistance; additional

process needed to make racks corrosionresistant

Conclusion. None of these materials wasfound suitable for the application.

Option 2: Use of Precipitation HardeningSteels. Steels considered:

• 17-4 PH• 13-8 Mo

Results were as follows:

• Attainable mechanical properties were not atspecified strength level

• Heat treat distortion was not predictable• Sensitive to grind burns• Problems with alloy segregation for any

post-heat treat finishing, in section sizeneeded

Conclusion. Materials were not suitable.Option 3: Use of an Age-Hardening Steel

(Maraging C-250). This maraging steel hashigh nickel (18% or more), very low carbon(under 0.03%), and is capable of developingvery high tensile and yield strengths by meansof an aging process. It is sold in the martensiticstate, which, because of the low carbon, is softenough to be readily machinable. Heating toapproximately 480 °C (900 °F) for aging, andcooling in the furnace, causes a change in mate-rial microstructure that increases the hardnessup to 52 HRC. This meets the required tensilestrength.

Results were as follows:

• Published literature indicated distortion ofmaraging C-250 steel is predictable.

• The material is available as forged, as wellas in bar form, to AMS 6412. Sheet or platestock available to AMS 6420 was notacceptable due to nonuniform distribution ofmechanical properties.Conclusion. Maraging C-250 forgings met

the design requirements and were selected forthis application.

Process SelectionHeat Treat Distortion of Racks Made of

C-250. Although published literature indicateddistortion of maraging C-250 material is pre-dictable, it was still necessary to find out howmuch the distortion would be for a rack toothused in this application. To determine thesecharacteristics, a preliminary investigation wasundertaken with racks made from readily avail-able C-250 of shorter lengths (305 mm, or 12in., long); longer lengths were not commerciallyavailable at the time of this investigation. Toexpedite the program further, a standard shapercutter was used to cut the teeth. The racks werethen heat treated.

Heat Treatment of Racks. Some prelimi-nary experiments were conducted to select asuitable heat treat furnace. The following fur-naces were considered:

• Partial vacuum furnace• Full vacuum furnace• Air furnace

Heat treatment in the air furnace was not accept-able due to:

• Oxidation of racks• Scale removal resulted in size change

Both full and partial vacuum furnaces producedoxidation-free racks.

Conclusion. Full vacuum furnace thatensures oxidation-free parts was selected todetermine heat distortion.

Twelve racks were selected for heat treat-ment. All critical dimensions of the racks wereinspected and recorded before heat treatment.

The heat treat procedure consisted of thefollowing steps:

• Vapor degrease racks• Wipe racks with a cleaning chemical such as

acetone• Select any two racks• Hold the racks together back to back with

nickel-plated bolts—processed horizontallyon a flat base in the furnace

• Heat treat racks along with one tensile testbar in each production lot, at 480 ± 6 °C (900± 10 °F) for 4.5 h at this temperature

• Furnace cool racks

Inspection consisted of:

• Critical rack dimensions after heat treatment• Mechanical properties of material such as

hardness and tensile strength


Fig. 2 Modified shaper cutter dimensions

Results. From the experimental results andinspection, the following conclusions weremade:

• Contraction rate of maraging steel wasbetween 0.0005 and 0.0007 mm/mm(in./in.) and found to be linear and consistentin each lot

• Parts remained flat after the hardeningprocess

• Pitch and accumulative pitch errors werewithin acceptable limit

• Teeth perpendicularity (lead errors) werebetween 0.013 and 0.025 mm (0.0005 and0.001 in.)

• Pitch dimensions measured over a pin wereheld to 0.038 to 0.076 mm (0.0015 to 0.003in.)

Recommendations included:

• Design of rack to include 0.076 mm (0.003in.) tolerance for pitch dimension over thepin

• Tooth perpendicularity (lead) error to 0.025mm (0.001 in.)

• A shaper cutter to be developed to include0.0006 mm/mm (in./in.) contraction rate ofrack tooth geometry with the expectationthat this might eliminate finish processing ofracks after heat treatment

New Shaper Cutter. With the proposedcontraction rate, a shaper cutter was designedand manufactured by a cutter manufacturingcompany. Figure 2 shows the dimensions of this

special cutter. An investigation was then carriedout with full-length racks.

Manufacturing method for full-lengthracks consisted of the following steps:

• Forge blanks• Solution anneal to 35 HRC• Machine (mill and drill), leaving ground

stock on sliding surfaces only• Shape rack teeth to final dimensions—

rough, semifinish, and finish• Straighten to 0.16 mm/m (0.002 in./ft)• Inspect• Heat treat (age) to 50 HRC—two pieces

bolted back to back• Clean• Grind sliding surfaces locating from the

pitch line of rack teeth• Inspect all rack dimensions before and after

heat treatment

Test results are shown in Tables 5 and 6.Analysis of the results indicates:

• Part remained flat after heat treatment within0.25 mm (0.010 in.)

• Pitch and accumulative pitch errors werewithin the specified tolerance

• Tooth perpendicularity (lead) error waswithin 0.025 mm (0.001 in.)

• Measurements of pitch line over the pinwere within the new tolerance

Conclusions. Racks met the required qualitylevel (AGMA class 9). In this case, the modifiedcutter and superior heat treat facilities made it


Table 5 Experimental results: full-sized racks dimensions before heat treatRack 1

Item Drawing dimension Left flank Right flank Left flank Right flank

Linear pitch, mm (in.) 9.9746 (0.3927) 9.9720–10(0.3927–0.3936)

9.977–9.9949(0.3936–0.3927)

9.9771–9.9949(0.3928–0.3935)

9.9771–9.9924(0.3928–0.3934)

Spacing error, mm (in.) 0.0330 (0.0013) max 0.0178 (0.0007) max 0.0229 (0.0009) max 0.0203 (0.0008) max 0.0178 (0.0007) maxAccumulated spacing

error, mm (in.)0.0762 (0.003) max,

over any 12 teeth0.1778 (0.007) max 0.1778 (0.007) max 0.0152 (0.006) max 0.0152 (0.006) max

Tooth perpendicularity(lead error), mm (in.)

0.0127 (0.0005) max 0–0.0533 (0–0.0021) 0–0.0533 (0–0.0021) 0–0.0406 (0–0.0016) 0–0.0406 (0–0.0016)

Dimension over pin, mm (in.)

20.1193–20.1574(0.7921–0.7936)

20.2946–20.7518(0.799–0.817)

20.2946–20.7518(0.799–0.817)

20.2692–20.5994(0.798–0.811)

20.2692–20.5994(0.798–0.811)

Surface finish, rms 63 �45 �45 �45 �45

rms, root mean square

Rack 2

Table 6 Experimental results: full-sized racks dimensions after heat treat and grinding back faceRack 1

Item Drawing dimension Left flank Right flank Left flank Right flank

Linear pitch, mm (in.) 9.9746 (0.3927) 9.9670–9.9873(0.3924–0.3932)

9.9720–9.990(0.3926–0.3933)

9.9593–9.9873(0.3921–0.3932)

9.9670–9.9924(0.3924–0.3934)

Spacing error, mm (in.) 0.0330 (0.0013) max 0.0152 (0.0006) max 0.0152 (0.0006) max 0.0152 (0.0006) max 0.0178 (0.0007) maxAccumulated spacing

error, mm (in.)0.0762 (0.003) max,

over any 12 teeth0.1778 (0.007) max 0.1778 (0.007) max 0.1143 (0.0045) max 0.1143 (0.0045) max

Tooth perpendicularity(lead error), mm (in.)

0.0127 (0.0005) max 0–0.0533 (0–0.0021) 0–0.0533 (0–0.0021) 0.0025–0.0279(0.0001–0.0011)

0.0025–0.0279(0.0001–0.0011)

Dimension over pin, mm(in.)

20.1193–20.1574(0.7921–0.7936)

20.1016–20.1422(0.7914–0.7930)

20.1016–20.1422(0.7914–0.7930)

20.1270–20.1955(0.7924–0.7951)

20.1270–20.1955(0.7924–0.7951)

Surface finish, rms 63 �45 �45 �45 �45

rms: root mean square

Rack 2

possible to manufacture the racks to AGMAclass 9 without any subsequent finishing opera-tion such as grinding.

Experiments of this nature are definitely use-ful in determining the distortion of heat treatedgears and planning for subsequent finishingoperation, if needed. When the quantity of gearsto be produced is limited, and the allocated pro-duction development time is short, there maynot be many choices other than to finish the gearafter heat treatment. For low distortion, honingis useful, while grinding is necessary for largedistortion. However, grinding after throughhardening is not recommended. Some manufac-turers, instead of honing a gear and the matingpinion individually, lap the gear and piniontogether with a slurry of fine abrasive com-pound in the mesh until the desired quality isobtained.

In general, gears designed and manufacturedto AGMA class 7 and below do not require anysuch process development due to the fact thatthe hobbing or shaping process can producegears to AGMA class 8 and above. It is expectedthat gears so produced will meet AGMA class 7after heat treatment.

ACKNOWLEDGMENT

This chapter was adapted from A.K. Rakhit,Through-Hardening Gears, Heat Treatment ofGears: A Practical Guide for Engineers, ASMInternational, 2000, p 21–32

SELECTED REFERENCES

• C.E. Bates, G.E. Totten, and R.L. Brennan,Quenching of Steel, Heat Treating, Vol 4,ASM Handbook, ASM International, 1991, p67–120

• B.L. Bramfitt and A.K. Hingwe, Annealingof Steel, Heat Treating, Vol 4, ASM Hand-book, ASM International, 1991, p 42–55

• T. Ruglic, Normalizing of Steel, Heat Treat-ing, Vol 4, ASM Handbook, ASM Interna-tional, 1991, p 35–41

• M. Schmidt and K. Rohrbach, Heat Treatingof Maraging Steels, Heat Treating, Vol 4,ASM Handbook, ASM International, 1991, p219–228

• M. Wisti and M. Hingwe, Tempering ofSteel, Heat Treating, Vol 4, ASM Hand-book, ASM International, 1991, p 121–136

CHAPTER 9

Carburizing

CARBURIZING is a process in whichaustenitized ferrous metal is brought into con-tact with an environment of sufficient carbonpotential to cause absorption of carbon at thesurface and, by diffusion, create a carbon con-centration gradient between the surface andinterior of the metal. The depth of penetration ofcarbon is dependent on temperature, time attemperature, and the composition of the carbur-izing agent. As a rough approximation, a car-burized depth of approximately 0.76 to 1.3 mm(0.030 to 0.050 in.) on a 6 diametral pitch (DP)gear tooth can be obtained in about 4 h at 930 °C(1700 °F) with a carburizing agent, which maybe solid, liquid, or gas.

The primary objective of carburizing andhardening gears is to secure a hard case and arelatively soft but tough core. For this process,low-carbon steels (up to a maximum of approx-imately 0.30% carbon), either with or withoutalloying elements (nickel, chromium, man-ganese, molybdenum), normally are used. Aftercase carburizing, the gear teeth will have highcarbon at the surface graduating into the low-carbon core.

Sometimes to prevent through hardening ofthe tooth tip, carbon penetration through tip oftooth needs to be controlled. This is accom-plished by plating or spraying the outside diam-eter of gear before cutting the teeth with somematerial that prevents the passage of the carbur-izing agent. However, the most widely usedmethod is copper plating. Several proprietarysolutions and pastes, which are quite effective inpreventing carburization, also are available.

There are five general methods of carburiz-ing, depending on the form of the carburizingmedium. These methods are:

• Solid or pack carburizing, employing solidcarburizing material

• Liquid carburizing, employing fused bathsof carburizing salts

• Gas or atmosphere carburizing, employingsuitable hydrocarbon gases

• Vacuum carburizing, employing a roughvacuum and a partial pressure of hydrocar-bon gas

• Plasma or ion carburizing, employing bothvacuum and glow-discharge technology(carbon-bearing ions are introduced to thesurface for subsequent diffusion below thesurface)

Today, gas (atmosphere) carburizing is consid-ered the de facto standard by which all othersurface hardening techniques are measured andwill be the emphasis of this chapter. However,more recently introduced carburizing methodssuch as vacuum carburizing are rapidly gainingacceptance in the gear industry. The final sec-tion of this chapter reviews vacuum carburizingand compares the attributes of conventional gascarburizing and vacuum carburizing. Figure 1compares the use (market breakdown) of vari-ous carburizing methods.

Gas Carburizing: Processing and Equipment

As shown in Fig. 1(a), it is estimated that90% of gear carburizing is performed in a car-bonaceous gas atmosphere. In this type of car-burizing, carbon is induced into the ferrous basematerial heated in the gaseous atmosphere witha carbon potential that allows the surface toabsorb carbon. The most commonly usedmedium is endothermic (commonly known as“endo”) gas produced by reacting natural gas(mainly methane, CH4) with air (1:2.5 to 2.7




Fig. 2 Depth of carbon penetration for different times and dif-ferent temperatures in gas carburizing a gear steel

Fig. 1 North American carburizing market. (a) Market in2000. (b) Anticipated market in 2010. Source: Ref 1

ratio) over a heated catalyst. The importantchemical reactions that take place can beexpressed as:

(Eq 1)

(Eq 2)

Varying the ratio of methane to air alters thecomposition of endo and the chemical reactionsslightly.

Free carbon resulting from chemical reactionis then dissolved in the austenite that is formedwhen gears are heated above 720 °C (1330 °F)and precipitates as iron carbide (Fe3C).

2COSC � CO2

2CH4 � O2S 2CO � 4H2

Recently, nitrogen-methanol has been usedfor supplying the carburizing atmosphere. Thistype of system offers a number of benefits overthe conventional endo gas generator. Here, N2plays the most important function to keep air outof the furnace and prevents the gears from beingoxidized. Typically, N2 is more than 90% of thenitrogen-methanol atmosphere. Carburizing innitrogen-methanol systems also ensures accu-rate carbon potential for improved carburizedcase properties. Because of higher cost withnitrogen methanol system, most of the gears arestill carburized in endo gas.

Carburizing TemperatureThe penetration of carbon into the steel

depends on the carburizing temperature, thetime at temperature, and the carburizing agent.Since the solubility of carbon is greatest abovethe Ac3 temperature, carburization takes placemost readily above this temperature. Further-more, the higher the temperature is, the greaterthe rate of carbon penetration will be, since therate of diffusion is greater. It is thus customaryto select a temperature approximately 55 °C(100 °F) above the Ac3 point. Again, the time atthe carburizing temperature is the most influen-tial factor in the control of the depth of carbonpenetration as illustrated in Fig. 2.

Temperatures as low as 790 °C (1450 °F) andas high as 985 °C (1800 °F) have been used forcarburizing gears, although it should be kept inmind that the life of a furnace deteriorates rap-idly above 955 °C (1750 °F). With the desiredamount of carbon absorbed into the tooth sur-

Chapter 9: Carburizing / 165

face, gears are quenched in a suitable medium(generally oil) to obtain the required case hard-ness. Quenching may be performed eitherdirectly from the carburizing temperature orfrom a somewhat lower temperature. In someinstances, parts after carburizing are completelycooled to room temperature, reheated to theaustenitizing temperatures, and then quenched.As already mentioned, the depth of case isdependent on time and temperature selectedduring carburizing. The following equationgenerally satisfies the relationship between thecase depth and carburizing time:

(Eq 3)

where d is the total case depth in inches, t is thecarburizing time in hours at temperature withsaturated austenite at the surface, and ϕ is theproportionality factor of material that varieswith the carburizing temperature.

For low carbon and alloy steels, the value ofϕ is found to be approximately 0.025 for gascarburizing at approximately 930 °C (1700 °F).Thus, Eq 3 can be rewritten for most alloy steelsas:

(Eq 4)

Another relationship used to determine d is:

(Eq 5)

where T is the carburizing temperature in °F.Both Eq (4) and (5) are used in industry and pro-vide satisfactory results.

Besides time and temperature, the quality ofcase also depends on the type of carburizing fur-nace and equipment used. A proper selection isthus essential for successful carburizing andhardening.

Furnaces and Equipment for Gas Carburizing

There are three basic types of furnaces usedfor gas carburizing: atmospheric, vacuum, andfluidized bed. Each of these has its own advan-tages and disadvantages, although a great major-ity of gears are gas carburized in atmosphericfurnaces because gas carburizing seems to offeracceptable control of case depth, surface carbon

d �31.62t

10 a 6700T � 460

b

d � 0.0252t p

d � �2t p

content, and diffusion of carbon into steel. Thegas mixture may be adjusted to provide either acarburizing or neutral atmosphere, making itpossible to diffuse the carbon in the case withoutthe further addition of surface carbon.

Atmospheric Furnaces. Two types ofatmospheric furnaces are used: batch and con-tinuous. The fundamental difference betweenthese, aside from size, is the method by whichthe work is handled. With a batch furnace, as thename implies, the workload is charged and dis-charged as a single unit or batch. With continu-ous furnaces, the load is fed on a continuousbasis at the charged end and is received at thedischarge end after processing. In a batch fur-nace, changes in composition of carburizingagent take place in both environment and work-pieces until equilibrium is reached. In continu-ous furnaces, the heating chamber is dividedinto zones. These zones may be separated byinternal doors. The atmospheres in each zonecan be controlled to different carbon potentials.Coupled with different temperatures in eachzone, atmosphere control provides the mainmeans of controlling the carburizing and diffu-sion portion of the carburizing cycle. The chiefadvantage of a batch furnace is its adaptabilityto a variety of cycles. Each batch usually con-sists of several individual gears. Very largegears may be carburized one at a time; smallgears may be loaded several hundred to a batch.One of the major disadvantages of this furnaceis that gears are transferred from ambient tem-perature into a furnace usually operating at thecarburizing temperature, causing thermal shockthat may lead to uncontrolled distortion.

Vacuum and Fluidized Bed Furnaces.Besides atmospheric-type furnaces, carburizingalso may be performed in vacuum furnaces orfluidized bed furnaces. In general, heat transfercharacteristics of these furnaces are superior toatmospheric-type furnaces, assuring better caseproperties and uniformity of case. But the oper-ating cost of these furnaces is higher thanatmospheric furnaces. Hence, such furnaceshave more limited use.

Carburizing in a vacuum furnace is a rela-tively new process. Any carburizing done in anatmospheric furnace also can be accomplishedin a vacuum furnace. However, vacuum carbur-izing offers some significant benefits in time,cost, and quality. A major reduction of time is inthe heating-up phase of the process, where the


parts are loaded into a cold furnace; parts andfurnace are then heated up together. Further-more, the process allows a stepped heat-upmode, which has also been found beneficial. Asopposed to conventional carburizing in atmo-spheric furnaces, where the carburizing mediumis adjusted to generate a near eutectoid surfacecomposition, vacuum carburizing is based on asupersaturated carbon reaction.

Selecting the most suitable alloy for vacuumcarburizing is very important for its success.Correct quench rates, commensurate with thealloy selection, offer a less drastic quench modefor fully hardened case and core, which atmo-spheric carburizing and quenching does notallow. This also results in reduced distortion ofparts. The major advantage of vacuum carburiz-ing is that it offers better control of case deptheven at the root fillet of the gear tooth.

Carburizing in a fluidized bed furnace is verysimilar to vacuum carburizing, in that supersat-uration through direct reaction with the carbur-izing media (natural gas, methane or propane)can take place at the face to control the surfacecarbon level, together with the controlled casedepth.

Quenching and Hardening

After carburizing, gears are quenched in acooling medium for hardening. Quenchingdevelops a martensitic or a bainitic case withcore microstructures other than a mixture ofproeutectoid ferrite and pearlite. Thus, theselection of a proper quenchant is of utmostimportance, and the cooling rate, ideally, shouldbe just fast enough to produce the desired corestructure but not so fast that the case cracks orthat an undue amount of austenite is retained.For industrial and automotive gears, however,quenching conditions often are chosen solely onthe basis of developing required surface hard-ness, especially in applications where the coreproperties are known to have little or no effecton product performance.

Depending on part size and shape, and ontransformation characteristics of the steel, gearsmay be quenched in water, oil, or any propri-etary fluids. Most often oil is used because it isa suitable quenchant for most carburizinggrades of steel, especially for relatively fine-pitch gears. Small DP gears may require a moredrastic quench, particularly if densely packed,and often are susceptible to quench cracks.

Regardless of the type of quenchant used, goodcirculation within the quench bath is extremelyimportant to promote uniform cooling of gears.

Sometimes, for some materials, the desiredproperties of the case can be developed withoutresorting to a liquid quench, in which case aircooling, furnace cooling, or gas cooling may beappropriate. Any of these three cooling mediacan be used when parts are to be reheated forhardening. If intermediate operations such asstraightening or machining are needed prior tohardening, furnace or gas cooling is preferred.Both are done under a protective atmospherethat keeps the gears clean and free of oxide scaleand prevents decarburization of the surface.

Direct QuenchingMost gas-carburized gears are quenched

directly after carburizing. Furnace temperatureusually is reduced to normal austenitizing tem-perature (approximately 790 °C, or 1450 °F)prior to quenching. In certain cases, quenchingdirectly from the carburizing temperature also isacceptable provided this does not induce ther-mal cracks in gears. On the other hand, some-times gears made of some high-alloy steels(alloy content above 5%), are first cooled in airto room temperature after carburizing and thenreheated and quenched for low distortion.

Nevertheless, direct quenching has gainedwider acceptance, primarily because of econ-omy and simplicity of the procedure. To mini-mize carbide network in the case, carburizingabove the Acm temperature is suggested. Directquenching reduces the amount of energy usedfor heating and eliminates or avoids some of theequipment and operating expense of the harden-ing operation. Labor costs are reduced, and nicksand other part damage are minimized becausethe parts are handled less frequently. The use offine-grain (ASTM 5 and above) steels, whichexhibit a relatively uniform response to heattreatment, and the development of equipmentand techniques for improved confidence in car-bon control have led to wider acceptance ofdirect quenching as a means of hardening car-burized gears made from a great variety of steels.

The fixtures required for adequately support-ing and separating individual gears during car-burizing also promote uniform direction andvelocity of the quenchant movement relative toeach part on the fixture. This leads to more con-sistent metallurgical and dimensional quality.Furthermore, a single direct-quench operationminimizes distortion by bringing about crystal-


lographic phase changes during only one heatingand one cooling cycle. Each such phase changeresults in volume change of grain microstructureand increase in internal stress that may producesubstantial dimensional change of a gear.

Both horizontal-batch and pusher-type con-tinuous furnaces are well suited for directquenching. Continuous furnaces sometimes aredesigned to remove one part at a time from the reduced-temperature section of the furnacefor press quenching with a fixture to controldistortion.

The degree of distortion in some gears, forexample, varies with case depth and the amountof retained austenite in the case, as well as withalloy and process variables. Good control ofcarbon-gradient shape, case depth, and surfacecarbon content are essential for direct quench-ing of dimensionally sensitive gears. In case thetemperature of gears is reduced prior to quench-ing to minimize thermal shock, carbon contentnear the surface must be held to below satura-tion; otherwise, carbides will precipitate. Agrain-boundary network of carbides in the caseis usually considered to be detrimental to gearlife, although slow cooling after carburizing andthen reheating before quench is one way toavoid or minimize the development of a carbidenetwork.

In the case of severe quench sometimesrequired to obtain high core hardness, the shapeof the gear section being quenched is of greatimportance since a combination of thick andthin sections (for example, annulus of epicyclicgearbox) may lead to cracking. Cracking resultsdue to a difference in the rate of cooling of thickand thin sections. The transformation of thickersections will take place when the thin sectionsare at a lower temperature. The expansion in thethick sections on transformation will set up veryhigh stress concentrations, which may causewarpage or cracking. If proper core hardnesscannot be achieved for a certain gear tooth size,an alternate material needs to be investigated.

Reheating of Carburized Gears and Quenching

Originally, only high-alloy steels were car-burized, because of the relatively unsophisti-cated steel-producing techniques required foralloy additions to yield a steel with uniformresponse to heat treatment. At that time, carbur-izing was done only by pack carburizing, whichhas a different set of material-handling and car-bon-control techniques than does gas carburiz-

ing. The original carburizing grade steels, whichwere high in nickel, required a reheat operationafter pack carburizing to produce a uniformmicrostructure in the case. Reheating was alsothe only effective method of reducing the surfacecarbon content below saturation. Later, althoughlow-alloy steels were introduced for gears, packcarburizing or crude gas-carburizing techniquesstill required gear reheating to control surfacecarbon and microstructure. Today, the moderncarburizing equipment is capable of producingthe desired microstructure in the case of bothhigh- and low-alloy steels. Even then, certaintypes of gear steels are still reheated beforequenching to ensure the quality of case micro-structure and low distortion.

Gears requiring individual quenching in a fix-ture sometimes are reheated as a practical meansof confining the tedious one-at-a-time hardeningoperation to a few simple hardening furnaces,while a larger, more-expensive continuous car-burizing furnace is permitted to operate at itsmaximum capacity for direct quench. Some-times, the total cost including labor and fuel canbe lower for a carburize, cool, and reheat proce-dure than for direct quenching. Also, this tech-nique of carburizing, followed by slow cooling,machining certain areas to remove the case, andthen hardening the entire gear sometimes is usedwhen selected areas must be free of a carburizedhardened case.

Furthermore, reheating of gears occasionallyis specified for “grain refinement.” However,there is considerable disagreement over theadvantage of a reheated microstructure over adirect-quenched microstructure, and whetherthe former is preferred because of tradition, orbecause of a real need, is unknown. The amountof retained austenite is usually lower, or at leastis less visible in microstructures of reheatedgears. Again, the effect of retained austenite ongear performance is controversial, but clearly itis not always detrimental. Also, if reheating isused, there is always the danger of greater ther-mal distortion. The choice between directquenching, and reheating and quenching shouldoften be decided on the basis of a specific appli-cation. Reheating generally is recommendedonly after high-temperature carburizing (above930 °C, or 1700 °F).

Surface Hardness Variations after Quenching

Variation in the surface hardness of gearswithin a lot is a problem that is often encoun-


Fig. 3 Variation of tooth surface hardness with tempering tem-perature of carburized and hardened AISI 8620H gears

Fig. 4 Influence of tempering temperature on core hardnessof some high alloy steels

tered when many small gears are heat treated inthe same basket. This variation is due to theparts being too densely loaded, especially at thecenter of the load. This restricts the flow ofquenchant in such a manner that gears near thebasket’s perimeter may attain full surface hard-ness while those in the center do not. If it is notpossible to space out the gears for economic rea-sons, at least divider screens should be insertedto “layer” the load.

Another possible cause of gear surface hard-ness variation in a lot is insufficient quench bathagitation. The obvious solution is to speed upthe circulation system of the quench tank inorder to move more quenchant through the loadfaster. Approximately 230 to 260 L/min (60 to70 gal/min) of gear is considered an ideal rate.This establishes the rate of cooling for idealmartensitic transformation of most gear steels.

Tempering of Carburized and Quenched Gears

Tempering is a process of reheating quench-hardened gears to a temperature below the trans-formation range of steel and holding at this tem-perature to reduce thermal stresses inducedduring quenching and improve dimensional sta-bility. Normal tempering temperature for car-burized and quenched gears varies between 115and 175 °C (240 and 350 °F). The surface hard-ness of quenched gears decreases as the temper-ing temperature increases as shown in Fig. 3. In

addition, tempering temperature has a signifi-cant effect on core hardness, as illustrated in Fig.4. Furthermore, higher tempering temperaturesreduce both case hardness and case depth. Inapplications where gears are required to main-tain high compressive and bending strengths atan elevated temperature, carburizing steels thatare least affected by tempering temperature arepreferred.

To enhance the effect of tempering, it shouldfollow soon after the quench but not until thegears can be comfortably touched with barehands. Tempering too early can cause seriousproblems by interrupting the martensitic trans-formation. To the other extreme, too long adelay before tempering might create a majordistortion problem and even cracking of thegears.

Tempering is a necessary finishing treatmentafter hardening. However, it also involves heat-ing and cooling. This may again generate newstresses in the gears being processed. Fortu-nately, the influence of these new stresses ongeometric shapes of gears is very small due tolow temperature levels involved. Nevertheless,uniform heating and cooling is advisable duringtempering to keep distortion-causing stresses ata minimum.

Some controversy still exists concerning thevalue of tempering carburized and quenchedgears. For critical applications, experience hasproved that tempering is definitely beneficial.Carburized and hardened gears used in aero-space applications invariably need to be tem-


pered. The reasoning is that tempering is notharmful and provides some benefit to resistcracking or chipping of gears under edge load-ing. However, in thousands of other less criticalapplications, it is difficult or sometimes impos-sible to prove the need of a tempering operationfor carburized and hardened gears.

Recarburizing

Occasionally after carburizing and harden-ing, gears in a certain lot are found to havelower surface carbon and case depth even whenall the furnace carburizing parameters are keptthe same. To salvage these under-carburizedgears by recarburizing sometimes creates anumber of potential problems. For example:

• Every time a gear is heated, there is moredistortion.

• If a hardened gear is charged into a hot fur-nace, it might crack.

• If the carburized case depth is shallow, car-burizing the second time will increase casecarbon content.

This also can result in excessive retained au-stenite or an undesirable carbide network. Thus,all scenarios are to be considered before recar-burizing gears.

Cold Treatment

The presence of retained austenite in a heattreated case can be the source of dimensionalinstability, excessive residual stress, or cracking,all of which may cause service problems with acarburized gear. Retained austenite is moreprominent at high surface carbon and alloy con-tents, and in cases where gears have been directquenched from high carburizing temperaturesrather than cooled, reheated, and quenched.High-carbon and high-alloy contents in steelsdepress the temperatures at which martensitictransformation begins and ends. In some in-stances, the transformation temperature may bewell below room temperature, which favors theretention of large amounts of austenite.

One way of reducing the amount of retainedaustenite in the case microstructure is to coldtreat a gear following quenching. Cold treatmentis basically a continuation of quenching, during

which retained austenite in the case is trans-formed to martensite. The percentage of trans-formation is related to temperature rather than totime at a temperature—lower temperatures yieldhigher levels of transformation. Multiple treat-ments produce diminishing improvement. Al-most all of the significant transformation isachieved by the first cold treatment.

The specific amount of martensitic transfor-mation achieved by a given subzero treatment isextremely difficult to predict. The degree ofreluctance to transform at a given temperature isinfluenced by:

• The amount of retained austenite at the startof cold treatment

• The elapsed time between quenching andcold treating

• Any intermediate thermal treatment, such astempering

• The general level of residual compressivestress in the part

• Any cold working of the material, such asstraightening of long slender pinions aftercarburizing and quenching

Temperatures in the range –75 to –100 °C (–100to –150 °F) are routinely used in cold treating.Equipment for cold treatment up to –75 °C(–100 °F) can be as simple as dry ice mixed withkerosene, trichloroethylene, or alcohol in abucket. Temperatures down to –100 °C (–150°F) is reached with relatively simple mechanicalrefrigeration. Liquid nitrogen can be used forchilling to any temperature down to –195 °C(–320 °F) but is seldom used.

Selection of Materials for Carburized Gears

There is a wide variety of carburizing gradematerials that offer different mechanical proper-ties (Table 1). Heat treat data for some of thesesteels are given in Table 2. In general, a materialthat can attain a tooth surface hardness around60 HRC and a core hardness between 32 and 48HRC after carburizing and hardening is se-lected. The choice determines the surface caseand core hardnesses. A low tooth surface hard-ness reduces the pitting life of gears. On theother hand, low core hardness reduces bendingfatigue life. As already discussed, the surface


Table 1 Chemical compositions of frequently used carburizing grade gear steels

Material C Mn P S Si Ni Cr Mo V W Co

AISI grades3310 0.08–0.13 0.45–0.60 0.025 max. 0.025 max. 0.20–0.35 3.25–3.75 1.40–1.75 . . . . . . . . . . . .3310H 0.07–0.13 0.30–0.70 0.035 max. 0.040 max. 0.20–0.35 3.20–3.80 1.30–1.80 . . . . . . . . . . . .4023 0.20–0.25 0.70–0.90 0.035 max. 0.040 max. . . . . . . . . . 0.20–0.30 . . . . . . . . .4027 0.25–0.30 0.70–0.90 0.035 max. 0.040 max. . . . . . . . . . 0.20–0.30 . . . . . . . . .4118 0.18–0.23 0.70–0.90 0.035 max. 0.040 max. 0.20–0.35 . . . 0.40–0.60 0.08–0.15 . . . . . . . . .4118H 0.17–0.23 0.60–1.00 0.035 max. 0.040 max. 0.20–0.35 . . . 0.30–0.70 0.08–0.15 . . . . . . . . .4140 0.38–0.43 0.75–1.00 0.035 max. 0.040 max. 0.20–0.35 . . . 0.80–1.10 0.15–0.25 . . . . . . . . .4320 0.17–0.22 0.45–0.64 0.035 max. 0.040 max. 0.20–0.35 1.65–2.00 0.40–0.60 0.20–0.30 . . . . . . . . .4330M 0.30–0.33 0.96 0.008 max. 0.006 0.30 1.82 0.88 0.44 0.09 . . . . . .4620 0.17–0.22 0.45–0.65 0.035 max. 0.040 max. 0.20–0.35 1.65–2.00 . . . 0.20–0.30 . . . . . . . . .4815 0.13–0.18 0.40–0.60 0.035 max. 0.040 max. 0.20–0.35 3.25–3.75 . . . 0.20–0.30 . . . . . . . . .4820 0.18–0.23 0.50–0.70 0.035 max. 0.040 max. 0.20–0.35 3.25–3.75 . . . 0.20–0.30 . . . . . . . . .8617 0.15–0.20 0.70–0.90 0.035 max. 0.040 max. 0.20–0.35 0.40–0.70 0.40–0.60 0.15–0.25 . . . . . . . . .8617H 0.14–0.20 0.60–0.95 0.035 max. 0.040 max. 0.20–0.35 0.35–0.75 0.35–0.65 0.15–0.25 . . . . . . . . .8620 0.18–0.23 0.70–0.90 0.035 max. 0.040 max. 0.20–0.35 0.40–0.70 0.40–0.60 0.15–0.25 . . . . . . . . .8620H 0.17–0.23 0.60–0.95 0.035 max. 0.040 max. 0.20–0.35 0.35–0.75 0.35–0.65 0.15–0.25 . . . . . . . . .8720 0.18–0.23 0.70–0.90 0.035 max. 0.040 max. 0.20–0.35 0.40–0.70 0.40–0.60 0.20–0.30 . . . . . . . . .8822H 0.19–0.25 0.70–1.05 0.035 max. 0.040 max. 0.20–0.35 0.35–0.75 0.35–0.65 0.30–0.40 . . . . . . . . .9310 0.08–0.13 0.45–0.65 0.025 max. 0.025 max. 0.20–0.35 3.00–3.50 1.00–1.40 0.08–0.15 . . . . . . . . .

Special quality gradesHP 9-4-30 0.30 0.20 0.005 0.007 0.01 7.50 1.00 1.00 0.08 . . . 4.0Pyrowear 0.10 0.37 . . . . . . . . . 2.15 1.05 3.30 0.12 . . . . . .17CrNiMo6 0.14–0.19 0.40–0.80 0.125 max. 0.005–0.020 0.15–0.35 1.40–1.70 1.50–1.80 0.25–0.35 0.06 max. . . . . . .VASCO X2M 0.15 0.30 0.15 max. 0.01 max. 0.90 . . . 5.0 1.40 0.45 . . . 1.35M50NiL 0.15 0.25 . . . . . . . . . 3.5 3.5 4.0 1.0 . . . . . .EX 30 0.13–0.18 0.70–0.90 0.04 0.04 0.20–0.35 0.70–1.00 0.45–0.65 0.45–0.60 . . . . . . . . .EX 55 0.15–0.20 0.20–1.00 0.04 0.04 0.20–0.35 1.65–2.00 0.45–0.65 0.45–0.80 . . . . . . . . .

Composition, wt%

hardness of a gear tooth is strictly dependent onthe percentage of carbon at the surface, whereasthe core hardness is related to the hardenabilityof the material and is determined by the alloyingelements in the steel. It is thus essential to havea clear understanding of the terms hardness andhardenability of gear materials. Metallurgi-cally, these two terms are quite different fromone another as discussed subsequently.

Hardness and HardenabilityHardness is a surface property, whereas hard-

enability of steels refers to depth and hardnessdistribution induced by quenching. Steels withlow hardenability can be hardened to a rela-tively shallow depth. In these types of steels,austenite-martensite transformation takes placein the area close to the surface only. The centerof heat treated section remains soft or trans-forms to a structure softer than martensite, suchas pearlite. Steels with high hardenability de-

velop a much deeper martensitic structure whensimilarly treated.

As explained previously, the higher the sur-face carbon is, the higher the surface hardnesswill be until surface carbon reaches around0.6%. To increase hardenability of steels thechemical compositions of steels need to bealtered to slow down martensitic transformation.This is achieved by alloying the steels. All alloy-ing elements, except cobalt, increase hardenabil-ity of steels. The common method to determinehardenability is by the Jominy, or end-quench,test where a test bar of the steel, 25 mm (1 in.) indiameter by 100 mm (4 in.) long, normalized andmachined to remove the decarburized surface, isheated to the hardening temperature for 30 min-utes. It is then quickly transferred to a fixture thatholds the bar in a vertical position, and a jet ofwater under controlled conditions is directedimmediately against the bottom end only (Fig.5a). The end of the bar is thus cooled very


Tabl

e 2

Hea

t tr

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ng d

ata

for

som

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ar s

teel

sN

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aliz

ing

tem

pera

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mpe

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ning

te

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ratu

re

AIS

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°F°C

°F°C

°F°C

°F°C

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3310

900–

950

1650

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086

015

7577

5–80

014

25–1

475

900–

930

1650

–170

079

0–81

514

50–1

500

350

655

3140

815–

930

1500

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079

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014

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550

815–

840

1500

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0..

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.31

059

040

2887

0–93

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700

830–

860

1525

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.87

0–93

016

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700

790–

815

1450

–150

040

075

040

4784

0–95

015

50–1

750

830–

860

1525

–157

580

0–84

014

75–1

550

...

...

...

4130

870–

930

1600

–170

079

0–84

014

50–1

550

840–

900

1550

–165

0..

...

.36

568

541

4087

0–93

016

00–1

700

790–

840

1450

–155

083

0–88

515

25–1

625

...

...

315

595

4320

870–

930

1600

–170

086

015

75..

.90

0–93

016

50–1

700

775–

800

1425

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538

072

034

4087

0–93

016

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700

590–

660

1100

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580

0–83

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525

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285

545

4620

930–

980

1700

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086

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.90

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700

800–

830

1475

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529

055

546

4087

0–93

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700

790–

840

1450

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079

0–84

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50–1

550

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320

605

4820

900–

950

1650

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087

515

75..

.90

0–93

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50–1

700

790–

815

1450

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036

568

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4587

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700

790–

840

1450

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0–83

014

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525

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6120

930–

980

1700

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087

016

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0077

5–80

014

25–1

475

400

760

6150

900–

950

1650

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084

0–90

015

50–1

650

840–

900

1550

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0..

...

.28

554

586

2087

0–93

016

00–1

700

860

1575

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930

1700

775–

840

1425

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039

574

593

1090

0–95

016

50–1

750

860

1575

...

900–

930

1650

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077

5–84

014

25–1

550

345

650

EX

24

900–

950

1650

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087

016

0087

016

0090

0–93

016

50–1

700

815–

840

1500

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044

583

0E

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990

0–95

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50–1

750

870

1600

870

1600

900–

930

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015

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550

445

830

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30

900–

950

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420

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Fig. 5 Jominy end-quench apparatus (a) and method for pre-senting end-quench hardenability data (b). Source: Ref 2

rically opposite flats approximately 6 mm (¼ in.)wide are ground along the length of the bar andRockwell hardness measurements are made atintervals of 1.6 mm (1 ⁄ 16 in.), on one or both theflat surfaces so prepared. The relationship ofhardness to distance from the quenched end is anindication of the hardenability of steel (Fig. 5band 6).

Carbon content in alloy steels also plays animportant role in developing hardenability. Fig-ures 7 and 8 show hardenability curves for somesteels with different content of carbon. Thedegree of hardness at the quenched end (sur-face) depends primarily on the carbon content,but the hardness at any point away from this enddepends on the alloy content in the steel as wellas carbon. Deep-hardening steels produce flatterhardenability curves (Fig. 6). Commerciallyavailable “H-band” steels assure high harden-ability. Producers of such steels usually indicateminimum and maximum hardnesses that areexpected at any depth from the quenched end ofthe bar.

Effect of Common Alloying Elements onHardness and Hardenability. There are fivefundamental factors that influence hardenabilityof steel:

• Mean composition of the austenite• Homogeneity of the austenite• Grain size of the austenite• Nonmetallic inclusions in the austenite• Undissolved carbides and nitrides in the

austenite

It has been found that the effect of dissolvedelements that combine with carbon in prefer-ence to dissolving in ferrite have the greatestinfluence in increasing hardenability if they aredissolved in the austenite before quenching. Acarbide-forming element that is not dissolved inthe austenite has no effect on hardenabilityexcept that as a carbide it may restrict graingrowth, thus reducing the hardenability of thesteel. Undissolved carbides reduce both thealloy and carbon content of the austenite. Sinceundissolved carbides restrict grain growth, insome instances, quenching from higher temper-ature that increases grain size promotes deeperhardening. In summary, the factors that increasehardenability are:

• Dissolved elements in austenite (exceptcobalt)

• Coarse grains of austenite• Homogeneity of austenite

quickly while cross sections remote from the endare cooled more slowly. The rate of cooling isdependent on the distance from the quenchedend. After the cooling is completed, two diamet-


Fig. 7 Comparative hardenability of 0.20% C AISI alloy steels

Fig. 8 Comparative hardenability of 0.40% C AISI alloy steels

Fig. 6 Hardenability curves for different steels with the same carbon content. A, shallow hardening; B, intermediate hardening; C,deep hardening


Fig. 9 Some typical Jominy curves showing end-quenchhardenability. Source: Ref 3

The factors that reduce hardenability are:

• Fine grains of austenite• Undissolved nonmetallic inclusions, car-

bides, or nitrides

Of the various alloying elements used incommonly used gear materials, the followingare considered to effect tooth surface and corehardnesses significantly:

• Nickel (Ni): The principal advantage lies inhigher tensile strength that can be obtainedwithout appreciable decrease of elongationand reduction area. Nickel also lowers thecritical temperatures, and hence, lower heattreat temperature can be used. It decreasesthe critical cooling rate; therefore, a lessrapid quench is required to obtain hardnessequal to that of plain carbon steel. Nickelincreases hardenability and fatigue strengthof steels.

• Chromium (Cr): It is essentially a hardeningelement and frequently used with other ele-ments such as nickel to improve strength andwear resistance and hardenability. Chro-mium has, however, the disadvantage ofbeing temper brittle, and hence, precautionsmust be taken when tempering in the rangeabove 540 °C (1000 °F).

• Molybdenum (Mo): The pronounced effectsof molybdenum when added in relativelysmall amounts (0.15 to 0.3%) are (a) greaterductility and toughness, (b) reduced temperbrittleness, (c) improved creep resistance athigh temperatures, and (d) greater harden-ability when present with chromium.

• Vanadium (V): When present with nickel,chromium, and molybdenum, vanadium (a)improves fatigue resistance, (b) providesfine grain structure, (c) reduces grain-growth tendencies, and (d) Improves hard-enability only when quenched from highertemperature

• Tungsten (W): Tungsten forms a hard, stablecarbide that imparts wear and abrasive resis-tance. In the dissolved form, tungstenincreases hardenability. In certain combina-tions with chromium and vanadium, tung-sten decreases the tendency to form cracksin case-core boundary, and distortion duringheat treatment.

• Cobalt (Co): Cobalt improves high temper-ature strength characteristics and corrosion

resistance. In addition, it imparts excellentwear resistance. But, the hardenability ofsteel is reduced with cobalt over 0.4%.

Selection of Gear Steel by Hardenabil-ity. Since there is a variety of steels with stan-dard and nonstandard analyses, the problem ofselecting just the right steel for a certain appli-cation can become quite confusing if chemistrycomparisons alone are used. The establishmentof end-quench hardenability curves demon-strates how alloys slow down the reaction ratesof steels. Also, mass has significant influence onhardenability. The rate of heat transfer is notuniform for gears with varied cross sections.Larger gears (heavier mass) experience morenonuniform heat transfer. There is danger ofcracking large gears if they are quenched drasti-cally enough to harden completely. A milderquench, on the other hand, may not developmicrostructures with the required strength. Inextreme cases, the part may be so large that evenwith considerable alloy content, it is not practi-cal to use a fast enough quench to develop fullhardness. In these cases, a gear designer needsto compromise by designing with low allowablestresses to get by with the properties that can beobtained in the steel after heat treatment. Figure9 shows end-quench hardenability curves forseveral kinds of gear steels frequently used inindustrial and aerospace applications.

Table 3 presents core hardness of some car-burized steels of different diameter sections.


Table 3 Effect of section size on core hardness and tensile properties of carburized steels

Heat treatment

Quenching temperature of oil

Tempering temperature Bar diam

Tensile strength

°C °F °C °F mm in. MPa ksi MPa ksi

4320 815 1500 150 300 13 ½ 415 1055 153 1124 163 12 4625 1 302 738 107 738 107 17 5150 2 255 593 86 593 86 22 56

102 4 248 517 75 517 75 24 574620 815 1500 150 300 13 ½ 255 876 127 621 90 20 60

25 1 197 676 98 462 67 26 7050 2 192 662 96 448 65 27 70

102 4 170 586 85 359 52 30 694820 800 1475 150 300 13 ½ 401 1441 209 1193 173 14 54

800 1475 25 1 352 1172 170 869 126 15 51800 1475 50 2 277 938 136 641 93 20 56800 1475 102 4 241 820 119 558 81 23 59925 1700 152 6 226 765 111 517 75 22 62

8620 845 1550 150 300 13 ½ 388 1379 200 1082 157 13 49845 1550 25 1 255 876 127 579 84 21 53845 1550 50 2 235 807 117 503 73 23 58845 1550 102 4 207 676 98 400 58 24 58925 1700 152 6 200 655 95 400 58 24 64

9310 790 1450 150 300 13 ½ 363 1234 179 986 143 16 5925 1 321 1096 159 848 123 16 5850 2 293 1000 145 745 108 18 67

102 4 277 938 136 655 95 19 62

Yield strength

Tensile properties

Elongation, %

Reduction of area, %

Steel type,AISI

Core hardness, HB

This table also shows how the tensile propertiesof the specimens vary with size.

Carbon Content and Case Properties

A carburized gear tooth may be regarded as acomposite structure consisting of a low carbonin the core and a high carbon of the same steelcomposition at the surface.

Increasing the carbon content of the case(within limits) increases wear resistance andresistance to contact fatigue. As the carbon levelincreases above 0.8%, there is a tendency toretain austenite and to produce carbide networksin the case. Heavy carbide networks can producebrittle cases, leading to tooth end chipping. It hasbeen shown that a level of 15 to 20% retainedaustenite is desirable both for sliding wear resis-tance and resistance to pitting fatigue. Excessiveretained austenite causes soft cases and lowerssurface hardness and should be avoided. Moder-ate quantities of retained austenite transform andwork harden under the contact load. A carbonlevel in the range 0.9 to 1.0% (for low-alloysteels) at the surface generally gives the opti-mum case properties to resist contact fatigue andsurface wear. Similar case properties in high-

alloy steels may be obtained with lower carbonlevel.

Case Depth of Tooth. Case depth is animportant parameter of carburized and hardenedgears and plays a significant role in determiningtheir pitting fatigue life. The case must be suffi-ciently deep to resist case crushing by theapplied load on the gear. In general, case depthof a carburized tooth is a function of diametralpitch. The bigger the tooth, the more case isneeded to carry the loads that will be imposedon the tooth. For each size of tooth there is anoptimum case depth. Too much case makes atooth brittle with the tendency to shatter off thetop of a tooth. However, too thin a case reducestooth resistance to pitting. A high-hardenabilitysteel with strong core structure may not need adeep case as with a lower hardenability steel.This makes it difficult to calculate an optimumcase depth with complete certainty for all typesof steels. A further practical point is that casedepths vary according to the heat treatmentcycle and equipment used. For example, in abatch-type furnace where a load is made up of alarge number of densely packed gears there willbe a variation in case depth throughout the load.This is due to variations in temperature and car-burizing atmosphere circulation. Using a lower


Fig. 10 Step-ground specimen for hardness-traverse methodof measuring depth of medium and heavy cases.

Arrows indicate location of hardness-indenter impression

Fig. 11 Variation of hardness with distance below the sur-face for a carburized and hardened gear made of

8620H steel

temperature for carburizing, much better con-trol over case depth is possible. At a tempera-ture of 900 °C (1650 °F), it is not unrealistic toexpect a case depth tolerance of 0.08 to 0.15mm (0.003 to 0.006 in.).

Measurement of Case Depth. In the gearindustry, two terms are frequently used to deter-mine the quality of a carburized case—totalcase depth and effective case depth. Thus, anaccurate and repeatable method for measuringthese case depths on a gear tooth is essential notonly to control the reliability of carburizingprocess but also for evaluation of gear perfor-mance. The total case depth is the perpendiculardistance from the surface of a carburized andhardened tooth to a point inside the tooth atwhich difference in chemical and mechanicalproperties of the case and core can no longer bedistinguished. Effective case depth, on the otherhand, is the perpendicular distance form the sur-face to the farthest point inside the tooth atwhich a hardness of 50 HRC is measured. Tomeasure case depths, a mechanical method isconsidered to be one of the most useful andaccurate of all the methods available. In thismethod, for gears in critical applications, a crosssection of a representative tooth from a pie-shaped test coupon prepared from the same“heat” of steel is preferred for reliability. How-ever, for vacuum melt steels with cleanliness ofAMS 2300 or 2304, the test coupon does notnecessarily have to be made from the same heatof steel to ensure a similar reliability of casemicrostructure. Nevertheless, considerable careshould be exercised in preparing such a speci-men. The tooth needs to be sectioned perpen-dicular to the hardened surface. Cutting orgrinding that would affect the original hardnessis to be avoided. Polishing of the specimen isquite important. This polishing should be donefinely enough so that hardness impressions areunaffected. A microhardness tester is recom-mended for case-depth measurements.

In noncritical gears, case depths are deter-mined by step grinding (0.13 mm, or 0.005 in.,step) a test coupon of rectangular cross sectionas illustrated in Fig. 10. Here, the hardness read-ings are taken on steps that are of known dis-tances below the carburized surface, and a stan-dard Rockwell hardness tester may be used. Ata particular step, if the hardness is found to begreater than 50 HRC and less than 50 HRC onthe next deeper step, the effective case depth is

taken to be between the two depths. Figure 11illustrates typical hardness versus case depthreadings taken at pitch line and root fillet of acarburized and hardened gear tooth. The effec-tive case depth at root fillet area is always some-what lower than at the pitch line. In a gear, theeffective case depth at pitch line is of impor-tance for gear pitting life, and hence, the valueat this line is regarded as the effective casedepth of a gear tooth. Case depth in root filletcontributes to higher bending fatigue life.

Effective Case Depth of High-Alloy SteelGears. Hardness versus case depth relationshipas depicted in Fig. 11 applies to low- to medium-alloy steels such as AISI 8620, 4320, and so on.In high-alloy steels such as HP 9-4-30 and AISI4330M, the core hardness after carburizing and


Fig. 12 Variation of hardness versus case depth in gearsmade of HP 9-4-30 steel Fig. 13 Gear tooth profile

hardening may be as high as 52 HRC. For thistype of steel, effective case depth cannot bedetermined as already outlined. Typical hard-ness versus case depth for a high-alloy and highcore hardness steel (HP 9-4-30) is shown in Fig.12. For such steels, 55 HRC instead of 50 HRC isconsidered a better approximation of effectivecase depth and is successfully used in variousaerospace applications.

Now the question is, how much case is neededon a gear tooth to prevent case failure due toHertzian contact stress that causes pitting? Ingeneral, high case depths adversely affect thequality of case and, hence, the gear life. So, thedetermination of proper case depth on a geartooth is quite important and is based on its capac-ity to resist contact stress-induced pitting.

Determination of Case Depth-ShearStress Theory. Of the several parameters usedin optimizing a gear design, the case depth, sur-face hardness, and core hardness of tooth are ofsignificant importance. These three parametersare normally selected on the basis of appliedload to a gear and its required life under theservice conditions. Research carried out showsthat a proper combination of case depth, surfacehardness, and core hardness provides the maxi-mum gear life. Analytically, these parametersare determined as outlined subsequently.

In transmitting torque, a gear tooth is sub-jected to at least two types of major stresses:contact and bending. These stresses cause toothfailure due to metal fatigue.

Gear tooth failure due to contact stress, com-monly known as pitting, occurs when small pits

initiated by fatigue cracks are formed on orbelow the tooth surface. These pits usuallyemanate at the highest point of single-tooth con-tact (HPSTC) for pinion and at the lowest pointof single-tooth contact (LPSTC) for the matinggear (Fig. 13). The occurrence of pits is alsofound to be influenced by other factors such assurface quality (surface finish, microstructure ofcase, etc.), surface hardness, lubricating condi-tions, and operating temperature. Empirically,to resist crack-initiated pit formation, a geardesigner considers maximum contact stress toact along the axis of load at HPSTC or LPSTC.There are two current theories that prevail toexplain formation of cracks on any of theseaxes. The most widely held theory for well-lubricated gears is based on shear stress inducedcracks below the surface due to contact load.The second one is based on cracks initiated atthe surface, which happens only when the coef-ficient of friction goes below 0.1. According toshear stress induced pit formation below thesurface, the maximum shear stress occurs on theaxis of maximum contact load at HPSTC forpinion and LPSTC for gear. Because of thepresence of sliding at these points, it is notknown at what angle to the load axis the planeof maximum shear stress lies. That the maxi-mum shear stress occurs at 45° to the load axisbelow the surface is true for pure rolling condi-tion. In gear mesh, pure rolling exists only at thepitch point. Above and below this point there issliding. This alters the location and magnitudeof shear stress and presents difficulty in deter-mining the point of maximum shear stress. Toovercome this difficulty, the peak value of shear


Fig. 15 Contact stress profile between two meshing gear teeth

Fig. 14 Shear stress distribution along the load axis of two parallel cylinders under contract pressure

stress is assumed to occur below the pitch pointand is quite valid for a well-lubricated gearmesh (coefficient of friction, μ ≈ 0.1, Fig. 14).Under these conditions, the value of the maxi-mum shear stress is found to be 0.140 (0.304) P0at a depth of 20 (0.786)b, where P0 is the maxi-mum contact load in kg (lb) and b is the halfwidth in mm (in.) of contact ellipse between twomeshing teeth (Fig. 15). The shear stress soinduced causes plastic flow in the outer corewhile the harder case still behaves elastically.

This makes a Poisson’s ratio for the core todeviate from 0.3 to approximately 0.5 while thatof the case remains near 0.3. Thus, the core willtend to contract more than the case, inducingtransverse stress, which, in turn, produces triax-ial tensile stress in the core. This in combinationwith the discontinuity in the compressive hoopstress at the case-core interface causes cracks toform.

Cracks formed by this mechanism at the case-core boundary are resisted by the toughness of


Fig. 16 Estimation of total case depth

core for propagation in the direction of the core.Facing such resistance, cracks then follow thepath of maximum tensile stress that exists in thecase and finally find their way out to the surface,resulting in a pitlike formation. Progressive pit-ting of this nature destroys the tooth profile, andthe gears run rough with increased vibrationlevels until the teeth break off.

To prevent destructive pitting of this nature, agear design engineer needs to make sure that themaximum shear stress lies well within the caseso as not to cause any plastic flow of material inthe case-core boundary. This does not mean thatone should specify case depth more than what isneeded. Deep cases have some adverse effectson the properties of case such as excessiveretained austenite, free carbides, internal oxida-tion, and so on. Many of these may be responsi-ble for modifying the residual stress distributionin the quenched case in a manner not quite ben-eficial to the gear life.

The theory as explained is quite useful andseems to satisfy the design requirements ofgears made from most low- and high-alloysteels. But it fails to explain crack formation ingears made of some high-alloy steels with highcore hardness. In these gears, pits are formed ator just below the tooth surface due to someinduced tensile stresses in the case, and thegears do not seem to require high case depth asin low core hardness steels. This is possible onlyif the coefficient of friction becomes less than0.1. The magnitude of maximum shear stressunder this condition is approximately 0.25 P0.Hence, case depth requirement may be reducedin comparison to shear stress induced pit belowthe surface theory. Experimental investigationsso far carried out show this theory to be true forgears made of materials such as HP 9-4-30 withcore hardness over 50 HRC. Further tests areneeded for its wider acceptance with high corehardness steels. Until then, the shear stressbelow the surface theory will be used to deter-mine case depth at pitch diameter of carburizedgears. Now, the question is how much casedepth is needed to resist bending fatigue failureof a tooth.

Gear tooth failure due to cyclic bending stressoccurs when the bending stress at the root filletsurface exceeds the allowable bending fatiguestrength, which is dependent on the core hard-ness. Higher core hardness results in higherallowable bending fatigue strength. But there isan optimum range of core hardness for maxi-

mum bending fatigue life of gears. On the otherhand, case depth at the root fillet does not seemto have any direct relationship with the bendingfatigue life, although it has been found that casedepth indirectly influences bending fatiguecharacteristics through altering the magnitudeof surface residual stress. In general, the case atthe root fillet develops high compressive sur-face residual stress that is considered beneficialfor improved bending fatigue life.

Total Case Depth. The shear stress theory,as explained, is used to determine the point ofmaximum shear stress below the surface at thepitch line (Fig. 16). Knowing this point, the totalcase depth (δc) may be calculated for gears withdifferent core hardness from the following rela-tionship:

(Eq 6)

where δτ is the depth at the point of maximumshear stress below the surface, and k is a con-stant that depends on core hardness of gear. Fora safe design, its value may be taken as: 2 forcore hardness up to 48 HRC, and 1.2 for corehardness above 48 HRC. Total case depthobtained with Eq 6 has been applied success-fully to industrial, automotive, and aerospacegears.

The total case depth obtained by considering k= 1.2 works well for some high-alloy steel gearssuch as HP 9-4-30 with core hardness above 48HRC. The case depth thus obtained does notdeteriorate pitting or bending fatigue life orinduce any failure due to case crushing. Further-more, this seems to improve bending fatigue life,particularly when carburizing is done in vacuumfurnaces. This is partly due to uniform case depthalong the tooth profile including root fillet that isachieved with vacuum furnace carburizing. Car-burizing in atmospheric furnaces cannot assuresuch consistency.

dc � kdt p


Table 5 Recommended case and corehardnesses at pitch line of low-alloy steel gears

ApplicationSurface hardness,

HRCCore hardness,

HRC

General-purpose industrial gearing 55 min 28–32High-capacity industrial gearing 58 min 32–38Aircraft gearing 60 min 38–48

Table 6 Recommended case depth at tooth tipMaximum case depth

mm in.

20 0.71 0.02816 0.86 0.03412 1.17 0.04610 1.40 0.0558 1.75 0.0696 2.34 0.0924 3.18 0.1252 3.56 0.140

Diametral pitch (DP)

Recommended Total Case Depth forLow-Alloy Steel Gears. As discussed, thecase depth required on a carburized tooth is pri-marily a function of its diametral pitch. The big-ger the tooth, the deeper the case needed to carrythe loads. Also, for each size of tooth there is anoptimum case depth. Too much case makes thetooth brittle with a tendency for the tip of thetooth to shatter. Too thin a case, on the otherhand, reduces tooth strength and resistance topitting. Table 4 shows the general practice oncase depth for different DP gear tooth based onmaximum shear stress theory.

Carburizing of gears with acceptable casemicrostructure below 1 DP is extremely diffi-cult because of tooth size. This is the reason,carburized and hardened gears below 1 DP arerarely used in industrial applications. If surfacehardening is needed for such gears, an alternatehardening process such as induction hardeningis recommended.

For extremely critical gears, it is advisable tohold case depth toward the maximum as shownin Table 4 and the minimum limit raised. Forexample, case depth on a critical 10 DP gearmight be held to 0.635 to 0.90 mm (0.025 to0.035 in.) case depth instead of 0.508 to 0.90mm (0.020 to 0.035 in.). The case depth sospecified is the total case depth as noted in anetched specimen. The effective case (hec) forsurface durability is taken to be about 75% ofthe total case or may be estimated by the fol-lowing equation:

(Eq 7a)

where Sc is the maximum contact stress psi, inthe region of 106 to 107 cycles; d is the pinionpitch diameter (in.); φt is the pressure angle; Ψbis the base helix angle; and mG is the tooth ratio.

In metric units:

(Eq 7b)

where Sc is the maximum contact stress,N/mm2; and dm is the pinion diameter, mm.

Recommended case and core hardness atpitch line for different applications are given inTable 5.

Case Depth at Tooth Tips. Under normalconditions, gear tooth tips do not experienceany load. In case of misaligned gears, the tipsmay be subjected to high contact load due to

hec �Sc# dm# sin ft

48,250 cosyb a mG

mG � 1b mm

hec �Sc# d # sin ft

7.0 � 106 # cosyb

a mG

mG � 1b in.

which they may fail, particularly if the tips arethrough hardened during carburizing. To avoidsuch failures, case depth in the region of toothtips, hem, should be between 0.3 and 0.4/DP ininches or 0.3 and 0.4 × module mm.

Recommended case depths at tooth tips aregiven in Table 6.

Grain Size and Case Depth. Besides timeand temperature, case depth also depends to acertain extent on grain size of steel. Coarse-grain steels (ASTM 4) develop a deeper case,whereas fine-grain steels (ASTM 10 to 12) pro-duce a shallow case. Grain size between ASTM5 and 7 is recommended for proper case depth.

The grain size usually is reported as a numberthat is calculated from the relation:

(Eq 8)n � 2N�1

Table 4 Recommended case depths at pitch lineCase depth

mm in.

20 0.25–0.46 0.010–0.01816 0.30–0.58 0.012–0.02310 0.50–0.90 0.020–0.0358 0.64–1.02 0.025–0.0406 0.76–1.27 0.030–0.0504 1.02–1.52 0.040–0.0602 1.78–2.54 0.070–0.1001 2.29–3.30 0.090–0.130



Table 7 ASTM grain sizeASTM No.

Mean No. of grains/in.2

ASTM No.

Mean No. ofgrains/in.2

1 1 7 642 2 8 1283 4 9 2564 8 10 5125 16 11 10246 32 12 2048

Fig. 18 Measurement locations of importance for core hard-nesses

where n is the number of grains per square inchat a magnification of 100×, and N is the grainsize number commonly called the ASTM grainsize.

Table 7 shows ASTM grain size and grainsper square inch.

Core Hardness of Gear Teeth

Core hardness of teeth, as already discussed,is an important parameter that determines thestrength of a gear tooth. Currently, it is a com-mon practice in the gear industry to accept hard-ness at the center of a tooth on form diameter asthe core hardness (Fig. 17). This considerationhas some merit. First, it allows a conservativeestimate of allowable bending fatigue strengthof a tooth because the hardness at the point ofmaximum bending stress that occurs near to theroot surface is higher than at the center of thetooth. Hence, the actual bending strength of atooth is always higher than what is considered toestablish its bending fatigue life. Second, itidentifies a definite spot in a tooth to measurehardness.

The major drawback of this practice is thehardness at this location is always low for low-hardenability steels. Hence, the allowablestrengths are low. This makes the gears made ofsuch steels large, and eventually, the gearboxbecomes large. In reality, the locations of maxi-mum stresses that cause failures are not at thecenter of the tooth. Recent investigations showmaximum tensile stress due to bending of atooth that causes failure occurs just below thecase at root, and also the stress that causes casecrushing is located in the case-core interfacearea on the pitch diameter. Hardness in theseareas is of importance because this is where fail-ures originate, and they are substantially higherthan at the center of tooth. Hence, it is logical todetermine bending or case crushing failures onthe basis of these strengths. Such considerationswould be beneficial in optimizing gear designsthat are bending-strength limited.

The main problem with the new approach liesin precisely identifying the locations for propercore hardness measurements. To avoid com-plexity in preparing a sample and subsequentdiscrepancy in measurements, the followinglocations are considered realistic as illustratedin Fig. 18:

• C1 for bending strength: Between root andcenter of tooth

• C2 for case crush support strength: Be-tween pitch point and center of tooth

Core Hardness versus Maximum BendingStrength. Metallurgically, for a carburized and

Fig. 17 Measurement locations of case and core hardnesses


Fig. 19 Core hardness vs. bending fatigue strength of geartooth

Table 8 Core hardness of tooth for some gearmaterials

Core hardness, HBDiametral pitch (DP) AISI 4620 AISI 8620 AISI 4320 AISI 9310

0.75 180–230 180–250 215–270 245–3401 180–245 180–260 225–300 260–3601.25 180–260 230–290 240–325 280–3701.5 200–280 230–310 255–343 285–3801.75 200–280 235–320 260–350 290–3802 225–310 240–335 270–370 300–3802.5 235–340 250–360 280–390 310–3903 235–340 260–390 300–400 310–3903.5 235–340 270–395 315–410 315–3904 255–375 290–400 315–410 315–3905 290–395 320–420 335–420 315–3906 310–405 320–420 340–430 315–3907 310–405 335–430 340–430 315–3908 310–405 335–430 340–430 315–39010 350–425 370–440 370–440 315–390

Core hardness ranges are based on min and max hardenability curves for Hgrades and quench temperatures between 80 and 95 °C (175 and 200 °F). Fig. 20 Austenitic grain size and bending fatigue strength of

a typical gear steel

hardened gear tooth, higher core hardness resultsin higher bending fatigue strength. But unfortu-nately, this relationship is not fully true for gears.Research shows maximum bending fatiguestrength of a gear tooth for low- and high-alloysteels is achieved with core hardness in the rangeof 34 to 46 HRC. It is easy to understand the rea-son for lower bending fatigue strength for corehardness below this range. Why bending fatiguestrength for such alloys does not increase abovethis range is difficult to explain. For very high-alloy (above 9%) steels such as HP 9-4-30, max-imum bending strength is achieved with corehardness between 46 and 50 HRC. It is believedat core hardness above 52 HRC, an unsatisfac-tory tensile residual stress is occasionally ob-

served. Figure 19 illustrates the relationship ofcore hardness with bending fatigue strength ofcarburized and hardened gears.

Table 8 shows achievable core hardnessrange (HB) versus DP of tooth for some com-monly used carburizing grade gear materials.

Surface Oxidation Effect. Oxidation at thesurface should be avoided during carburizing.The most undesirable effect of surface oxidationis a loss of hardenability because O2 reacts pref-erentially with the alloying elements. It is less ofa problem for steels with high-alloy content.

Grain Size and Core Hardness. Some-times, full core hardness is not achieved in gearsmade from a “heat” of very fine grain steel(ASTM 10 to 12) instead of normally usedASTM 5 to 7. It is not unusual to see approxi-mately one point HRC hardness gain or lossaccompanied with each grain size change ingear tooth size from 3 to 6 DP. In general, corehardness drops as grain size becomes finer andincreases when it coarsens. Similarly, bendingfatigue strength increases with increase ofaustenitic grain size as illustrated in Fig. 20. Pit-ting fatigue strength, on the other hand, in-creases with finer grain size. It is to be noted thatthe temperature to which a steel is heated has amarked influence upon the austenitic grain size.It is necessary, therefore, when determining theaustenitic grain size of carburized steels, tomake the determination under conditions thatare similar to the heat treating procedure.

Effect of Carburizing Processes on Sur-face Carbon. Surface hardness and hardnessbelow the surface are dependent on carbon gra-


Fig. 21 Carbon gradients by different carburizing processes.Material: HP 9-4-30

Fig. 22 Carbon profiles for two different AISI steels (carbur-ized with carbon potential of 0.7%)

Fig. 23 Carbon profiles for the same two steels shown in Fig.22 (carburized with carbon potential of 1.0%)

dient. For higher surface hardness without alarge carbide network, 0.80% carbon is pre-ferred on the surface. For low carbon potential(below 0.70%), some decarburization may takeplace at the surface of steel during carburizingby any of the processes such as endothermic,vacuum, fluidized bed, and vacuum pulsation.Decarburization results in lower surface hard-ness after quenching. This is why it is importantto maintain proper carbon potential during car-burizing. Also, the penetration of carbon intothe surface depends on the carbon gradient,which is found to vary with the carburizingprocess selected. Figure 21 illustrates variouscarbon gradients for gears made of HP 9-4-30with different carburizing processes. It showsthat carburizing in a vacuum pulsating-type fur-

nace offers the highest carbon on the surface forthe same carbon potential. Figures 22 and 23illustrate typical carbon profiles for AISI 9310and 8620 steels for different carbon potentials inan endothermic carburizing furnace.

Microstructure of Carburized CasesThe microstructure of a carburized gear tooth

changes from the surface to the core. Dependingon carbon content and post carburizing heattreatment, the microstructure at the surface willbe pearlitic or martensitic, with or withoutgrain-boundary carbides. Toward the interior,there is a gradual transition in microstructure totransformation products that are characteristicsof lower carbon contents until the core isreached. In some steels, there is only a transitionfrom high-carbon martensite to low-carbonmartensite, but in other steels, there is a transi-tion from pearlite with proeutectoid cementitethrough eutectoid pearlite to a predominantlyferritic structure. Such a gradation in micro-structure is useful to measure case depth bymicroscopic examination.

In planning carburizing of a gear, it is thusnecessary to consider both the carburizing cycleand the post carburizing heat treatment. Theproper control of heat treatment develops therequired properties in the core and at the sametime, develops the required tooth surface hard-ness and hardness gradient in the case. Caseproperties depend strongly on carbon contentand carbon gradient. It is only through adjust-ment of carbon content and carbon gradient that


Table 9 Hardness and microstructure requirements in case and core for different classes ofcarburized and hardened gears

Hardness

Gearclass(a) Process Material

Case surface(Knoop 500 g)

Core HRC

Area ofpart Requirement

A Carburize andharden

Carburizinggrade

720 min ontooth surfaces

710 min at rootfillet areas

34–44 Case High-carbon refined tempered martensite.Retained austenite 10% max. Continuouscarbide network or cracks are not acceptable.Scattered carbides are acceptable provided themax carbide particle size does not exceed0.005 mm (0.0002 in.) in any direction.Transformation products such as bainite,pearlite, proeutectoid ferrite, or cementite notpermitted in excess of the amount. No whitemartensite (untempered) permitted.

Core Low carbon (tempered) martensite. No blockyferrite, pearlite, or bainite. Ferrite patches notto exceed 1.6 mm (1/16 in.) in width or lengthas measured at 250× magnification. Excessivebanding not permitted.

B Carburize andharden

Carburizinggrade

690 min (all areas)

30–44 Case High-carbon tempered martensite. Retainedaustenite 20% max. No continuous carbidenetwork is acceptable. Scattered carbides areacceptable provided the maximum carbideparticle size does not exceed 0.010 mm(0.0004 in.) in any direction. Surfaceoxidation not to exceed 0.013 mm (0.0005in.). Transformation products not permitted inexcess of the amount shown. No whitemartensite permitted.

Core Essentially low-carbon martensite with sometransformation products permissible. Ferritepatches up to 3.18 mm (1/8 in.) wide andlength permissible as measured at 250×.Excessive banding not permitted.

C Carburize andharden

Carburizinggrade

630 min (all areas)

28–45 Case andcore

Defects such as laps and cracks are notpermitted. Retained austenite, 30% max. Casedepth shall meet drawing requirements.Excessive inclusions that may affect thefunction of the part shall be cause forrejection.

(a) A, critical applications where a gear failure may result in loss of life; B, not as critical as A but still requires high reliability; C, industrial application

Microstructure

the heat treatment can be made to develop goodcase properties.

The microstructures of case and core also areinfluenced by the heat treatment after carburiz-ing. Because of the generally low carbon con-tent in the core, its structure may consist of low-carbon martensite to mostly ferrite. On the otherhand, the case structure, because of higher car-bon content, may contain martensite, bainite, orpearlite, depending on the rate of cooling fromthe austenitizing temperature. Some proeutec-toid ferrite may appear near the case-core inter-face, especially if the cooling rate is slow. Insome alloy steels, retained austenite may appearnear the surface, particularly if the surface car-bon content and the austenitizing temperatureare high or the cooling rate is too fast. Steels

containing nickel are especially susceptible tosuch austenite retention. Microstructure re-quirements of case and core generally vary withthe class of gears. Table 9 shows recommendedmicrostructures for different classes of gears.Metallographic standards for carburized gearsteel structures are shown in Fig. 24 and 25.More detailed information on the microstruc-tures of carburized steels can be found in Ref 4and 5.

Problems Associated with Carburizing

During carburizing, gear tooth tips experiencehigher carbon absorption than at the roots. Thereason for this is the convergence of carburizing


Fig. 24 Metallographic standard for carburized, hardened, and tempered cases in grades A, B, and C gears. (a) Desired high car-bon, carburized, hardened, and tempered martensitic case. No retained austenite. No surface oxidation. Acceptable for

grade A. (b) Case structure 10% retained austenite and small amounts of transformation products. Maximum austenite permissible forgrade A. (c) Case structure with 20% retained austenite and some transformation products. Maximum permissible for grade B. (d) Casestructure with over 30% retained austenite and a considerable amount of transformation products. Continuous grain boundary carbides,massive carbides. Not acceptable for grade A or B

gas flow at the tips, whereas divergence exists atthe root area as illustrated in Fig. 26. As a result,the case thickness does not run parallel to thetooth profile. The thickness is deeper at the tipand shallower at the root. Consequently, this dif-ference results in the slope variation of hardnessversus case depth relationship taken at differentpoints on a gear tooth as depicted in Fig. 27. Thedifference in case depth becomes more critical asthe gear tooth geometry also changes. For exam-ple, with an increase in pressure angle, the casethickness at the tip increases significantly, mak-ing it almost through hardened. Figure 28 showsthis condition. Such tooth tips are very brittleand subject to chipping in case of any misalign-ment of gears.

Copper Plating of Gear to Control CaseDepth at Tooth Tip. To overcome the prob-lem of high case depth at tooth tips, very fre-quently gear blanks are plated with copperbefore cutting the teeth. After the teeth are cut,plating is still left on the tooth land, which actsas a buffer during carburizing and reduces casedepth at and near the tips of the gear teeth.Results obtained so far show that copper platinghelps the reduction of case near the tips ofcoarse pitch (up to 10 DP) and small pressureangle (up to 20°) gear teeth where an apprecia-ble top land exists. In finer-pitch (20 DP andhigher) and higher-pressure angle gears (above20°), the tooth land is relatively small, and cop-per plating offers only limited case depth con-


Fig. 25 Metallographic standards for carburized, hardened, and tempered core structure. (a) Desired low-carbon, tempered marten-site, free from ferrite patches and with some transformation products. Acceptable for grade A. (b) Low-carbon, tempered

martensite with maximum allowable transformation products. Acceptable for grade A. (c) Low-carbon, tempered martensite with maxi-mum allowable transformation products. Acceptable for grade B. (d) Tempered martensite with block ferrite patches. Not acceptable forgrades A and B

trol at the tips. On the basis of recent experi-mental work, the following recommendations(Table 10) are put forward with regard to copperplating of gears before carburizing.

In industries where in-process inspection iscritical, a note on the gear drawing is helpful(e.g., “peeling of plating on the edges of teethresulting from gear cutting should not be thecause of rejection of plated gears”). Also, strip-ing of plating after carburizing is not necessaryprovided a small amount of peeled copper plat-ing is acceptable in the gearbox lubricating oilsystem.

Tip and Edge Radii. For good heat treat-ment and performance of gears, tooth tips andedges are to be rounded as suggested in Table11.

Retained Austenite and Its Effect on GearPerformance. After carburizing and harden-ing, it is possible that some retained austenitemay exist near the surface of the gear teeth.Steels containing nickel are especially suscepti-ble to such austenite retention. The retainedaustenite is not generally considered harmful togear life when present in the amount not exceed-ing 15 to 20% by volume. In fact, retainedaustenite present between 15 to 20% by volumeseems to increase bending fatigue resistance ofgear teeth (Fig. 29). On the other hand, retainedaustenite in the martensitic microstructure ofthe case lowers the surface hardness, which isnot at all desirable for contact fatigue life. Also,a high percentage of retained austenite (above20% by volume) is found to be detrimental dur-


Fig. 26 Gas flow over a gear tooth during carburizing

Fig. 27 Hardness profiles at different locations of a tooth

Fig. 28 Case depth profile vs. tooth pressure angle. Dashedline indicates case depth profile

ing the service life of gears where the volumeaccompanying austenite-martensite transforma-tion causes dimensional change in gear toothgeometry. Furthermore, martensite formed inthis manner is untempered and brittle and mayaccelerate crack formation in the case. Hence, itis essential to control the amount of retainedaustenite for maximum service life of gears.Recent research indicates that finely dispersed,retained austenite in the amount of up to 15% isnot detrimental to the contact fatigue (pitting)life of gears. Retained austenite above 20% maycause “grind burn,” discussed later in this chap-ter, particularly if the gears are ground on wetgear grinding machines with vitrified aluminumoxide wheels.

A number of variables during carburizingaffect retained austenite in gears. These vari-ables include carbon potential, quench tempera-ture, cooling rate, and so on. Holding the carbonpotential between 0.7 and 0.85% and usingquench oil temperature below 95 °C (200 °F)and fast cooling rate, the retained austenite canbe significantly reduced. Another way of reduc-

ing the amount of retained austenite in the casemicrostructure is to cold treat the gears follow-ing quenching.

The specific amount of transformationachieved by a given subzero treatment isextremely difficult to predict. The degree ofreluctance to transform at a given temperature isinfluenced by:

• The amount of retained austenite at the startof cold treatment

Table 10 Copper plating of gearsDiametral pitch (DP)

Pressure angle (PA) Copper plating

15 and higher 20° and above Plating not recommended10–14 20° and above May use plating on selective basis10 and lower 20° and below Use plating

Table 11 Recommended tip and edge radii ofteeth

Tip and edge radii

mm in.

1–4 0.51–0.76 0.020–0.0305–8 0.38–0.64 0.015–0.02510–12 0.25–0.51 0.010–0.02016–20 0.13–0.25 0.005–0.010



Fig. 30 Typical near-surface case microstructure of direct-quenched carburized steel. Martensite plates etch

dark and retained austenite appears white. Gas-carburized AISI8719 steel (1.06% Mn, 0.52% Cr, 0.5% Ni, 0.17% Mo). Lightmicrograph, nital etch

Fig. 29 Influence of retained austenite on bending fatiguestrength

• The elapsed time between quenching andcold treatment

• Any intermediate thermal treatment such astempering

• The general level of residual compressivestress in the parts

• Any cold working of material such asstraightening

Tempering of gears at 150 to 175 °C (300 to350 °F) prior to cold treating is a common prac-tice. It decreases the tendency to form subsur-face microcracks. Also, tempering tends to sta-bilize retained austenite. After tempering, aslightly lower temperature is required to attainthe same degree of transformation upon coldtreating. Holding gears at room temperature forsome time probably has a stronger stabilizingeffect than tempering immediately after quench-ing. Because a volume increase accompaniessuch transformation, higher levels of compres-sive residual stress after quenching tend to retardtransformation until lower temperatures arereached. Temperatures in the range of –75 to–100 °C (–100 to –150 °F) are routinely used incold treating as already discussed.

To make sure the carburized case has theproper amount of retained austenite, it is neces-sary to have a proper measurement technique.Currently, there is no exact method to determinethe percentage of retained austenite in a carbur-ized case. Of the various methods available,metallographic examination and x-ray diffrac-

tion are frequently used. In metallographicexamination, austenite is not attacked by nital,and therefore, it appears white when the nital-etched specimen is examined (Fig. 30). Metal-lographic method, however, is not a reliablemethod of estimating the percentage of retainedaustenite. X-ray diffraction technique is consid-ered to be more reliable. Even this method failsto positively identify the percentage when theretained austenite is below 10%.

Heat Treat Distortion of Carburized and Hardened Gears

Distortion is always a problem in all heattreating processes, and it is most severe in car-burizing and hardening. Thus, its reduction orelimination is a very important factor in themanufacture of high-quality gears. In gears, twotypes of distortion occur. One is a body distor-tion, which, for gears, is measured in terms ofout-of-roundness, out-of-flatness, or run-out di-mensions. The second is the distortion in geartooth geometry. Body distortion also influencestooth geometry distortion a great deal. In gen-


eral, distorted gears need a finishing operationafter carburizing and hardening to improve theirquality.

The mechanism of heat treat distortion isquite complex for any component and more sofor gears. It is expected that the following briefdiscussion on this phenomenon will be helpfulto manufacture high quality gears at an opti-mum cost.

Mechanics of Heat Treat DistortionAfter carburizing, gears are quenched either in

oil, water, or gas to increase tooth surface hard-ness. As the gear body cools during quenching,two types of internal stresses are induced: ther-mal and grain microstructure transformation.

Thermal Stress. Thermal stress is induceddue to exterior surfaces of the gear cooling morerapidly and contracting than the inner ones, thusdeveloping a temperature gradient. In alloysteels, the various alloying elements with differ-ent densities result in different specific volumesthat cause additional thermal stresses. Theseinternal stresses may cause extensive deforma-tion as the gear cools down to room tempera-ture. In general, the more drastic the quench is, the greater the thermal stress causing geardistortion.

Transformation Stress. During the carbur-izing process, as a gear is heated up to the firstcritical temperature, its volume increases. Thisvolume then decreases as ferrite transforms intoaustenite. Once the austenitic transformation iscomplete, volume increases again with highertemperature. However, the coefficient of volu-metric expansion is different for austenite thanfor ferrite. After the austenitic transformation, asthe temperature is lowered, thermal contractiontakes place until the temperature falls to quench-ing temperature. As the temperature drops duringquenching, austenite is transformed to marten-site and the volume increases again. This trans-formation goes on until the temperature drops toroom temperature. Even at this temperature, allmartensitic steels contain some austenite, theamount increasing with the amount of alloyingelements dissolved during austenitization. Thelarger the quantity of retained austenite in thesteel after hardening is, the smaller the increasein volume. Also, the volume of austenite in-creases with the amount of dissolved carbon.

Furthermore, all gear steels are basically ani-sotropic, which means the volume change oc-

curring during the heat treat process will not bethe same in the direction of rolling from whichgear blanks are made as in the direction of rightangles (90°) to it. The volume change in gearsalso is affected by the configuration and geom-etry of gear blanks (with or without web). Allsuch volumetric changes induce additionalstresses in a gear body that cause distortion.

Material and Heat Treat Process Factors

Besides thermal and transformation stresses,the factors discussed below contribute signifi-cantly to the distortion of carburized and hard-ened gears.

Quality of steel plays an important role inthe process of distortion. The better the qualityof the steel is, the lower the distortion. For ex-ample, alloying segregation in any gear materialmay cause variations in hardness in a givencross section, which, in turn, initiates a differen-tial response during machining operations. Theresult is various degrees of cold work with un-predictable dimensional change during heattreatment. Another material property is grainstructure. A uniform grain structure is desirablefor predictable distortion. Furthermore, the non-metallic inclusions in the material need to beminimized, preferably by selecting vacuum-melted steels. Low inclusions make the me-chanical properties of vacuum-melted steels farsuperior to the air-melted variety. In the follow-ing section, the primary advantages and limita-tions of vacuum-melted steels are discussed indetail. Also, it is important that gears of thesame material heat code provided by steel millsare processed together to maintain uniform heattreat response.

Material cleanliness is an important crite-rion that needs to be considered for acceptablequality of gear materials. Also, material cleanli-ness plays an important role that determines theconsistency of heat treat response. The cleanerthe material (low nonmetallic inclusions) is, themore predictable the heat treat distortion ofgears. The degree of cleanliness usually is con-trolled by an Aerospace Material Specification(AMS). Of the various applicable specifica-tions, the following are frequently applied togear steels:

• AMS 2300: “Steel Cleanliness, PremiumAircraft Quality Magnetic Particle Inspec-tion Procedure”


• AMS 2301: “Steel Cleanliness, AircraftQuality Magnetic Particle Inspection Proce-dure”

• AMS 2304: “Steel Cleanliness, SpecialQuality Magnetic Particle Inspection Proce-dure”

As the titles indicate, these specifications alsocall for strict magnetic particle inspection stan-dards to control surface integrity. AMS 2300specifies the highest cleanliness standard andcan only be achieved in vacuum arc remelt(VAR) steels. On the other hand, AMS 2301quality steels are generally achieved by air melt-ing, whereas AMS 2304 quality may be attainedeither with VAR or air melting under strict con-trol of nonmetallic inclusions.

Sometimes, AMS 2300 quality steels are notreadily available because of strict control ofinclusions. Thus, it may create some unaccept-able bottlenecks in manufacturing. Also, in-house inspection of such materials presents quitea bit of difficulty for gear manufacturers notequipped with proper measuring equipment.Furthermore, these materials are not easilymachinable due to lack of sufficient sulphur,which causes cutting speeds and feeds to beslowed down considerably. Even then, highstresses may be induced in the gears duringmachining. For predictable heat treat distortion,it is thus a good practice to stress relieve gearsmade of these materials before any heat treat-ment. In addition, experimental results show thatmaterial cleanliness affects some importantmechanical properties such as allowable contactfatigue stress and bending fatigue stress in gears.

Studies on the effect of steel cleanliness ongear performance led to the development ofcleanliness standards for three different materi-als by the American Gear Manufacturers Asso-ciation (AGMA):

• Grade 3 materials call for AMS 2300. Gearsmade of these materials are used in criticalapplications. Allowable contact fatiguestress is 1900 MPa (275 ksi).

• Grade 2 materials call for AMS 2301. Gearsused in these applications are not as criticalas those made of grade 3 materials but havebeen successfully used in high-speed appli-cations up to 185 m/s (36,000 ft/min). Thesematerials are easy to machine and procure.Cost/pound is significantly lower than grade3 materials. Allowable contact fatigue stressis 1550 MPa (225 ksi).

• Grade 1 materials do not specify any specialcleanliness quality and nonmetallic inclu-sions may vary widely. A great percentageof industrial-type gears are made with thesematerials. Allowable contact fatigue stressfor such steels is 1240 MPa (180 ksi). Amajor disadvantage with this grade of mate-rials is significant uncontrolled heat treatdistortion of gears.

Although there is no separate AGMA gradefor materials that meet AMS 2304, theirmechanical properties are far superior to AMS2301 quality materials. Allowable contact fa-tigue stress may be considered to be similar tograde 3 materials. Also, heat treat response ofthese materials is as predictable as AMS 2300materials. Besides, AMS 2304 materials areeasily available and their cost/pound is less thanAMS 2300 materials. All of these featuressometimes make AMS 2304 material quiteattractive even for some critical applications.

The Hardenability of Steel. Steels withhigher hardenability, in general, experiencemore heat treat distortion. On the other hand,lower hardenability steels exhibit low distortionbut may not meet the design requirements.

Alloy Elements. The higher the alloy con-tent, the larger the heat treat distortion will be.

Method of Quenching. Direct quenchingresults in lower distortion. However, distortionmay increase when gears are cooled after carbur-izing and then reheated before quenching (dou-ble heating cycle and related thermal stress).

Flow of Quench Media. Whether oil orgas, an insufficient and turbulent quenchantflow increases distortion because of slow heattransfer between the gears and quench media.

Temperature of Quench Media. Lowquench media temperature increases thermalshock and gear distortion. High quench temper-ature reduces distortion but may not produceacceptable case properties.

Speed of Quench Media. Low-speed oilmedia (16 s and lower) causes higher distortion.Higher than 18 s is suitable for low distortionbut may not produce the desired case micro-structure.

Gear Blank Design (Solid or WebbedConstruction). Solid construction seems tohave smaller distortion than the webbed config-uration. However, larger gears are usuallywebbed in order to reduce weight and oftenhave asymmetric sections as well. Distortion ofthis type of gear blank could be large. Again,


webbing is needed for uniform heat treatmenttooth along the face width. Without web, thecenter of tooth does not have the same metallur-gical properties as the end of a tooth as depictedin Fig. 31.

Vacuum-Melted versus Air-Melted Alloy Steels

Because of high strength, ductility, andtoughness, alloy steels are frequently used forgears, particularly in aerospace and other criti-cal applications. These steels are available ineither vacuum- or air-melted condition. Vac-uum-melted steels have fewer nonmetallicinclusions, are much cleaner than the air-meltedvariety, and offer several advantages as dis-cussed previously. Even then, gear engineersare reluctant to use these types of steel due tohigher material cost per pound without any con-sideration for the total manufacturing cost. Vac-uum-melted steels offer optimum designs inseveral applications because of low heat distor-tion that significantly reduces gear grindingtime. Also, the rejection rate of gears after car-burizing for improper case microstructure isvery low. It is advisable, therefore, to considerall pros and cons before selecting a proper gearmaterial. To enable design engineers to decideon the type of material, it is considered helpful

to summarize the major benefits of vacuum-melted steels:

• Lower unwanted gas content• Fewer nonmetallic inclusions• Less center porosity and segregation• Increased transverse ductility• Increased fatigue properties

Typical average gas contents (wt%) of twowidely used steels before and after consumableelectrode vacuum melting, as determined by thevacuum fusion technique, are shown in Table12. It can be seen that the gas contents of AISI4340 and 9310 steels have been reduced toextremely low levels by vacuum melting. Thelow hydrogen content in steels reduces the sus-ceptibility to flaking, while the low oxygen con-tent reduces the amount of oxygen available forformation of nonmetallic inclusions.

There are two methods available for compar-ing the cleanliness of vacuum-melted and air-melted steels. One is the magnetic particle testthat has been extensively used in the aircraftindustry for rating steels such as AISI 4340 and9310. The other method for rating cleanliness isthorough microexamination, whereby the num-ber, sizes, and types of nonmetallics are counted.

The magnetic particle inspection of vacuum-melted steel requires that indications of inclu-

Fig. 31 Effect of gear blank web on uniformity of tooth hardness

Table 12 Gas contents of two gear steels before and after consumable electrode vacuum melting

Alloy H2 O2 N2 H2 O2 N2

AISI 4340 0.00014 0.0025 0.010 0.00009 0.0004 0.0053AISI 9310 0.00019 0.0035 0.011 0.00008 0.0006 0.0072

Gas content, wt%

Before vacuum melting After vacuum melting


sions as small as 0.40 mm (1 ⁄ 64 in.) long becounted, whereas, in testing air-melted steel, it isrequired only to count indications down to 1.6mm (1 ⁄ 16 in.) in length. A comparison of vacuum-melted, and air-melted heats of AISI 4340 and9310 steels was made where indications down to0.40 mm (1 ⁄ 64 in.) in length were counted in thesteel produced by both vacuum and air melting.In every case, the vacuum-melted steels were 5to 10 times cleaner than the air-melted products.The Jern Konntoret (JK) chart (Fig. 32) de-scribed in ASTM E 45 is one method for ratingcleanliness of steels. Row 1 in this figure showsthe least amount of inclusions while row 5 hasthe highest amount of inclusions.

Improvements in fatigue resistance aredirectly related to the cleanliness of steel. It hasbeen shown that large nonmetallic inclusionslower the fatigue strength of a metal. In vacuum-melted steels, there are no large nonmetallicinclusions. This increases their fatigue strengths.The transverse ductility of steels produced in a

vacuum also shows improvement, especially atthe ultra-high-strength level. The improvementin transverse ductility of AISI 4340 (AMS 6485)and 300M steels after vacuum melting is denotedby higher elongation as shown in Table 13.These materials are extremely brittle at the 2070MPa (300 ksi) strength level in the air-meltedcondition; however, after consumable electrodevacuum melting, they have sufficient transverseductility to be fabricated into aircraft landinggears and missile components. The higher, moreuniform quality of the consumable-electrodevacuum-melted steels makes them popular foraerospace applications where fatigue life (over10 billion cycles) and high reliability are fre-quently a requirement.

Cost of Material. Although air-melted steelcosts are approximately 50% less, the use ofVAR steels permits cost savings in several areas:

• Magnetic particle test rejections are reducedto almost zero. Each finished gear that is

Fig. 32 Jern Konntoret (JK) chart for determining the inclusion in steel. (a) Sulfide-type inclusion. (b) Alumina-type inclusion. (c) Sil-ica-type inclusion. (d) Globular-type inclusion


Table 13 Comparison of transverse mechanical properties between air-melted and consumable-electrode, vacuum-melted steels

Tempering temperature Tensile strength

Alloy Type of melt °C °F MPa ksi MPa ksi

AISI 4340 Air 230 450 1944 282 1586 230 6.0 14480 900 1379 200 1193 173 8.0 16538 1000 1241 180 1103 160 10.0 22

Vacuum 230 450 1931 280 1634 237 6.5 17480 900 1379 200 1207 175 9.0 20530 1000 1241 180 1103 160 10.5 24

300M Air 315 600 1958 284 1620 235 5.0 11425 800 1758 255 1538 223 7.0 14538 1000 1586 230 1482 215 9.0 22

Vacuum 260 500 2020 293 1620 235 7.0 25425 800 1758 255 1551 225 10.0 34538 1000 1586 230 1482 215 11.0 35

Yield strengthElongation,

%Reductionof area, %

scrapped due to mag-particle inspection rep-resents a loss of 10 to 30 times raw materialcost.

• VAR material would eliminate the need forforged blanks in gear sizes under 130 mm (5 in.) outside diameter. Forging dies andforgings are a significant cost item in gears.

• VAR material can be procured with aboutthree times closer control on chemical com-position. Heat treat practice, a high source ofgear rejections, can be much more easilyperfected by having large quantities of steelthat are almost exactly the same composi-tion and hardenability.

• Problems of “banding” (grains not properlydiffused in certain areas of a forging orrolled bar) and alloy segregation can beeliminated. In gear blanks made of air-melted steels, such a condition may exist.Banding is the result of improper solidifica-tion of steel in an ingot and may causereduced core hardness in the range of 1 to 2points in HRC scale. Minor banding is gen-erally eliminated during subsequent heattreatment, particularly normalizing andaustenitizing as diffusion occurs duringthese processes. Severe banding that occa-sionally exists in air-melted steels destroysmaterial microstructure, and the hardnessmay be reduced as high as 10 HRC points,which are detrimental to gear life.

• Early failure of a gear due to undetectednonmetallic inclusions is minimized.

• VAR material gears carry more load thanair-melted steels because there is only about1⁄20 the amount of macro and micro impuri-ties present. Allowable gear rating could be

raised when VAR material is matched upwith a skilled and disciplined heat treat prac-tice. For example, a 1200 hp gearbox (gearsmade of air-melted steel) may be upgradedto transmit 1500 hp with the same center dis-tance if gears are made of VAR steels, pro-vided other components such as bearingsand shafts in the gearbox can carry the addi-tional load.

Measurement of Gear DistortionsThe distortion associated with gears is usu-

ally characterized by the following changes ingear geometry:

• Profile change: Due to greater growth nearthe root of gear teeth than at the tips givingthe appearance of collapsed tips

• Lead change: A condition, experiencedquite often, with gears of wide face widthresulting in a change of tooth helix angle(spur gear tooth: 0° helix angle)

• Size change: Determined by measurementsof pitch diameter (PD) before and after heattreatment. Change in dimension over orbetween pins bears a direct relationship withthe change in PD of gears.

• PD runout• Change in blank dimension: Flatness of rim

and hub

Some Recommendations to Minimize Distortion

Steel Cleanliness. Material needs to be asclean as possible (AMS 2300 or 2304), prefer-ably vacuum melted and of homogeneous com-


Fig. 33 Acceptable and unacceptable grain flow in a gear forging

position—alloy segregation or banding is to beavoided. AMS 2300 is highly recommended forcleanliness. If difficulty is experienced inprocuring material under this specification, thenAMS 2304 may be considered.

Lot Verification. The material in each lotof gears shall conform to the specification on thedrawing. A lot shall consist of gears of one partnumber, manufactured from one heat of steel,and should not be mixed with another heat ofsteel during heat treatment. Each part must beidentified with the lot number.

Heat Verification. Verification of confor-mance of heat for the steel shall be performedprior to manufacture of gears. The verificationshall include chemical analysis, hardenabilitycheck, magnetic particle inspection rating,microinclusion rating, and macroetch examina-tion, as applicable.

Grain Flow. When a forging is required foran application, the forge die and upset ratio shallbe determined by examination of a sample forg-ing prior to production. Evaluation for approvalshall be made on a section cut through the cen-terline, or longitudinal axis of the sample forg-ing. After approval, the forge die and upset ratioshall not be changed. Figure 33 shows someacceptable and unacceptable grain flow patternsin a gear forging. Grain flow parallel to gear axisis not acceptable.

Proper normalizing of material is essentialprior to machining with subsequent microstruc-ture analysis for verification. It is an importantoperation for uniformity of grain structure. It iscarried out by heating gears to the austeniticregion and then cooling in “still air.” The nor-malizing temperature should be selected toslightly exceed the carburizing temperature, sothat grain size changes will not again occur dur-ing carburizing. Normally, carburizing is per-formed between 870 and 930 °C (1600 and1700 °F) for which an optimum normalizingtemperature would be between 940 and 950 °C(1725 and 1750 °F).

Materials after normalizing with hard-ness above acceptable machining range(HRC 34) may be annealed at a lower temper-ature to obtain proper hardness. Grain sizebetween ASTM 5 and 7 (Fig. 34) after normal-izing is quite effective for low distortion. Testcoupons must accompany parts.

Normalizing refines grain structure,whereas annealing reduces hardness. Gears may be normalized before or after roughmachining. An adequate normalizing procedureis as follows:

1. Load the part into a furnace that is at orbelow 870 °C (1600 °F), if part is of uni-form section size. Limit the furnace tem-


perature to 540 °C (1000 °F) maximum,when loading a part with more than onesection thickness (to avoid cracking).

2. Furnace temperature rise shall not exceed170 °C (300 °F) per hour.

3. Normalizing temperature will be between940 and 950 °C (1725 and 1750 °F)—slightly above the carburizing temperatureplanned, not by more than 30 °C (50 °F).

4. Hold at temperature for ½ h of maximumsection thickness or 2 h, whichever isgreater.

5. Remove from furnace and allow to cool instill air. Do not accelerate or inhibit airmovement.

6. Stress relieve before gear cutting. Stressrelief is also suggested after rough gear cut-ting for gears below 5 DP.

7. Uniform carburizing atmosphere: Theentire load needs to be at a narrow temper-ature band (930 ± 8 °C, or 1700 ± 15 °F) toensure uniform result. The vacuum fur-naces are generally capable of maintainingtemperature within ±6 °C (±10 °F) in thework zone.

8. High, uniform laminar flow (225 to 300L/min, or 60 to 80 gal/min, for each 0.45

kg, or 1 lb, of gears) of quench oil, prefer-ably an oil that allows quenching at approx-imately 120 °C (250 °F) for acceptablehardness profile of gear teeth; gas quench ifcarburized in a vacuum furnace.

9. Speed of oil: approximately 18 s10. Press quench: This and other means of

quenching in fixture such as plug, and colddie are the most effective methods used tokeep the gears flat and minimum PDrunout.

Load arrangement in the furnace has asignificant effect on the outcome of directlyquenched gears. Small, lightweight, more intri-cate gears should be loosely hung on rodsmounted on special carburizing fixtures or laidflat on their faces. Larger and heavier gearsshould either rest vertically on their teeth withoverhead wiring for added stability or lie flat onthe faces.

When arranging a load for heat treatment in anin-and-out furnace, it may be necessary to exper-iment in order to find the best method suitable forthe gears in question. In one load arrangement(Fig. 35), 510 mm (20 in.) outside diameter(OD), 98 tooth spur gears made from forging

Fig. 34 Standard ASTM grain sizes of steel


Fig. 35 Arrangement of 510 mm (20 in.) OD spur gears in acarburizing furnace

(AISI 8620) with 13 mm (½ in.) face width(gears numbered 1 through 5 and 14) distortedexcessively, while those numbered 6 through 13did not. During the production run, instructionwas given not to place gears in the positions withexcessive distortion. This improved overallquality of gears after heat treatment.

In addition to these factors, control of the car-burizing process itself is considered vital foreffective carburizing with minimum distortion.There are many ways in which a carburizingfurnace and its controls can malfunction. Forinstance, failure of a thermocouple can causethe process to go out of control; soot buildup inthe furnace can interfere with carburizing reac-tions. An operator can detect these and manyother relatively common occurrences and takecorrective action before there is an adverseeffect on parts in the furnace. The following is apartial check list of items to be considered insetting up the furnace for production:

• Temperature distribution: Hot or cold spotsin the furnace are not acceptable. Thermo-couples need to be properly installed.

• Variation of carbon concentration: Testbars for carbon determination should beplaced at varying locations on trays withgears to be carburized. Results of prelimi-nary tests are to be analyzed statistically toascertain the process capability of the fur-nace.

• Carburizing atmosphere: For shallow cases,most of the enriching gas is to be deliveredinto the furnace close to the discharge end.For deep cases, it is to be nearer to the charg-ing end, keeping in mind that in eitherinstance, the enriching gas should enter atthe point where the work load has reachedthe carburizing temperature.

• Dew point control: It should be ascertainedwhether the last furnace zone (diffusionzone) can develop the required dew point,with some latitude for adjustment. A small,measured quantity of air may be introducedto increase the dew point and lower the car-bon potential.

Preheating of GearsIt is advisable to preheat gears prior to load-

ing into a carburizing furnace. This process gen-erally is done in a draw furnace. Preheatinghelps to control distortion that results fromintroducing gears from room temperature di-rectly to the austenitizing temperature.

Distortion Characteristics of Some Gear Materials

The distortion characteristics of carburizinggrade gear materials depend on a large numberof variables. Research work on distortion ofhigh-strength steels suggests the degree of dis-tortion depends not only on the steel composi-tion, but also on the type of heat treat process.For example, step quenching, or so-called aus-bay quenching, significantly reduces distortionby as much as a factor of three compared withnormal quenching procedure. Furthermore, heattreating the steel to a bainitic structure com-pared with martensitic structure reduces thedegree of distortion. Table 14 shows compara-tive distortion ratings of some commonly usedcarburizing grade gear steels in industrial andaerospace applications.

An analysis of data presented in Table 14shows gear materials that exhibit good mechan-ical properties with acceptable distortion gener-ally cost more than materials with higher dis-tortion. But the finishing cost of gears made of


Fig. 36 Standard gear blanks for high distortion

Table 14 Distortion ratings of common gear materialsHardness, HRC

Material AMS specification AMS quality Quench media Case Core Distortion rating(a)

AISI 8620 6276, 6277 2304 Oil 58–60 28–32 FairAISI 9310/9315 6265(b), 6414(c) 2300/2304 Oil 58–62 34–42 FairAISI 4320 6299 2300/2304 Oil 58–60 36–40 FairAISI 4330 M(e) 6411, 6429 2300 Oil 58–62 42–50 PoorAISI 4130 6370 2300/2304 Oil 58–62 34–42 PoorHP 9-4-30(e) 6526 2300 Oil 58–62 48–52 GoodM50 Nil 6490D 2300 Oil 58–62 35–45 GoodVASCO X2M N/A(d) 2300 Oil 58–62 38–44 GoodCBS 600 6255 2300 Oil 58–62 34–42 GoodAISI 4620 6294 2300/2304 Oil 58–62 34–40 PoorPyrowear 53 6308 2300 Oil 59–64 36–42 Good

(a) Distortion ratings: poor, degradation of AGMA quality by 2 to 3 classes; fair, degradation of AGMA quality by 1 to 2 classes; good, degradation of AGMA qualityby 0 to 1 class. (b) AMS 6265, consumable electro-vacuum-melted steel. (c) AMS 6414, consumable electro-remelted steel. (d) N/A, not available. (e) Effective casedepth determination is difficult due to high core hardness of these materials.

high distortion materials is significantly higher.Thus, it is important to consider all aspectsbefore selecting a proper gear material. Frommechanical properties, manufacturing, and costpoints of view, AISI 9310 is considered to beone of the best materials currently available.This material is available both in vacuum- andair-melted conditions. Vast field data of suc-cessful applications are also available. How-ever, AISI 8620 steels are extensively used for industrial gears because of their low cost. Itis found that gears up to 410 mm (16 in.) OD made of these materials could maintain

AGMA class 9 gear quality after carburizingand hardening.

Improvement in Gear Design toControl Heat Treat Distortion

Gear blank design has a profound effect ondistortion. To minimize distortion, blank designshould address not only uniform metallurgicalproperties of teeth along the face width but alsodistortion. For example, gear blanks as depictedin Fig. 36 are found to distort more than blanksshown in Fig. 37 under similar heat treat condi-

Fig. 37 Improved gear blanks for low distortion


Fig. 39 Distortion of slender pinion. (a) Before heat treat-ment. (b) After heat treatment Fig. 40 Pinion blank dumb-bell-type configuration

Fig. 38 Improved pinion design for low distortion. (a) Origi-nal design (blind end teeth). (b) Improved design

(open end teeth)

tions. Holes and reduced mass are beneficial forgood heat treatment and low distortion. Pinionteeth with blank ends as illustrated in Fig. 38(a)seem to have large distortion of lead. Such dis-tortion can be minimized with a small properlydesigned relief at the end of the teeth as shownin Fig. 38(b).

Carburizing of Long Slender Pinions. Inthis type of pinion, Fig. 39(a), after carburizingand hardening, in addition to distortion of toothgeometry, the shaft bows. Such a bow can beminimized by press or die quenching the pin-ions. Furthermore, if the design of the pinion issuch that the teeth are located at the center ofshaft, they will experience the maximum bow asillustrated in Fig. 39(b). Because the teeth needto be ground for higher quality (AGMA class 10and above) with respect to the centerline of bear-ing journals, which are at the minimum bowposition, grinding may remove most of the casefrom the teeth. To ensure minimum caseremoval from teeth after grinding, pinion shafts

of this type are sometimes straightened under apress before grinding of the journals and teethwith proper control. An uncontrolled straighten-ing operation could damage the parts for the fol-lowing reasons:

• Stress induction during straightening mayinitiate cracks in the hard case.

• After straightening, the part can be in an un-stable condition and is likely to return, atleast partially, to its unstraightened shapewhen put into service, causing impropercontact between meshing teeth that maydeteriorate gear life.

Because straightening is such a potentially dam-aging and expensive operation, everything prac-tical should be done to eliminate the need for it.If it is still necessary, a reasonably satisfactorysolution to the problem is to heat the parts to justbelow tempering temperature and straighten,followed by air cooling to room temperature.All parts shall then be magnetic particle or dyepenetrant inspected for cracks.

Dumb-Bell Shape Pinion. The design asillustrated in Fig. 40 presents a high degree ofdifficulty in controlling heat treat distortionafter carburizing and hardening. For acceptabledistortion, the ratio between largest and smallestoutside diameters in the shaft is recommendedto be less than 1.5:1. Pinion configuration of thistype should be avoided, if possible.

Blank Design for Uniform Hardness ofWide Face Width Gears. Of the variousparameters that control the heat treat quality ofcarburized and hardened gear teeth, the rate ofheat transfer between the teeth and quenchmedia plays an important role. In general,besides material hardenability, fast heat transferresults in acceptable surface hardness, effectivecase depth, and core hardness of gear teeth. Inachieving these properties, configuration of the


Fig. 41 Effect of blank design on hardness. (a) Typicalwebbed gear tooth. (b) Surface hardness vs. case

depth at different locations of a tooth along the face width Fig. 42 Drilling of blank for uniform core hardness

gear blank (with or without web), size of gear,face width of tooth, and DP also contribute sig-nificantly. Design of a gear blank with or with-out web depends largely on the form of materialused—bar or forging. Bars are used for smallgears, whereas large alloy steel gear blanks(above 250 mm, or 10 in., diameter), in particu-lar for high production, are made primarily fromforgings with web. Occasionally, for small pro-duction quantities, large gear blanks with webare machined out of “pancake” forgings. In anycase, when large gears with or without web arecarburized and hardened, hardnesses at the sur-face and core, and case depth are found to belower at the center region “a” of tooth facewidth (Fig. 41a) than at the outer regions “b.”Figure 41(b) illustrates an approximate differ-ence in surface hardness versus case depth gra-dient at “a” and “b”. On the other hand, such a

difference is not greatly pronounced in smallgears (less than 250 mm, or 10 in., diameter)because of their smaller mass. Nevertheless,with high l/d (face width/pitch diameter) ratioover 1.5:1, lower case depth and hardness resultat the center region of teeth in all gears, large orsmall, the variations being quite distinct in largegears.

The cause of lower effective case thicknessand core hardness is attributed mainly to differ-ential heat transfer rate during quenching—slowest at the center region. Large mass of theweb below the center region acts as a barrier tofast heat transfer rate required for high hardnessand uniform case depth along the face width.Without web (solid blank) the differential heattransfer extends from the outer ends to the cen-ter region of teeth that results in higher hardnessand case depth at the ends gradually decreasingtoward the center.

Although small variations in hardness andcase thickness along the face width may not beof any concern for gears in industrial applica-tions, these can play an important role in ensur-ing the reliability of carburized and hardenedgears in critical applications. An improvementto the blank design is recommended to ensureboth uniform hardness and case depth along theface width of gears.

This can be partly achieved by designing ablank with a small fillet radius at the web that isacceptable from a stress concentration point ofview. Also, heat transfer from the middle sec-tion of the tooth could be improved by drillingsmall holes in the tooth spaces as illustrated inFig. 42. Small fillet radius and holes in toothspaces not only improve uniformity of case andcore hardnesses along the face width of tooth


Fig. 46 Helical tooth with chamfer on tooth edge

Fig. 43 Pinion design with threads in the shaft

Fig. 44 Helical tooth without chamfer on tooth edges

Fig. 45 Gear quenched in flat position

but also provide better lubrication, especially inhigh-speed gearing with pitch line velocityabove 50 m/s (10,000 ft/min).

Pinion Shaft with Threads. The threads ona pinion shaft as depicted in Fig. 43 grow anddistort similar to pinion teeth after carburizingand hardening to the extent that may require thethreads to be ground. To eliminate such a costlyoperation, it is advisable not to carburize thethreads, which could be achieved either by cop-per plating or covering with noncarburizing-type solution before carburizing. Any small dis-tortion during heat treat process may beremoved by thread chasing, a fairly inexpensiveoperation compared with grinding.

Heat Treat Cracks at Tooth Edges. In hel-ical gears, unchamfered tooth edges, which, inparticular, form acute angles with the face width(Fig. 44), are frequently found to developmicrocracks after carburizing and heat treat-ment. These types of cracks are more pro-nounced on the side that enters the quenchmedia first (Fig. 45). This is due to high thermalshock and stress—the cooler the quench media,the higher the shock.

Experimental investigations showed thatcracks emanating from the tooth edges could be

avoided by a proper chamfer (Fig. 46) that helpsto eliminate the sharpness of the acute angleedges. In chamfering the tooth edges, it isimportant to note that the amount of chamfermay not be equal on the acute and obtuse anglesides—smaller on the edge with the acute angle.Because cracks are found primarily on the edgewith acute angle, chamfering on this edge isimportant. The following chamfer dimensionsare found to be adequate and recommended foravoiding cracks from tooth edges of helicalgears:

• 4 DP and lower: 1 mm (0.04 in.) × 45°• Above 4 DP: 0.75 mm (0.03 in.) × 45°

Also, quenching of gears hanging from fixturingrods (Fig. 47) helps to reduce cracks at toothedges. Certainly, this method of quenching islimited to smaller gears with low mass; large


Fig. 47 Gear quenched hanging from bar

gears with heavy mass are not suitable becauseof higher distortion (PD runout). Cracks of thisnature are not common with spur gears becausespur gear tooth edges do not form any acuteangles.

Grinding Stock Allowance on ToothFlanks to Compensate for Distortion

For gears that do not meet the quality require-ments after heat treatment and grinding isrequired, additional stock is provided on toothflank. For a ground root, stock is also needed onthe root. Grind stock is determined on the basisof cleaning of all the surfaces of teeth consider-ing distortion and growth of gears after carburiz-ing and hardening. The grind stock allowance ongear teeth should not deemphasize the process-ing control required for minimum distortion. Infact, the control is just as necessary for gears thatwill be ground as it is important for gears that arenot ground after heat treat. The reason is that ifthe distortion is high and corrected by grinding,it may result in uneven case depth or sometimesno case at all on some teeth. Furthermore, theaddition of extra stock increases grinding timeand cost. So, for good quality gears at optimumcost, the distortion during heat treat needs to becontrolled. Distortion control will not only allowminimum removal of stock during grinding butalso ensures “sound” gears from the metallurgi-cal viewpoint.

In a well-controlled carburizing and harden-ing process, distortions could be held to within

one AGMA class below the pre-heat-treat qual-ity for gears made of commonly used materialssuch as AISI 4320H and 8620H. Such a processallows the establishment of a minimum grindstock on a tooth surface and the maintenance ofthe minimum surface hardness required aftergrinding. This satisfies the design requirementfor minimum gear pitting life in most applica-tions. Unfortunately, the state-of-the-art carbur-izing and quenching technology is unable toassure low gear distortion consistently in a pro-duction mode of operation. Sometimes, distor-tions within the same batch of gears are found tovary widely. Hence, it is very likely to find somegears after heat treatment with distortion farmore than others. Grinding of such gears forminimum stock removal necessitates inspectionof every gear in a batch for distortion severity.This increases the cost of gears. Furthermore,tooth surface hardness and effective case depthmay not be acceptable after grinding.

Besides grinding, surface hardness reductionof carburized and hardened teeth is also influ-enced by the slope of hardness versus case depthgradient of gear steel. Each carburizing gradesteel has its own unique slope and is primarilycontrolled by its alloying elements. The steeperthe slope is, the greater the hardness reductionon tooth surface after grinding will be. In addi-tion, grinding machine setup plays an importantrole in the equal amount of stock removal fromeach flank of the gear teeth and its associatedhardness reduction.

To establish an ideal grind stock, detailed dis-tortion characteristics and growth data of gearsare beneficial. For gears without any preproduc-tion or historical data on heat treat distortion,general knowledge on heat treat response of thegear material helps to establish effective grindstock.

Grinding of Distorted GearsWith the grind stock so determined either by

a preproduction investigation or from data ofsimilar gears, grinding of carburized and hard-ened gears is performed by properly positioningthe grinding wheel in the tooth space. In moderngear grinding machines with advanced mea-surement systems, a probe measures the helix(lead) deviation on a predetermined number ofright and left flanks of teeth at different loca-tions that include teeth at maximum PD runout.The measured values not only contain the effect


Fig. 49 Hardness gradient of a carburized and hardenedgear tooth. Material: 17CrNiMo6

Fig. 50 Hardness gradient of a carburized and hardenedgear tooth. Material: AISI 8620H

Fig. 48 Schematic of materials ground from a carburized andhardened gear tooth. (a) Tooth with no distortion;

equal stock removal from both flanks. (b) Tooth with distortion;more stock removal from one flank

of all helix deviations and PD runouts, but alsothe effect of profile and cumulative pitch varia-tions. The computer in the machine control cal-culates the optimum angular position of the gearbefore grinding starts. This method ensures thatthe grinding wheel will be positioned at the cen-ter between two flanks, allowing equal stockremoval from each flank starting with teeth atthe maximum PD runout. The method workswell as long as the distortions are comparativelysmall and their variations are distributed withina narrow band—one AGMA class below thepre-heat-treat quality.

For gears made of high-alloy steels such asAISI 9310 and AISI 8620 that exhibit uncon-trolled distortion after carburizing and harden-ing, the selection of an effective grind stock isquite difficult. Tests carried out show gearsmade of these materials have larger variationsof PD runouts and spacing of teeth. Further-more, the distortion seems to vary in a randommanner. Hence, considerable difficulty is expe-rienced for equal stock removal from all theflanks of distorted teeth even with moderngrinding machines. This leads to more-than-planned stock removal from some teeth flanksduring grinding as illustrated in Fig. 48.

Actual Stock Removal and Tooth Surface Hardness

The more stock that is removed from the sur-face of a carburized and hardened tooth, thelower the tooth surface hardness will be. Thedegree of hardness reduction is dependent alsoon the slope of the hardness gradient of thetooth. Figures 49 and 50 illustrate hardness gra-dients of two low-alloy steels, the first one for17CrNiMo6 and the other for AISI 8620H aftercarburizing and hardening. In comparison with17CrNiMo6, the hardness gradient of 8620Hexhibits a lower hardness at the tooth surfacefollowed by a gradual increase in hardness withthe maximum at a depth of 0.05 to 0.08 mm(0.002 to 0.003 in.) below the surface. This isbelieved to be due to higher than normal per-


Fig. 51 Hardness gradient of a carburized and hardenedgear tooth. Material: AISI 9310H

centage (about 20%) of retained austenite at thesurface of these gears after quenching. On theother hand, the percentage of retained austeniteafter cold treatment is much better controlled inmost of the high-alloy steels. Consequently,these materials do not exhibit the characteristicof some low-alloy steels. This is depicted in Fig.51 for AISI 9310H.

It is clear from the hardness gradients of var-ious alloy steels that stock removal over 0.13mm (0.005 in.) (normally allowed for grinding)from the flanks of distorted carburized and hard-ened gear teeth may result in lower than theminimum surface hardness required for theexpected pitting life. Because of the steeperslope, a usual characteristic of low alloy steels(Fig. 50), the surface hardness reduction of gearteeth made of these materials is generally higherthan those made of high-alloy steels. Again, dis-tortion associated with low-alloy steel gears iscomparatively less, and hence, these warrantsmaller stock removal during grinding. Thus,the actual tooth surface hardness reduction aftergrinding is almost of the same magnitude forboth low- and high-alloy steel gears. Some-times, carburizing with boost-diffuse cycle pro-duces a flatter hardness gradient. Because it isgenerally cost prohibitive, this type of carburiz-ing is very seldom used. This allows the consid-eration of similar amounts of grind stock for allgear materials. Furthermore, grind stock re-quired on each tooth flank for both low- andhigh-alloy steel gears with controlled heat treatdistortion is found not to exceed an average of0.13 mm (0.005 in.). Removal of stock to thisdepth does not seem to reduce tooth surface

hardness below the minimum considered indesign with carburized and hardened gears.

In a production-type carburizing and harden-ing operation, which is frequently associatedwith uncontrolled distortion, stock over 0.13mm (0.005 in.) is very often removed from teethlocated at maximum distortion. Such stockremoval in some gears may result in surfacehardness reduction as high as two points on theHRC scale, particularly for materials with asteep hardness gradient slope. As an example, ingears made of 17CrNiMo6, the hardness reduc-tion for an additional 0.05 mm (0.002 in.) stockremoval over planned 0.10 mm (0.005 in.) isapproximately one point on the HRC scale. Thisis a significant hardness reduction below theminimum considered during design. Lower sur-face hardness will definitely reduce pitting life.The new pitting life may be calculated from theequation derived from the pitting life versuscontact stress relationship.

New Pitting LifeThe equation for pitting life in terms of stress

cycles (L1) of a gear at any power level can beestimated as:

(Eq 9)

where Sac1is the allowable contact stress for the

gear material at minimum hardness, Sc is theactual contact stress due to applied load, and αis the slope of S-N curve for gear durability =17.62 (AGMA standard 2001-B88). Similarly,the new pitting life (L2) for a lower allowablecontact stress (Sac2

) due to reduced tooth surfacehardness of the same gear and at the same powerlevel is:

(Eq 10)

Equations 8 and 9 yield:

(Eq 11)

From Eq 11, the pitting life of a gear can be cal-culated at any allowable contact stress that cor-responds to a specific tooth hardness. For exam-ple, if due to additional stock removal (0.05mm, or 0.002 in., over the allowed 0.10 mm, or0.005 in.), the surface hardness of teeth reduces

L2 � L1 a Sac2

Sac1

b a

L2 � 107 a Sac2

Scb a

L1 � 107 a Sac1

Scb a


Fig. 52 Allowable contact stress number for carburized andhardened steel

from 58 to 57 HRC (Fig. 49), the allowable con-tact stress (Sac2

) for AGMA grade 1 material(Fig. 52) becomes:

Brinell hardness number (HB) of tooth surface� 1475 MPa (214 ksi)

The allowable contact stress (Sac1) at mini-

mum hardness (58 HRC) per design is 1500 MPa(218 ksi). Using Eq 11 the new pitting life is:

(Eq 12)

This is a significant reduction of gear pittinglife. Hence, for true pitting life of carburized,hardened, and ground gears, it is essential toconsider heat treat distortion. Certainly, thisnecessitates the availability of heat treat distor-tion data for all newly designed gears—a diffi-cult task to accomplish. One possible solution tothe problem is to develop distortion-deratingfactors for various gear materials from knownheat treat data and apply them to derate pittinglife.

Distortion Derating FactorThe distortion derating factor (DDF) is

defined as the ratio of actual pitting life to therequired pitting life of gears. For realistic valuesof distortion derating factors, it requires compre-hensive knowledge on composite distortioncharacteristics that include different gear materi-als, configuration and size of gears, gear diame-

L2 � 0.72 L1

Sac2� 26,000 � 327 HB

tral pitch and helix angle, heat treat process andequipment, and hardness gradient of each ofthese materials. Such a task is beyond the scopeof this discussion. Table 15 lists derating factorsfor some commonly used materials based ongear distortion characteristics. These are basedon an additional 0.05 mm (0.002 in.) stockremoval above 0.10 mm (0.005 in.) normallyallocated. Similar derating factors for other gearmaterials can be established from their compos-ite gear distortion data.

Sometimes, to avoid the task of developingsuch distortion derating factors, an extra grindstock with additional case depth is suggested.The extra stock no doubt allows grinding of allthe teeth to the required quality and geometrybut does not help to maintain the surface hard-ness equally on all the teeth surfaces. Also,deeper case creates some serious heat treatproblems for gears. First, it will increase car-burizing cycle time and, hence, the cost. Sec-ondly, it does not help to increase case hardness.Finally, a deeper case may cause some severeadverse effects such as:

• Through hardening of teeth, particularly forfine-pitch gears and gears with large pres-sure angle, above 20°

• Higher surface carbon—a potential sourcefor inducing grind burn

• Additional grinding time—higher cost• Larger step at the intersection of root radius

and tooth profile for unground roots—higherstress concentration

• Increased percentage of retained austenite—lower surface hardness

• Increased level of undesirable carbide net-work in the case microstructure—mechani-cal properties of teeth may be affected

Considering all of these potential problems, adeeper case than what is needed is not recom-mended.

Additional Effects of GrindingCarburized and Hardened Gears

Carburized and hardened gears are generallyground to improve distorted tooth geometrycaused by heat treatment. To maintain the re-quired case depth and tooth surface hardnessafter grinding, a certain amount of grind stock isprovided to pre-heat treat tooth flanks, and thecarburizing process is adjusted for case depth


Table 15 Distortion derating factors for true pitting life of carburized and ground gearsHardness versus case depth gradient

Gear materialHigh orlow alloy

Hardness drop less than half apoint HRC for every 0.05 mm(0.002 in.). Stock overallocated

(0.127 mm, or 0.005 in.)

Hardness drop more than half apoint HRC for every 0.05 mm(0.002 in.). Stock overallocated

(0.127 mm, or 0.005 in.)

Low (within 1AGMA class

below pre-heat-treat quality)

High (over 1AGMA class

below pre-heat-treat quality)

Distortion derating

factor (DDF)

Air melt

4320 High X X 0.808620H Low X X 0.809310H High X X 0.8017CrNiMo6 Low X X 0.75

Vacuum melt

4320 High X X 0.854330M High X X 0.809310H High X X 0.85HP 9-4-30 High X X 0.90

Distortion severity

that includes grind stock. Besides improving thetooth geometry and maintaining an acceptablecase depth and surface hardness, grinding has aprofound effect on the tooth surface integritysuch as grind burn and removal of residual sur-face compressive stress. Both grind burn ontooth surface and surface compressive stress re-duction detrimentally affect the fatigue life ofground carburized and hardened gears. In thissection, some discussion on the causes of andremedy for grind burn is presented.

Gear Grind Burns. Gears and, as a matterof fact, any surface that is carburized, hardened,and subsequently ground, are subjected to re-tempering of localized areas popularly knownas grind burn. The reasons for such burns onground surface are generally attributed to im-proper carburizing and grinding operation. Alarge number of researchers have endeavored toidentify the causes of the grind burn phenome-non, but none of them has come up with anyuseful solution to the problem. Nevertheless,the results of all these investigations indicatethat a large number of carburizing process andgrinding parameters influence grind burn. Car-burizing factors that cause grind burn are:

• High surface carbon—0.9% and above• High surface hardness—61 HRC and higher• High retained austenite—above 20%

Grinding parameters that can contribute to grindburn are:

• High stock removal rate during grinding• Sudden increase in stock removal from a

tooth surface due to nonuniform heat treatdistortion

• Too fine grit of abrasives on vitrified grind-ing wheel

• High grinding wheel hardness• Unbalance in grinding wheel• Infrequent dressing of grinding wheel result-

ing in glazing of wheel• Improper type of coolant• Inadequate flow rate and direction of coolant

flow• Presence of grind sludge in coolant due to

malfunction of gear grinding machine cool-ant filters

• High coolant temperature• Unstable machine

Any one or a combination of these factors cancontribute to grind burn on a gear tooth surfacethat is ground, possibly by wet grinding thatuses vitrified aluminum oxide wheel and cuttingfluid. Gears are less vulnerable to such defectwhen ground in machines that operate dry.Unfortunately, such dry grinding machines areno longer used due to their long grind cycletime. Wet grinding machines recently devel-oped for cubic boron nitride (CBN) wheels arefound to be quite effective in ensuring grind-burn-free gear teeth. In any case, improperlycarburized gears ground by an improperly con-trolled grinding process can result in grind burnon tooth surfaces.

Grind burn lowers surface hardness on theburnt areas usually in the range of 2 to 3 pointson the HRC scale. A burnt tooth, particularly atthe point of maximum contact stress, lowers thecontact fatigue life of the gear. Furthermore, aburnt tooth surface is frequently accompaniedby microcracks. Although these cracks are very


Fig. 53 Experimental gears after nital etch for surface dam-age. Grinding patterns were observed after surface

nital etch on both gears. Microscopic examination of sectionsremoved from the gears did not reveal microstructural changesin the case hardened matrix in either gear.

minute, they still can affect the fatigue life of agear subjected to high cyclic load or that operat-ing near a resonant condition. To ensure grind-burn free teeth, it is thus essential to inspectgears after grinding.

There are two different methods available inthe gear industry to inspect gear burns—one isdestructive and the other nondestructive. Thedestructive method provides a positive identifi-cation of burnt surfaces and is based on themicrohardness reading of the surface below theburnt area. Such a method is not quite practical,whereas a properly controlled nondestructivemethod currently available can provide suffi-cient evidence of grind burn. The most commonone is the nital, or temper etch, method.

Gear Grind Burn Identification. A gooddeal of controversy exists over the accuracy ofthe temper etch method results. Generally, nitaletch inspectors are specially trained to distin-guish between burnt and regular tooth surfaces,but sometimes they fail, as was the case withone gear manufacturing company discussed inthis section. At one point during normal manu-facturing, this company was experiencing con-tinual rejection of carburized and ground gearsdue to grind burns identified with nital etch.Even after implementing all necessary controlsduring carburizing and subsequent grinding, theproblem of grind burn showed up from time totime. An external metallurgical inspection com-pany was then employed to investigate whetherthe gears were definitely burnt or not. Figure 53shows photographs of two such apparentlyburnt and rejected gears after nital etch. Thegears were made of AISI 8625H, carburized andhardened, and the teeth ground on a wet grind-ing machine. Being unable to draw a definiteconclusion, the company employed destructivemicroscopic examination of sections taken atthe burnt areas. Surprisingly, the results did notreveal any rehardening or retempering of theseareas at 1000× magnification. It was then con-cluded that the visible burn indications afternital etching were caused by differential skinetch reflection. A subsequent successful full-load test of the gears confirmed this conclusion.This is why each gear manufacturing companyneeds to develop its own criteria of acceptanceand rejection of grind burns.

Inspection and Limited Acceptance Cri-teria of Grind Burns. Because it is extremelydifficult to grind gears except by CBN grinderswithout any grind burn in a production type

environment, a discussion on inspection and itslimited acceptance is considered helpful toestablish optimum carburizing and heat treatconditions.

Gears shall be inspected visually for evidenceof grind burns following the etching procedureunder a light source of 200 footcandles (ftc)minimum at the surface being inspected. Sur-faces not burnt will be uniformly gray to lightbrown in color, depending on the alloy used.Surfaces burnt will appear dark gray to black incolor. These could be either overtempered orrehardened areas. Overtempered (burnt) area isdue to localized overheating during grindingand will appear dark to black in color. Thisresults in a lower surface hardness. A rehard-ened (burnt) area is due to transformation ofretained austenite to untempered martensite andwill appear as a white or light gray spot sur-rounded by black overheated area. Rehardenedareas are usually associated with grind cracks.

The hardness of overtempered areas may bemeasured with a Rockwell superficial hardnesstester using the 15 N scale in accordance with


Fig. 54 Gear tooth nomenclature discussed in the section“Inspection and Limited Acceptance Criteria of Grind

Burns”

ASTM E 18. For comparison, similar readingsmay be taken on adjacent areas of grind burn.

Acceptance Criteria. Basically, there shallbe no rehardened and overtempered areas onany ground teeth of fracture-critical gears. Lim-ited overtempering may be acceptable on non-fracture-critical gears. A number of aircraft andnon-aircraft industries have been consulted todevelop the acceptance or rejection criteria forgrind burn. Refer to Fig. 54 for nomenclature ofa gear tooth.

Overtempering of the active profile of a geartooth is not acceptable. Limited overtemperingbelow the form diameter and above the toothroot fillet area (transition zone) may be accept-

able if the total burnt area does not extend morethan the area designated in Fig. 55. Overtemper-ing is also acceptable on the end faces of teeth aslong as it complies with the figure and applies togears that might experience tip and edge loading.Figure 56 shows acceptable overtempering ofthe active profile of gear tooth near the edges.This is applicable to gears that do not experienceedge loading even with misalignment betweenmeshing teeth designed with proper crowning on tooth lead. Figure 57 depicts acceptableovertempering of the active profile near theedges and the tip of a gear tooth that does notexperience either edge or tip loading.

Fig. 55 Overtempering of gear tooth

Fig. 56 Acceptable overtempering of active profile geartooth near the edges

Fig. 57 Acceptable overtempering of active profile geartooth near the edges and tip of a gear tooth that does

not experience either edge or tip loading


Fig. 58 Different configuration of tooth surfaces after grind-ing Fig. 59 Principle of shot peening

Shot Peening of Carburized and Hardened Gears

In general, all carburized and hardened gearsare either ground or honed. Gears with low dis-tortion and low tooth quality requirement(AGMA class 9 or below) are normally honed.Conversely, gears with high distortion and highquality requirement (AGMA class 10 andabove) are finish ground. Honing does notremove much stock—less than 0.01 (0.0005 in.)from a tooth surface. Thus, the hardness profileof tooth remains approximately the same asobtained after carburizing and hardening. Thiskeeps the compressive stress induced at the sur-face during carburizing intact. However, inground gears this is not the case. Very oftenstock up to 0.13 mm (0.005 in.) stock or more isremoved from a tooth surface that reduces thesurface hardness as well as removes the inducedcompressive stress during carburizing. Thesedual effects lower pitting life of ground gearssignificantly.

To improve pitting life of ground gears, toothsurfaces (ground and unground part of the pro-file as indicated in Fig. 58) are frequently shotpeened after grinding to induce compressive

residual stress at and below the surface. Thus,some knowledge of the proper shot peeningprocess that enhances the performance of car-burized, hardened, and ground gears is consid-ered beneficial.

Shot peening is basically a mechanical pro-cess for improving fatigue strength of a part andhas been in practice for a long time. In medievaltimes, a knight’s armor was cold worked to finalshape and hardness by hammering with a round-edged hammer. The repeated hammering im-proved armor fatigue life. Today, hammering isreplaced with shot peening, which consists ofbombarding a surface with small sphericalmetallic balls at a high velocity. Each shot acts asa tiny peenhammer, making a small dent on thesurface of metal and stretching the surface radi-ally as it hits (Fig. 59). The impact of the shotcauses a plastic flow of the surface fibers extend-ing to a depth depending upon degree of impactof the shot and the physical properties of the sur-face being peened. The effect of shot peening issimilar to cold working to distinguish it frommetal flow at high temperatures. Furthermore, itdoes not affect case thickness or case propertiesof ground, carburized, and hardened gears.

Experimental work indicates the surfacecompressive stress after shot peening to be sev-eral times greater than the tensile stress in the


interior of the section. Figure 60 shows a typicalcompressive stress profile developed on a geartooth fillet that was shot peened after grinding.

Because all fatigue failures originate withcracks, compressive stresses induced on the geartooth fillet surface provide considerable increasein gear fatigue life because cracks do not initiateor propagate in compressively stressed zones.This makes the bending fatigue life of properlyshot-peened gears 1.5 to 2 times the life ofunpeened gears as illustrated in Fig. 61. In somegears, shot peening is limited to root fillet alone,which makes it necessary to mask the rest of thegear tooth surface. The masking needs to beremoved after peening and this increases the costof gear manufacture. Active tooth profiles usedto be masked because it was believed shot peen-ing deteriorated the tooth profile and surface,and thereby reduced the pitting life of the gear.Thus, gear engineers were not very enthusiasticabout shot peening the entire tooth surface untilrecent research showed a considerable increasein pitting fatigue life of gears besides increasedbending fatigue life when the active tooth profilealso was peened. Such an improvement wasachieved with a precisely controlled and moni-tored shot peening process. Now that shot peen-ing is widely accepted to enhance gear life, thefollowing are some of the guidelines for theprocess.

Type of Shot. From the standpoint of econ-omy of operation, steel shots are preferred overcast iron shots. For good peening, the shots mustbe hard in the range of 42 to 50 HRC. Also, theshots need to be approximately round and uni-formly sized at all times. As the shots break up,broken particles must be removed because

sharp corners of broken or uneven shot may pro-duce harmful effects that lead to a lower fatiguelife. Shot supply is to be monitored in themachine so that no more than 20% of the parti-cles, by weight, pass through the screen sizespecified for the shots, which come in differentsizes such as S230, S170 (number indicates thediameter of the shot: 0.023 in. for S230, and0.017 in. for S170).

Shot Size. The basic rule for shot size is thatits diameter should not be greater than one-halfas large as the root fillet radius of gear tooth.Shot size also should be correlated to the inten-sity of peening required, but without violatingthis rule. For low intensity, small shot should bespecified and for high intensity, large shot.However, the peening machine, nozzles, airpressure, and volume also dictate, to a largeextent, the most appropriate shot size. In gen-eral, the smallest shot size that will produce therequired intensity should be used. The smallerthe shot is, the faster the coverage rate and theshorter the peening time will be.

Intensity. The depth of the compressivelayer on tooth surface is proportional to the shotintensity used. Thus, calibration of the impactenergy from shot peening is essential for a con-trolled process. The energy of the shot stream is found to be a function of the shot size, mate-rial, hardness, velocity, and impingement angle.Specifying all of these variables would be diffi-cult and impractical. The job is simplified by amethod of measuring and duplicating shot-peening intensity on standard steel control strips

Fig. 60 Stress profile of carburized gear tooth root groundand shot peened

Fig. 61 Fatigue strength chart of carburized gears. Courtesyof Metal Improvement Company, Inc. (Shot Peening

Applications)


developed many years ago by J.O. Almen ofGeneral Motors Research Laboratories. In hismethod, a flat strip of cold-rolled spring steel(AISI 1070) with a hardness of 44 to 50 HRC isclamped to a solid steel block and exposed to ashot stream for a given period of time (Fig. 62).Upon removal from the block, the residual com-pressive stress and surface plastic deformationproduced by the peening impacts will cause thestrip to curve, concave on the peened surface(Fig. 62). The height of this curvature serves asa measure of peening intensity.

There are three standard strips used to pro-vide for different ranges of intensities: “A” strip(1.3 mm, or 0.051 in. thick), “C” strip (2.4 mm,or 0.094 in., thick), and “N” strip (0.8 mm, or0.031 in., thick). The approximate relationshipbetween the A, N, and C strips is: 3N = A =0.3C. The A strip is the one most commonlyused. If the arc height of the A strip is less than0.10 mm (0.004 in.), the N strip should be used.For A strip readings greater than 0.51 mm(>0.020 in.), the C strip should be used. A read-

ing of 10 A intensity means 0.25 mm (0.010 in.)arc height on the A strip.

Coverage. Amount of coverage is an essen-tial element of a peening operation. Full, or100%, coverage is defined as the uniform andcomplete dimpling of tooth surface as deter-mined visually by a magnifying glass or the peenscan process. Most carburized and hardenedgears require 200 to 300% coverage (double andtriple peening process). Peening of gears beyondthis range will not produce much improvement.Saturation or full coverage is defined as thatpoint when doubling the peening time results ina 10% or less increase in height of Almen strips.

Angle of Shot Impingement. In case theshots do not impinge the surfaces at a properangle, sometimes tensile stresses are introducedon tooth surfaces. For fine DP (above 20 DP)gears, the angle is particularly important toensure that the shots impinge the root fillet aswell as the profile of the tooth.

Whenever possible, microprocessor-controlled shot peening is recommended for pre-

Fig. 62 Shot peening intensity control. Source: Ref 6


dictability, reproducibility, and verifiability ofthe process. This allows optimum level of eachvariable to be maintained, thereby improving thequality of shot peening.

Residual Stress. Compressive stress at andbelow the surface after shot peening of gears isshown in Fig. 63. The figure definitely showsthe benefits of shot peening carburized, hard-ened, and ground gears.

Some guidelines of shot peening parametersfor different DP carburized and hardened gearsare given in Table 16.

Tooth Surface Profile. A typical gear toothsurface profile after shot peening is shown inFig. 64. It clearly shows there is not much dete-rioration of the surface after shot peening.

Shot Peening Specification. In specifyingshot peening requirements on a gear, the fol-lowing parameters identified on a drawing helpto minimize confusion:

• Area to be shot peened• Areas to be masked• Optional areas that can be shot peened or

masked• Shot size, hardness, and material• Intensity• Coverage• Equipment: microprocessor controlled or

standard

Some typical shot peening parameters forcarburized and hardened gears (AISI 9310material) are:

Parameter Value

Shot size 70Shot type Cast steelShot hardness 45 to 50 HRCIntensity 0.178 to 0.229 mm

(height of Almen strip; type A) (0.007 to 0.009 in.)Coverage (profile and root) 200%

Applications and Costs

Applications. The vast majority of gearsused in industrial applications today are carbur-ized and hardened. It is because the processoffers the highest power density in a gearboxthrough optimum gear design. High surfacehardness, high case strength, favorable com-pressive residual stress in the hardened case,and suitable core properties, based on appropri-ate grade of steel, result in the highest gear rat-ing. Furthermore, carburized gears offer supe-rior heat resistance compared with other casehardening processes. These gears are also capa-ble of withstanding high shock load. In general,smaller gears are carburized. Nonetheless, gears

Table 16 Recommended shot peening parametersShot diam

mm in. × 10–4

20 0.006A 0.178 70 Cast steel 20016 0.008A 0.178 70 Cast steel 20010 0.010A 0.279 110 Cast steel 2007 0.014A 0.432 170 Cast steel 2005 0.018A 0.584 230 Cast steel 2004 0.021A 0.711 280 Cast steel 2003 0.007C 0.838 330 Cast steel 2002 0.010C 1.168 460 Cast steel 200

(a) Almen strips: A, 1.3 ± 0.025 mm (0.051 ± 0.001 in.); C, 239 ± 0.025 mm (0.094 ± 0.001 in.). (b) 200% indicates a double shot-peening process.

Diametral pitch (DP) Shot peening intensity(a) Shot type (HRC 42–50) Coverage(b), %

Fig. 63 Residual compressive stress below surface for stan-dard and shot-peened gears


Fig. 64 Tooth surface finish of standard ground and shot-peened gears

Table 17 Case depth versus costCase depth

requirementCost

factorRejection,

%Scrap,

%mm in.

0.25 0.010 1.0 5 3 80.51 0.020 1.1 3 2 40.76 0.030 1.2 3 2 41.02 0.040 1.3 4 2 61.27 0.050 1.4 6 3 81.52 0.060 1.6 8 4 91.78 0.070 1.8 8 4 10

The control of carbon concentration and case depth is more difficult in long car-burizing cycles. Also, very low case presents higher manufacturing difficulty asdoes excessive case. (a) Higher number indicates more difficulty.

Manufacturingdifficulty index(a)

Table 18 Case depth tolerance versus costCase depth tolerance(a)

Cost factor

Rejection,%

Scrap, %in.

±0.05 ±0.002 2.0 20 10 10±0.08 ±0.003 1.4 15 8 9±0.10 ±0.004 1.2 4 2 7±0.13 ±0.005 1.0 3 2 5±0.18 ±0.007 0.8 0 0 4±0.25 ±0.010 0.7 0 0 2

(a) Case depth tolerance must be greater than the carburizing process controlcapability to allow for various stock removal requirements. (b) Higher numberindicates more difficulty.

mm

Manufacturingdifficulty index(a)

Table 19 Special features versus costCarburizing features

Cost factor

Rejection, %

Scrap, %

Manufacturingindex(a)

Single case 1.0 3 1.5 5Dual case 2.5 25 12.0 10

(a) Higher number indicates more difficulty.

Table 20 Surface coverage versus costSurface coverage

Cost factor

Rejection, %

Scrap, %

Manufacturingindex(a)

All over 1.0 4 2 5Partial 3.5 4 2 10

The cost of masking and copper plating for selective carburizing is significant.(a) Higher number indicates more difficulty.

up to a 2030 mm (80 in.) diameter have beensuccessfully carburized.

Today, gas carburizing is extensively used tocarburize gears because a great deal of improve-ment has been made in this technology since thedays of pack or liquid carburizing. This is car-ried out mostly in air furnaces, although partialand full vacuum furnaces and fluidized-bed fur-naces with improved controls also are used forhigh quality of carburized and hardened case.

The major disadvantage of carburizing andhardening is high heat treat distortion; although,recent advancements in carburizing furnacetechnology and equipment, press quenching,selection of proper steel, and control of manu-facturing process have contributed greatly incontrolling and minimizing this distortion. Lowdistortion helps to reduce gear finishing cost.

Costs. Tables 17 to 20 show how carburiz-ing cost varies with case depth, tolerance, andany special features.

Vacuum Carburizing

Vacuum carburizing, also referred to as low-pressure carburizing, is a non-equilibrium,boost-diffusion-type carburizing process inwhich the steel being processed is austenitizedin a rough vacuum, carburized in a partial pres-sure of hydrocarbon gas, diffused in a roughvacuum, and then quenched in either oil or gas.Compared to conventional atmosphere (gas)carburizing, vacuum carburizing offers excel-lent uniformity and repeatability because of thehigh degree of process control possible with

vacuum furnaces; improved mechanical proper-ties due to the lack of intergranular oxidation;and potentially reduced cycle times, particularlywhen the higher process temperatures possiblewith vacuum furnaces are used. As a result ofthese benefits, the vacuum process is being usedincreasingly to carburize gears in the automo-tive, off-highway, heavy truck, and aerospaceindustries (Ref 7).


Process OverviewVacuum carburizing of steel is typically a

four-step process:

1. Heat and soak step at carburizing tempera-ture to ensure temperature uniformitythroughout steel

2. Boost step to increase carbon content ofaustenite

3. Diffusion step to provide gradual case-coretransition

4. Quenching step. This may be carried out bydirect quenching in oil or in a high-pressuregas quenching system.

Heat and Soak Step. The first step is toheat the steel being carburized to the desiredcarburizing temperature, typically in the rangeof 845 to 1040 °C (1550 to 1900 °F), and to soakat the carburizing temperature only long enoughto ensure that the steel is uniformly at tempera-ture. Oversoaking, particularly above 925 °C(1700 °F), can result in a reduction in toughnessdue to grain growth.

During the first step, surface oxidation must beprevented, and any surface oxides present mustbe reduced. In a graphite-lined heating chamberconsisting of graphite heating elements, a roughvacuum in the range of 13 to 40 Pa (0.1 to 0.3 torr)is usually satisfactory. In a ceramic-lined heatingchamber with silicon carbide heating elements, apartial pressure of approximately 40 to 67 Pa (0.3to 0.5 torr) of hydrogen is effective. Steels with ahigh chromium content (M-50 NiL, X-2 Modi-fied), a high silicon content (Pyrowear Alloy 53),or other high-oxygen affinity alloying elementsusually require a higher vacuum level prior tocarburizing but do not normally require preoxi-dizing.

Boost Step. Second is the boost step of theprocess. This step results in carbon absorptionby the austenite to the limit of carbon solubilityin austenite at the process temperature for thesteel being carburized. The boost step isachieved by backfilling the vacuum chamber toa partial pressure with either a pure hydrocarbongas (for example, propane or acetylene) or amixture of hydrocarbon gases. Ammonia can beadded if nitrogen alloying of the case is desired.An inert gas such as nitrogen can also be addedto the gas or gas mixture.

Carbon transfer occurs by dissociation of thehydrocarbon gas on the surface of the steel, withdirect absorption of the carbon by the austenite

and hydrogen gas being liberated. The reactionwith propane is:

(Eq 13)

At typical carburizing temperatures, thisreaction proceeds rapidly from left to right ofthe equation. Because such reactions are diffi-cult to measure in situ, they cannot be used tocontrol carbon potential when vacuum carburiz-ing. Because there is no oxygen present, theoxygen-base methods of carbon-potential con-trol used in conventional atmosphere carburiz-ing cannot be used either. However, at least onefurnace manufacturer has designed a system forvacuum carburizing that measures and controlsthe carbon potential of the carburizing gas.

A minimum partial pressure of hydrocarbongas is required to ensure rapid carburizing of theaustenite. The minimum partial pressure re-quired varies with the carburizing temperature,the carburizing gas composition, and the fur-nace construction. Above the minimum partialpressure, the partial pressure of carburizing gasused has no relationship to the carburizing po-tential of the atmosphere. Typical partial pres-sures vary between 1.3 and 6.6 kPa (10 and 50torr) in furnaces of graphite construction and 13and 25 kPa (100 and 200 torr) in furnaces ofceramic construction. Partial pressures inexcess of 40 kPa (300 torr) are not normally rec-ommended because of the excessive carbondeposition within the furnace that accompanieshigher partial pressures.

Diffusion Step. Third in the process is thediffusion step. If a steel were hardened with the carbon gradient resulting from the boost step only, particularly if no means of carbon-potential control were employed during theboost step, an undesirable microstructure adja-cent to the carburized surface and an extremelyabrupt case-core interface would result. The dif-fusion step enables the diffusion of carboninward from the carburized surface, resulting ina lower surface carbon content (relative to thelimit of carbon solubility in austenite at the car-burizing temperature) and a more gradual case-core transition. The diffusion step is usually per-formed in a rough vacuum of 67 to 135 kPa (0.5to 1.0 torr) at the same temperature used for car-burizing. If carbon-potential control was usedduring the boost step, the diffusion segmentmight be shortened or eliminated.

C3H8 � 3Fe � 3Fe1C 2 � 4H2


Oil Quenching Step. The fourth step of theprocess is quenching. If a reheat step is not goingto be employed, and/or no further machining isrequired, the steel is directly quenched in oil,usually under a partial pressure of nitrogen.

When vacuum carburizing is performed at ahigher temperature than is normally used withconventional atmosphere carburizing, cooling toa lower temperature and stabilizing at that tem-perature prior to quenching is usually required.Alternatively, if a reheat step is going to beemployed for grain refinement, and/or furthermachining is required, the steel is gas quenchedfrom the diffusion temperature to room tempera-ture, usually under a partial pressure of nitrogen.

Reheating usually consists of austenitizing inthe 790 to 845 °C (1450 to 1550 °F) range fol-lowed by oil quenching. When aircraft-qualitygearing or bearings are being processed, reheat-ing is usually preceded by a subcritical anneal.A diagram of temperature and pressure versustime for a typical vacuum carburizing cyclewith a reheat cycle is shown in Fig. 65.

High-Pressure Gas Quenching Step. In-creasingly, vacuum carburizing is being carriedout in conjunction with high-pressure gasquenching in 20 bar (2,000 kPa, or 300 psi) nitro-gen or nitrogen-helium mixtures. High-pressuregas quenching is ideally suited for light loads,thin sections, and moderate-to-highly alloyedsteels. An advantage of gas quenching comparedto liquid quenchants (oil, water, and aqueouspolymers) is that quenching with gas proceeds

more uniformly, minimizing residual stressesand distortion. In addition to improved quenchuniformity, gas quenching is a “clean” process,eliminating the need for a vapor degreasing step often used for oil quenching processes.Potential fire hazards and disposal problems arealso eliminated.

Furnace DesignVacuum carburizing is usually performed in

a furnace specifically designed for this applica-tion. Units have been developed to operate incell manufacturing operations found in com-mercial heat treating shops or just-in-time man-ufacturing plants. The standard line of furnacesconsists of both one- and two-zone models. Thetwo-zone model has one chamber for heatingand the other for quenching.

The furnace can be of either graphite con-struction (graphite insulation and heating ele-ments) or ceramic construction (refractoryboard insulation and silicon carbide heating ele-ments). Graphite construction permits higheroperating temperatures useful for a multipur-pose furnace, whereas ceramic construction iswell suited for vacuum carburizing, because itcan be safely operated in air at process temper-atures for die quenching or for facilitating sootremoval. Figure 66 shows a typical continuousceramic construction vacuum carburizing fur-nace. Figure 67 shows a typical batch-graphiteconstruction vacuum furnace with carburizingcapability.

Fig. 65 Plot of temperature and pressure versus time for a typical vacuum carburizing process with a reheat cycle


Fig.

66

A c

ontin

uous

cer

amic

vac

uum

car

buri

zing

furn

ace


Fig. 67 A batch-graphite integral oil quench vacuum furnace with vacuum carburizing capability

High-Temperature Vacuum Carburizing

The reduction in carburizing time associatedwith a higher carburizing temperature has longbeen appreciated. However, typical atmospherefurnace construction generally restricts themaximum carburizing temperature to approxi-mately 955 °C (1750 °F). The higher tempera-ture capability of vacuum furnaces, as com-pared to typical atmosphere furnaces, permitsthe use of higher carburizing temperatures withcorrespondingly reduced cycle times.

High-temperature vacuum carburizing cansignificantly reduce the overall cycle timerequired to obtain effective case depths in excessof 0.9 to 1.0 mm (0.035 to 0.040 in.). For obtain-ing smaller case depths, high-temperature vac-uum carburizing does not offer any advantages,because a grain-refining step is required, and the

boost times tend to be too short for acceptableuniformity. Table 1 compares the time requiredto obtain 0.9 mm (0.035 in.) and 1.3 mm (0.050in.) effective case depths via vacuum carburiz-ing at both 900 °C (1650 °F) and 1040 °C (1900°F) for an AISI 8620 steel. As is apparent fromTable 21, significant reductions in the total cycletime can be obtained by using high-temperaturevacuum carburizing.

Metallurgists not familiar with high-tempera-ture vacuum carburizing are often concerned thatalthough reduced cycle times can be obtained byhigh-temperature carburizing, a degraded micro-structure with reduced mechanical propertiesresults. There is no evidence that any reduction ineither monotonic or cyclic mechanical propertiesresults from high-temperature vacuum carburiz-ing, provided that the process is properly speci-fied and controlled. One aircraft-quality gearinguser has performed extensive work in the area of

high-temperature vacuum carburizing and con-cluded that there is no loss of properties when either AISI 9310 or X-2 Modified are high-temperature vacuum carburized to aircraft-qual-ity gearing process specifications.

There is also concern that the high processtemperatures involved result in excessive distor-tion and size change. Although it is true thatsome geometries are sensitive to the ultimateprocess temperature used, distortion can be min-imized by using proper preheating/heating tech-niques, minimizing times at temperature, properfixturing, and quenching techniques that are onlysevere enough to result in the desired micro-structure and do not develop excessive nonuni-form stresses within the part. Gas pressurequenching helps alleviate residual stresses, par-ticularly with the new moderate- to high-alloygrades of carburizing steels being developed. Asfar as any dimensional change greater than nor-mal is concerned, the uniformity and repeatabil-ity of the vacuum carburizing process, even atelevated temperatures, allows for dimensionalchange during manufacturing planning.

Comparison of Atmosphere and Vacuum Carburizing

As indicated in Fig. 1, atmosphere or gas car-burizing remains the most popular carburizingmethod, because it represents a good compro-mise between cost and performance. In recentyears, improvements in the reliability of thevacuum carburizing process have allowed itsbenefits to be realized, and a number of papershave been published that compare the benefitsof atmosphere and vacuum carburizing (Ref 1and 8–10). This section reviews the variousadvantages and disadvantages associated withthese carburizing methods and presents the rel-

ative technical merits of each process (Table22). The section that follows describes a casestudy that compares the properties of a low-alloy gear steel processed by both atmosphereand vacuum carburizing.

Atmosphere Carburizing Characteristics(Ref 1). Atmosphere carburizing is an empiri-cally based, time-proven process in which a car-bon-rich atmosphere surrounding a workload isused to chemically react with the surface of theparts to allow an adequate quantity of carbon tobe absorbed at the surface and diffuse into thematerial.

Advantages of atmosphere carburizing in-clude:

• The lowest initial capital equipment invest-ment cost

• Adequate process control; that is, all of theprocess variables are understood, and reli-able control devices are available to providea measure of process repeatability.

• Capability of high-volume output using awide variety of equipment styles, types, andworkload sizes. Furnace types include box,pit, mechanized box (integral- and sealed-quench furnaces), pusher, conveyor (meshbelt and cast link belt), shaker hearth, rotaryhearth, rotary drum (rotary retort), and car-bottom.

• Full automation capability, with recipe andpart-number control of heat treat cycles

• Well-understood process problems allowingtroubleshooting based on an established the-oretical and empirical knowledge base

Disadvantages of atmosphere carburizinginclude:

• The need to “condition” equipment if idledor shut down prior to processing work


Table 21 Comparison of time required to obtain a 0.9 mm (0.035 in.) and 1.3 mm (0.050 in.)effective case depth in an AISI 8620 steel at carburizing temperatures of 900 °C (1650 °F) and 1040 °C (1900 °F)

Effective depth

mm in. °C °F

Heating to carburizing temperature

Soaking prior to

carburizing Boost Diffusion

Gas quench to 540 °C(1000 °F)

Reheat to845 °C

(1550 °F)

Soak at 845 °C

(1550 °F)Oil

quench Total

0.9 0.035 900 1650 78 45 101 83 (a) (a) (a) 15 >3221040 1900 90 30 15 23 20 22 60 15 275

1.3 0.050 900 1650 78 45 206 169 (a) (a) (a) 15 >5131040 1900 90 30 31 46 20 22 60 15 314

(a) Not available

Carburizing temperature

Time, min

• A requirement of knowledge through empir-ically gained experience to achieve repeat-able results. This is due to a wide variabilityin the type of equipment, its operation, main-tenance, and constantly changing processconditions.

• The need for large material allowances forpostprocessing operations due to accuracyand finish requirements. Case depths typi-cally are specified in wide ranges (e.g., 0.75to 1.25 mm, or 0.030 to 0.050 in.) to com-pensate for cycle-induced variability.

• Case depth quality issues; the best part of thecase often is lost due to the amount of stockremoval required.

• The need to constantly monitor environmen-tal pollution issues, including air quality (forpotentially hazardous gases such as CO andNOx), water quality (for contamination con-cerns such as oil, minerals, etc.), waste dis-posal (quench oils), and safety issues (e.g.,fire from combustible gases and quench oils,hot contact surfaces, and pinch points)

Vacuum Carburizing Characteristics (Ref1). Vacuum carburizing is a proven method ofpure carburizing and pure diffusion in which

carbon penetrates into the surface of the steelbeing processed without interference from ex-ternal influences, such as gas chemistry or sur-face contaminants.

Advantages of vacuum carburizing include:

• Easy integration into manufacturing. Theprocess is clean, safe, simple to operate, andeasy to maintain. Also, working conditionsare excellent (that is, there are no openflames, heat, and pollution).

• Full automation capability using recipe orpart-number control of heat treating cycles

• Capability of higher temperatures and flexi-ble cycles, due to the type of equipment andthe nature of the process

• Precise process control achieved using com-puter simulations, which allow adjustmentsto established cycles

• Consumption of energy by the equipmentand process only when needed, due to thenature of the vacuum operation

Disadvantages of vacuum carburizing in-clude:

• Higher initial capital equipment cost thanatmosphere carburizing equipment


Table 22 Comparison of atmosphere and vacuum carburizing technologiesCriteria Atmosphere carburizing Vacuum carburizing

Temperature range, °C (°F) 790–980 (1450–1800) 790–1100 (1450–2000)Case uniformity, mm (in.)(a) ±0.25 (±0.010) ±0.05 (±0.002)Carbon-transfer control Yes Limited to control of time and temperatureLoad density, kg/m3 (lb/ft3)(b) 45–70 (100–150) 22.5–45 (50–150)Carburizing time, min x minutes x minutes minus 10–20%Carbonitriding(c) NH3 additions NH3 additionsMicrostructure Acceptable (in most cases) Optimal (in most cases)Internal oxidation, mm (in.) 0.0076–0.0127 (0.0003–0.0005) common NoneCarbides Suppression difficult Suppression possibleDealloying Yes(d) NoneDecarburization Possible NoneHydrogen pickup Yes (at high temperature) Slight (internal porosity diffusion)Furnace conditioning Required (4 h typical) NoneShell temperature, °C, or °F Warm (typically >65, or 150) Cold (typically �65, or 150)Environmental impact CO/NOx emissions Slight or noneEnergy consumption Low (~30%) Lower (<30%)Gas consumption High (x cfh) Low (1/3–1/6 x cfh)Integration with cellular manufacturing Difficult EasyInvestment cost Average High

(a) Atmosphere and vacuum carburizing processes typically are different with respect to when gas additions are introduced, and this has the greatest impact on caseuniformity. In atmosphere carburizing, enriching gas typically is added after the furnace set point is reestablished. Depending on the mass and configuration of theworkload, a large temperature differential can exist between different locations within the workload. In the case of vacuum carburizing, a soak or stabilization periodis built into the cycle to allow the workload to reach carburizing temperature prior to gas additions. (b) Loading density in vacuum carburizing equipment often is lim-ited, due to the use of high-gas-pressure quenching chambers. (c) Techniques for vacuum carbonitriding using low pressure, <25 mbar (20 torr), are still being devel-oped. (d) Due to oxidation at the part surface. Source: Ref 1


• Empirical process control, which requiresprocessing loads to determine optimal set-tings or to fine tune simulator

• Formation of soot and tar, which occur dueto the type, pressure, and quantity of hydro-carbon gas introduced

It is important to note that research duringrecent years has succeeded in finding combina-tions of pressure, gas type (e.g., acetylene), andflow parameters to minimize soot and tar for-mation as a concern in the vacuum carburizingprocess.

Case Study: Property Comparisons of aGear Steel Processed by Atmosphereand Vacuum Carburizing (Ref 8)

Case Study Overview. The purpose of thestudy described in this section was to investi-gate whether vacuum carburizing could be usedto improve the fatigue life of steels used for off-road vehicle transmission gearing. Fatigue is amajor cause of gear failure, where the primaryfailure modes are gear tooth root bending andtooth pitting. Test samples were:

• Atmosphere carburized and oil quenched• Vacuum carburized and oil quenched• Vacuum carburized and high-pressure gas

quenched

The effects of postheat grinding and shot peen-ing were also examined.

The methods used to compare the vacuumand atmosphere carburizing processes in thisstudy were x-ray diffraction (XRD) and micro-hardness testing.

Coupons of AISI 8620 low-alloy steel wereheat treated using the different carburizingmethods and subjected to identical post-heattreat grinding and shot peening operations.

X-ray diffraction was selected as an evalua-tion tool, because it can be used to measureresidual stresses. Residual stresses are additivewith applied stress, which makes their level animportant factor in fatigue-critical componentssuch as gears. Residual compressive stresses aredesirable, because they oppose the applied, re-petitive, and undesirable tensile stresses thatcause fatigue failure. For gears, the areas ofmost concern are the flanks, which are subjectedto contact loads that could cause pitting fatigue,and the roots, which experience tensile bendingfatigue loads.

The greater the magnitude and depth of resid-ual compressive stress, the greater the ability toimprove fatigue properties. To enhance resis-tance to fatigue crack initiation, it is particularlyimportant to have a higher compressive stresslevel at the outer surface. Also note that a deeperlayer of compressive stress provides resistanceto fatigue crack growth for a longer time than ashallower layer.

Carburizing Process Basics. Carburizingof a metal surface is a function of both the rateof carbon absorption into the steel and the diffu-sion of carbon away from the surface and intothe interior of the part. Once a high concentra-tion of carbon has developed at the surface dur-ing what is commonly called the boost stage, theprocess normally introduces a diffuse stage,where solid-state diffusion occurs over time.This step results in a change in the carbon con-centration gradient between the carbon-rich sur-face and the interior of the steel. The result is areduction of carbon concentration at the surfaceof the part, accompanied by an increase in thedepth of carbon absorption.

The carburization process also induces desir-able residual compressive stresses through thecase-hardened layer. This stress state resultsfrom the delayed transformation and volumeexpansion of the carbon-enriched surface of thesteel.

In atmosphere carburizing, parts areheated to austenitizing temperature in a neutralor carrier gas atmosphere that contains approxi-mately 40% H2, 40% N2, and 20% CO. Smallpercentages of carbon dioxide (CO2, up to1.5%), water vapor (H2O, up to 1%), andmethane (CH4, up to 0.5%), along with traceamounts of oxygen (O2), also are present. Thecarburizing process also requires the addition ofa hydrocarbon enriching gas, usually naturalgas.

Of the 180 chemical equations that describethe reactions occurring during atmosphere car-burizing, one of the most important is the water-gas reaction:

(Eq 14)

Control of the atmosphere carburizing processis done by looking at the CO/CO2 and H2O/H2ratios of this equation using instruments such asdewpoint analyzers, infrared analyzers, andoxygen (carbon) probes.

CO � H2O � CO2 � H2


Fig. 68 Microhardness profiles at pitch line and tooth rootfor an atmosphere carburized and oil quenched AISI

8620 gear. For resistance to bending fatigue, it is desirable toachieve a deeper case in the root.

In atmospheres containing CO and H2, car-bon transfer is dominated by the CO adsorption(ad) and the oxygen desorption reactions:

(Eq 15)

(Eq 16)

These two reactions yield an alternate form ofthe water-gas reaction:

(Eq 17)

Thus, the transfer of carbon in atmospherescontaining CO and H2 is connected with a trans-fer of oxygen, giving rise to an oxidation effectin steel containing oxide-forming alloying ele-ments such as silicon, chromium, and man-ganese. This phenomenon is known as internalor intergranular oxidation of steel (Ref 4).

Atmosphere Carburized and OilQuenched Hardness Profile. Figure 68 showsKnoop (500 gf) microhardness profiles for anatmosphere carburized and oil quenched AISI8620 steel gear.

Atmosphere carburizing to a depth of 0.36mm (0.014 in.) produced a hardness of 58 HRCat both the gear tooth pitch line and root. Fromthis depth, the hardness values quickly diverge.The effective case depth (at 50 HRC) is 0.76mm (0.030 in.) in the root and 1.33 mm (0.0525in.) at the pitch diameter. These values are typi-cal of the vast majority of carburized gears cur-rently in service.

For resistance to bending fatigue, it is desir-able to achieve a deeper case in the root. This

CO � H2 � �C� � H2O

Oad � H2SH2O

COSCOadS �C� � Oad

produces a deeper level of high-hardness, high-strength material with the benefit of residualcompressive stress.

Vacuum carburizing, by comparison, doesnot use a carrier gas atmosphere but instead usesvacuum pumps to remove the atmosphere fromthe chamber before the process begins. For car-burizing to take place in a vacuum furnace, allthat is needed is a small, controlled addition ofa hydrocarbon gas.

Unlike atmosphere carburizing, the break-down of hydrocarbons in vacuum carburizing isvia nonequilibrium reactions. This means thatthe carbon content at the surface of the steel isvery rapidly raised to the saturation level of car-bon in austenite. By repeating the boost and dif-fuse steps, any desired carbon profile and casedepth can be achieved.

Today, vacuum carburizing is best performedusing low-pressure techniques under 20 torr (25mbar) and typically at temperatures between790 and 1040 °C (1455 and 1900 °F). Hydro-carbon gases currently being used for vacuumcarburizing are acetylene (C2H2), propane(C3H8), and, to a lesser degree, ethylene (C2H4).Methane (CH4) is not used, because it is nearlynonreactive at these low pressures, unless thetemperature is at or above 1040 °C (1900 °F).

Carbon is delivered to the steel surface invacuum carburizing via reactions such as these:

(Eq 18)

(Eq 19)

(Eq 20)

In the past, propane has been the primaryhydrocarbon gas used for vacuum carburizing;however, propane dissociation occurs beforethe gas comes in contact with the surface of thesteel, thus producing free carbon or soot. Thisuncontrolled soot formation results in poor car-bon transfer to the part and loss of up-time pro-ductivity due to the need for additional heat treatequipment maintenance.

Development work done in the past few yearshas demonstrated that acetylene is a good per-forming gas for vacuum carburizing. This isbecause the chemistry of acetylene (Eq 18) isvastly different from that of propane or ethylene(Eq 19 and 20). Dissociation of acetylene deliv-ers two carbon atoms to the one produced bydissociation of either propane or ethylene andavoids formation of nonreactive methane.

Control of the vacuum carburizing process ison a time basis. Carbon transfer rates are a func-

C2H4SC � CH4

C3H8SCH4 � C2H4SC � 2CH4

C2H2S 2C � H2


Fig. 69 Microhardness profiles at pitch line and tooth rootfor a vacuum carburized and oil quenched AISI

8620 gear. The overall case depth of maximum hardness isdeeper than that of the atmosphere carburized part in Fig. 68

tion of temperature, gas pressure, and gas flowrate. Simulation programs have been written todetermine the boost and diffuse times of thecycle.

Vacuum Carburized and Oil QuenchedHardness Profile. Figure 69 shows hardnessprofiles for a vacuum carburized and oilquenched AISI 8620 steel gear.

The overall case depth of maximum hardnessfor the vacuum carburized part is noticeablydeeper than that of the atmosphere carburizedpart in Fig. 68. The vacuum carburized casedepth of approximately 0.81 mm (0.032 in.) at58 HRC is more than double that obtained withatmosphere carburizing, while the effectivecase depths (depth at 50 HRC) are similar. Alsonote the much greater consistency in root andpitch line hardnesses through a depth of 0.81mm (0.032 in.) for vacuum carburizing versusatmosphere carburizing (Fig. 69 versus Fig. 68).

Vacuum Carburized and Gas QuenchedHardness Profile. The hardness profilesshown in Fig. 70 are for an AISI 8620 steel gearthat has been vacuum carburized and then high-pressure gas quenched (HPGQ) in 20 bar (2,000kPa, or 300 psi) nitrogen.

A comparison of Fig. 68 and 69 shows thatuse of HPGQ instead of oil quenching in vac-uum carburizing results in a more uniform casedepth between gear pitch line and root. Theabsence of a vapor layer in gas quenchingresults in a more uniform cooling rate along thegear tooth and root profile.

The Test Procedure. The following proce-dure was used to properly evaluate the effect ofdifferent heat treatments and post-heat treat-ment processes on residual stress in coupons ofAISI 8620 low-alloy gear steel:

• Five coupons from the same heat lot of AISI8620 were cut to size: 76 by 19 by 13 mm,±0.05 mm (3.00 by 0.75 by 0.505 in., ±0.002in.). The coupons were stamped, and a sepa-rate manufacturing process was defined foreach (Table 23).

• Coupons were sent out for heat treatment—vacuum or atmosphere carburizing—according to the parameters in Table 24.Required surface hardness: 59 to 61 HRC.Vacuum carburized coupons were nitrogengas quenched, while atmosphere carburizedcoupons were oil quenched.

• Heat treated coupons were ground to 12.7 ±0.013 mm (0.5000 ± 0.0005 in.), removing

Fig. 70 Microhardness profiles at pitch line and tooth rootfor a vacuum carburized and high-pressure gas

quenched AISI 8620 steel gear. Use of gas quenching instead ofoil quenching (Fig. 69) results in a more uniform case depthbetween pitch line and root.

Table 23 Test coupon manufacturing processesCoupon Identification Process

1 EX2470 Vacuum carburize (VC)2 EX2470-1 Vacuum carburize and shot peen

(VC and SP)3 EX2470-2 Atmosphere carburize (AC)4 EX2470-3 Atmosphere carburize and shot peen

(AC and SP)5 EX2470-4 Vacuum carburize and dual shot peen

(VC and DSP)


Table 24 Test parameters for atmosphere andvacuum carburized couponsParameter Atmosphere Vacuum

Temperature, °C (°F) 940 (1725) 940 (1725)Boost time, min 300 32Diffusion time, min 120 314Hardening temperature,

°C (°F)845 (1550) 845 (1550)

Quenching method Oil at 60 °C (140 °F) Nitrogen gas at20 bar

Tempering temperature, °C (°F)

175 (350) 175 (350)

Tempering time, h 2 2

no more than 0.15 mm (0.006 in.) from thenon-stamped side where XRD was to takeplace.

• Three of the five coupons were sent out forshot peening.

• All five coupons were sent out for XRD onthe nonstamped side.

The Benefits of Shot Peening. The pri-mary purpose of shot peening gears is toenhance their fatigue life by inducing a highresidual compressive stress at the surface of thetooth roots. Shot peening is most effective forparts subject to high-cycle fatigue loading.

A basic explanation is provided by the graphin Fig. 71, a typical stress-number of cycles (S-N) curve. It plots (tensile) stress, S, versus thenumber of load cycles, N. It is important to notethat the vertical scale is linear, whereas the hori-zontal scale is logarithmic. This means that as

tensile stress is reduced, fatigue life improvesexponentially. An ~35% reduction of stress from760 MPa (110 ksi) to 485 MPa (70 ksi) results inan improvement in fatigue life from 40,000cycles to 160,000 cycles (400%). Additionalreductions in tensile stress result in significantlymore fatigue enhancement. At 415 MPa (60 ksi),for example, the anticipated fatigue life is~400,000 cycles.

The residual compressive stresses producedby shot peening counteract applied tensilestresses. The compressive stresses are inducedby impacts of small, spherical media (shot). Theimpact of each individual shot stretches the sur-face enough to yield it in tension. Because thesurface cannot fully restore itself due to themechanical yielding that has taken place, it isleft in a permanent compressed state.

Shot peening results in a residual compres-sive stress at the surface—where most fatiguecracks initiate—that is ~55 to 60% that of thematerial ultimate tensile strength. For carbur-ized gears, the surface compression is typically1170 to 1725 MPa (170 to 250 ksi), whichresults in a significant improvement in fatigueproperties.

The grinding process is applied to compo-nents so often and in so many forms (automatic,manual, with and without coolant) that it isoften overlooked from a residual stress stand-point. However, its influence should not be dis-counted, especially when dealing with fatigue-critical parts.

Fig. 71 Typical S-N curve, or plot of (tensile) stress, S, vs. number of load cycles, N. The primary purpose of shot peening gears isto enhance their fatigue life by inducing a high residual compressive stress at the surface of the tooth roots. Shot peening is

most effective for parts subject to high-cycle fatigue loading (>104 to 105 cycles).


During grinding, residual tensile stress maybe created from generation of excessive, local-ized heat. The localized surface area beingground heats from friction and attempts toexpand but cannot, because it is surrounded bycooler, stronger metal. If the temperature gener-ated from grinding is high enough, however, themetal yields in compression due to the resis-tance to its expansion and reduced mechanicalproperties at elevated temperature. On cooling,the yielded material attempts to contract. Thesurrounding material resists this contraction,thus creating residual tensile stress. Becauseheat is the major cause of residual tensile stressfrom grinding, the importance of coolant forcontrolling these stresses is paramount.

X-Ray Diffraction Residual Stress Mea-surements. X-ray diffraction was used tomeasure the residual stresses at surface and sub-surface locations. The technique measures strainby measuring changes in atomic distances. It is adirect, self-calibrating method that measurestensile, compressive, and neutral strains equallywell. Strains are converted to stresses by multi-plying by elastic constants appropriate for thealloy and atomic planes measured.

For this study, chromium Kα radiation wasused to diffract the (211) planes at approxi-mately 156° 2θ. The area measured was nomi-nally 4 mm (0.16 in.) in diameter. Because onlya few atomic layers are measured, the techniqueis considered a surface analysis technique. The subsurface measurements were made byelectrochemically removing small amounts ofmaterial. These subsurface measurements weresubsequently corrected for stress gradient andlayer removal effects using standard analyticalcalculations.

Comparing the Processes. Hardness pro-files for vacuum carburized (coupon 1) andatmosphere carburized (coupon 3) AISI 8620steel coupons are compared in Fig. 72. A majoradvantage of vacuum carburizing over atmo-sphere carburizing is a deeper case of high hard-ness. Hardness values for the two carburizingprocesses are given in Table 25.

Effect of Peening. Residual stress distribu-tions in the three carburized, ground, and shotpeened coupons—coupons 2, 4, and 5—areplotted in Fig. 73.

From a fatigue standpoint, the solid layer ofcompression demonstrated for all three couponsimplies excellent resistance to initiation andgrowth of fatigue cracks. The tensile stress re-

quired for a fatigue crack to develop must firstovercome compressive stresses that are ~1035MPa (150 ksi) at the surface and ~1515 MPa(220 ksi) at 0.05 mm (0.002 in.) below the sur-face. A tensile stress of 1035 MPa (150 ksi) pro-duces a net stress of 0 MPa (0 ksi) at the surfacewhen added to the residual compressive stress.

Coupons 2 (vacuum carburized and shotpeened) and 4 (atmosphere carburized and shotpeened) were shot peened at an Almen intensityof 14 to 16. (Almen intensity is a measure of theenergy of the shot stream.) The steel shot had ahardness of 55 to 62 HRC and a nominal diam-eter of 0.58 mm (0.023 in.).

The residual stress curves in Fig. 73 haveshapes typical of shot peened material. All threehave a similar maximum compressive stress of~1515 MPa (220 ksi). This value is ~55 to 60%that of the steel ultimate tensile strength at thesurface. Because all three coupons were hard-

Fig. 72 Microhardness profiles for vacuum carburized andgas quenched (coupon 1) and atmosphere carbur-

ized and oil quenched (coupon 3) AISI 8620 steel coupons. Amajor advantage of vacuum carburizing is a deeper case of highhardness. VC, vacuum carburized; AC, atmosphere carburized

Table 25 Comparison of atmosphere andvacuum carburizing resultsProperty Atmosphere Vacuum

Depth to 58 HRC, mm (in.) 0.20 (0.008) 0.58 (0.023)Surface hardness before

grinding, HRC59 60

Surface hardness after removal of 0.1 mm (0.004 in.) stock bygrinding, HRC

58 62


Fig. 73 Residual stress distributions in the three carburized, ground, and shot peened coupons (coupons 2, 4, and 5) of AISI 8620.Each contains a solid layer of compression that implies excellent resistance to initiation and growth of fatigue cracks. Note

that the residual stress curve for dual-peened coupon 5 is –0.025 to 0.05 mm (0.001 to 0.002 in.) deeper than those for the single-shot-peened coupons. See Table 23 for definition of process abbreviations for coupons.

ened to 59 to 62 HRC, they also had similar ten-sile strengths (at the surface).

The depth of the compressive stress layer is afunction of the Almen intensity. It can beincreased by increasing shot size and/or veloc-ity. The depth is the location where the residualstress versus depth curves would cross the neu-tral axis (into tension) if the positively slopedlines were extended. A greater depth of com-pression is desired, because this layer is whatresists fatigue crack growth. Coupons 2 and 4were shot peened to the same intensity, so thatthe depth of their compressive stress layers isalso essentially the same at ~0.18 to 0.20 mm(0.007 to 0.008 in.).

Dual Peening. The trade-off to increasingshot peening intensity is that there is additionalcold work and material displacement at thepoint of shot impact. This generally results inless compression right at the surface (depth = 0)and a more aggressive surface finish.

Dual peening is performed to make up for the reduced compression resulting from high-intensity peening. The technique consists of shotpeening the same surface twice—peening at ahigher intensity is followed by peening at alower intensity, usually with smaller media. The second peening reduces the degree of cold work at the surface, improving the surface

finish, which, in turn, makes the surface morecompressed.

Coupon 5 was dual peened. The process spec-ified: MI-230H shot at 18 to 20 Almen followedby MI-110H shot at 8 to 10 Almen. The residualstress curve for this coupon (Fig. 73) is ~0.025to 0.05 mm (0.001 to 0.002 in.) deeper than thecurves for the coupons single shot peened at 14to 16 Almen using MI-230H shot.

This would be expected for a carburized gearsteel. The surface stress of coupon 5 (at depth =0) is the same as that of the other two shotpeened coupons. What most likely occurred isthat it was less compressed after the first peen-ing step. When the second was performed, thesurface became even more compressed, to the~930 MPa (135 ksi) level shown in Fig. 73.Therefore, coupon 5 would be expected to havethe best fatigue performance of the three,because it has the most compressive stressthroughout its depth. This is particularly evidentbetween 0.08 and 0.20 mm (0.003 and 0.008 in.)below the surface. At 0.10 mm (0.004 in.) belowthe surface, for example, there is still 1380 MPa(200 ksi) of compression for coupon 5, com-pared with 1170 MPa (170 ksi) for coupon 4 and1000 MPa (145 ksi) for coupon 2.

Effect of Grinding. Testing of coupons thathad been ground gave unexpected results that


required further investigation. All coupons wereground at the same time. Grinding was per-formed using a wheel that had coolant flow. Theoperator was instructed to remove no more than0.025 mm (0.001 in.) of stock per pass, for atotal of 0.10 mm (0.004 in.) of material removedfrom each coupon. This appeared to be accept-able grinding practice, and little thought wasgiven to the technique prior to testing.

X-ray diffraction measurements indicatedthat tensile stresses existed on the surface of thevacuum carburized coupon (coupon 1) as highas 255 MPa (37 ksi) at 0.013 mm (0.0005 in.)below the surface. At a depth of ~0.10 mm(0.004 in.), the values crossed the neutral axisinto compression. These results were immedi-ately questioned. However, retesting at severallocations using XRD verified that the originalvalues were correct.

The explanation lies in the fact that additionalheat was generated when grinding vacuum car-burized coupon 1. The coupon was 1 HRC pointharder at the surface and 4 HRC points higherafter 0.10 mm (0.004 in.) of stock removal.These values are higher than those for theatmosphere carburized specimen (coupon 3).Additional heat from an increase in frictionresulted in the generation of residual tensilestresses on the vacuum carburized coupon.

This is an excellent example of why it isimportant to carefully evaluate the amount ofheat generated when grinding fatigue-criticalparts. It also demonstrates that XRD is an effec-tive tool for determining the residual stress stateof components before they enter service.

Test Results Reviewed. This study com-pared atmosphere and vacuum carburizing ofAISI 8620 gear steel and evaluated the influenceof the subsequent manufacturing operations ofshot peening and grinding. The primary goal ofthe study was to determine which carburizingprocess was more suitable for heavy-duty trans-mission gears. Gears are subject to both slidingand rolling-contact stresses on their flanks inaddition to bending stresses in tooth roots. Tomeet these demanding performance criteria, thesteel gears ideally would be hardened forstrength and contact properties and have resid-ual compressive surface stresses for bendingfatigue resistance.

It was concluded that vacuum carburizing issuperior to atmosphere carburizing for heattreating heavy-duty transmission gears and en-joys the following advantages:

• Higher hardness (XRD coupons): Surface(before grinding), 1 HRC point higher (60versus 59 HRC); subsurface (after 0.10 mm,or 0.004 in., stock removal), 4 HRC pointshigher (62 versus 58 HRC)

• Greater depth of high, ≥58 HRC, hardness(XRD coupons): 58 HRC depths were vac-uum, 0.58 mm (0.023 in.); atmosphere, 0.20mm (0.008 in.)

• Greater depth of high, ≥58 HRC, hardness(pitch line and root of actual gears): 58HRC depths were vacuum, 0.81 mm (0.032in.); atmosphere, 0.38 mm (0.015 in.)

• Deeper effective case in tooth root (actualgears): Vacuum, 1.0 mm (0.040 in.); atmo-sphere, 0.699 mm (0.0275 in.)

• Higher surface residual compression (XRDof coupons without shot peening or grind-ing): Vacuum, 135 MPa (19.6 ksi); atmo-sphere, 98 MPa (14.2 ksi)

• Improved consistency between the caselayer at the pitch line of the gear flank andgear roots (actual gears): Vacuum, 0.28mm (0.011 in.) variation; atmosphere, 0.648mm (0.0255 in.) variation

Shot Peening Results Reviewed. Both thevacuum carburized and atmosphere carburizedsurfaces responded equally to shot peening:

• Maximum compressive stress: ~1515 MPa(220 ksi)

• Compressive layer depth: ~0.18 to 0.20 mm(0.007 to 0.008 in.)

Dual shot peening at first a higher and then alower intensity resulted in a greater depth ofcompression by ~0.025 to 0.05 mm (0.001 to0.002 in.). The surface stress of the dual-peenedcoupon was very similar, at ~930 MPa (135ksi), to that of the conventionally shot peenedcoupons. The higher-intensity first peen wouldhave produced a less compressed surface, butthe second, lower-intensity peen would haverestored compressive stress to the ~930 MPa(135 ksi) level. The dual-peened coupon shouldhave significantly better high-cycle fatigueproperties than the single-peened coupons.

Fatigue. In terms of fatigue performance,the additional 34.5 MPa (5 ksi) of compressionmeasured for the vacuum carburized coupon(not shot peened or ground) should yield signif-icant increases in gear life under high-cyclefatigue loading, compared with that for theatmosphere carburized coupon.


ACKNOWLEDGMENTS


• J.R. Davis, Ed., Vacuum and Plasma Car-burizing, Surface Hardening of Steels:Understanding the Basics, ASM Interna-tional, 2002, p 91–114

• A.K. Rakhit, Carburizing and HardeningGears, Heat Treatment of Gears: A Practi-cal Guide for Engineers, ASM Interna-tional, 2000, p 33–132

REFERENCES

1. D.H. Herring, Pros and Cons of Atmo-sphere and Vacuum Carburizing, Ind.Heat., Jan 2002, p 45–48

2. J.R. Davis, Ed., Hardenability of Steels,ASM Specialty Handbook: Carbon andAlloy Steels, ASM International, 1996, p 138–166

3. D.W. Dudley, Handbook of Practical GearDesign, McGraw-Hill Book Company,1984, p 4.13

4. J.R. Davis, Ed., Gas Carburizing, SurfaceHardening of Steels: Understanding theBasics, ASM International, 2002, p 17–89

5. G.F. Vander Voort, Ed., Metallography andMicrostructures of Case-Hardening Steel,Metallography and Microstructures, Vol 9,ASM Handbook, ASM International, 2004,p 627–643

6. Gear Materials and Heat Treatment Man-ual, ANSI/AGMA 2004-B89, AmericanGear Manufacturers Association, 1989, p 48

7. F.J. Otto and D.H. Herring, Gear HeatTreatment, Part II, Heat. Treat. Prog.,July/Aug 2002, p 27–31

8. G.D. Lindell, D.H. Herring, D.J. Breuer,and B.S. Matlock, Atmosphere versus Vac-uum Carburizing, Heat Treat. Prog., Nov2001, p 33–41

9. W.J. Titus, Considerations when Choosinga Carburizing Process: Traditional BatchAtmosphere Carburizing versus Vacuumand Ion Carburizing, Ind. Heat., Sept 1987

10. B. Edenhofer, Overview of Advances inAtmosphere and Vacuum Heat Treatments,Heat Treat. Met., Vol 4, 1998, and Vol 1,1999

CHAPTER 10

Nitriding

NITRIDING is a surface hardening heattreatment that introduces nitrogen into the sur-face of steel at a temperature generally in therange of 500 to 575 °C (930 to 1065 °F) while itis in the ferritic condition. Nitriding, therefore,is similar to carburizing in that surface compo-sition is altered, but different in that the nitrogenis added into ferrite instead of austenite. Thefact that nitriding does not involve heating intothe austenite phase field and a subsequentquench to form martensite means that nitridingcan be accomplished with a minimum of distor-tion and excellent dimensional control.

Although nitriding can be carried out using agaseous, liquid, or solid medium, gas nitridingusing ammonia (NH3) as the nitrogen-carryingspecies is the most commonly employedprocess and will be the emphasis of this chapter.Steels that are nitrided are generally medium-carbon steels that contain strong nitride-formingelements such as aluminum, chromium, molyb-denum, tungsten, and vanadium. Prior to nitrid-ing, the steels are austenitized, quenched, andtempered. Tempering is performed at tempera-tures between 540 and 750 °C (1000 and 1380°F), a range above which the nitriding is per-formed. Tempering above the nitriding temper-ature provides a core structure that is stable dur-ing nitriding.

Nitriding produces a wear- and fatigue-resist-ant surface on gear teeth and is frequently usedin applications where gears are not subjected tohigh shock loads or contact stress above 1340MPa (195 ksi) for American Gear Manufactur-ers Association (AGMA) grade 3, and 1190MPa (172 ksi) for grade 2 materials. It is partic-ularly useful for gears that need to maintaintheir surface hardness at elevated temperature.Gears used in industrial, automotive, and aero-space applications are commonly nitrided.

The Gas Nitriding Process

Gears to be nitrided are placed in an airtightcontainer or oven and an atmosphere of NH3 issupplied continuously while the temperature israised and held between 500 and 575 °C (930and 1065 °F) to produce the best combination ofsurface hardness and case depth. At this temper-ature, NH3 breaks down into atomic nitrogen andhydrogen according to the following reaction:

(Eq 1)

The atomic nitrogen slowly penetrates into thesteel surface and combines with the base metaland the alloying elements such as aluminum,chromium, vanadium, and molybdenum thatmight be present in the steel selected to formhard nitrides of such elements. Of these, alu-minum nitrides offer the highest surface hard-ness, whereas chromium, vanadium, andmolybdenum nitrides result in a deeper andtougher case. Because nitriding takes place at atemperature well below the critical temperatureof steel, no molecular change in the grain struc-ture is expected. Therefore, properly nitridedgears exhibit very little distortion and it is acommon practice to finish machine gears priorto nitriding. Ideally, the only work requiredafter nitriding is stripping of the mask used forselective nitriding. The masking is generallydone with fine-grained copper or nickel platingof thickness not less than 0.025 mm (0.001 in.).Gas nitriding is carried out with gears that arealready heat treated, quenched, and temperedfor core hardness. This provides a strong, toughcore with a hard wear-resisting case, usuallyharder than obtained by carburizing. Steelsselected have carbon content somewhat higherthan is employed for carburizing grades to pro-

2NH3 4 2N � 3H2




Table 1 Chemical compositions of nitriding steels commonly used in gearsSteel C Mn Si Cr Al Mo Ni

Nitralloy 135 0.35 0.50 0.30 1.20 1.00 0.20 . . .Nitralloy 135M 0.41 0.55 0.30 1.60 1.00 0.35 . . .Nitralloy N 0.23 0.55 0.30 1.15 1.00 0.25 3AISI 4340 0.40 0.70 0.30 0.80 . . . 0.25 1AISI 4140 0.40 0.90 0.30 0.95 . . . 0.20 . . .31CrMoV9 0.30 0.55 0.30 2.50 . . . 0.20 . . .

vide support for the hard, brittle case. Thechemical compositions of nitriding steels com-monly used in gears are shown in Table 1.

To improve the quality of nitriding, somepre-nitriding requirements are important,including:

• Gears are to be free from decarburization.Nitriding a decarburized steel causes exces-sive growth and the case becomes very brit-tle and susceptible to cracking and spalling.

• Normalizing and subcritical annealingshould occur prior to core hardening.

• Gears are to be core hardened and tempered.• Nitriding temperature is to be at least 28 °C

(50 °F) below the tempering temperature ofcore-hardened gears.

Gas Nitriding Parameters

Case Depth in Nitriding. Nitrided gears donot require as much case depth as required in car-burized gears. This is due to the fact that nitrid-ing is used basically to increase the wear life ofgears under a moderate load. The depth of caseand its properties are greatly dependent on theconcentration and type of nitride-forming ele-ments in the steel. In general, the higher the alloycontent, the higher the case hardness. However,higher alloying elements retard the N2 diffusionrate, which slows the case depth development.Thus, nitriding requires longer cycle times toachieve a given case depth than that required forcarburizing. It is also to be noted that higher casedepth does not increase the contact fatigue life ofnitrided gears in the same ratio as it does in car-burized gears. This is due to the fact that hard-ness drops quickly below the surfaces of nitridedcase, whereas, in a carburized case, the drop inhardness is very small. Recommended casedepths on different diametral pitch (DP) gearteeth are given in Table 2.

Nitriding Cycle Time. Nitriding is a slowprocess and it takes hours to develop useful casedepths on tooth surfaces. Figure 1 shows some

typical cycle times for nitriding versus casedepth relationship for commonly used materi-als, such as the nitriding steels listed in Table 1.

The effective case depth of a nitrided geartooth should be the depth below the tooth sur-face at which the minimum hardness of 50 HRCis met for aluminum and high-chromium steels.On the other hand, low-chromium steels do notdevelop surface hardnesses above 50 HRC. Forthese steels, effective case depth at 40 HRCworks very well (Ref 1). In the case of somegear materials with core hardness approaching40 HRC, a higher hardness, such as 45 HRC,may be considered for an effective case depthmeasurement.

Effective case depth is determined by a prop-erly calibrated microhardness tester using a 500g load and Knoop indenter. The microhardnessimpressions should be spaced so that they arenot disturbed by adjacent impressions. Thereshould be positive assurance that the surfacebeing tested is normal to the indenter. Surfacesto be microhardness tested should be properlypolished (scratch-free) and lightly etched in 4%nital solution. When microhardness tests indi-cate unacceptable results, two additional sets ofreadings should be obtained—if possible, oneon each side of the original set. On small gears,the additional sets may be obtained on adjacentteeth. The three sets of readings should then beaveraged. The hardness values are then plottedagainst their depth from the surface, and a curveis drawn connecting the points. Determine thedepth at which the minimum hardness level of50 HRC crosses the curve.

Total case depth should be determined met-allographically using a suitable etch procedure.On an etched tooth section two identifiable bandsappear, dark and light. The depth of the dark bandis considered to be the total case depth.

Surface Hardness. Because case depth ofnitrided gears is generally low, surface hardnessmeasurements are recommended to be taken inRockwell 15-N scale. Some typical surface

Chapter 10: Nitriding / 229

Fig. 1 Nominal time for different nitrided case depths

Table 2 Recommended case depths fornitrided alloy steel gears

Case depthDiametral pitch (DP) of tooth mm in.

20 0.127–0.254 0.005–0.01016 0.203–0.330 0.008–0.01310 0.305–0.457 0.012–0.0188 0.356–0.508 0.014–0.0206 0.406–0.559 0.016–0.0224 0.508–0.711 0.020–0.028

Table 3 Properties of Nitralloy 135M and Nitralloy N

Tensile strength Yield point

Alloy MPa ksi MPa ksiElongation in 2 in., %

Reduction of area, %

Brinell hardnessat core

Nitralloy 135 M

Before nitriding 950 138 830 120 26 60 320After nitriding 950 138 760 110 4 17 310

Nitralloy N

Before nitriding 910 132 790 114 2 59 277After nitriding 1310 190 1240 180 6–15 43 415

hardnesses that can be attained after nitridingdifferent alloy steel gears are:

Material Minimum hardness, Rockwell 15-N

Nitralloy 135M 92.5Nitralloy N 92.5Nitralloy EZ 92.5AISI 4140, 4330, 4340 85.5

Both Nitralloy 135M and Nitralloy N are out-standing materials for gears. Some typical coreproperties of these two steels before and afternitriding are shown in Table 3.

Core hardness. As with carburized gears,core hardness of nitrided steels is measured inthe center of a tooth. See the discussion of “CoreHardness of Gear Teeth” in Chapter 9, “Carbur-izing,” for details (see, in particular, Fig. 17 inChapter 9).

Recommended Tip and Edge Radii ofTeeth. To avoid chipping tooth edges in caseof any misalignment of gears during service, itis important to remove sharp corners of gearteeth before nitriding. This is achieved byrounding off the edges. Suggested tip and edgeradii are given in Table 4.

White Layer in Nitrided Gears

The microstructure of nitrided steels is com-prised of three distinct regions: the compoundlayer, the diffusion zone, and the core (Fig. 2).The compound layer remains unetched in nital(3% nitric acid in ethyl alcohol) and appearswhite under the microscope. For this reason, thecompound layer is called the “white layer” andconsists of a mixture of gamma prime andepsilon iron nitrides. Below the compoundnitride layer is the diffusion zone containing pre-cipitated alloy nitrides. From the mechanicalstrength viewpoint, the white layer is very hardand brittle. The brittleness of this layer is detri-mental to gear life, particularly when gears expe-rience misalignment during service. The thick-ness of the white layer may vary from onematerial to the other. It is also found that theprocess used during nitriding has a significanteffect on the thickness of this white layer. Forexample, single-stage gas nitriding may result ina white layer of 0.025 to 0.076 mm (0.001 to0.003 in.) on materials normally used for gears.On the other hand, it is possible to hold thisthickness to 0.0127 mm (0.0005 in.) or less witha two-stage gas nitriding process, also known asdiffusion or Floe process. This double-stage


Table 5 Double-stage gas nitriding cyclesEffective case depth

at 50 HRCMaximum white layer thickness

Steel Cycle mm in. mm in.

Minimum hardnessat surface,

Rockwell 15-N

Core hardness,

HRC

Nitralloy 135M 10 h at 525 °C (975 °F),28% dissociation, 50 h at 550 °C (1025 °F),84% dissociation

0.457 0.018 0.0127 0.0005 91–92 32–38

Nitralloy N 10 h at 525 °C (975 °F),28% dissociation, 50 h at 525 °C (975 °F), 84%dissociation

0.356 0.014 0.0127 0.0005 91–92 38–44

AISI 4140 10 h at 525 °C (975 °F),28% dissociation, 50 h at 525 °C (975 °F), 84%dissociation

0.635 0.025 0.0178 0.0007 85–87 32–38

AISI 4340 10 h at 525 °C (975 °F),28% dissociation, 50 h at 525 °C (975 °F), 84%dissociation

0.635 0.025 0.0178 0.0007 84.5–86 32–38

31CrMoV9 10 h at 525 °C (975 °F),28% dissociation, 50 h at 525 °C (975 °F), 84%dissociation

0.559 0.022 0.0178 0.0007 89.3–91 27–33

Table 4 Tip and edge radiiMaximum edge radius Maximum tip radius

Diametralpitch (DP) mm in. mm in.

2–5 1.524 0.060 0.381 0.0156–10 1.270 0.050 0.254 0.01012–20 0.762 0.030 0.127 0.005

Fig. 2 Typical nitrided case structure showing the white layer(top), the diffusion zone, and the core below the diffu-

sion zone

process uses two nitriding cycles, the first simi-lar to the single-stage process (except for dura-tion). In the first stage, gears are nitrided at a 15to 30% dissociation rate of NH3 for 4 to 12 h at atemperature of approximately 505 to 560 °C(940 to 1040 °F). The longer second stage takes

place at a temperature of 525 to 565 °C (975 to1050 °F) with a dissociation rate of 80 to 85%.To get this high dissociation rate of NH3, anexternal dissociator is used. Some typical casehardnesses and depths achieved with double-stage nitriding cycles are shown in Table 5. Moredetailed information on single- and double-stagenitriding can be found in Ref 2.

Any presence of white layer (above 0.025mm, or 0.001 in.) on the tooth surface is consid-ered very detrimental to the fatigue life ofnitrided gears. To improve fatigue life of suchgears, as much of this white layer as possiblemust be removed after nitriding. The most com-monly used processes for the removal of thislayer are honing, acid pickling, and fine sand-blasting. Of these, sandblasting is the mostexpeditious method, but it destroys the surfacefinish and profile of gear teeth. Honing is amuch superior process, but it is extremely slow.Frequently, a combination of these processes isused to remove the white layer and ensure thequality of the tooth surface and optimize cost.For gear quality (AGMA class 10 and above),honing is recommended.

In case the gears need to be finish-machinedto reduce white-layer thickness, it is importantto make sure there is only minimal removal ofthe case. Removal of the case is detrimental tothe life of nitrided gears, due to the fact that thehardness of a nitrided surface drops very rapidlyalong the depth of the case, as shown in Fig. 3.This figure also shows the differences in hard-


Fig. 3 Comparison of hardness gradients for a carburizedtooth and a nitrided tooth

ness versus case depth gradient of a nitrided sur-face compared to a carburized and hardenedsurface. The difference in these two gradientsnarrows as DP of gears increases. For 20 DP andhigher, to avoid removal of any case, completeremoval of white layer from a nitrided case isnot advocated. Recent investigation on this sub-ject also shows that a white layer on the order of0.0127 mm (0.0005 in.) or below does not affectthe fatigue properties of single-stage nitridedgears, particularly gears that are not heavilyloaded (contact stress of 1030 MPa, or 150 ksi,or below). In this region of contact stress, theelastic deformation of contact surface betweentwo mating teeth is usually negligible, and, con-sequently, tensile stress that develops at theinterface of the contact zone is also negligible.Furthermore, the maximum shear stress belowthe surface at the load center is also relativelysmall for gears that are not heavily loaded.Hence, the failure of such gears is not due to pit-ting fatigue but rather to simple wear. Toenhance wear life of nitrided gears it is thus nec-essary to have good surface finish (0.61 μm, or24 μin., or better) and high surface hardness (60HRC and higher) on gear teeth. While surfacefinish depends primarily on the gear cutting andfinishing processes, the surface hardnessdepends on the alloying elements in the gearmaterial. As discussed earlier, aluminum alloyin nitriding type steels (Nitralloy 135M) helpsto achieve higher surface hardness, whereasalloying elements such as chromium (AISI4330) help to obtain higher case depth. Withgood process controls, Nitralloy 135M providessurface hardness of 60 to 62 HRC and is con-sidered very suitable for gears that are not very

heavily loaded. These gears, when nitrided witha diffusion cycle (two-stage process), are notexpected to have more than 0.0127 mm (0.0005in.) of white layer on tooth surfaces.

Now, the question is whether a white layer inthe range of 0.0127 mm (0.0005 in.) is accept-able for highly loaded gears (contact stress ofapproximately 1340 MPa, or 195 ksi, forAGMA grade 3 materials). This, of course,depends on the mechanical properties of thewhite layer and the magnitude of contact stressthat is induced by the applied load. In analyzingthe properties of the white layer, an interestingcharacteristic is revealed. It is found that thewhite layer produced in a two-stage process issomewhat softer and more ductile than thewhite layer produced in the single-stageprocess. This allows the white layer of a two-stage process to withstand some elastic defor-mation. Results obtained so far indicate such awhite layer of 0.0127 mm (0.0005 in.) does notdetrimentally affect the fatigue life of heavilyloaded nitrided gears. The failure in these appli-cations is predominantly controlled by resis-tance to case crushing at the case-core bound-ary. To resist this type of crushing, a deeper casewith high core hardness is desirable. Materialssuch as Nitralloy N and AISI 4340 offer thesecharacteristics.

General Recommendations for Nitrided Gears

Several guidelines should be followed whennitriding gears:

• Use a two-stage nitriding process whereverpossible.

• Use Nitralloy 135M or a similar materialwith aluminum alloying addition for gearsthat are not very heavily loaded. Allow amaximum 0.0127 mm (0.0005 in.) of whitelayer on tooth surface. A minimum corehardness of 30 HRC is recommended.

• For highly loaded gears where the mode offailure is primarily due to case crushing,select steels with chromium, such as Nitral-loy N and AISI 4340. Core-harden tooth to aminimum of 35 HRC.

• All nitrided gear teeth should have proper tiprelief on their profile to avoid tip loadingthat may occur due to tooth deflection ormisalignment of gears. No sharp corners areallowed on tooth tips.

• Honing or grinding (not to exceed 0.025mm, or 0.001 in., stock removal) is accept-


Table 6 Recommended material, attainable hardness, and case microstructure for differentapplications of nitrided gears

Hardness

MaterialCased surface min,Knoop 500 gram

Uncased surface, HRC

Core, HRC Requirement

Grade A, gas nitrided (double stage)

Nitralloy 135Nitralloy NAISI 4140AISI 4340

754732540540

32–3838–4432–3832–38

32–3838–4432–3832–38

Case: Maximum white layer of 0.0127 mm (0.0005 in.)permitted on working surfaces of gear and spline teeth, othersurfaces 0.0203 mm (0.0008 in.) max. No soft spots,microcracks, or heavy nitrogen penetration along grainboundaries. No evidence of improper heat treatment in priorprocessing, excessive ammonia, or excessive temperature.Heavy continuous iron nitride network at tooth tip may because for rejection.

Core: The core structure should be essentially temperedmartensite. Ferrite patches and transformation products(bainite and pearlite) should not exceed 1.586 mm (1/16 in.) inlength and width as measured at 250×.

Grade B, gas nitrided (double stage)

AISI 4130AISI 4140AISI 4340Nitralloy 135

500500500754

28–3628–3628–3630–38

23–3628–3628–3630–38

Case: Maximum white layer of 0.0203 mm (0.0008 in.).Tempered martensite with nitride needles. No evidence ofdecarburization or improper heat treatment. Complete grainboundary network is acceptable.

Nitralloy N 732 38–44 38–44 Core: Tempered martensite. Ferrite patches and transformationproducts should not exceed 3.175 mm (⅛ in.) in width andlength as measured at 250×.

Grade C, liquid salt and gas nitrided (single stage)

AISI 4340AISI 4140AISI 4130Nitralloy 135

466466466754

28–3628–3628–3628–36

28–3628–3628–3628–36

Case: Compound layer 0.025 mm (0.001 in.) max. Diffusionzone per drawing requirements. Microstructure per AMS2755

able to remove the white layer, but only ifsuch removal is essential.

• For satisfactory nitriding, liquid-abrasiveblast (200–1200 grit size) surfaces prior tonitriding. Burnished or polished surfaces donot nitride satisfactorily.

• No shot peening is necessary for nitridedgears.

Microstructure of Nitrided Cases and Cores

As with carburizing, the microstructure of anitrided gear tooth changes from the surface tothe core. Preferred microstructures for variousgrades of nitrided gears are given in Table 6.Metallographic standards for core structuresand nitrided case are illustrated in Fig. 4 and 5.

Overload and Fatigue Damage of Nitrided Gears

One major drawback of nitrided gears is thereduction of fatigue life subsequent to anymomentary overload. The most popular theoryof adequately representing the fatigue life of amechanical element, such as gear teeth sub-jected to a cumulative fatigue damage, was

developed by Palmgren and Miner. This theoryis popularly known as Miner’s Rule and is nowwidely used to calculate both bending and pit-ting fatigue life of gears (Ref 3). According tothis theory, failure occurs when the following issatisfied:

(Eq 2)

where Di is the damage done to a part due to acertain stress level, ni is the number of cyclesthe part experienced at this stress level, and Ni isthe number of cycles to failure at that stresslevel.

Figure 6 shows a typical endurance (S-N)curve of a gear steel. For gears carburized andhardened, the S-N curve for original and dam-aged material due to momentary overload re-mains more or less the same. But unfortunately,this is not the case with gears that are nitrided.Tests show that the nitrided gears do not have thesame overstressing capability as the carburizedones. In fact, the damaged endurance limit ofmomentarily overloaded nitrided gears seems tobe quite a bit below than that of virgin material,

ai

Di � ai

ni

Ni

� 1


Fig. 5 Metallographic standards for nitrided case structure. (a) Desired nitrided case showing small amount of grain boundary nitride;acceptable for grade A. Dark field illumination. (b) Nitride case with some continuous grain boundary nitrides; maximum

acceptable for grade A. Dark field illumination. (c) Nitride case with an increase in continuous grain boundary nitride; maximumacceptable for grades A and B tooth tip. Dark field illumination. (d) Nitride case with complete grain boundary nitrides; not acceptablefor grades A or B. Dark field illumination

Fig. 4 Metallographic standards for nitrided core structure. (a) Desirable tempered martensite core structure for grades A and B. (b)Maximum acceptable large-grained tempered martensite core structure for grades A and B


Fig. 6 Bending-fatigue life of original and damaged carbur-ized and hardened gears

Fig. 7 Bending-fatigue life of original and damaged nitridedgears

as depicted in Fig. 7. Therefore, it is advisable toconsider this phenomenon while determiningthe fatigue life of nitrided gears that may be sub-jected to occasional overload. However, that thelife of nitrided gears may also deteriorate whenthey are subjected to a rated load that varieswidely in a very short time period is relativelyunknown. A case study on the failure of suchgears under wide fluctuating load is presentednext.

Case History: Fatigue Failure of Nitrided Gears

As discussed in the preceeding section, casecarburized and hardened gears are known tooperate satisfactorily both under steady andoverload conditions. Nitrided gears, on the otherhand, seem to perform well only under steadyload. Shock loads detrimentally affect the life ofnitrided gears. Thus, nitrided gears are rarely

used in applications that experience occasionalshock loads. However, that the life of nitridedgears may also deteriorate when subjected to arated load that varies widely in a very short timeperiod is relatively unknown. Although, suchload spectrums are not very common, sometimesthese are observed in gas turbogenerator appli-cations. An analysis of a gas turbogenerator loadduring startup shows that load fluctuations occurwhenever the fuel-control system malfunctions.In this case study, the failure of nitrided gearsused in a gearbox subjected to a load with widefluctuations is presented.

Failed Gearbox. The gearbox is of starepicyclic configuration and is used as a speedreducer in between a 10.4 megawatt (MW) gasturbine and an electric generator. The generalcharacteristics of the gearbox are:

• Horsepower rating: 16,500 hp• Input speed: 8,625 rpm• Output speed: 1,500 rpm

The sun pinion and planet gears are nitrided,whereas the ring gear is just through-hardened.The design life of the gears is a minimum of100,000 h.

Failure Incident. According to a field rep-resentative, gearbox failure occurred after 3 h ofoperation following a scheduled online turbinewater wash cycle. In general, all turbines gothrough a water wash cycle after a few thousandhours of operation. During such a cycle for thisturbine, the generator load is brought down toapproximately the 8 MW level and then water isinjected through the compressor section of theturbine. Following wash, the load is raised to themaximum continuous level of 10.4 MW. Afterthe last wash cycle, high vibration levels of thegearbox were reported just before the gearboxfailed. Unfortunately, no data were taken. Thegearbox had a total of approximately 16,000 hof service before the failure.

Following this incident, to ensure the failurewas not caused by misalignment of equipment orany malfunction of components, such as bear-ings, couplings, or a shaft, a thorough inspectionwas conducted. The equipment alignment of thepackage was found to be within the allowabletolerance. Also, no visible damage of any com-ponent was noticed. This led the inspectiontoward the internal components of the gearbox.

Visual inspection of the disassembled gear-box revealed severe mechanical damage to allgears. The failure was so catastrophic that one


Fig. 9 View of dislocated tooth

Fig. 8 Overall view of one damaged planet gear

complete tooth fell off one of the planet gearsand was found at the bottom of the housing. Fig-ure 8 shows the damaged planet gear, and Fig. 9shows the severed tooth.

Tooth debris was noticed in various gearmeshes. No abnormal distress was found onplanet sleeve bearings, although the thrust facesof output shaft sleeve bearings were completelywiped out. Also, sealing surfaces of the outputshaft and labyrinth seal were found to be burnt.

To determine if there were any discrepancieswith the quality of gear material and heat treat-

ment, detailed metallurgical evaluation was car-ried out with a section from the failed tooth.

Metallurgical Evaluation. Examination ofthe fragmented tooth revealed some well-defined beach marks (Fig. 10) suggesting a typ-ical fatigue failure. The tooth segment was alsoanalyzed by an energy-dispersive x-ray spectro-scope (EDS) and examined with a scanningelectron microscope (SEM). The primary frac-ture surface was relatively flat and showed well-defined crack growth marks, as illustrated inFig. 11. Features of transgranular fatigue propa-


Fig. 10 Detail view of the received fragment from the primary failed tooth. Arrows indicate the crack propagation direction. 4×

Fig. 11 Scanning electron microscope view of the fracture surfaces of the gear fragment. Arrows indicate the crack propagationdirection. 100×

gation were identified on the fracture surfaces(Fig. 12), confirming cracking of the tooth dueto a bending-fatigue mechanism. Material certi-fication shows gears were made from Europeannitriding grade steel (EN-4B), and the chemical

composition seems to meet the requirements asshown below:

• C: 0.2–0.28• Si: 0.10–0.35


Fig. 12 Scanning electron microscope view of the fracture surfaces of the gear fragment showing transgranular fatigue propagation.500×

• Mn: 0.45 max• Cr: 3.00–3.50• Mo: 0.45–0.65• S: 0.025 max• P: 0.025 max

The case-hardness profile and the effective casedepth of teeth were determined by a microhard-ness tester and are shown in Fig. 13. The effec-tive case depth was found to be 0.381 mm(0.015 in.). This satisfies the design require-ments for these gears. The core hardness oftooth varied from 25.8 to 27.5 HRC. The de-sired minimum core hardness is 28 HRC.

Failure Analysis. In a mature design of agearbox as in this case, the failure is believed tobe due to the influence of one or more of the fol-lowing factors:

• Defective gear material or forging• Improper heat treatment of gears• Sudden overload beyond design considera-

tion• High fluctuating load

In this analysis, failure initiation due to inade-quate lubrication is ruled out because no evi-dence, such as discoloration of tooth or any burnmarks, was observed on teeth surfaces. Also,vibration was not believed to be the cause be-

cause no abnormal vibration levels were re-ported while the generator set was running fol-lowing the turbine wash cycle. Thus, it is justi-fied to assume that gearbox health wasreasonably satisfactory for some time before thefailure occurred.

In regard to material, the chemical analysisshows an acceptable alloy composition. Also,there were no adverse reports on forging qual-ity, such as banding or grain flow. Therefore,material quality did not seem to play any signif-icant role in the failure mechanism.

Hardness and case depth profile, along withthe case microstructure, indicate there was notmuch discrepancy during heat treatment. Lowercore hardness of the planet gears has some influ-ence on the reduction of bending fatigue life butnot to the extent as in this case. Because therewere no records of any sudden overload, it isbelieved the major cause of failure was loadfluctuation.

Analysis of the generator load spectrum (Fig.14) subsequent to an online engine wash cycleshows quite a bit of load fluctuation—from 4 to12 MW in a short interval of time (1.5 cycles persecond for approximately 25 seconds). Fieldreports indicate this type of loading occurredmany times since the generator set was com-missioned. Nobody paid any attention to this


Fig. 13 Gear tooth microhardness profile

Fig. 14 Fluctuation of generator load after online enginewashing

loading pattern because it did not represent areal overload condition for the gearbox de-signed with an overload capacity of four timesthe nominal rating. That a high fluctuating nom-inal load could be as damaging as overload tothe nitrided gears was simply unknown. Al-though reduced allowable bending fatiguestrength was considered in designing the planetgears for reverse bending, it did not take intoaccount any possible change in the slope of theS-N curve (damage line) due to the high magni-tude of a fluctuating load.

It has been shown that the slope of S-N curvesfor both bending and pitting shifts downwardwhen nitrided gears are subjected to any over-load, as illustrated in Fig. 7. Conversely, theslope of S-N curves for carburized and hardenedgear steels changes very little, as shown in Fig.

6. Therefore, it is certain that the allowablefatigue strengths for both sun and planet gearsthat were nitrided had been reduced due to highfluctuating load. With reduced allowable fa-tigue strength, one of the planet gears that mighthave been metallurgically weakest of all failedfirst. It is believed the fragments of the failedtooth then went into mesh, causing the prema-ture failure of the gearbox.

Discussion. The fluctuating load followinga turbine water wash cycle was due to someinstability in the fuel-control system. This sortof instability and, hence, load fluctuation maybe avoided by replacing the online wash of theturbine with a stationary wash procedure. Suchan arrangement will definitely improve the lifeof such gearboxes.

Conclusions. The fatigue life of nitridedgears is reduced not only under overload butmay also be reduced under highly fluctuatingnominal load. The failure due to overload orfluctuating nominal load definitely accelerateswith the level of fatigue already induced by pre-vious stress cycles in the nitrided gears. In thiscase, it is believed that 16,000 h of turbine oper-ation contributed to some extent in the failure ofgears. Therefore, it is advisable to considerlower allowable fatigue strengths when design-ing nitrided gears that are subjected to overloador occasional highly fluctuating load. Also, acleaner material that meets AMS 2300 or 2304is recommended in such applications for reli-able and high-fatigue strength.

Bending-Fatigue Life of Nitrided Gears

To increase bending-fatigue life it is benefi-cial to have compressive stress at the surface ofthe tooth root fillet, the location of maximumbending stress. The mechanism for obtainingthe compressive stress on a nitrided surface is torestrict the growth of case by the core duringnitriding process. For small DP gear teeth withthe section size much greater than the hardenedcase, the expansion in the nitrided layer cannotalter the dimensions of the tooth. This actionsimply tends to stretch the core and, in so doing,places the surface in compression. On the otherhand, in large DP (smaller tooth section) gears,the case growth cannot be restricted by a thinnersection of the tooth and results in greatergrowth, which generates excessive tensile stressin the case. This lowers the residual compres-sive stress in the case and thereby reduces thefatigue life. This is why small DP nitrided gears


Table 7 Distortion ratings of common nitriding gear materialsHardness, HRC

Material AMS specification AMS quality Case Core Distortion rating

Nitralloy 135M 6471 2300 60–65 32–36 GoodNitralloy EZ 6475 2300 60–65 34–38 GoodNitralloy N 6475 2300 60–65 40–44 GoodAISI 4140 6349 2300 50–55 25–32 GoodAISI 4340 6414 2300 48–53 28–34 GoodMaraging 300 6419 2300 57–59 52–54 Excellent

show higher bending fatigue life than large DPnitrided gears.

Distortion in Nitriding

As with any other heat-treating process,nitriding causes gears to experience distortion,although its severity is less in comparison to thatwith other processes because this process is car-ried out at a relatively low temperature, approx-imately 510 °C (950 °F). Because of the lowtemperature, no phase transformation of steel,the major cause of distortion, takes place. Thesmall dimensional changes that occur are due toheating and cooling mechanisms and the gearblank configuration. Sometimes, higher distor-tion is observed due to high case depth require-ments in some gears that require many hours ofnitriding. In general, gas-nitrided gears with acase depth less than 0.254 mm (0.010 in.) domaintain the same AGMA quality level afternitriding. Gears with case deeper than 0.254mm (0.010 in.) experience some distortionresulting in lower quality level. Furthermore,pitch diameter (PD) and DP of a gear tooth arealso important parameters that influence distor-tion. Large PD with a small DP tooth distortsmore than a small PD with a large DP tooth.Distortion is also influenced by the materialselected. Some materials distort more than oth-ers. In general, distortion of gears after nitridingis low. Occasionally, the distortion becomeshigh due to large size and configuration of gears(e.g., internal gears in epicyclic arrangements).Higher distortion is also noticed in gears withselective nitriding (e.g., nitriding of teeth only).Table 7 presents general distortion ratings ofvarious steels after single-stage gas nitriding.

Although some distortion is always present inany type of nitriding, the process has a uniqueadvantage: reproducibility of the distortion inbatch after batch of gears. Gears of identicalgeometry and similar metallurgical quality dis-

tort exactly the same way. This means compen-sation for expected distortions can be made dur-ing tooth cutting prior to nitriding.

Gas Nitriding Applications and Costs

Applications. While carburizing is the mosteffective surface-hardening method, nitridingexcels when gear tooth geometry and tolerancesbefore heat treating need to be maintained with-out any finishing operation, such as grindingafter heat treatment. Although, through-harden-ing is capable of maintaining close tooth dimen-sional tolerances, the process cannot providesufficient wear and pitting resistance. This iswhy nitriding is an alternative to carburizingespecially for lightly loaded gears.

The major disadvantage of nitrided gears istheir inability to resist shock load due to inher-ent brittleness of the case. Also, nitrided gearsdo not perform well in applications with possi-ble misalignment during which the highly brit-tle nitrogen oxides on tooth edges break off andmay go into the gear mesh.

The quality of nitrided gear teeth is not asgood as carburized, hardened, and ground gears.Grinding to improve tooth geometry is not rec-ommended for nitrided gears because this maydetrimentally affect their load carrying capabil-ity if more than 0.025 mm (0.001 in.) stock isremoved.

Costs. Higher case depth requires a longernitriding cycle with an increase in cost. Steelswith chromium need shorter nitriding cyclesthan steels with aluminum for the same casedepth. Cost factors for one nitriding steel, Nitral-loy 135M, are given in Table 8.

Wider case depth tolerance is preferred forreduced costs. Table 9 gives case depth toler-ances and costs for Nitralloy 135M.

Partial coverage increases cost and should beavoided if possible. As shown in the table givenbelow, the cost of masking and copper plating


Table 8 Case depth and cost for Nitralloy135M

Case depth

mm in. Cost factor

0.254 0.010 1.00.004 0.012 1.00.356 0.014 1.40.406 0.016 1.60.457 0.018 2.0

Table 9 Case depth tolerances and cost forNitralloy 135M

Case depth tolerance

mm in. Cost factor

±0.051 ±0.002 1.4±0.076 ±0.003 1.0±0.102 ±0.004 0.8±0.127 ±0.005 0.7

Note: Similar cost factor is applicable to all other nitriding materials.

for selective nitriding contribute to a high costfactor:

Surface coverage Cost factor

Complete 1.0Partial 3.5

Controlled Nitriding (Ref 4, 5)

Controlled nitriding is a further developmentof the traditional gas nitriding in which all of theprocess parameters are computer controlled.The key to the success of the process lies in itsability to effectively control the concentrationof nitrogen in the surface layer of the treatedparts. By controlling the activity of nitrogen inthe gas atmosphere, it is possible to control theactivity of nascent nitrogen, a factor that deter-mines the nitriding capability of the atmo-sphere. The technology involves measuring andadjusting what is termed the nitriding potential,Np, which is expressed by the formula:

(Eq 3)

where PNH3is the partial pressure of ammo-

nia, and PH2is the partial pressure of hydrogen

in the furnace atmosphere.It should be noted that the term potential is in

no way equivalent to what is meant by carbonpotential in carburizing atmospheres. It is,rather, the reaction constant for the dissociation

Np � PNH3

1PH22 1>2

of ammonia. Its control allows the formation ofpredictable case structures and depths for arange of steels, including some tool and stain-less grades. Higher Np values produce highersurface concentrations of nitrogen and steeperconcentration gradients. Lower potentials allowthe development of nitrided cases without anybrittle-compound (white) layer in high-alloysteels. This can be of particular advantage incertain applications, such as aerospace gearssubject to higher contact stresses. In these appli-cations, the brittleness and/or unpredictabilityof the white layer produced by conventionalnitriding is detrimental.

The controlled nitriding process differs fromconventional gas nitriding in that it does not usepure ammonia. Instead, other gas components—including nitrogen, previously dissociated am-monia, hydrogen, argon, and oxygen—are addedin a controlled way to conventional ammonia.The effect of these additions, with the exceptionof argon, is to reduce the nitriding potential of theatmosphere; argon has no effect on Np. Con-trolled gas nitriding expands on the advantagesof nitriding, such as corrosion resistance and lowdistortion, and expands the range of metals suit-able for this surface-hardening process.

How the Process Works. This systemmakes it possible to adjust the availability ofatomic nitrogen at the gas-metal interface and toprecisely control the properties by changing thecomposition of the gas mix. This is done not onlyby selecting the correct atmosphere compositionfor a given material and process temperature butalso by maintaining the preset nitriding potentialvalue for each stage of the process.

Temperature and gas-flow controls, linked bya computer connected to a nitriding potential-sensing device, allow the programming of thecomplete process cycle to produce predictableand reproducible surface-layer characteristicsfor a given material. The control system can storea number of process recipes that may be selectedfor specified materials and applications. Whenthe operator selects a process from the software’s“library,” the time, temperature, atmospherecomposition, and nitriding potential for eachstage of the cycle are automatically controlled.

The computer program also controls func-tions such as opening and closing of valves,switching electric motors on and off, and main-taining optimal pressure inside the retort. Theoperator may manually select less critical fac-tors, such as printout frequency and the tempera-ture at which the process is to stop after cooling.


Fig. 15 Microhardness profiles of EN 19 chromium-molybdenum steel produced by controlled and conventional gas nitridingprocesses. Source: Ref 5

Process Advantages. The control of thenitrogen concentration in the surface zone bymaintaining a preset nitriding potential of theatmosphere offers several advantages over tra-ditional gas nitriding and other competitive sur-face treatment methods:

• Improved ductility and toughness of thecompound layer, reducing the risk of crack-ing or spalling

• Improved surface roughness values• Improved microhardness profiles (Fig. 15)• Cost-effectiveness through optimized cycle

times• Often, even lower temperatures than con-

ventional nitriding, thus further minimizingdistortion

• A broader range of treatable steel grades• Enhanced corrosion resistance through the

introduction of additional compounds intothe surface layer

In addition, by eliminating the white layerwhere it is not wanted, the process expands onthe traditional advantage of nitriding not need-ing mechanical finishing operations. It also lim-its the surface roughness that accompaniesnitriding by appropriately structuring the nitrid-ing stages. The process is ecologically more“friendly” than conventional gas nitriding, be-cause less ammonia is used overall.

Ion Nitriding

Ion, or plasma, nitriding is a vacuum processthat takes place in the plasma of high current

glow in a vessel. The workpiece, in this case, agear, forms the cathode, whereas the vessel wallis the anode. The vessel is evacuated prior tonitriding. Gas containing nitrogen is then intro-duced, and the treatment pressure in the vessel isset to between 0.1 to 10 torr (0.13 to 13.3 × 102

Pa). At this point, electric voltage is switched onand a glow discharge takes place; the nitrogenions thus produced strike the surface of the cath-ode with high kinetic energy emitting heat thatresults in a sputtering of the cathode, whichatomizes the cathode (gear) surface material. Thetemperature inside the vessel may vary from 350to 580 °C (660 to 1080 °F). The atomized ionsthen combine with nitrogen ions in the plasma toform iron nitride, which then is deposited as aneven iron nitride layer on the cathode. In turn, theiron nitrides are partially broken down on the sur-face of the cathode, whereby the nitrogen dif-fuses into the gear material.

As the process continues, the iron from theiron nitrides is partially dusted off in the plasmain front of the workpiece surface. Based on thiscontinual dusting process, the surface of gearsbeing treated is kept active longer. The advan-tage is that the nitride produced does not imme-diately act as a diffusion blocker, as in the caseof conventional gas nitriding. The case pro-duced by plasma nitriding is thus thicker andfree of pores because of the constant ion bom-bardment. Also, in comparison with the caseproduced in gas or liquid nitriding process, ion-nitrided cases are more ductile and more resis-tant to wear.

In ion nitriding, as in other nitriding pro-cesses, the nitrided layer has a diffusion zone


Table 10 Results after ion nitriding of common gear materials

Steel group

Core hardness,

HRC

Nitriding temperature,

°C (°F)

Surface hardness, 15-N scale

Total case depth, mm (in.)

Thickness of white layer,

mm × 10–4 (in. × 10–4)

White layer

composition

AISI 9310 28–32 520–550 (970–1020) 89.0 0.305–0.711 (0.012–0.028) 38.10–80.01 (1.50–3.15) Fe4NAISI 4130 28–36 510–550 (950–1020) 89.0 0.203–0.660 (0.008–0.026) 38.10–80.01 (1.50–3.15) Fe4NAISI 4140 34–38 510–550 (950–1020) 89.0 0.203–0.610 (0.008–0.024) 38.10–80.01 (1.50–3.15) Fe4N or noneAISI 4340 38–42 510–550 (950–1020) 89.0 0.254–0.635 (0.010–0.025) 38.10–80.01 (1.50–3.15) Fe4N or noneNitralloy 135M 28–32 510–550 (950–1020) 92.0 0.203–0.508 (0.008–0.020) 20.32–100.33 (0.8–3.95) Fe4NNitralloy N 25–32 510–550 (950–1020) 92.0 0.203–0.508 (0.008–0.020) 25–100.33 (1–3.95) Fe4N

and a compound layer. In the diffusion zone,nitrogen diffuses in steel according to classicalprinciples producing a hardened zone by precip-itation and solid solution hardening. This zoneis detected as a dark etching region below thesurface, varying in hardness from the surface tothe core. This region is measured as case andmay be as deep as 0.9 mm (0.035 in.), depend-ing on the type of steel, nitriding cycle time, andtemperature. On the other hand, the compoundlayer above the diffusion zone known as “whitelayer” is essentially composed of pure nitridesof iron and is very brittle. In ion nitriding, thewhite layer is usually below 0.0127 mm (0.0005in.). It is possible to reduce the thickness of thislayer further by controlling the ratio of nitrogenin the nitrogen and hydrogen gas mixture duringion nitriding.

Basically, any type of ferrous gear materialscan be ion nitrided. Heat treatable steels are par-ticularly suitable. Table 10 shows the results ofion nitriding for some typical gear materials.

To maintain the properties as listed in Table10 after ion nitriding, it is essential that there areno traces of rust, paint, or grease on gears be-cause these would prevent nitrogen from beingabsorbed into the tooth surfaces. Also, it is ad-visable to have lower arithmetic surface rough-ness average (Ra) value of these surfaces beforenitriding because surface roughness increases inmost materials after nitriding due to nitrogenabsorption into the surface. The longer theprocess is, the greater the increase of roughness,although the level of roughness can be returnedto its original state by honing or lapping at anadditional cost.

Honing or lapping also may be used to re-move the white layer. If grinding (not to exceed0.025 mm, or 0.001 in., stock removal) is usedinstead, the part shall be stress relieved at 160 to280 °C (325 to 540 °F) after grinding. Removalof white layer by chemical means is not advis-able. Allowable white layer should not exceed

0.0127 mm (0.0005 in.) and shall be of single-phase Fe4N (gamma prime iron) composition.

For selective ion nitriding, masking bymechanical means such as plate covers, whichact as barriers between the glow of dischargeand the part surfaces, is advisable. Maskingwith copper plating causes sputtering and is notadvisable. As an alternate to masking, parts maybe nitrided all over first and then the surfacesground where case is not desired or required.

Dimensional growth is minimal during ionnitriding. The growth is dependent on the quan-tity of nitrogen deposited. High-alloy steels takeup more nitrogen than those with a low-alloycontent. Hence, there is more growth of high-alloy steel gears. In case of insufficiently an-nealed and normalized steels, the annealingeffect of ion nitriding may cause disintegrationof the stable retained austenite, leading to a dis-proportional growth and distortion. Also, ionnitriding can cause a decrease in volume in gearsmade of martensitic steels. As in other heat treatprocesses, dimensional change of gears is betterdetermined by a preproduction run. In theabsence of such data, a growth of 0.025 mm per0.127 mm (0.001 in. per 0.005 in.) diffusiondepth may be considered for most gear steels.

In ion nitriding, the discharge parameters ofvoltage and current determine the supply ofactive ions, and that nitriding potential of thelow-pressure atmosphere in the chamber isessentially independent of the temperature of thecharge, unlike conventional gas nitriding. Thiscapability results in a number of unique advan-tages; for example, materials that would losetheir core strength under conventional nitridingconditions can be ion nitrided because theprerequisite for maintaining the core strength is that nitriding temperature be below the tem-per temperature. This also reduces distortionconsiderably.

Ion-Nitriding Time and Case Depth. Forthe same processing time, case depth attained


Fig. 16 Comparison of case depth vs. process time for ionand conventional nitriding

Fig. 17 Case depth vs. square root of ion-nitriding time fortwo materials

Fig. 18 Microhardness traverse of AISI 4140 steel gear sam-ple

Table 11 Summary of metallographicmeasurements of ion nitrided specimensMeasurement 4140 Sample 4340 Sample Requirement

Case depth, mm(in.)

Over 0.889(over 0.035)

0.508 (0.020)

0.51 (0.02)

Surface hardness,HK

690 604 540 min.

Core hardness,HRC

36 35 32–38

Grain size(ASTM)

No. 7 No. 6 No. 5 or finer

White layerdepth, mm (in.)

0.0025 (0.0001)

0.0051 (0.0002)

None

with ion nitriding is higher than gas nitriding.Figure 16 shows the results of case depth versustreatment time for AISI 4140 steel ion nitridedat 510 °C (950 °F) and gas nitrided at 525 °C(975 °F). Similar results also are achieved withNitralloy 135M steel. As in gas nitriding, highercase depth is obtained with AISI 4140 steel thanwith Nitralloy 135M. But Nitralloy 135M pro-duces higher surface hardness. Similar to gasnitriding, time for ion nitriding varies with casedepths and material. Figure 17 depicts timerequired for different case depths and two gearmaterials.

Hardness and Case Depth. Case-hardenedsamples of AISI 4140 and 4340 steels producedby ion-nitriding process showed encouragingresults as tabulated in Table 11. The majorshortcoming of earlier ion-nitriding processeswas the large variation in case depth from areato area of teeth. However, the current improved

process offers fairly uniform case depths. Sometypical microhardness traverses for gear toothmade of AISI 4140 and 4340 steels are illus-trated in Fig. 18 and 19, respectively.

Improved Case Property. Ion-nitrided sur-faces, especially with high-alloy steels, show

Fig. 19 Microhardness traverse of AISI 4340 steel gear sam-ple


Table 12 Distortion ratings of some ion-nitriding materialsHardness, HRC

Material AMS specification AMS quality Nitriding temperature, °C (°F) Case Core Distortion rating

AISI 9310/9315 6265 2300/2304 520–550 (970–1020) 50/58 28/32 GoodAISI 4340 6414 2300/2304 510–550 (950–1020) 54/58 38/42 GoodNitralloy 135M 6471 2300/2304 510–550 (950–1020) 60/62 28/32 GoodNitralloy N 6475 2300/2304 510–550 (950–1020) 60/62 26/32 Good

comparatively good ductility. This characteris-tic is due to the ability to closely control theamount and type of white layer. High ductilityresults in high fatigue properties.

Distortion. Because gears are ion nitridedunder vacuum, only the stresses originatingfrom the thermal and preliminary treatmentslead to distortion. For this reason, to minimizedistortion, gears are stress-free annealed beforeion nitriding. The temperature of the stress reliefis maintained at least 25 °C (75 °F) over the ion-nitriding temperature. Also, slower coolingafter the stress relief is recommended. A secondstress relief is sometimes beneficial after roughmachining. If done properly, the distortion isexpected to be minimal. Should the core hard-ness be diminished through stress relieving to avalue too low, an alternate material should beused. Table 12 presents comparative distortionratings of some ion-nitriding materials.

ACKNOWLEDGMENTS


• A.K. Rakhit, Nitriding Gears, Heat Treat-ment of Gears: A Practical Guide for Engi-neers, ASM International, 2000, p 133–158

• A.K. Rakhit, Modern Nitriding Processes,Heat Treatment of Gears: A Practical Guidefor Engineers, ASM International, 2000, p159–169

• J.R. Davis, Ed., Nitriding, Surface Harden-ing of Steels: Understanding the Basics,ASM International, 2002, p 141–194

REFERENCES

1. D.W. Dudley, Gear Materials, Handbookof Practical Gear Design, McGraw-HillBook Company, 1984, p 4.1–4.61

2. Gas Nitriding, Heat Treating, Vol 4, ASMHandbook, ASM International, 1991, p387–409

3. R. Errichello and D.R. McVittie, PredictingGear Life with Miner’s Rule, Power Trans-mission Design, Vol 31 (No. 3), March1989, p 33–38

4. G.J. Tymowski, W.K. Liliental, and C.D.Morawski, Typical Nitriding Faults andTheir Prevention Through the ControlledNitriding Process, Ind. Heat., Jan 1995, p 39–44

5. G.J. Tymowski, W.K. Liliental, and C.D.Morawski, Take the Guesswork Out ofNitriding, Adv. Mater. Process., Dec 1994,p 52–54

SELECTED REFERENCES

• Plasma (Ion) Nitriding, Heat Treating, Vol4, ASM Handbook, ASM International,1991, p 420–424

• D. Pye, Nitriding Techniques and Methods,Steel Heat Treatment Handbook, G.E. Tot-ten and M.A.H. Howes, Ed., MarcelDekker 1997, p 721–764

• D. Pye, Practical Nitriding and Ferri-tic Nitrocarburizing, ASM International, 2003

CHAPTER 11

Carbonitriding

CARBONITRIDING is a modified form ofgas carburizing, rather than a form of nitriding.The modification consists of introducing ammo-nia into the gas carburizing atmosphere to addnitrogen to the carburized case as it is beingproduced. Nascent nitrogen forms at the worksurface by the dissociation of ammonia in thefurnace atmosphere; the nitrogen diffuses intothe steel simultaneously with carbon. Typically,carbonitriding is carried out at a lower tempera-ture and for a shorter time than is gas carburiz-ing, producing a shallower case than is usual inproduction carburizing.

Carbonitriding is performed in a closed fur-nace chamber with an atmosphere enriched withgaseous compound of carbon and nitrogen.Many types of gas are used. Common practice isto use an endothermic gas, such as natural gas,as a carrier for the ammonia and hydrocarbons.The process primarily imparts a hard, wear-resistant case. A carbonitrided case has betterhardenability than a carburized case. Also, thepresence of N2 in the case, as in nitriding,increases its hardness. Most carbonitriding isdone between 770 and 890 °C (1425 and 1625°F) for gears to be liquid quenched and between650 and 790 °C (1200 and 1450 °F) for gearsnot requiring liquid quench.

The addition of nitrogen has four importanteffects:

• It inhibits the diffusion of carbon, whichfavors production of a shallow case.

• It enhances hardenability, which favorsattainment of a very hard case.

• It makes it possible to form martensite inplain carbon and low-alloy steels that ini-tially have low hardenability.

• Nitrides are formed, increasing the surfacehardness further.

Nitrogen, similar to carbon, manganese, andnickel, is an austenite stabilizer, so retainedaustenite is a concern after quenching. Lower-ing the ammonia percentage reduces the amountof retained austenite and should be done ifdecreases in hardness or wear resistance cannotbe tolerated. Another consequence of too-highnitrogen is the formation of voids or porosity. Ingeneral, the nitrogen content at the surfaceshould be no greater than 0.40% (Fig. 1).

The nitrogen in the carbonitrided case alsoincreases the resistance of steel to softening atslightly elevated temperatures. The greater thenitrogen content, the greater the resistance tosoftening. This is why higher tempering tem-peratures—up to 225 °C (440 °F)—are often

Fig. 1 Surface layers produced by carbonitriding of steel at850 °C (1560 °F), where carbon predominates in

the formation of a martensitic layer. Source: Ref 1




used on carbonitrided parts. The resistance tosoftening manifests itself in improved wearresistance. Carbonitrided gears, for example,often exhibit better wear properties than carbur-ized gears.

Applicable Steels and Applications

Gear steels commonly carbonitrided in-clude carbon steels (1018, 1022, 1117) and alloysteels in the 4100, 4300, 5100, and 8600 series,with carbon contents up to approximately 0.25%.Also, many alloy steels in these same series witha carbon range of 0.30 to 0.50% are carbonitridedto case depths up to approximately 0.3 mm (0.01in.) when a combination of a reasonably tough,through-hardened core and a hard, long-wearingsurface is required (for example, transmissiongears). Steels such as 4140, 5130, 5140, 8640,and 4340 for applications such as heavy-dutygearing are treated by this method at 845 °C(1550 °F). High-density powder metallurgysteels are also often carbonitrided for improvedwear resistance and toughness.

Applications. Carbonitriding is limited toshallower cases for fine pitch gearing used pri-marily in aerospace applications. Deep casedepths require prohibitive time cycles. The car-bonitrided case has better wear and temper resis-tance than a carburized case. For many applica-tions, carbonitriding of low-alloy steels providescase properties equivalent to those obtained ingas carburized high-alloy steels. But the coreoften has low hardness. This is why the processis generally applied to gears of low-duty cycle.

Depth of Case

Preferred case depth is governed by serviceapplication and by core hardness. Case depthsof 0.025 to 0.075 mm (0.001 to 0.003 in.) arecommonly applied to thin parts that requirewear resistance under light loads. Case depthsup to 0.75 mm (0.030 in.) may be applied toparts for resisting high compressive loads. Casedepths of 0.63 to 0.75 mm (0.025 to 0.030 in.)may be applied to gears that are subjected tohigh tensile or compressive stresses caused bytorsional, bending, or contact loads.

Medium-carbon steels with core hardnessesof 40 to 45 HRC normally require less casedepth than steels with core hardnesses of 20HRC or below. Low-alloy steels with medium-

carbon content, such as those used in automo-tive transmission gears, are often assigned min-imum case depths of 0.2 mm (0.008 in.).

Measurements of the case depths of carboni-trided parts may refer to effective case depth ortotal case depth, as with reporting case depthsfor carburized parts. For very thin cases, usuallyonly the total case depth is specified. In general,it is easy to distinguish case and core micro-structures in a carbonitrided piece, particularlywhen the case is thin and is produced at a lowcarbonitriding temperature; more difficulty isencountered in distinguishing case and corewhen high temperatures, deep cases, and me-dium-carbon or high-carbon steels are involved.Whether or not the core has a martensitic struc-ture is also a contributing factor in case-depthmeasurements.

Hardenability of Case

One major advantage of carbonitriding is thatthe nitrogen absorbed during processing lowersthe critical cooling rate of the steel. That is, thehardenability of the case is significantly greaterwhen nitrogen is added by carbonitriding thanwhen the same steel is only carburized (Fig. 2).This permits the use of steels on which uniformcase hardness ordinarily could not be obtained ifthey were only carburized and quenched. Wherecore properties are not important, carbonitridingpermits the use of low-carbon steels, which costless and may have better machinability orformability.

Fig. 2 End-quench hardenability curve for 1020 steel car-bonitrided at 900 °C (1650 °F) compared with curve

for the same steel carburized at 925 °C (1700 °F). Hardness wasmeasured along the surface of the as-quenched hardenabilityspecimen. Ammonia and methane contents of the inlet carboni-triding atmosphere were 5%; balance, carrier gas.

Chapter 11: Carbonitriding / 247

Quenching and Tempering

Quenching. Carbonitrided steels may bequenched in water, oil, or gas depending on theallowable distortion, metallurgical requirements(such as case and core hardness), and type of fur-nace. For the alloy gear steels discussed earlier,oil quenching is most commonly employed.Quenching oil temperatures may vary fromapproximately 40 to 105 °C (100 to 220 °F). Spe-cial high-flash-point oils may be used at thehigher temperatures to minimize distortion;sometimes, molten salt is used for the same rea-son. In the normal range of oil temperature(approximately 50 to 70 °C, or 120 to 160 °F), amineral oil with a minimum flash point of 170 °C(335 °F) and a viscosity of 21 × 10–6 m2/s at 38 °C(21 centistokes, or 100 Say-bolt universal sec-onds, or SUS, at 100 °F) is commonly used. Spe-cial oils containing additives for increasing thequenching rate also may be used. To maintainmaximum quenching effectiveness, quenchingoils should have a low capacity for dissolvingwater. Quenching oils that dissolve even smallamounts of water may lose effectiveness in 3 to 6months; those that shed water completely may beused significantly longer.

Tempering. Because tempering a carboni-trided case at 425 °C (795 °F) and above results ina marked increase in notch toughness (see Table1), parts that are to be subjected to repeated shockloading are invariably tempered to avoid impactand impact fatigue failures. Most carbonitridedgears are tempered at 190 to 205 °C (375 to400°F) to reduce surface brittleness and yetmaintain a minimum case hardness of 58 HRC.Alloy steel parts that are to be surface ground aretempered to minimize grinding cracks.

Distortion

Distortion in carbonitrided gears is far lessthan that of carburized gears because of lowerprocess temperatures and shorter time cycles.Nevertheless, it is more than any nitridingprocess. But one major advantage of carboni-triding is that the hardenability of the case is sig-nificantly greater than carburizing or nitridingprocess. This permits in many cases to finishgrind teeth (0.076 to 0.102 mm, or 0.003 to0.004 in., stock removal) without any signifi-cant loss of hardness.

ACKNOWLEDGMENT

This chapter was adapted from Carbonitrid-ing, Surface Hardening of Steels: Understand-ing the Basics, J.R. Davis, Ed., ASM Interna-tional, 2002, p 127–139

REFERENCE

1. D.H. Herring, Comparing Carbonitridingand Nitrocarburizing, Heat Treat. Prog.,April/May 2002, p 17–19

SELECTED REFERENCES

• R. Davies and C.G. Smith, A Practical Studyof the Carbonitriding Process, Met. Prog.,Vol 114 (No. 4), 1978, p 40–53

• J. Dossett, Carbonitriding, Heat Treating,Vol 4, ASM Handbook, ASM International,1991, p 376–386

Table 1 Effect of tempering on Charpy V-notch impact strength of carbonitrided 1041 steelSpecimens were carbonitrided at 845 °C (1550 °F) for 3 h in an atmosphere containing 7% ammonia, and were oil quenched fromthe carbonitriding temperature. Specimens were copper plated before machining of V-notch to permit exposure of the notch to thecarbonitriding atmosphere.

Tempering temperature Impact strength

Test °C °F J ft · lb Surface(b) Core0.075

(0.003)0.15

(0.006)0.25

(0.01)0.38

(0.015)0.64

(0.025)1.0

(0.04)1.4

(0.055)

1 AQ AQ 1.4 1 60 53 63 64 64 63 61 61 582 370 700 2, 2 1.5, 1.5 47 46 57 57 55 54 49 50 503 425 800 29, 29 21.5, 21.5 42.5 43 57 57 56 55 49 47 474 480 900 69, 60 51, 44 38 38 54 54 52 50 42 38 385(c) 480 900 47, 52 35, 38 . . . . . . . . . . . . . . . . . . . . . . . . . . .6 540 1000 78, 81 57.5, 60 35 32 49 50 50 47 36 33 32

AQ: as-quenched. (a) Converted from Vickers hardness. (b) Surface hardness is less than hardness at 0.075 mm below the surface because of retained austenite. (c)Tested at –18 °C (0 °F); all other tests at room temperature

Hardness, HRC(a) Distance below surface, mm (in.)

CHAPTER 12

Induction and Flame Hardening

INDUCTION AND FLAME HARDENINGare methods of hardening the surfaces of com-ponents, usually in selected areas, by the short-time application of high-intensity heating fol-lowed by quenching. The heating and hardeningeffects are localized, and the depth of hardeningis controllable. Unlike thermochemical casehardening treatments (carburizing, nitriding,and carbonitriding) applied to steels, inductionand flame hardening do not promote chemicalenrichment of the surface with carbon or nitro-gen but rely on the presence of an adequate car-bon content already in the material to achievethe hardness level required. The properties ofthe core remain unaffected and depend on mate-rial composition and prior heat treatment.

Induction and flame hardening have beenused successfully on most gear types (spur, heli-cal, bevel, herringbone, etc.). These processesare used when gear teeth require high hardness,but size or configuration does not lend itself tocarburizing and quenching the entire part. Bothprocesses may also be used when the maximumcontact and bending strength achieved by car-burizing is not required. Induction and flamehardening are also used in place of the morecostly nitriding process which cannot economi-cally generate some of the deeper cases required.The characteristics of induction and flame hard-ening methods are compared in Table 1.

Induction Hardening

In the induction hardening process, rapidheating is generated by electromagnetic induc-tion when a high-frequency current is passedthrough a coil surrounding a gear. The depth towhich the heated zone extends depends on thefrequency of the current and on the duration ofthe heating cycle. Because of an electrical phe-

nomenon called skin effect, the depth of theheated area is inversely proportional to the fre-quency used. It means the finer the pitch of geartooth is, the higher the frequency of currentneeded will be. The time required to heat thesurface layers to above the material transforma-tion range is surprisingly brief, a matter of a fewseconds. Selective heating and, therefore, hard-ening, is accomplished by suitable design of thecoils or inductor blocks. At the end of the heat-ing cycle, the steel usually is quenched by waterjets passing through the inductor coils. Precisemethods for controlling the operation, such asthe rate of energy input, duration of heating, andrate of cooling, are thus necessary. These fea-tures are incorporated in induction hardening

Table 1 Comparison of flame- andinduction-hardening processesCharacteristics Flame Induction

Equipment Oxyfuel torch,special headquench system

Power supply,inductor, quenchsystem

Applicable material

Ferrous alloys,carbon steels,alloy steels, castirons

Same

Speed of heating Few seconds to fewminutes

1–10 s

Depth of hardening 1.2–6.2 mm(0.050–0.250 in.)

0.4–1.5 mm(0.015–0.060 in.);0.1 mm (0.004 in.)for impulse

Processing One part at a time SamePart size No limit Must fit in coilTempering Required SameCan be automated Yes YesOperator skills Significant skill

requiredLittle skill required

after setupControl of process Attention required Very preciseOperator comfort Hot, eye protection

requiredCan be done in suit

CostEquipment Low HighPer piece Best for large work Best for small work




Fig. 1 Variations in hardening patterns obtainable on gearteeth by induction hardening

equipment, which usually is operated entirelyautomatically.

Induction hardening employs a wide variety ofinductors ranging from coiled copper tubing toforms machined from solid copper combinedwith laminated materials to achieve the requiredinduced electrical currents. Coarser pitch teeth(below 20 diametral pitch, DP) generally requireinductors powered by medium-frequency motorgenerator sets or solid-state units. Finer-pitchgearing uses encircling coils with power pro-vided by high-frequency vacuum tube units.Wide-faced gearing is heated by scanning-typeequipment, while more limited areas can beheated by stationary inductors. Parts are rotatedwhen encircling coils are used. Induction heatingdepth and pattern are controlled by frequency,power density, shape of the inductor, workpiecegeometry, and workpiece area being heated.

Quenching after induction heating can be inte-gral with the heat source by use of a separate fol-lowing spray or by using an immersion quenchtank. Oil, water, or polymer solutions can beused, in addition to air, depending on hardenabil-ity of the steel and hardening requirements.

Applicable MaterialsA wide variety of materials can be induction

hardened, including (cast and wrought) carbonand alloy steels, martensitic stainless steels, andductile, malleable, and gray cast irons. Gener-ally, steels with carbon content of approximately0.35 to 0.50% are suitable for induction harden-ing. Alloy steels with more than 0.5% carbon aresusceptible to cracking. The higher the alloycontent with high carbon is, the greater the ten-dency to crack will be. Some of the common gearmaterials that offer acceptable case and coreproperties after induction hardening are AISI1040, 1050, 4140, 4340, and 5150 steels.

Selection of the material condition (hotrolled, cold rolled) can affect the magnitude andrepeatability of induction hardening. Hot-rolledmaterials exhibit more dimensional change andvariation than cold drawn because of densifica-tion of material from cold working. A quenchand tempered material condition before heattreatment, however, provides the best hardeningresponse and most repeatable distortion.

Preheat TreatmentFor more consistent results, it is recom-

mended that coarser pitch gears of leaner alloysteels receive a quench and temper pretreat-

ment, for example, 4140 steel with teeth coarserthan 4 DP.

Both carbon and alloy steels with normalizedor annealed structures can be induction hard-ened. These structures do, however, requirelonger heating cycles and a more severe quench,which increase the chance of cracking. Theannealed structure alone is the least receptive toinduction hardening.

Hardening PatternsThere are two basic methods of induction

hardening gears: spin hardening and tooth-to-tooth, or contour hardening. Figure 1 showsvariations of these processes and the resultanthardening patterns. In spin hardening that uses acircular inductor, the teeth are hardened fromthe tips downward. While such a pattern may beacceptable for splines and some gearing, heav-ily loaded gears need a hardness pattern that ismore like a carburized case. This is achievedwith contour hardening.

The spin or induction coil method is generallylimited to gears of approximately 5 DP and finer.The maximum diameter and face width of gearscapable of being hardened by this method aredetermined by the area of gear outside diameterand kW capacity of the equipment. Long slenderparts can be induction hardened with lower kWcapacity equipment by having coils scan thelength of part while it is rotating in the coil.

Contour hardening can be applied to almostany tooth size with appropriate supportingequipment and kW capacity. However, forgears of approximately 16 DP and finer, thismethod does not produce satisfactory results. In

Chapter 12: Induction and Flame Hardening / 251

Fig. 2 Quench ring and solenoid coil surrounding a gear tobe induction hardened.

Table 2 Current frequency versus case depthfor induction hardeningFrequency, kHz Approximate case depth, mm (in.)

3 3.81 (0.150)10 1.52–2 (0.060–0.080)500 0.51–1 (0.02–0.04)1000 0.25–0.51 (0.01–0.02)

Table 3 Recommended depth of hardness inroot region for induction-hardened teethDiametralpitch (DP)

Hardness depth, mm (in.)

Frequency, kHz

20 0.25–1 (0.010–0.040) 500–100016 0.38–1.52 (0.015–0.060) 500–100010 0.51–2.54 (0.020–0.100) 300–5008 0.76–3.18 (0.030–0.125) 300–5006 1.14–3.81 (0.045–0.150) 100–3004 1.52–4.45 (0.060–0.175) 6–10

Depth reading taken at the center of root fillet.

such cases, an induction coil method is recom-mended.

Heating with InductionAccurate heating to the proper surface tem-

perature is a critical step. Inductor design, heatinput, and cycle time must be closely controlled.Underheating results in less than specified hard-ness and case depth. Overheating can result incracking. For effective heating, recommendedcurrent frequencies used for different DP ofgears are:

Diametral pitch (DP) Frequency, kHz

20 500–100010 300–5008 300–5006 10–5004 6–102 6–10

Quenching and TemperingQuenching. Heat must be removed quickly

and uniformly to obtain desired surface hard-ness. The quenchant should be such that it pro-duces acceptable as-quenched hardness, yetminimize cracking. Quenchants used are water,soluble oil, polymer, oil, and air.

Parts heated in an induction coil usually arequenched in an integral quench ring (Fig. 2) orin an agitated quench media. Contour hardeningis equipped with an integral quench followingthe inductor, or the gear may be submerged in aquench media.

Tempering is performed only when speci-fied. However, judgment should be exercisedbefore omitting tempering. It is a good practice

to temper after quenching to increase toughnessand reduce residual stress and crack susceptibil-ity. Tempering should be done for sufficienttime to ensure hardened teeth reach the speci-fied tempering temperature.

Surface Hardness and Case DepthFrequency and power density of electrical

power and its time duration govern the depth ofheating, which eventually controls the surfacehardness and case depth that can be achievedafter induction hardening. Surface hardness isprimarily a function of carbon content. It alsodepends on alloy content, heating time, mass ofthe gear, and quenching considerations. Hard-ness achieved is generally between 53 and 55HRC. The core hardness is developed byquenching and tempering prior to inductionhardening. As already discussed, high fre-quency of current can control heat to a shallowdepth on the tooth surfaces, whereas low fre-quencies produce greater depth of heat penetra-tion. For example, a case depth of 0.254 mm(0.010 in.) can be produced with a frequencybetween 100 kHz and 1 MHz.

For larger case depths, frequencies between 3and 25 kHz are used. Table 2 shows approxi-mate case depths that are normally achievedwith the induction hardening process.

In an induction-hardened tooth that requireshigh bending strength, it is necessary to get areasonable hardness depth at the root fillet.Table 3 shows how much is needed for differentsize gear teeth.


Fig. 3 Recommended maximum surface hardness and ef-fective case depth hardness vs. carbon percent for

induction-hardened gears

Fig. 4 Case depth profiles at different current frequency

Fig. 5 Comparison of hardness gradients—induction-hardened and carburized gears

Even though the correct hardness depth isobtained in the root region, it still is difficult toobtain high bending strength with induction-hardened gears made of any alloy steel. There-fore, a proper material selection is critical.Another drawback of induction hardening isresidual tensile stress. With a clever develop-ment program, it is usually possible to work onan induction-hardening cycle so that the timingof the heating, the delay before quench, and thequenching are such that gears are free from dan-gerous residual tensile stresses.

Effective Case Depth. Effective case depthfor induction-hardened gears normally isdefined as the distance below the surface at the0.5 tooth height where hardness drops 10 HRCpoints below the surface (Fig. 3). In case a toothis through hardened (finer DP gears), effectivecase depth does not apply. When root is to behardened, depth of case at the root may be sep-arately specified.

Core Hardness of Tooth and FatigueStrength. For every gear material, there is anoptimum core hardness for maximum fatiguestrength, provided the tooth is not through hard-ened. As the size of tooth decreases (higher DP), teeth tend to become through hardened. In case of induction-hardened teeth, throughhardening takes place for tooth size above 10DP, meaning allowable fatigue strength forinduction-hardened gears above 10 DP needs tobe reduced.

Induction Hardening ProblemsIt is quite difficult to obtain uniform case

depth on a gear tooth with induction hardening.Typical case profiles of induction-hardenedteeth are shown in Fig. 4. Furthermore, it also isdifficult to obtain a reasonable depth of hard-ness at the center of root fillet. This results inlower bending strength compared with a carbur-ized and hardened gear tooth. Furthermore, themaximum attainable surface hardness withinduction hardening is about 55 HRC, whichlimits the durability of gears.

Another problem with an induction-hardenedgear is residual stress in the case/core interface.In this region, there are high residual stressesdue to drastic differences of the case and coremicrostructures and the fact that the transitionoccurs in a very short distance, as illustrated inFig. 5. This figure also shows the differences incase hardness gradients for induction-hardenedand carburized gear teeth. If the induction hard-ening process is not properly controlled, the

case/core interface area could be susceptible tocracking.

In any case, considering all the merits anddemerits, induction hardening is a viable gear


Table 4 Distortion ratings of some induction-hardening materials

Material (AISI) AMS specification AMS quality Case Core Distortion rating(a)

1040 . . . 2300/2304 54 30 Good1050 . . . 2300/2304 54 30 Good4140 6382 2300/2304 55 40 Good4340 6414 2300/2304 55 40 Poor5140 . . . 2300/2304 55 40 Poor

Note: Alloy steels with 0.5% carbon and above are susceptible to cracking. (a) Compared with carburizing and hardening

Hardness, HRC

heat treat process. For successful use of theprocess, it is necessary to go through severaldevelopmental steps similar to other heat treatprocesses.

Heat Treat Distortion. As with other heattreat processes, there is some distortion of gearsafter induction hardening. Hot-rolled materialsexhibit more dimensional change and variationthan cold-drawn materials that are subjected todensification due to cold working. A quenchand tempered material condition or pre-heattreatment, however, provides the best hardeningresponse and most repeatable distortion. Table 4shows comparative ratings of some commoninduction-hardening type materials. In general,after induction hardening, the quality level ofgears does not go down by more than oneAGMA quality level. Thus, in most applica-tions, induction-hardened gears do not requireany post-heat-treat finishing except for high-speed applications (pitch line velocity above50.8 m/s, or 10,000 ft/min); mating gears some-times are lapped together.

Dual-Frequency ProcessThe dual-frequency process uses two differ-

ent frequencies for heating: high and low. Atfirst, the gear is heated with a relatively low-frequency source (3–10 kHz), providing theenergy required to preheat the mass of the gearteeth. This step is followed immediately byheating with a high-frequency source, whichranges from 100 to 270 kHz, depending on theDP of the gear. The high-frequency source rap-idly heats the entire tooth surface to the harden-ing temperature. The gear is then quenched forthe desired hardness.

The process is usually computer controlled.Because it is fast, surfaces remain clean and freefrom carbon depletion and scale, and the corematerial retains its original properties. Theprocess puts only the necessary amount of heatinto the part (much less than single-frequency

induction); hence, case depth and gear qualitylevel can be met precisely.

Residual (compressive) stress levels in agear tooth induction hardened by the dual-frequency method are considerably higher than those in the single-frequency inductionmethod. Figure 6 shows comparative stress lev-els between single-frequency induction, dual-frequency induction systems, and carburizedand hardened gear tooth.

Distortion. Because the amount of heatapplied by the dual-frequency process is consid-erably less than single frequency, heat treat dis-tortion is significantly lower. In a test with gears(8 DP; 54 teeth; 29.21 mm, or 1.15 in., facewidth) made from AISI 5150, results showeddistortion on any gear geometry dimension to beless than ±0.0102 mm (±0.0004 in.).

Materials. A variety of materials can beused. Materials that have been successfully con-tour hardened by the dual-frequency methodinclude AISI 1050, 4140, 4340, 4150, and 5150.

Applications. Dual-frequency process is su-perior to regular induction hardening and is par-ticularly useful for higher root hardness andclose control of case depth.

Flame Hardening

Flame hardening involves the direct impinge-ment of oxyfuel gas flames from suitablydesigned and positioned burners onto the surfacearea to be hardened, followed by quenching. Theresult is a hard surface layer of martensite over asofter interior core. There is no change in com-position, and therefore, the flame-hardened steelmust have adequate carbon content for thedesired hardness. The rate of heating for thisprocess is rapid, although not as fast as withinduction heating.

Equipment. Flame-hardening equipmentmay be a single torch with a specially designed


Fig. 7 Variations in hardening patterns obtainable on gearteeth flanks by flame hardening

Table 5 Response of steels to flame hardening

Material Air(a) Water(b)

Plain carbon steels

1025–1035 . . . 33–501040–1050 . . . 55–601055–1075 50–60 60–631080–1095 55–62 62–651125–1137 . . . 45–551138–1144 45–55 55–621146–1151 50–55 58–64

Carburized grades of plain carbon steels(c)

1010–1020 50–60 62–651108–1120 50–60 62–65

Alloy steels

1340–1345 45–55 55–623140–3145 50–60 60–643350 55–60 63–654063 55–60 63–654130–4135 . . . 55–604140–4145 52–56 55–604147–4150 58–62 62–654337–4340 53–57 60–634347 56–60 62–654640 52–56 60–6352100 55–60 62–646150 . . . 55–608630–8640 48–53 58–628642–8660 55–63 62–64

Carburized grades of alloy steels(c)

3310 55–60 63–654615–4620 58–62 64–668615–8620 . . . 62–65

(a) To obtain the hardness results indicated, those areas not directly heated mustbe kept relatively cool during the heating process. (b) Thin sections are suscep-tible to cracking when quenched with water. (c) Hardness values of carburizedcases containing 0.90 to 1.10% C

Typical hardness, HRC, as affected by quenchant

head or an elaborate apparatus that automati-cally indexes, heats, and quenches parts. Gearsthat are so large that conventional furnace treat-ments are not practical or economical are flame

hardened. The quality requirement for suchgears is generally below AGMA class 7. Itshould be noted that high operator skill is nec-essary when flame hardening is carried out man-ually using a single torch.

Gases. Three basic gases are used for flamehardening: acetylene, MAPP (methylacetylenepropadiene), and propane. These gases are eachmixed with air in particular ratios and areburned under pressure to generate the flamewhich the burner directs on the workpiece.

Applicable Materials. Any type of harden-able steel can be flame hardened. For bestresults, the carbon content should be at least0.35%, the usual range being 0.40 to 0.50% asshown in Table 5.

Quenching. Plain carbon steels usually arequenched by a water spray, whereas the rate ofcooling of alloy steels may be varied from arapid water quench to a slow air cool, dependingon the composition of the steel. Typical hard-nesses obtained by quenching in air or water aregiven in Table 5.

Applications. The general application offlame hardening is to the tooth flanks only. Thiscan be accomplished by spin flame hardening ortooth-to-tooth flame hardening (Fig. 7). Induc-tion contour hardening is preferred over flamehardening when root hardness and closer con-trol of case depth is required. Although the spinflame hardening process is capable of hardeningthe whole tooth and also below the root, reducedcore ductility and increased distortion result.

ACKNOWLEDGMENT

Portions of this chapter were adapted fromA.K. Rakhit, Induction Hardening Gears, Heat

Fig. 6 Residual compressive stress distribution—inductionhardening and carburizing


Treatment of Gears: A Practical Guide forEngineers, ASM International, 2000, p 175–184

SELECTED REFERENCES

• R.E. Haimbaugh, Practical Induction HeatTreating, ASM International, 2001

• P.A. Hassell and N.V. Ross, Induction HeatTreating of Steel, Heat Treating, Vol 4,

ASM Handbook, ASM International, 1991, p164–202

• T. Ruglic, Flame Hardening, Heat Treating,Vol 4, ASM Handbook, ASM International,1991, p 268–285

• S.L. Semiatin and D.E. Stutz, InductionHeat Treatment of Steel, American Societyfor Metals, 1986

• S. Zinn and S.L. Semiatin, Elements ofInduction Heating: Design, Control, andApplications, ASM International, 1988

CHAPTER 13

Gear Failure Modes and Analysis

GEARS can fail in many different ways, andexcept for an increase in noise level and vibra-tion, there is often no indication of difficulty untiltotal failure occurs. In general, each type of fail-ures leaves characteristic clues on gear teeth, anddetailed examination often yields enough infor-mation to establish the cause of failure. Despitethe variety of ways in which gears fail, servicefailures of gears are relatively rare (Ref 1).

Classification of Gear Failure Modes

Several failure analysists have classified gearfailure modes in different ways. As shown inTable 1, the American Gear ManufacturersAssociation (AGMA) has classified 36 modesof gear failure under the broad categories ofwear, scuffing, plastic deformation, contactfatigue, cracking, fracture, and bending fatigue.Each of these failure modes are described in theAGMA gear failure nomenclature publication(Ref 2).

Errichello (Ref 3) has classified gear failuresinto two broad groups:

• Nonlubrication-related failures• Lubrication-related failures

As shown in Table 2 in Chapter 2, “Gear Tri-bology and Lubrication,” nonlubricated-relatedfailures include both overload and bendingfatigue types of failure. Lubricated-related fail-ures include Hertzian fatigue (pitting), wear,and scuffing.

In Ref 4, gear failure modes were brokendown into two groups:

• Failure modes on gear tooth flanks, includ-ing pitting, scuffing, and wear

• Failure modes on gear root fillets, includingbending fatigue and impact

Alban (Ref 1) has classified gear failures intofour groups: fatigue, impact, wear, and stressrupture. Table 2 lists these failure modes inorder of decreasing frequency (the primarycause of failure is fatigue, the second cause isimpact, and so on). In a composite analysis ofmore than 1500 studies, the three most commonfailure modes, which together account for morethan half the failures studied, are tooth-bendingfatigue, tooth-bending impact, and abrasivetooth wear (Ref 1).

Fatigue Failures

Fatigue failure results from cracking underrepeated stresses much lower then the ultimatetensile strength. This type of failure:

• Ordinarily depends upon the number of rep-etitions of a given stress range rather thanthe total time under load

• Does not occur below some stress amplitudecalled the fatigue limit

• Is greatly encouraged by notches, grooves,surface discontinuities, and subsurface im-perfections that will decrease the stress am-plitude that can be withstood for a fixednumber of stress cycles

• Is increased significantly by increasing theaverage tensile stress of the loading cycle

There are three stages within a fatigue failurethat must be studied closely: the origin of thefracture, the progression under successive cyclesof loading, and final rupture of the part when thespreading crack has sufficiently weakened thesection. Most attention is devoted to the firststage to answer the question, Why did it start atthis point? The second stage is observed to deter-mine the direction of the progression. It appearsthat a fatigue crack will follow the path of least



resistance through the metal. The final fracturingmay be by shear or tension, but in either case, thesize of the final-fracture area can be used to cal-culate the apparent magnitude of stress that hadbeen applied to the part.

Bending Fatigue

The origins of bending fatigue failures typi-cally are imperfections in the surface of the root


Table 1 Gear failure nomenclaturerecommended by the American GearManufacturers Association (AGMA)Category Failure mode

Wear AdhesionMildModerateSevere

AbrasionMildModerateSevere

PolishingCorrosionFretting corrosionScalingCavitationErosionElectrical dischargeRippling(a)

Scuffing Mild scuffingModerate scuffingSevere scuffing

Plastic deformation IndentationCold flowHot flowRollingTooth hammerRippling(a)RidgingBurrRoot fillet yieldingTip-to-root interference

Contact fatigue Pitting (macropitting)InitialProgressiveFlakeSpall

MicropittingSubcase fatigue

Cracking Hardening cracksGrinding cracksRim and web cracksCase/core separationFatigue cracks

Fracture Brittle fractureDuctile fractureMixed mode fractureTooth shearFracture after plastic deformation

Bending fatigue Low-cycle fatigueHigh-cycle fatigue

Root fillet cracksProfile cracksTooth end cracks

(a) Rippling is generally associated with plastic deformation, but it may also bea form of wear. Source: Ref 2

Table 2 Gear failure modes proposed byAlban in Ref 1Failure mode Type of failure

Fatigue Tooth bending, surface contact (pitting orspalling), rolling contact, thermal fatigue

Impact Tooth bending, tooth shear, tooth chipping,case crushing, torsional shear

Wear Abrasive, adhesiveStress rupture Internal, external

fillet (e.g., tooling “witness” marks) or non-metallic inclusions near the surface. Cracksslowly propagate around the origin until theyreach the critical size for the case material at the prevailing stress level. For hardened high-carbon material typically used for gears, whenthe crack reaches this critical size, it “pops”through the case (i.e., the entire case fractures).At this point, the rigidity of the tooth is reduced(compliance increases), and dynamic loadincreases significantly. This produces a readilydetectable increase in noise and vibration andrepresents failure.

As stated earlier, bending fatigue is the mostcommon mode of fatigue failure in gearing.There are many variations of this mode of fail-ure, but the variations can be better understoodby first presenting the classical failure.

The classical bending fatigue failure is thatwhich occurs and progresses in the areadesigned to receive the maximum bendingstress. Figure 1 shows such an example. Thereare five conditions that make Fig. 1 a perfecttooth-bending fatigue failure:

• The origin is at the surface of the root radiusof the loaded (concave) side of the tooth

Fig. 1 Spiral bevel pinion showing classic tooth-bendingfatigue. The origin is at midlength of the root radius on

the concave (loaded) side. Original magnification at 0.4×

Chapter 13: Gear Failure Modes and Analysis / 259

• The origin is at the midpoint between theends of the tooth where the normal load isexpected to be

• One tooth failed first, and the fracture pro-gressed slowly toward the zero-stress pointat the root, which shifted during the progres-sion to a point under the opposite root radiusand then proceeded outward to that radius

• As the fracture progressed, the tooth de-flected at each cycle until the load waspicked up simultaneously by the top cornerof the next tooth, which (because it was nowoverloaded) soon started a tooth-bendingfatigue failure in the same area. The fractureof the second tooth appears to be of morerecent origin than the first fracture

• The material and metallurgical characteris-tics are within specifications

If any of the above five conditions is changed,there will be a variation of bending fatigue awayfrom the classical example

The rudiments of the classical bending fa-tigue can be studied using photoelastic models.Once the crack at the root radius is initiated andis progressing toward the zero-stress point (Fig.2), the point moves away from the leading edgeof the crack and shifts laterally until it reaches aposition under the opposite root. At that time,the shortest remaining distance is outward to theroot, and the point terminates there. In themeantime, as the failing tooth is being deflected,the top of the adjacent tooth has picked up theload. The load on the first tooth has now beenrelieved, allowing a slower progression due tolower cyclic stress. It is now only a matter oftime until the next tooth initiates a crack in thesame position. Variations from the classicalbending fatigue appear for many reasons.

Bending fatigue of a spur-gear tooth with theorigin along the surface of the root radius of theloaded side but at a point one-third the distancefrom the open end (Fig. 3) can be considered aclassical failure in that the maximum crown ofthe teeth had been placed intentionally at thearea where the failure occurred; therefore, themaximum applied loads were at the same area.This, then, is the area that was designed for thepoint of initiation of normal bending fatigue.The progression was directly to the bore, whichwas the shortest direction of least resistance.

Bending fatigue of a spur-gear tooth meetingall but one of the conditions for a classical fail-ure is shown in Fig. 4. The origin was at one endof the tooth and not at the midlength. Therecould have been several reasons for this point ofinitiation; in this instance, a severe shock loadhad twisted the parts until a momentary over-load was applied at the end of the tooth, causinga crack to form. The crack became a high stress-concentration point from which fatigue progres-sion continued.

An example of bending fatigue that did notconform to classical conditions is shown in Fig.5. Crack initiation was at a nonmetallic inclu-sion at the case/core interface; it did not origi-nate at the surface. Subsequent progression was

Fig. 2 Photoelastic study of mating teeth indicates the shift ofthe zero-stress point during crack propagation until

final fracture reaches the opposite root radius. At the same time,deflection of the tooth allowed the adjacent tooth to pick up theload

Fig. 3 Spur tooth pinion at 0.5× (top) and 1.5× (bottom).Tooth-bending fatigue originating at the root radius

(arrows), loaded side, one-third the distance from the open end.Progression was to the bore


through the case to the surface as well asthrough the core toward the zero-stress point.

Another example of bending fatigue that didnot conform is shown in Fig. 6. The failure wasat the root radius and at the midlength, but theorigin was not at the surface. The origin was atthe apex of a tapped bolt hole that had beendrilled from the back face of the gear and had ter-minated less than 6.4 mm (0.25 in.) from the rootradius. Subsequent progression of the fatiguecrack was to the surface at the root radius as wellas into the core toward the zero-stress point.

Additional examples of gear failures due tobending fatigue fracture can be found in Fig. 7to 10.

Bending Fatigue Properties. Detailed in-formation on the bending fatigue characteristicsof gear steels can be found in Chapter 3, “Fer-rous and Nonferrous Alloys,” and Chapter 9,“Carburizing.”

Contact Fatigue

Contact fatigue is the cracking of a surfacesubjected to alternating Hertzian stresses pro-duced under controlled rolling and sliding load-ing conditions (Ref 5). In addition to cracking,contact fatigue can result in microstructural al-terations, including changes in retained austen-ite, residual stress, and martensite morphology.

When sliding is imposed on rolling, the tan-gential forces and thermal gradient caused byfriction alter the magnitude and distribution ofstresses in and below the contact area. The alter-nating shear stress increases in magnitude and ismoved nearer to the surface by sliding forces.Thus, initiation of contact-fatigue cracks in gearteeth, which are subjected to significant amountsof sliding adjacent to the pitchline, is found to bein the surface material. These cracks propagateat a shallow angle to the surface, and pits resultwhen the cracks are connected to the surface bysecondary cracks. If pitting is severe, the bend-ing strength of the tooth may be decreased to thepoint at which fracturing can occur.

The existence of several distinctly differentmodes of contact-fatigue damage has been rec-ognized, but the factors that control the nucle-ation and propagation of each type are onlypartially understood. The contact fatigue ofhardened steel has been the subject of exten-

Fig. 4 Spur pinion failure. Tooth-bending fatigue with originat root radius of loaded side at one end of the tooth.

Original magnification at 0.6×

Fig. 5 Spur pinion failure. Tooth-bending fatigue is atmidlength of the tooth at the root radius, but the ori-

gin is at an inclusion located in the case/core transition. Originalmagnification at 55×

Fig. 6 Spiral bevel gear tooth failure. Tooth-bending fatiguewith origin at the apex of the drilled bolt hole, which

terminated just below the root radius. Original magnification at0.5×


sive research using analytical and experimentalmethods, and publications have revealed a largevariation in the contact fatigue strength of simi-lar materials when tested under different condi-tions of contact geometry, speed, lubrication,temperature, and sliding in combination withrolling. These variations result from a poorunderstanding of the basic mechanism of con-tact fatigue. Although the cause of the fatigueand the locations of the origins are somewhatdifferent, these are true fatigue fractures that arecaused by shear-stress origins due to contactstresses between two metal surfaces.

Table 3 lists terminology used by the gearindustry to describe the fracture appearance ofcontact-fatigue failed components. The follow-ing sections describe the types of damage fromcontact fatigue based in the categories in Table3 as previously published in Ref 5.

The macro- and micropitting failures listed inTable 3 are divided into the following three cat-egories based on the location of the origin:

• Surface-origin pitting: This is the type ofpitting characteristic of combined rollingand sliding, such as occurs on gear teethslightly away from the exact pitch line,where only rolling is present. The maximumshear stress is no longer buried within themetal, but is now brought to the surfacebecause of the friction at the interface.Because the character of the surface is inti-

mately involved, the lubricant becomes crit-ical. It is for this reason that transmissions,final drives, and various other types of gearsystems require lubricants with special ad-ditives. Everything possible must be done to reduce surface friction, expand the con-tact area, and reduce the load in order toreduce the contact stress and provide a hard,fatigue-resistant structure in the metal. Un-fortunately, if those things are already nearoptimum, little can be done to improve thefatigue life. Only minimal improvements, ifany, can be expected. Improvements canbest be obtained, if at all, by changes in thelubricant.

• Subsurface-origin pitting is the result offatigue below the surface in the region ofhighest shear stress. Subsurface origin pit-ting typically occurs only in cases where theelastohydrodynamic (EHD) lubricant filmthickness is great enough to prevent signifi-cant asperity interaction. This pitting occursin high-speed power gearing and in aero-space power drives. It is also typical inantifriction bearings (which operate withpure rolling as at the pitch diameter on spurgears). The origin is typically a nonmetallicinclusion or discontinuity in the structure, inthe area of highest shear stress below thesurface. Crack propagation is initially quiteslow, until a crack penetrates the surface,allowing lubricant to enter. It can be difficult

Fig. 7 Bending-fatigue fracture in the heel of one tooth of a spiral bevel pinion of AISI 8617 steel, carburized and hardened to 57HRC in the case. Fracture resulted from severe pitting. Note that pitting had begun in an adjoining tooth (near top). Original

magnification at 0.75×


to tell the difference between surface andsubsurface origin pits, although subsurfaceorigin pits often do not have the arrow shapetypical of surface origin pits. As with sur-face origin pits, when the pit becomes largeenough to cause a readily detectable in-crease in noise and vibration, it is considereda failure. Because most pits start small andprogressively grow large, some criticalhigh-speed drives incorporate a chip detec-tor in the lubrication system to provideadvance warning of imminent failure.

• Subcase fatigue: The previous types of con-tact-stress fatigue result in small, often tiny,pits in the contacting surfaces. Subcase-origin fatigue is different because very largecavities may be formed, apparently in a veryshort time. The fatigue originates near thecase/core interface where the shear stresses.Because the basic cause is inadequate metal

strength in the subcase region, the logicalsolution should be to strengthen the metalthere. This can be done by increasing the casedepth and/or the core hardness. This must bedone carefully, however, because thechanges could lead to through-hardening andbrittle fracture, particularly on gear teeth.

Macropitting

Macropitting is a general term that includesspalling and other forms of macroscale damage(Table 3) caused by Hertzian contact fatigue.Macropitting of gear teeth is generally due tocontact fatigue, which occurs from localizedplastic deformation, crack initiation, and finallymacropitting from crack propagation in andnear the contact surface.

Macropitting results from the subsurfacegrowth of fatigue cracks, which may have a sur-face or subsurface origin. Figure 11 showsmacropit formation by subsurface growth of sur-face-origin pitting on a gear tooth. The bottom ofinclusion-origin macropits form first, and soforth. When circumstances cause surface-originpitting, crack growth often occurs within andbeyond the range of maximum shear stresses inthe contact stress field (so-called hydraulic-pressure propagation crack paths that may bedue to chemical reactions at the crack tip as wellas to lubricant viscosity effects).

When fully developed, the craters exist at adepth comparable to that of the maximum alter-nating Hertzian shear stress. A macropit doesnot result from the gradual enlargement of asmall cavity, but rather it results from the sub-surface growth of a fatigue crack, which even-tually separates from the main body of material.In the example of a gear damaged by crater for-mation due to surface-origin macropitting (Fig.11), the craters are generally steep walled andessentially flat bottomed, as the walls and bot-

Fig. 9 Bending-fatigue fractures in several teeth of a spur gear of AISI 8620 steel, carburized and hardened to 60 HRC in the case.The tooth marked A apparently broke first, as the result of a fatigue crack that originated in the fillet to the left of the tooth

(arrow). After this tooth broke off, fracturing of the teeth on each side of it was accelerated. Original magnification at 2×

Fig. 8 Bending-fatigue fracture in two teeth of a reverse idlergear of AISI 8617 steel, carburized and hardened to 60

HRC in the case. Arrows point to the root fillets on both sides ofeach tooth, where fracture began due to excessive stress in theselocations. Original magnification at ~2×


tom are formed by fracture surfaces. The bot-toms of macropits usually form first, and thenthe crack extends through the contact surface,creating the walls of the crater. However, thereare circumstances in which macropits are initi-ated at or near the contact surface and the crackpropagates through the Hertzian shear stressfield, forming the walls and then the bottom ofthe crater (Ref 5).

Macropitting fatigue life is inherently statisti-cal because defect severity and location are ran-domly distributed among macroscopically iden-tical contact components. Two major classes ofmacropitting damage are distinguished accord-ing to the location of the initiating defect: sub-surface- and surface-origin macropitting.

Subsurface-origin macropitting resultsfrom defects in the bulk material subjected to theHertzian cyclic stress field. Subsurface-originmacropits are characterized by a smooth areaparallel to the contact surface with a steep wallexit (inclined by more than 45° with respect tothe contact surface). Sometimes the subsurfacedefect that caused the damage remains visibleafter the macropit forms. The defects that causesubsurface-origin macropits are inclusions and/or material microstructure alterations. The de-fects that most likely produce this type of macro-pit are located above the depth of maximumalternating Hertzian shear stress. Variables gov-erning the life of a component with respect tothis type of macropit are Hertzian shear stresslevel, material matrix fatigue resistance, defectseverity, and defect location.

Inclusion-origin fatigue is normally initiatedat nonmetallic inclusions below the contact sur-face. The initiation and propagation of fatiguecracks are the result of cyclic stresses that arelocally intensified by the shape, size, and distri-bution of nonmetallic inclusions in steels. Oxideinclusions from deoxidation, reoxidation, orrefractory sources are the most frequently ob-served origins of inclusion-origin fatigue dam-age. Sulfide inclusions alone are rarely associ-ated with contact fatigue cracks. The ductility ofsulfide inclusions at hot working temperatures

Fig. 10 Surface of a bending-fatigue fracture in a tooth(upper tooth in this view) of a large spiral bevel pin-

ion of AISI 8620 steel carburized and hardened to 60 HRC at thesurface. The arrow marks the fatigue-crack origin, in the root fil-let. The absence of this tooth resulted in fracture of the toothbelow by overload. Original magnification at 1.65×

Table 3 List of contact fatigue terminologyused to describe the different fatiguemechanismsCategory Fatigue mechanisms

Macroscale

Macropitting PittingInitial pittingDestructive pittingFlakingSpallingScabbingShellingFatigue wear

Subcase fatigue Case crushing

Microscale

Micropitting MicrospallingFrostingGlazingGray stainingSurface distressPeeling

Source: Ref 5 Fig. 11 Fractograph showing the advanced stages of macro-pitting fatigue for a helical pinion tooth


and a relatively low interfacial energy makethem less effective stress concentrators than theharder, incoherent oxide inclusions. In addition,oxide inclusions are often present as stringers,or elongated aggregates of particles, which pro-vide a much greater statistical probability for apoint of stress concentration to be in an area ofhigh contact stress.

When a nonmetallic inclusion as describedabove results in significant stress concentration,two situations are possible: (a) localized plasticflow occurs; and/or (b) a fatigue crack begins topropagate with no plastic flow as observedmicroscopically. If localized plastic deforma-tion occurs, microstructural alterations begin todevelop and the effective stress concentration ofthe inclusion is reduced. The probability offatigue crack initiation/propagation is less thanbefore the plastic flow occurred, so a macropitmay not form. However, if a fatigue crack formsdue to the inclusion, prior to any plastic defor-mation, the stress concentration is increased andcrack propagation results in macropitting fa-tigue. This hypothesis includes the possibility ofa fatigue crack originating from an inclusionthat is associated with some sort of microstruc-tural alteration, but also proposes that micro-structural alterations are not a necessary step inthe initiation/propagation of inclusion originfatigue.

Early macroscopic propagation of inclusion-origin fatigue takes on a characteristic pattern.Many branching subsurface cracks are formedaround the inclusion, with propagation oftenbeing most rapid perpendicular to the rollingdirection, with a resulting elliptical shape for the incipient macropit. In some instances, thecracked material around the inclusion macropitsearly and further propagation is relatively slow,leaving a small macropit with very few subsur-face cracks to cause further damage. However,when material has macropitted from the contactsurface, the result may be debris bruising anddenting of other contact areas with subsequentsurface-origin macropitting.

Surface-origin macropitting is caused bydefects in the immediate subsurface materialsubject to asperity scale cyclic stress fields andaggravated by surface tractive forces. Thesedefects are either preexisting defects, such asnicks, dents, grinding furrows, surface disconti-nuities, and so forth, or microscale pits, whichare described subsequently. The distinguishingfeatures of a surface-origin macropit are in theentrance zone of the macropit. The entrance

zone may exhibit a shallow-angle entry wall(inclined less than 30° to the contact surface), anarrow-head configuration (Fig. 12), the pres-ence of a visible surface defect, or an associa-tion with a stress concentration due to designgeometry. Surface-origin macropits have beenclassified by the nature of the defect: geometricstress concentration (GSC) and point surfaceorigin (PSO).

Geometric stress concentration macropits aredistributed on the contact surface at the ends ofline contact. When the contact geometry,deflection under applied loads, and alignmentcause the contact stress to be higher at the end ofline contact, fatigue occurs within a narrowband in which the contact stresses are moresevere than those associated with inclusions.The GSC macropits can propagate more rapidlyin either direction—parallel or transverse to therolling direction. This mode of contact fatigue ismore frequently observed in life tests acceler-ated due to overload conditions because contactgeometry is designed to produce uniform load-ing under expected service loads.

Crowning of gear teeth in line contact situa-tions has been shown to be an effective methodof prolonging life or preventing the GSC modeof macropitting. The fact that GSC macropitscan occur simultaneously at both ends of a linecontact indicates that this mode of contactfatigue is truly the result of end stress concen-trations and not simply misalignment. However,misalignment can aggravate the situation byincreasing end contact stresses. Early stages of

Fig. 12 Gear with arrow-shaped surface-origin pit. Source:Ref 4


GSC macropitting exhibit cracks extending tothe surface, but it is not clear whether the firstcracks always originate at the surface or slightlysubsurface. However, the origins are rarelyassociated with a nonmetallic inclusion, butoccasionally an inclusion at the end of line con-tact will serve as the nucleus for a GSC fatiguemacropit.

Point surface origin macropits occur ran-domly distributed on the contact surface, similarto inclusion-type macropits. However, PSOmacropits are different in two important as-pects: first, there is no consistent associationwith nonmetallic inclusions; second, the originis located at or near the contact surface, whereaswith inclusion-origin macropits, the initiationsite is located subsurface. These characteristicsresult in a distinct arrowhead appearance, inwhich the tip of the arrowhead is the origin andthe advanced stages of the macropit develop ina fanned-out appearance with respect to the tipin the rolling direction.

Micropitting

Micropitting is damage of rolling/sliding con-tact metal surfaces by the formation of a glazed

(burnished) surface, asperity scale microcracks,and asperity scale micropit craters. Micropittingdamage is a gradual type of surface fatigue dam-age that is a complex function of surface topogra-phy and its interaction with the lubricant. (Evenunder high contact loads, a thin film of lubricantbetween the contacting surfaces from EHD lubri-cation is present.) Cumulative plastic deforma-tion first results in a surface with a mirrorlikereflection known as a glazed surface. The surfaceand immediate subsurface material of a glazedsurface are heavily deformed and with continuedcyclic stressing, the ductility of the materialdecreases and microcracks form. The cracks tendto propagate parallel to the contact surface atdepths comparable to that of asperity scale shearstresses. A microcracked surface is not usuallydistinguishable from a glazed surface by theunaided eye, but with microscopy, microcracksopening to the surface may be visible in glazedareas. As the microcracks multiply and propa-gate, the surface becomes undermined (in asper-ity dimensions), and multiple microscopic pitsform. A micropitted surface appears frosted tothe unaided eye, with black spots representingthe micropits. An example is shown in Fig. 13.

Fig. 13 Gear with micropitting (frosting) failure. Source: Ref 4


If extensive, the micropitting is considered afailure.

The occurrence of micropitting is controlledby the EHD film-thickness-to-roughness ratioand surface microgeometry. In the presence of a sufficiently high EHD film-thickness-to-surface-roughness height ratio, micropittingdoes not occur because the film prevents high-contact microstress in asperity interactions.However, film thickness may be sufficient toprevent generalized micropitting, but not localmicropitting in the vicinity of surface defectssuch as nicks and dents that locally depressurizeand thereby thin the EHD film. Tribology fea-tures that effect micropitting are both the heightand sharpness (root-mean square height andslope) of the asperities. There is also some evi-dence that the normal wear in boundary-lubricated gear contacts removes incipient sur-face-origin pitting, which is one reason gearsmay be less prone to macropitting from surface-origin macropitting under some circumstances.

Micropitting is characterized by the limiteddepth of cracking and propagation over areasrather than propagation in depth. Micropittingfatigue cracks usually propagate parallel to thesurface at depths from 2.5 to 13 mm (0.098 to 0.511 in.) and rarely as deep as 25 mm (0.984 in.). The high-stress gradient that exists inthe vicinity of asperities explains why suchcracks do not propagate to greater surface depthsof the macro-Hertzian contact stress field. In essence, micropitting removes the asperityridges and relieves the high-stress gradient. Anadditional visual characteristic is that the micro-pitting occurs more or less in the rolling direc-tion, following finishing lines.

Macropitting fatigue is the most hazardousconsequence of micropitting. The principaloperating factor influencing the rate of macro-pitting from micropits is tractive interfacialstress. When friction is high, macropits formrapidly from the micropits on the surface. Ifearly macropitting does not terminate the oper-ation of a component that has suffered micropit-ting, then surface material delamination mayoccur. The original surface is thereby lost overwide areas, and the component becomes inoper-ative through loss of dimensional accuracy,noise, or secondary damage.

In many cases, micropitting is not destructiveto the gear-tooth surface. It sometimes occursonly in patches and may stop after the tribologi-cal conditions have been improved by run-in.Run-in is defined as an initial transition process

occurring in newly established wearing contacts,often accompanied by transients in coefficient offriction, wear rate, or both, that are uncharacter-istic of the long-term behavior of the given tribo-logical system. Gears appear less sensitive to theconsequences of surface distress than rolling-element bearings. This may be due to the greaterductility of lower-hardness materials.

Subcase Fatigue

Subcase fatigue is fracture of case-hardenedcomponents by the formation of cracks below thecontact surface within the Hertzian stress field.However, the depth at which the cracks form ismuch greater than those that cause macropittingfatigue, and it is a function of material strength inconjunction with the alternating Hertzian shearstresses. Subcase fatigue is also sometimes re-ferred to as case crushing, but because it resultsfrom a fatigue crack that initiates below the effec-tive case depth or in the lower-carbon portion ofthe case, the former nomenclature is used.

In case-hardened components—produced bycarburizing, nitriding, or induction hardening—a gradient of decreasing hardness (shearstrength) exists from the case to the core. If thematerial shear strength gradient is steeper thanthe gradient in Hertzian shear stress, then theapplied-stress-to-strength ratio is least favor-able at some depth below the normal maximumHertzian shear-stress region. This depth is usu-ally located at (or near) the case/core interfacedue to shear strength and stress gradients, inaddition to unfavorable tensile residual stresses.The reversal in the sign of the residual stressfrom compression in the case to tension in thecore occurs at or very near the case/core inter-face, and therefore the Hertzian shear stressesare increased due to the tensile residual stresses.

The fatigue originates near the case/coreinterface where the shear stresses, which arestill fairly high, exceed the strength of the rela-tively low-strength core metal in that region.Fatigue cracks propagate parallel to the surfacebut underneath the case, then they join and formcracks that come up through the case to the sur-face, resulting in macropit formation. A typicalexample of this type of failure in gear teeth isshown in Figure 14.

Subcase fatigue is usually caused by too thina case, such as on a nitrided gear tooth, by insuf-ficient core hardness on carburized or induc-tion-hardened parts, or in heavily loaded case-hardened rolling-element bearings. Factors thattend to promote the various types of contact


Fig. 14 Pinion with several very large cavities where metal from the surface down to the depth of the case has fallen out due to sub-case fatigue. Shown at actual size

fatigue are listed in Table 4. It should be notedthat three of the five modes of fatigue damageare influenced by lubrication, including all sur-face-origin damage modes.

Location of Pitting Initiation on the Gear Tooth Profile

The initiation of pitting is mostly confined tothree areas along the profile of a gear tooth.First, the pitchline is the only area of line con-tact that receives pure rolling pressure. The pitsforming directly at the pitchline are usually verysmall and may not progress beyond the point oforiginal initiation. Some analysts claim that thistype of pitting repairs itself and is not detrimen-tal. That may be true when the pitting is formedby the breakdown of a rough surface. Note, too,that lubrication will not deter the origin of pit-ting along the pitchline. Oil is noncompressibleand will not cushion the pressures exerted in thearea of pure rolling.

Second, the area immediately above or belowthe pitchline is very susceptible to pitting. Notonly is the rolling pressure great at this point butsliding is now a real factor. The mechanics ofsurface-subsurface pitting can be best under-stood when looking at the resultant appliedstresses illustrated in Fig. 15. The extra shear

stress of the sliding component when added tothat of the rolling component often results innear-surface fatigue at the point of maximumshear below the surface. In many instances, it isdifficult to determine whether some pittingcracks actually initiate at or below the surface.Figure 16 shows initiation of pitting fatigueboth at the pitchline of a helical-gear tooth anddirectly above the pitchline. Progression up theaddendum in some areas makes it difficult todifferentiate the two. A surface-pitted area nearthe pitchline is illustrated in Fig. 17. Althoughthe surface was in a rolling-sliding area, theimmediate surface shows no catastrophic move-ment. It is then most probable that cracking ini-tiated by shearing fatigue below the surface.The freedom from surface movement alsospeaks well for the lubrication of the gear teeth.

Third, the lowest point of single-tooth contactis that point which receives the tip of the matingtooth as it makes first contact low on the activeprofile. Tip contact will produce high pressures,even if a small fraction of the actual load istransferred by the tip. Also, the maximum slid-ing speed, both in approach and recess, occurs atthe tip contact.

There are two types of pits that prevail at thisarea. One is the type shown in Fig. 18, whichappears to be a swift-shear and lift-out type.


Table 4 List of contact fatigue modes andtheir controlling factorsMode of failure Factors that control occurrence

Subsurface

Inclusion origin Size and density of oxide or otherhard inclusions

Absence of other modes of failureSubcase fatigue Low core hardness

Thin case depth relative to radiusof curvature and load

Surface

Point-surface origin Low lubricant viscosityThin EHD film compared with

asperities in contactTangential forces and/or gross

slidingGeometric stress End contact geometry

Misalignment and deflectionsPossible lubricant film thickness

effectsMicropitting Low lubricant viscosity

Thin EHD film compared withasperities in contact

Loss of EHD pressureSlow operating speeds

Source: Ref 5

concentration

Fig. 15 Stress distribution in contacting surfaces due torolling, sliding, and combined effect

Fig. 16 Pitting initiated along and immediately above thepitchline in helical gear teeth. In some areas, the

progression has been continuous. Shown at actual size

Fig. 17 Near-pitchline pitting fatigue in a spiral pinion tooth.Origin is subsurface at plane of maximum shear.

Original magnification at 180×

Perhaps the question whether this is fatigue orimpact can be answered, but if it is shearingfatigue, it is certainly rapid and would call for astudy of tip interference and lubrication. Thesecond type of pit is the same as that illustratedin Fig. 17 and shows failure only by compres-sive loads. This is not uncommon in spur-gearteeth or helical-gear teeth, but, when found, ispuzzling because one does not expect to find tipinterference pits other than those previously dis-cussed. However, it must be remembered thatdynamic effects are to be taken into account.

Gear vibration is a fact, but is seldom ever rec-ognized as such. Studies indicate that gearvibration at high speeds, excited by static trans-mission error, may cause corner contact eventhough the tip relief is sufficient to prevent cor-ner contact at low speed. Also, with sufficientlubrication, the pressures of tip interference willresult in compressive-type pitting (Fig. 17)rather than the adhesive type (Fig. 18).

Other than the three specific and most com-mon areas of surface-fatigue pitting just dis-cussed, there are always the random areas that


Fig. 18 Spiral bevel tooth failure. Pitting at the lowest pointof single-tooth contact illustrating contact path of the

tip of the mating tooth. Nital etch. Original magnification at 90×

Fig. 19 Rolling-contact fatigue in a gear tooth section. Crackorigin subsurface. Progression was parallel to sur-

face and inward away from surface. Not etched. Original mag-nification at 60×

Fig. 20 Rolling-contact fatigue in a gear tooth section. Crackorigin subsurface. Progression was parallel with sur-

face, inward, and finally to the surface to form a large pit or spall.Not etched. Original magnification at 60×

crop up to demand recognition, such as pittingat only one end of the face, at opposite ends ofopposite faces, along the top edge of the adden-dum, or at one area of one tooth only. The ran-dom incidences are without number and aremost baffling; but each one is present because ofa reason, and that reason must be found if at allpossible.

Rolling-Contact Fatigue

Rolling-contact fatigue can only be describedby using Fig. 15. Under any conditions of rolling,the maximum stress being applied at or very nearthe contact area is the shear stress parallel to therolling surface at some point below the surface.For normally loaded gear teeth, this distance isfrom 0.18 to 0.30 mm (0.007 to 0.012 in.) belowthe surface just ahead of the rolling point of con-tact. If sliding is occurring in the same direction,the shear stress increases at the same point. If theshear plane is close to the surface, then light pit-ting will probably occur. If the shear plane is deepdue to a heavy rolling load contact, then the ten-dency is for the crack propagation to turn inward(Fig. 19). The cracks will continue to propagate

under repeated stress until heavy pitting orspalling takes place (Fig. 20).

There is always one characteristic (and oftentwo) of rolling-contact fatigue that will distin-guish it from other modes of surface-contactfatigue. Both characteristics can be observedonly by an examination of the microstructure. Inrolling contact, the surface will not show a cata-strophic movement; it will remain as the originalstructure. For example, an unetched, polishedsample taken near the origin of a subsurfacefatigue crack (Fig. 21) very clearly shows undis-turbed black oxides at the surface. The subsur-face cracking could not have been caused byeither abrasive or adhesive contact; it had to be byrolling. This is always the first evidence to lookfor when determining the type of applied stress.

The second characteristic is common only ina martensitic case that contains very little or noaustenite and is found only at, along, or in line


Fig. 21 Rolling-contact fatigue in a gear tooth section distin-guished by subsurface shear parallel to surface. Note

the undisturbed black oxides at the surface, indicating no sur-face-material movement. Not etched. Original magnification at125×

Fig. 22 Same sample as in Fig. 21, only etched in 3% nital,showing details of submicrostructure called butterfly

wings. (a) Original magnification at 125×. (b) Original magnifi-cation at 310×

Fig. 23 Spalling of spiral bevel gear teeth. Original pittinglow on the active profile gives initiation to a fast and

extensive progression of spalling over the top face and down theback profile. This is often called the cyclone effect. Originalmagnification at 0.25×

with the shear plane. This is a microstructuralfeature that has been termed butterfly wings. Ifthe sample in Fig. 21 is etched properly with 3%nital, the result is the microstructure shown inFig. 22(a). Increasing the magnification to 310 ×shows more detail (Fig. 22b).

The original discussion presented by rolling-element bearing manufacturers had no explana-tion as to the origin of this microstructural alter-ation except that it was always in conjunctionwith and radiated from an inclusion. It is truethat many times there is an inclusion present,

but not always. One could argue that the frac-ture is a plane and not a line, such as could beseen on a polished sample; therefore, an inclu-sion could be present somewhere else along theplane being observed.

Two other extensive and very detailed studiesof rolling-contact fatigue refer to the gray sub-structure as white bands of altered martensite. Itis believed that these substructures are causedwhen, under an extreme shearing stress, move-ment is called for but is restrained and containedto such an extent that the energy absorbed insti-tutes a change in the microstructure ahead of aprogressing crack. They are never observedwhen significant amounts of austenite are pres-ent; austenite will quickly absorb the energy andwill be converted to untempered martensite.They are also in an area that has not beendeformed but has definitely been transformed.Each area has distinct boundaries, and the on-coming cracks appear to follow these bound-aries. It has been noted that some academicstudies refer to this same structure as being atransformed shear band product formed by adi-abatic shear.

Spalling

Spalling, in general, is not considered an ini-tial mode of failure but rather a continuation orpropagation of macropitting and rolling-contactfatigue. It is very common to reference this fail-ure mode as pitting and spalling. For example,Fig. 23 shows a spiral-gear tooth with pitting lowon the profile that subsequently progressed untilspalling occurred over the top face and back sideprofile. This apparent rapid and extensive pro-gression can be referred to as the cyclone effect.


Fig. 24 Applied stress versus case depth (net strength)

Fig. 25 Subsurface cracking that subsequently resulted inspalling at a gear-tooth edge. Unetched section of a

carburized AMS 6260 steel gear tooth. Cracking initiated in thetransition zone between the carburized case and the core. Orig-inal magnification at 500×

Fig. 26 Spalling on a tooth of a steel spur sun gear shaft. (a)Overall view of spalled tooth. (b) Micrograph of an

unetched section taken through the spalled area showing pro-gressive subsurface cracking. Original magnification at 100×

Spalling, in the true sense of the word, is amode of fatigue failure distinct in itself andunique in its origin. It originates below the sur-face, usually at or near the case/core transitionzone. As illustrated in Fig. 24, the origin is at thatpoint where the sum of all applied and misap-plied stresses intersect the net strength of thepart. The applied stresses are substantially inshear, and the intercept point is most likely undera carburized case. Fatigue fractures will gener-ally progress under the case (Fig. 25 and 26) andwill eventually spall away from the gear tooth.

Gear failures due to spalling in conjunctionwith other failure modes are also common. Fig-ure 27 shows a pinion that failed because ofspalling, abrasive wear, and plastic deformation.

Thermal Fatigue

Thermal fatigue in gearing, although not nec-essarily correct, is most often synonymous with

frictional heat. This is perhaps the only type ofalternating heating and cooling that is applied inthe field. Then, too, it is not commonly found onthe active profile of the gear teeth, but on a rotat-ing face that is exerting a high amount of thrust.Figure 28(a) shows an example of high endthrust that resulted in frictional heat. The ther-mal expansion and contraction initiated a largenumber of radial cracks that progressed as afatigue fracture (Fig. 28b) into the bore of thepart and along the roots of the teeth.

Impact

Tooth-Bending Impact. When a tooth isremoved from a gear within a very few cycles(usually one or two), the fracture is uniform instructure and does not show the striations com-mon to the fatigue mode of failure. They areusually random, due to a sudden shock load,either in a forward or reverse direction, and donot necessarily originate at the root radius. Infact, if the fracture did originate at the root


Fig. 27 Surface of a spalling-fatigue fracture in a single tooth of a heavily loaded final-drive pinion of AISI 8620 steel, carburizedand hardened to 60 HRC in the case, showing vertical scratches, which indicate that appreciable abrasive wear took place

also. The surface ripples at right suggest that a small amount of plastic flow occurred under the applied load. Original magnification at ~4×

Fig. 28 Thermal fatigue cracking of a spur gear. (a) Radial cracking due to frictional heat against the thrust face. Original magnifi-cation at 0.4×. (b) Progression of thermal fatigue produced by the frictional heat. Original magnification at 1.5×

radius, it would follow a rather flat path acrossto the opposite root radius rather than traveldownward toward the zero-stress point.

Tooth Shear. When the impact is very highand the time of contact is very short, and if theductility of the material will allow it, the resul-tant tooth failure mode will be shear. The frac-tured area appears to be highly glazed, and thedirection of the fracture will be from straightacross the tooth to a convex shape. For example,a loaded gear and pinion set were operating at ahigh rate of speed when the pinion stoppedinstantaneously (Fig. 29). The momentum ofthe gear was strong enough to shear the contact-ing pinion teeth from the reverse direction, leav-ing the remaining teeth in excellent condition.The gear teeth were partially sheared and were

all scrubbed over the top face from the reversedirection.

Most commonly, bending impact and shearare found in combination (Fig. 30). Tooth-bend-ing impact fractures supersede the shearingfractures; thus, the direction of impact can bedetermined.

Tooth chipping is certainly a type ofimpact failure, but is not generally considered tobe tooth-to-tooth impact. It is usually accom-plished by an external force, such as a foreignobject within the unit, a loose bolt backing outinto the tooth area, or even a failed tooth fromanother gear. Figure 31 shows a chipping condi-tion that existed during the operation of the part.Most chipping, however, is caused by mishan-dling before, during, or after the finished parts


Fig. 29 Spiral bevel gear and pinion set that sheared in thereverse direction. The pinion came to a sudden and

complete stop at the instant of primary failure of the unit, allow-ing the gear to shear the contacting teeth and to continue rotat-ing over the failed area. Original magnification at 0.4×

Fig. 30 Spur-gear tooth showing combination failure modes.(a) Tooth-bending impact. (b) Tooth shear. Arrows

indicate direction of applied force.

Fig. 31 Tooth chipping resulting from impact of a foreignobject within the assembled unit

are shipped from the manufacturer and are notfield failures. This is one of the modes that mustbe identified by a cause.

Wear

Surface deterioration of the active profile ofthe gear teeth is called wear. There are two dis-tinct modes of wear—abrasive and adhesive.Additional information on these wear failuremodes can be found in Chapter 2, “Gear Tribol-ogy and Lubrication.”

Abrasive wear occurs as the surface isbeing freely cut away by hard abrasive particles.It can happen only as two surfaces are in slidingcontact. The dissociated material must be con-tinually washed away and not allowed to accu-mulate on the sliding surfaces, or adhesion maytake place. The first evidence of abrasive wear isthe appearance of light scratches on the surface,followed by scuffing. As the scuffing continuesto deepen, the result is scoring. Figure 32 illus-trates an excellent example of pure abrasivewear that shows the entire tooth profile cleanlycut away with no microstructural damage to theunderlying material.

Abrasive wear cannot be deterred by lubrica-tion, because the lubricant is often the vehiclethat contains and continually supplies the abra-sive material as a contaminant. When this is thecase, all moving parts within the assembly areaffected, such as seals, spacers, bearings,pumps, and matching gears.


Fig. 32 Spiral bevel gear teeth showing contact wear. Insert A shows a tooth area exhibiting no wear. Insert B shows abrasive wearclearly cutting away 3.2 mm (⅛ in.) of the surface without damage to underlying material.

When abrasive wear is isolated to only onepart, that is, either gear or pinion, it is impera-tive to examine closely the surface of the match-ing part. For example, a very large amount ofmassive carbides embedded in the surface mayeasily cut into a softer matching surface.

Adhesive wear occurs on sliding surfaceswhen the pressure between the contactingasperities is sufficient to cause local plasticdeformation and adhesion. Whenever plasticdeformation occurs, the energy expended toproduce the deformation is converted to heat.

The first indication of trouble is a glazed sur-face, followed by galling, then by seizure. Aglazed surface may not have any dimensionalchanges, but the microstructure shows a cata-strophic movement of surface material (Fig.33). As frictional heat increases, the surfacebecomes softer, the adhesive tendency becomesgreater, there is more plastic deformation, thelocal temperature becomes high enough tochange completely the microstructure at the sur-face (Fig. 34), and galling occurs. Galling con-tinues, the sliding surfaces begin weldingtogether, and adhesion takes place. Large areasmay be pulled away from the surface (Fig. 35).Some of these welded particles are so hard dueto change of microstructure that they becomesharp points that cut into the matching parts. Asthe adhesive wear continues with the parts stillin service, there is the distinct possibility thatthe part will ultimately fail (Fig. 36).

Adhesive wear on gear teeth may not alwayspoint to that set as the culprit. There have beeninstances when a severe case of adhesion is of asecondary nature. In other words, particles of

material from a primary failure of another com-ponent in the assembly may have impingedupon the gear-tooth surfaces and thus started thesequence of events leading to seizure anddestruction.

Wear-Resistant Coatings (Ref 6). Al-though the gear industry has been slow to imple-ment gear coatings, there have been a fairlywide variety of coating methods/materials thathave been used to coat gears. Their uses rangefrom cosmetic to doubling the wear life of agear set. They include technologies that are justemerging, such as the coatings applied by phys-ical vapor depostion (PVD) discussed below, aswell as well-established coating systems thathave been used for more than 50 years includingblack oxide conversion coatings, electrolessnickel coatings, electroplated coatings (chromeand nickel), and phosphate coatings. The fol-lowing represent some of the more recentlydeveloped wear-resistant options available forsteel gears:

• Boron carbide (B4C) is a very hard, amor-phous ceramic material applied using themagnetron sputtering PVD process. Thiscoating has been used for coating transmis-sion gears for major auto makers. The coat-ing thickness is about 2 to 3 μm.

• Diamond-like carbon (DLC) is a hard(1000–3000 HV) low-friction coating of anamorphous form of carbon with diamond-like bonds. It is applied by ion-beam PVD.This gear coating is the focus of intenseresearch by automotive manufacturers andthe aerospace community.


Fig. 34 Pinion tooth profile. The pinion was plasticallydeformed by frictional heat and sliding pressures.The surface layer has locally rehardened, and galling

is evident. Original magnification at 80×

Fig. 35 Carburized AMS 6260 steel gear damaged by adhe-sive wear. (a) Overall view of damaged teeth. (b)

Etched end face of the gear showing excessive stock removalfrom drive faces of teeth

Fig. 33 Pinion tooth profile. Glazed surface showing thestart of catastrophic movement of surface material.

Frictional heat has already started to temper the surface. Originalmagnification at 75×

works well in a vacuum. For lower precisiongears, it can be used in powder form orapplied by special techniques such as spray-ing or dipping, followed by curing in anoven. It can also be applied by PVD sputter-ing, which allows much tighter tolerancesand thinner films.

• Tungsten carbide-amorphous carbon(WC/C) coatings are applied by the reactivesputtering PVD process. Application areas,both present and potential, for these coatingsinclude motorcycle gears, concrete mixergears, bevel gear actuators for aircraft land-ing gear flaps, highly-stressed, fast-runninggears, and worm gear drives.

Scuffing

Scuffing, which is sometimes also referred toas scoring, is a lubrication failure, frequentlybrought on by an increase in the operating tem-perature. The lubricant film breaks down,allowing metal-to-metal contact at high spots(asperities) on the flank surfaces. Under suffi-cient conditions of load and temperature, this

• Molybdenum disulfide (MoS2) has becomethe workhorse of dry-film lubrication forgears. It combines a low coefficient of fric-tion with high load-carrying capacity, and it


Fig. 36 Extreme wear of steel pinions. (a) Hypoid pinionwith teeth worn to a knife-edge from both sides. (b)

A similar pinion with teeth worn completely away by adhesivewear

metal-to-metal contact causes asperities to weldtogether and then tear apart as the motion con-tinues. The surface is characterized by torn orfurrowed markings in the direction of sliding.Figure 37 shows a typical scuffed gear. Similardamage can occur without the instantaneouswelding of the contact surfaces. This damage issometimes caused by foreign material beingcarried through the mesh but is more frequentlycaused by high asperities on one contacting sur-face plowing through the other. This damage istermed cold scoring (or scuffing), or burnishing,and is differentiated from that described previ-ously by the absence of tearing. More detailedinformation on scuffing can be found in Chapter2, “Gear Tribology and Lubrication.”

Stress Rupture

When the internal residual stresses build to amagnitude beyond the strength of the material,the part will rupture. The rupture will occur atthe point where this critical value is exceeded,either internally or externally.

Internal Rupture. The most likely pointwithin a gear that would attract a buildup ofresidual stresses is the case/core interface nearthe top face or the corner of a tooth. Figure 38shows an excellent example of case/core sepa-ration due to internal residual stresses exceed-ing the strength of material at the case/core tran-sition zone. In severe cases, the entire top of thetooth might pop off (Fig. 39).

External rupture is much easier to under-stand because it almost always originates from astress raiser. For example, a part not yet in serv-ice ruptured starting at the end face (Fig. 40)from a grinding crack; this was confirmed byexamination of the fractured face (Fig. 41). Thegrinding cracks were not the entire cause of thefailure, but they supplied the notch in the highlystressed area.

Causes of Gear Failures

Analysis of the actual part that failed willshow the mode of failure, but the cause of fail-ure is often found in the mating or matchingpart. One should always inspect both parts veryclosely for the correct answer to the problem. Infact, if there are several components to anassembly, each component must be suspectuntil eliminated.

The cause of a specific gear failure may beobvious enough to be recognized by anyone orsubtle enough to defy recognition by the mostexperienced analyst. At times, one almostbelieves that the number of causes may equalthe number of failures. This is close enough tobeing correct that each failure must be treatedindividually as a complete case in itself.

It is very difficult in many instances to sepa-rate cause from mode. In fact, a single cause caninitiate several different modes, dependingupon the forces being applied. Conversely, aspecific mode of failure could have been initi-ated by one of several causes. It must be empha-sized that one should not match a fracture pat-tern of a failed gear to a picture in this chapterand conclude that the cause and effect are the


Fig. 37 Specimen gear with scuffing failure. Source: Ref 4

same. They may be, but not necessarily. Thepictures of a reference book should be used onlyas a guide. Causes, as listed in Table 5, areunder five major headings and several subhead-ings. Undoubtedly, there may be more. Theheadings are not listed in order of importance(they are all important), but in sequence ofprobable occurrence. An example of a gear fail-ure due to improper heat treatment is shown inFig. 42 and 43.

Conducting the Failure Analysis (Ref 7)

When gears fail, there may be incentive torepair or replace failed components quickly andreturn the gear system to service. However,because gear failures provide valuable data thatmay help prevent future failures, a systematicinspection procedure should be followed beforerepair or replacement begins.

The failure investigation should be plannedcarefully to preserve evidence. The specificapproach can vary depending on when andwhere the inspection is made, the nature of thefailure, and time constraints.

Ideally, the analyst should visit the site andinspect failed components as soon after failureas possible. If an early inspection is not possi-ble, someone at the site must preserve the evi-dence based on instructions from the analyst.

The failure conditions can determine whenand how to conduct an analysis. It is best to shut

down a failing gearbox as soon as possible tolimit damage. To preserve evidence, carefullyplan the failure investigation and conduct in-situ inspections and plan to become involved ingearbox removal, transport, storage, and disas-sembly. If the gears are damaged but still func-tional, the company may decide to continueoperation and monitor damage progression. Inthis case, be certain to become involved in es-tablishing the gear system monitoring process.In most applications, inspection and monitor-ing include visual inspection and temperature,sound, and vibration measurements. Addition-ally, for critical applications, nondestructiveinspection of the gears (e.g., magnetic particleinspection) should ensure the absence of cracksbefore operation is continued. Before the sys-tem is restarted, be certain to collect samples oflubricant for analysis, drain and flush lubricantreservoirs, and replace the lubricant. Examinethe oil filter for wear debris and contaminants,and inspect magnetic plugs for wear debris.

The high cost of shutdown frequently limitstime available for inspection. Such cases call forcareful planning. Dividing tasks between two ormore analysts may reduce time required andprovide varied insight into the failure analysistask.

Prepare for Inspection

Before visiting the failure site, the analystshould interview a contact person and explain


Fig. 38 An internal rupture in a gear tooth at the case/coretransition zone. The rupture does not reach the sur-

face. This condition can be discovered by ultrasonic testing.

Fig. 39 Spiral bevel gear tooth failure. Internal rupture is lift-ing the entire top of a tooth.

Fig. 40 Spur gear failure. External rupture (assembled, butnot in service) with origin at the end face. See also

Fig. 41.Fig. 41 Spur gear. External rupture originating from a grind-

ing check. See also Fig. 40.

evidence. Emphasize that failure investigationis different from a gearbox rebuild, and the dis-assembly process may reveal significant facts toa trained observer.

Verify that gearbox drawings, disassemblytools, and adequate facilities are available. In-form the contact person that privacy is requiredto conduct the investigation, and access to allavailable information is necessary.

Ask for as much background information aspossible, including specifications of the manu-facturer, service history, load data, and lubricantanalyses. Send a questionnaire to the contactperson to help expedite information gathering.

the failure analysis process and outline specificneeds. Emphasize the need to inspect the gear-box, interview personnel, examine equipment,and assess working conditions.

A skilled technician should be requested todisassemble the equipment under the directionof the analyst. However, if safety permits, it isbest if no work is done on the gearbox until theanalyst arrives. This means no disassembly,cleaning, or draining oil. Otherwise, a well-meaning technician could inadvertently destroy


Table 5 Summary of a statistical report oncauses of gear failures (%) over a 35-yearperiod

Basic material 0.8SteelForgingsCastings

Engineering 6.9DesignMaterial selectionHeat treat specificationsGrinding tolerances

Manufacturing 1.6Tool undercutting, sharp notchesTooth characteristicsGrinding checks, burnsHeat treat changes

Heat treatment 16.0Case propertiesCore propertiesCase/core combinationsHardeningTemperingMiscellaneous operations

Service application 74.7Set-matchingAssembly, alignment, deflection, vibrationMechanical damage, mishandlingLubricationForeign materialCorrosionContinuous overloadingImpact overloadingBearing failureMaintenanceOperator errorField application

Source: Ref 1

Fig. 42 Fatigue fracture of AISI 4140 bull gear due to improper heat treatment. The one-of-a-kind replacement gear had a servicelife of just 2 weeks. Heat treatment did not produce full hardness in gear teeth. Hardness at tooth face, 15 HRC; at tooth

core, 82 HRB. (a) Outside diameter of gear showing where teeth broke off. Fatigue pattern on fracture surfaces is typical of reversedbending even though the gear was driven in only one direction. Original magnification at 0.6×. (b) Fracture surfaces of four teeth.Fatigue cracks propagated from both roots of each tooth. Arrows point to area of final overload on one tooth. Original magnification at0.84×. See also Fig. 43.

Inspect In Situ

Before starting the inspection, review back-ground information and service history with thecontact person. Try to interview those involvedin design, installation, startup, operation andmaintenance, and anyone present when failureof the gearbox occurred or was discovered.Encourage the interviewees to share everythingthey know about the gearbox and associatedsystems even if they feel it is not important.

External Examination. Before removingand disassembling the gearbox, take photo-graphs and thoroughly inspect the exterior. Usean inspection form to ensure that important data(data that may be lost once disassembly begins)is recorded. For example, the condition of sealsand keyways should be recorded before disas-sembly or it may be impossible to determinewhen these parts were damaged.

Before cleaning the exterior of the gear hous-ing, inspect for signs of over-heating, corrosion,contamination, oil leaks, and damage, and pho-tograph the areas of interest. Photographic doc-umentation is frequently a key to any good fail-ure analysis, including a gear failure analysis.

Gear Tooth Contact Patterns. To observethe condition of the gears, shafts, and bearings,clean the inspection port cover and the immedi-ate area around it, and then remove the cover.Be careful not to contaminate the gearbox dur-


Fig. 43 Structure of fractured tooth from AISI 4140 bull gear in Fig. 42. (a) Tooth cross section. Arrows show depth to which tem-perature exceeded Ac1 during heat treatment. (b) Near-surface hardened region of tooth. Large ferrite indicates that com-

plete austenitization was not obtained during heat treating. 2% nital, original magnification at 200×

ing cleaning or during the removal of the portcover.

The way gear teeth contact indicates howthey are aligned. Record tooth contact patternsunder loaded or unloaded conditions. No-loadpatterns are not as reliable as loaded patterns fordetecting misalignment, because marking com-pound is relatively thick and no-load tests do notinclude misalignment caused by load, speed, ortemperature. Therefore, follow no-load testswith loaded tests whenever possible. See ANSI/AGMA 2000 Appendix D for information re-garding contact pattern tests.

No-Load Contact Patterns. For no-loadtests, paint the teeth of one gear with soft mark-ing compound and roll the teeth through meshso compound transfers to the unpainted gear.Turn the pinion by hand while applying a lightload to the gear shaft by hand or brake. Lifttransferred patterns from the gear with cleartape and mount the tapes on white paper to forma permanent record.

Loaded Contact Patterns. For loadedtests, paint several teeth on one or both gearswith machinist’s layout lacquer. Thoroughlyclean teeth with solvent and acetone, and brushpaint with a thin coat of lacquer. Run the gearsunder load for sufficient time to wear off the lac-quer and establish the contact patterns. Photo-graph patterns to obtain a permanent record.

Record loaded contact patterns under severalloads, for example, 25, 50, 75, and 100% load.Inspect patterns after running approximatelyone hour at each load to monitor how patternschange with load. Ideally, the patterns shouldnot change much with load. Optimum contactpatterns cover nearly 100% of the active face of

gear teeth under full load, except at extremes ofteeth along tips, roots, and ends, where contactis lighter as evidenced by traces of lacquer.

Endplay and Backlash. Inspect endplayand radial movement of the input and outputshafts and gear backlash.

Remove Gearbox

Mounting Alignment. Measure alignmentof shaft couplings before removing the gearbox.Note the condition and loosening torque of allfasteners including coupling and mountingbolts. To check for possible twist of the gearhousing, measure movement of the mountingfeet as mounting bolts are loosened. Install fourdial indicators, one at each corner of the gear-box. Each indicator will record the same verti-cal movement if there is no twist. If not, calcu-late the twist from relative movements.

Transport Gearbox

Fretting corrosion is a common problem thatmay occur during shipping. Ship the gearbox onan air-ride truck, and support the gearbox onvibration isolators to help avoid fretting corro-sion. If possible, ship the gearbox with oil. Tominimize contamination, remove the breatherand seal the opening, seal labyrinth seals withsilicone rubber, and cover the gearbox with atarpaulin.

Store Gearbox

It is best to inspect the gearbox as soon aspossible. However, if the gearbox must bestored, store it indoors in a dry, temperature-controlled environment.


Disassemble Gearbox

Explain analysis objectives to the attendingtechnician. Review the gearbox assembly draw-ings with the technician, checking for potentialdisassembly problems. Verify that the work willbe done in a clean, well-lighted area, protectedfrom the elements, and that all necessary toolsare available. If working conditions are not suit-able, find an alternate location for gearbox dis-assembly.

Because technicians usually are trained towork quickly, it is wise to remind him or herthat disassembly must be done slowly andcarefully.

After the external examination, thoroughlyclean the exterior of the gearbox to avoid con-taminating the gearbox when opening it. Disas-semble the gearbox and inspect all components,both failed and undamaged.

Inspect Components

Inspect Before Cleaning. Mark relative po-sitions of all components before removingthem. Do not throw away or clean any partsuntil they are examined thoroughly. If there arebroken components, do not touch fracture sur-faces or fit broken pieces together. If fracturescannot be examined immediately, coat themwith oil and store the parts so fracture surfacesare not damaged.

Examine functional surfaces of gear teeth andbearings and record their condition. Beforecleaning the parts, look for signs of corrosion,contamination, and overheating.

Inspect After Cleaning. After the initialinspection, wash the components with solventsand re-examine them. This examination shouldbe as thorough as possible because it is often themost important phase of the investigation andmay yield valuable clues. A low-power magni-fying glass and 30× pocket microscope are help-ful tools for this examination.

It is important to inspect bearings becausethey often provide clues to the cause of gearfailure. For example:

• Bearing wear can cause excessive radialclearance or endplay that misaligns gears.

• Bearing damage may indicate corrosion,contamination, electrical discharge, or lackof lubrication.

• Plastic deformation between rollers andraceways may indicate overloads.

• Gear failure often follows bearing failure.

Document Observations. Identify andmark each component (including gear teeth andbearing components) so it is clearly identified inwritten descriptions, sketches, and photographs.It is especially important to mark all bearings, in-cluding inboard and outboard sides, so their loca-tions and positions in the gearbox are identified.

Describe components consistently. For exam-ple, always start with the same part of a bearingand progress through the parts in the samesequence. This helps to avoid over-looking anyevidence.

Describe important observations in writingusing sketches and photographs where needed.The following guidelines help maximize thechances for obtaining meaningful evidence:

• Concentrate on collecting evidence, not ondetermining cause of failure. Regardless of how obvious the cause may appear, do not form conclusions until all evidence isconsidered.

• Document what is visible. List all observa-tions even if some seem insignificant or ifthe failure mode is not easily recognizable.Remember there is a reason for everything,and some details may become importantlater when all the evidence is considered.

• Document what is not visible. This step ishelpful to eliminate certain failure modesand causes. For example, if there is no scuff-ing, it can be concluded that gear tooth con-tact temperature was less than the scuffingtemperature of the lubricant.

• Search the bottom of the gearbox. Often, thisis where the best-preserved evidence isfound, such as when a tooth fractures andfalls free without secondary damage.

• Use time efficiently. Be prepared for theinspection. Plan work carefully to obtain asmuch evidence as possible. Do not be dis-tracted by anyone.

• Control the investigation. Watch every stepof the disassembly. Do not let the technicianproceed too quickly. Disassembly shouldstop while the analyst inspects and docu-ments the condition of a component; thenmove on to the next component.

• Insist on privacy. Do not let anyone distractattention from the investigation. If askedabout conclusions, answer that conclusionsare not formed until the investigation iscomplete.

Gather Gear Geometry. The load capacityof the gears should be calculated. For this pur-


pose, obtain the following geometry data fromthe gears and housing or drawings:

• Number of teeth• Outside diameter• Face width• Gear housing center distance• Whole depth of teeth• Tooth thickness (both span and topland

thickness)

Specimens for Laboratory Tests. Duringinspection, the analyst will begin to formulatehypotheses regarding the cause of failure. Withthese hypotheses in mind, select specimens forlaboratory testing. Take broken parts for labora-tory evaluation or, if this is not possible, pre-serve them for later analysis.

After the inspection is completed, be sure allparts are coated with oil and stored properly sothat corrosion or damage will not occur.

Oil samples can be very helpful. However, aneffective analysis depends on how well the sam-ple represents the operating lubricant. To takesamples from the gearbox drain valve, first dis-card stagnant oil from the valve. Then, take asample at the start, middle, and end of the drainto avoid stratification. To sample from the stor-age drum or reservoir, draw samples from thetop, middle, and near the bottom. These samplescan uncover problems such as excessive waterin the oil due to improper storage.

Ask whether there are new, unused compo-nents. These parts are helpful to compare withfailed parts. Similarly, compare a sample offresh lubricant to used lubricant.

Before leaving the site, be sure that allnecessary items—completed inspection forms,written descriptions and sketches, photos, andtest specimens—have been collected.

It is best to devote two days minimum for thefailure inspection. This affords time after thefirst-day inspection to review the inspection andanalyze collected data. Often, the initial inspec-tion discloses a need for other data, which canbe gathered on the second day.

Determine Failure Mode

Now it is time to examine all information anddetermine how the gears failed. As describedearlier in this chapter, several failure modesmay be present and an understanding of thesemodes—bending fatigue, contact fatigue, wear,scuffing, impact, and so on—will enable identi-fication of the cause of failure.

Tests and Calculations. In many cases,failed parts and inspection data do not yieldenough information to determine the cause offailure. When this happens, gear design calcula-tions and laboratory tests are necessary to de-velop and confirm a hypothesis for the probablecause.

Gear Design Calculations. Gear geometrydata aids in estimating tooth contact stress, bend-ing stress, lubricant film thickness, and geartooth contact temperature based on transmittedloads. Calculate values according to AGMAstandards such as ANSI/AGMA 2001. Comparecalculated values with AGMA allowable valuesto help determine risks of micropitting, macro-pitting, bending fatigue, and scuffing.

Laboratory Examination and Tests. Mi-croscopic examination may confirm the failuremode or find the origin of a fatigue crack. Lightmicroscopes and scanning electron microscopes(SEM) are useful for this purpose. A SEM withenergy-dispersive x-ray is especially useful foridentifying corrosion, contamination, or inclu-sions.

If the primary failure mode is likely to beinfluenced by gear geometry or metallurgicalproperties, check for any geometric or metallur-gical defects that may have contributed to thefailure. For example, if tooth contact patternsindicate misalignment or interference, inspectthe gear for accuracy on gear inspection ma-chines. Conversely, where contact patterns indi-cate good alignment and loads are within ratedgear capacity, check teeth for metallurgicaldefects.

Conduct nondestructive tests before any de-structive tests. These nondestructive tests, whichaid in detecting material or manufacturingdefects and provide rating information, include:

• Surface hardness and roughness• Magnetic particle inspection• Acid etch inspection• Gear tooth accuracy inspection

Then, conduct destructive tests to evaluatematerial and heat treatment. These tests include:

• Microhardness survey• Microstructural determination using acid

etches• Determination of grain size• Determination of nonmetallic inclusions• Scanning electron microscopy to study frac-

ture surfaces


Form and Test Conclusions

When all calculations and tests are com-pleted, the analyst should form one or morehypotheses for the probable cause of failure,then determine whether the evidence supportsor disproves the hypotheses. Evaluate all evi-dence that was gathered, including:

• Documentary evidence and service history• Statements from witnesses• Written descriptions, sketches, and photos• Gear geometry and contact patterns• Gear design calculations• Laboratory data for materials and lubricant

Results of this evaluation may make it neces-sary to modify or abandon initial hypotheses orpursue new lines of investigation.

Finally, after thoroughly testing the hypothe-ses against the evidence, a conclusion will bereached regarding the most probable cause offailure. In addition, secondary factors that con-tributed to the failure may be identified.

Report Results

The failure analysis report should describe all relevant facts found during analysis, inspec-tions and tests, weighing of evidence, conclu-sions, and recommendations. Present data suc-cinctly, preferably in tables or figures. Goodphotos are especially helpful for portraying fail-ure characteristics.

If possible, include recommendations for re-pairing equipment or making changes in equip-ment design, manufacturing, or operation to pre-vent future failures.

Examples of Gear Failure Analysis

No failure examination has been successfullycompleted until an evaluation of the results ismade and it is only when the failure mechanismis understood that effective corrective measurescan be devised. The purpose now is to take theknown facts of a specific failure, to place themin a systematic context to arrive at a logical con-clusion, and to indicate a corrective measure.Obviously, one cannot detail the hundreds ofexaminations available, but a chosen few will bepresented to illustrate a systematic approach tothe examination, regardless of its apparent sim-plicity or complexity.

Example 1: Catastrophic Failure of aHoist Worm Caused by Destructive WearResulting From Abusive Operation. A farm-

silo hoist was used as the power source for ahomemade barn elevator. The hoist mechanismconsisted of a pulley attached by a shaft to aworm that, in turn, engaged and drove a wormgear mounted directly on the hoist drum shaft.The worm was made of leaded cold-drawn 1113steel with a hardness of 80 to 90 HRB; the wormgear was made of class 35–40 gray iron that hadbeen nitrided in an aerated salt bath. Drivingpower was applied to the pulley, which actuatedthe worm and worm gear and rotated the drumto which the elevator cable was attached. Afterless than 1 year of service, the hoist failed cata-strophically from destructive wear of the worm(Fig. 44). The hoist was rated at 905 kg (2000lb) at a 200-rpm input. It was determined that atthe time of failure the load on the hoist was only325 kg (720 lb).

Investigation. When examined, the gearboxwas found to contain fragments of the wormteeth and shavings that resembled steel wool. Itwas determined that both fragments and shav-ings were steel of the same composition as theworm, ruling out the possibility that these mate-rials may have derived from a source other thanthe gearbox. The teeth of the worm had worn toa thickness of approximately 1.6 mm (₁/₁₆ in.)from an original thickness of 3.2 mm (⅛ in.).More than half of the worm teeth had beensheared off.

Further investigation revealed that the drivepulley had been replaced with a pulley of differ-ent diameter and that the pulley was rotating at975 rpm instead of at the rated maximum of 200rpm. By calculation, with a load of 325 kg (720lb), the gearbox was forced to develop 0.24 kW(0.32 hp)—almost twice the specified rating of0.13 kW (0.18 hp) (2000 lb at 200 rpm).

Conclusions. The failure mode was adhe-sive wear of the steel worm, which resultedfrom operation of the gearbox at a power levelthat far exceeded the maximum specified by thegearbox manufacturer. The cause of failure wasmisuse in the field.

Example 2: Failure of Carburized SteelImpeller Drive Gears Due to Pitting and aWear Pattern. Two intermediate impellerdrive gears were submitted for metallurgicalexamination when they exhibited evidence ofpitting and abnormal wear after production testsin test-stand engines. Both gears were made ofAMS 6263 steel and were gas carburized, hard-ened, and tempered. Figure 45 shows the pittingand the wear pattern observed on the teeth ofgear 1.


Fig. 44 Destructive wear of an 1113 steel worm used in a silo hoist

According to the heat-treating specification,the gears were required to satisfy the followingrequirements: (1) a carburized case depth of 0.4to 0.6 mm (0.015 to 0.025 in.), (2) a case hard-ness of 77 to 80 HR30N, and (3) a core hardnessof 36 to 44 HRC.

Investigation. Sections of both gears wereremoved with a cutoff wheel and examined forhardness, case depth, and microstructure of caseand core. Results were as follows:

Gear 1 Gear 2

HardnessCase, HR30N 70–73 77–78Core, HRC 40 40

Case depth, mm (in.) 0.5–0.6 (0.02–0.024) 0.6–0.7(0.024–0.028)

MicrostructureCase Lean carbon (<0.85% C) NormalCore Normal Normal

Both the pitting and the wear pattern were moresevere on gear 1 than on gear 2.

Conclusions. Gear 1 failed by surface-con-tact fatigue (pitting) because the carbon contentof the carburized case and consequently the casehardness were below specification and inade-quate for the loads to which the gear was sub-jected. The pitting and wear pattern observed ongear 2 were relatively mild because case-carboncontent and case hardness were within specifiedrequirements. Nevertheless, it was evident thatcase depth, as specified, was not adequate for

this application—even with case-carbon con-tent and hardness being acceptable.

Recommendations. It was recommendedthat the depth of the carburized case on impellerdrive gears be increased from 0.4 to 0.6 mm(0.015 to 0.025 in.) to 0.6 to 0.9 mm (0.025 to0.035 in.), an increase that would still allow aminimum of 30% core material across the toothsection at the pitchline. This increase wouldensure improved load-carrying potential andwear resistance. It was also recommended thathardness readings on gears be made using a 60 kg (132 lb) load (Rockwell A scale) and thatthe minimum case-hardness requirement be setat 81 HRA, an additional safeguard to ensureadequate load-carrying capacity.

Example 3: Failure of a Carburized SteelGenerator-Drive Idler Gear by Pitting Due toDecarburization and Subsurface Oxidation.Following test-stand engine testing, an idler gearfor the generator drive of an aircraft engineexhibited evidence of destructive pitting on thegear teeth in the area of the pitchline; as a conse-quence, the gear was submitted for metallurgicalexamination. The gear was made of AMS 6263steel and was gas carburized to produce a case 0.4to 0.6 mm (0.015 to 0.025 in.) deep.

Investigation. Sections of the gear were re-moved and examined for hardness, case depth,and microstructure of case and core. The resultsof the examination and the specified require-ments were:


Fig. 45 Pitting and wear pattern on a carburized AMS 6263steel impeller drive gear. Original magnification

approximately 2.3×

Fig. 46 Metallurgical causes of destructive pitting thatoccurred in a carburized AMS 6263 steel gear. (a)

Specimen etched 15 to 20 s in 2% nital showing a surface layerof decarburized material. Original magnification at 500×. (b)Same specimen repolished and etched 3 s in 2% nital showing aheavy subsurface layer of oxide scale. Original magnification at500×. The white band immediately above the decarburized andoxidized layers is electrodeposited nickel that was applied toprevent edge-rounding during polishing.

Required Actual

Case depth, mm (in.) 0.4–0.6 0.6–0.7 (0.015–0.025) (0.024–0.028)

HardnessCase, HR30N 77–80 74–76

(HR15N88–89)Core, HRC 36–44 40–41

When it was determined that the case hard-ness of the gear was below specification, addi-tional hardness measurements were made usinga 15 kg (33 lb) load. These measurements con-firmed the low hardness and suggested that ithad resulted from one or more surface defects.

A specimen from the pitted area of one geartooth was prepared for metallographic examina-tion. The results of this examination are shownin Fig. 46. When the specimen was etched in 2%nital for 15 to 20 s, a decarburized surface layerwas observed in the vicinity of pitting (Fig.46a). When the specimen was repolished andthen etched in 2% nital for only 3 s, a heavy sub-surface layer of oxide scale was observed in thevicinity of pitting (Fig. 46b).

Conclusions. Based on low case-hardnessreadings and the results of metallographicexamination, it was concluded that pitting hadresulted due to a combination of surface decar-burization and subsurface oxidation. Because ofprevious failure analyses and thorough investi-gation of heat-treating facilities, the source ofthese defects was well known. The oxide layerhad been developed during the carburizingcycle because the furnace retort had not beenadequately purged of air before carburization.Decarburization had occurred during theaustenitizing cycle in a hardening furnace con-

taining an exothermic protective atmospherebecause of defects in the copper plating appliedto the gear for its protection during austenitiz-ing. These defects had permitted leakage ofexothermic atmosphere to portions of the car-burized surface, and, because of the low carbonpotential of the exothermic atmosphere, theleakage had resulted in decarburization.

Recommendations. It was recommendedthat steps be taken during heat treatment toensure that furnaces are thoroughly purgedbefore carburizing and that positive atmo-spheric pressure be maintained throughout thecarburizing cycle. Further, it was recommendedthat more effective control be exercised over allaspects of copper plating of carburized gears,including final inspection, before releasing thegears for hardening.

Example 4: Fatigue Failure of a Carbur-ized 4817 Steel Spiral Bevel Gear at Acute-Angle Intersections of Mounting Holes andTooth-Root Fillets. A spiral bevel gear set wasreturned to the manufacturer because the gear


Fig. 47 Carburized 4817 steel spiral bevel gear failure. Thegear broke from fatigue at acute-angle intersections

of mounting holes and tooth-root fillets as a result of throughhardening. Dimensions given in inches

broke into three pieces after about 2 years ofservice. Damage to the pinion was minor. Thegear broke along the root of a tooth intersectedby three of the six 22 mm (0.875 in.) diam holes(Fig. 47) used to mount the gear to a hub. Theintersection of the hole and root fillet created anacute-angle condition (Section A-A, Fig. 47).

The ring gear, machined from a forged blankmade of 4817 steel, had been gas carburized at925 °C (1700 °F), cooled to 815 °C (1500 °F),press quenched in oil at 60 °C (140 °F), thentempered at 175 °C (350 °F) for 1½ h to producea case hardness of 61 to 62 HRC, as measured ata tooth land.

Investigation. Examination of the gearrevealed fatigue progression for about 6.4 mm(¼ in.) at acute-angle intersections of threemounting holes with the root fillets of threeteeth. Subsequent fracture progressed rapidlyuntil the entire section failed. Cracking betweenthe holes and the bore of the gear started beforethe tooth section failed. Magnetic-particleinspection revealed cracks at the intersections

of the remaining three mounting holes and theadjacent tooth-root fillets.

Microstructure of the carburized and hard-ened case was fine acicular martensite withabout 5% retained austenite. The core was com-posed principally of low-carbon martensite.

Metallographic examination revealed that theacute-angle intersections of the mounting holesand tooth-root fillets were carburized to a depththat comprised the entire cross section and con-sequently were through hardened.

Conclusions. The gear failed in fatigue,slowly to a depth of about 6.4 mm (¼ in.), thenrapidly until final fracture. Design of the gearand placement of the mounting holes were con-tributing factors in the failure because theyresulted in through hardening at the acute-angleintersections of the mounting holes and tooth-root fillets.

Example 5: A Spiral Bevel Pinion ThatHad Two Failure Modes Occurring Inde-pendently of Each Other. This spiral bevelset was the primary drive unit for the differen-tial and axle shafts of an exceptionally largefront-end loader in the experimental stages ofdevelopment.

Visual Examination. The tooth contact areaof the pinion appeared to have been heavy at thetoe end and low on the profile of the concave(drive) side. The entire active profile showedsurface rippling for more than half the length ofthe tooth from the toe end (Fig. 48). Pitting orig-inated at the lower edge of the profile 50 mm (2 in.) from the toe end of the concave side (Fig.48a) and subsequently progressed in both direc-tions along the lower edge of the active profileand upward toward the top of the tooth, chang-ing the mode from pitting to spalling (Fig. 48b).Both photographs show evidence of a doublecontact: the original setting, and a secondarypattern with the pinion moved out and awayfrom the center of the gear. The convex(reverse) sides were slightly worn and scuffedhigh over the profile.

All of the gear teeth were intact and highlypolished along the top of the profile toward thetoe end of the convex (forward) side. Somescuffing was evident low on the profile of theconcave sides.

Physical Examination. Magnetic-particle in-spection showed no evidence of tooth-bendingfatigue on either part. The several cracks indi-cated are associated with the spalling surfaceson the concave sides of the pinion teeth. Thegear teeth showed no crack indications.


Fig. 48 Spiral bevel pinion of 4820H steel. (a) Rippled surface for three-fourths of the length of the tooth starting from the toe end.Pitting originated low on the active profile 50 mm (2 in.) from the toe end. (b) The pitting area extended in both directions

and broadened. The central profile has an area of spalling that appears to be contiguous with the pitting. The microstructure indicatesthat the two modes occurred independently. Original magnification at 0.5×. See also Fig. 49 and 50.

Tooth Characteristics. The original settingtest charts taken on this set in December 1979are on file and document a very good and nor-mal tooth contact pattern. The secondary toothpattern that prevails at this time could not beduplicated on the gear tester. It appears that thepinion had moved away from the center of thegear, thus activating a very heavy low-profilecontact toward the toe end.

Surface-Hardness Tests. The surface hard-ness of both parts was 58 to 59 HRC, which iswithin the specification of 58 to 63 HRC.

Metallurgical Examination. The proceduresto implement are determined as follows. Therippling (Fig. 48) was extensive and covered theentire area of the initial contact pattern. Rip-pling is a reflection of apparent movement or ofa tendency to move. It can be a superficialadjustment of a surface being heavily rolledwhile sliding, or it can be an adjustment of thesurface during absorption of energy by retainedaustenite. Rippling is not always associatedwith a failure, nor is it detrimental in itself. Itdoes usually indicate, however, a rolling-slidingcondition that is highly compressive.

The pitting originated in a localized area, andthe spalling appeared to be a contiguous event,although this type of spalling could easily havebeen found as an independent mode without theassociation of surface pitting. It was, therefore,necessary to section the pinion tooth normal tothe active profile near the spalled area shown inFig. 48(b) and to prepare this section for amicrohardness traverse of the case and for amicroscopic examination.

Microscopic Examination. The core struc-ture of the pinion showed an equal admixture oflow-carbon martensite and lamellar pearlite.The case structure consisted of very fine acicu-lar martensite retaining less than 5% austenite.

The pitted area low on the active profileshowed evidence of a heavy metal-to-metal slid-ing action which tended to produce adhesion.The central profile area, being subjected tospalling, had a surface that was relatively unal-tered (Fig. 49). In the same area, there was a sub-surface display of butterfly wings reaching to adepth of 0.7 mm (0.027 in.) from the surface.

Case-Hardness Traverse. Figure 50 showsthe case-hardness traverse of the section usedfor Fig. 49. The results are self-explanatory.

Conclusions. The material and process spec-ifications were met satisfactorily. The primarymode of failure was rolling-contact fatigue of theconcave (drive) active tooth profile. The spalledarea was a consequence of this action. The pit-ting low on the profile appeared to have origi-nated after the shift of the pinion tooth awayfrom the gear center. The shift of the pinion ismost often due to a bearing displacement or mal-function. The cause of this failure appeared to becontinuous high overload, which may also havecontributed to the bearing displacement.

Example 6: Fatigue Failure of a Carbur-ized Steel Bevel Pinion Because of Misalign-ment. The bevel pinion shown in Fig. 51(a)was part of a drive unit in an edging mill. Thepinion had been in service about 3 months whenseveral teeth failed. Specifications required thatthe pinion be made from a 2317 steel forging


Fig. 49 Section normal to surface of tooth profile taken nearthe spalled area shown in Fig. 48(b). The surface

shows no catastrophic movement; the butterfly wings are gener-ally parallel to the surface, but extend 0.7 mm (0.027 in.) belowthe surface. Microstructure is very fine acicular martensite retain-ing less than 5% austenite. Original magnification at 200×

Fig. 50 Case-hardness traverse of section used for Fig. 49taken from tooth shown in Fig. 48(b)

Fig. 51 2317 steel bevel pinion that failed by fatigue breakage of teeth. (a) Configuration and dimensions (given in inches). (b) Viewof area where two teeth broke off at the root. (c) Fracture surface of a broken tooth showing fatigue marks

and that the teeth be carburized and hardened toa case hardness of 56 HRC and a core hardnessof 250 HB (24.5 HRC).

Investigation. Chemical analysis of themetal in the pinion showed that it was 2317 steelas specified. Case hardness was 52 to 54 HRC,and core hardness was 229 HB (20.5 HRC).


Both hardness values were slightly lower thanspecified, but acceptable.

Visual inspection of the pinion showed thattwo teeth had broken at the root (Fig. 51b). Thesurfaces of these fractures exhibited fatiguemarks extending across almost the entire tooth(Fig. 51c). Magnetic-particle inspection of thepinion showed that all of the teeth were cracked.Each crack had initiated along the tooth root, atthe toe (small) end of the tooth, extending to thecenter of the crown. Spalling was also noted onthe pressure (drive) side of each tooth at the toeend. A metallographic specimen taken trans-versely through a broken tooth showed it to becase carburized to a depth of 4.8 mm (₃/₁₆ in.),hardened, and tempered.

Conclusions. The pinion failed by tooth-bending fatigue. Some mechanical misalign-ment of the pinion with the mating gear causeda cyclic shock load to be applied to the toe endsof the teeth, as exhibited by the spalling. Thiscontinuous pounding caused the teeth to crackat the roots and to break off.

Example 7: Overload Failure of a BronzeWorm Gear. Overload failures, from the per-spective of the materials failure analyst, refer tothe ductile or brittle failure of a material whenstresses exceed the load-bearing capacity of thematerial from either excessive applied stress ordegradation of the load-bearing capacity of thematerial from damage, embrittlement, or otherfactors (Ref 8). Ductile overload failures aresimply those that exhibit significant visiblemacroscopic plastic deformation. Brittle over-load failures, in contrast to ductile overload fail-ures, are characterized by little or no plasticdeformation. For ductile and brittle fractures,distinguishing characteristics at different scalesof observations (1× to >10,000×) are brieflysummarized in Table 6. In this example, amixed-mode failure (ductile plus brittle frac-ture) is described.

Background. A very large diameter wormgear that had been in service in a dam for morethan 60 years exhibited cracks and wasremoved. It was reported that the cast bronzegear was only rarely stressed during service,associated with infrequent opening and closingof gates. Due to the age of the gear and the timeframe of its manufacture, no original materialspecifications or strength requirements could belocated. Likewise, no maintenance records ofpossible repairs to the gear were available.

Investigation. As part of the investigation, anumber of representative sections excised from

the gear were submitted for metallurgical analy-sis. The cracks were primarily located on thegear faces and were not associated with tradi-tional regions of high service stresses, such asthe tooth roots. Some portions of the gear faceexhibited light discoloration, which was sugges-tive of weld repairs. The cracks were evidentwithin the base metal, at the repair weld fusionlines, and within the weld metal. Figure 52(a)shows the opened crack features in an area wherea weld and remaining casting imperfection wereapparent. The macroscopic fracture features dif-fered substantially between the base metal andthe welds. Some of the cracking did not occur atcasting imperfections or repair welds.

Scanning electron microscopy revealed thetypical weld and base metal fracture featuresshown in Fig. 52(b) and (c), respectively. Theweld exhibited fine features that consisted ofboth dimple rupture and grain-boundary dim-ple-rupture evidence. The base metal exhibitedrather large-grain intergranular brittle crackingfeatures with many types of inclusions.

Chemical analysis revealed a standard high-strength, manganese bronze composition, andthe weld filler metal was considered compatible.Tension testing of specimens removed fromgear segments remote to repairs revealed tensilestrengths near 690 MPa (100 ksi), yieldstrengths near 517 MPa (75 ksi), and 5% elon-gation at fracture. Weld and base metal hard-nesses were similar.

Table 6 Distinguishing characteristics ofbrittle versus ductile behavior depending on thescale of observationScale of observation Brittle Ductile

Structural engineer Applied stress atfailure is less than the yieldstress

Applied stress atfailure is greaterthan the yieldstress

By eye (1×) No necking, shinyfacets, crystalline,granular

Necked, fibrous,woody

Macroscale (<50×)

“Low” RA or ductility

Medium to high RA

Microscale, scanning electronmicroscopy(100–10,000×)

Brittle microprocess,cleavage orintergranular

Ductilemicroprocess,microvoidcoalescence

Transmission electronmicroscopy(>10,000×)

May have a largelevel of localplasticity

High amount ofplasticityglobally

RA, reduction of area. Source: Ref 8


Fig. 52 Overload failure of a bronze worm gear (example 4). (a) An opened crack is shown with a repair weld, a remaining castingflaw, and cracking in the base metal. (b) Electron image of decohesive rupture in the fine-grain weld metal. Scanning elec-

tron micrograph. Original magnification at 119×. (c) Morphology in the large-grain base material at the same magnification as (b), show-ing intergranular brittle fracture features. Scanning electron micrograph. Original magnification at 119×. (d) Metallographic imageshowing the weak grain-boundary phase in the weld. Potassium dichromate etch. Original magnification at 297×

ACKNOWLEDGMENTS


• L.E. Alban, Failures of Gears, FailureAnalysis and Prevention, Vol 11, MetalsHandbook, 9th ed., American Society forMetals, 1986, p 586–601

• R. Errichello, Tutorial: How to AnalyzeGear Failures, Practical Failure Analysis,Vol 2 (No. 6), December 2002, p 8–16

• R.S. Hyde, Contact Fatigue of HardenedSteel, Fatigue and Fracture, Vol 19, ASMHandbook, ASM International, 1996, p 691–703

• B.A. Miller, Overload Failures, FailureAnalysis and Prevention, Vol 11, ASMHandbook, 2002, p 671–699

• D.R. McPherson and S.B. Rao, MechanicalTesting of Gears, Mechanical Testing and

The microstructure at the transition betweenthe base metal and weld metal is shown in Fig.52(d). The continuous grain-boundary phase inthe weld metal responsible for the decohesiverupture features is evident.

Conclusions. It was concluded from theinvestigation that the bronze gear cracked viamixed-mode overload, rather than by a progres-sive mechanism such as fatigue or stress-corrosion cracking (SSC). The cracking was not associated with regions that would be highly stressed and did not appear to be consis-tently correlated to casting imperfections, repairwelds, or the associated heat-affected zones.The cast gear was a high-strength, low-ductilitybronze. Cracking across the gear face suggestedbending forces from misalignment were likelyresponsible for the cracking, and further reviewof this potential root cause could be recom-mended.


Evaluation, Vol 8, ASM Handbook, ASMInternational, 2000, p 861–872

REFERENCES

1. L.E. Alban, Systematic Analysis of GearFailures, American Society for Metals,1985

2. Appearance of Gear Teeth—Terminologyof Wear and Failure, ANSI/AGMA 1010-E95, American Gear Manufacturers Asso-ciation, 1995

3. R. Errichello, Friction, Lubrication, andWear of Gears, Friction, Lubrication, and Wear Technology, Vol 18, ASM Hand-book, ASM International, 1992, p 535–545

4. D.R. McPherson and S.B. Rao, MechanicalTesting of Gears, Mechanical Testing andEvaluation, Vol 8, ASM Handbook, ASMInternational, 2000, p 861–872

5. R.S. Hyde, Contact Fatigue of Hardened

Steel, Fatigue and Fracture, Vol 19, ASMHandbook, ASM International, 1996, p 691–703

6. W.R. Scott, Myths and Miracles of GearCoatings, Gear Technology, July/Aug1999, p 35–44

7. R. Errichello, Tutorial: How to AnalyzeGear Failures, Practical Failure Analysis,Vol 2 (No. 6), December 2002, p 8–16

8. B.A. Miller, Overload Failures, FailureAnalysis and Prevention, Vol 11, ASMHandbook, 2002, p 671–699

SELECTED REFERENCES

• R. Errichello, “Analysis Techniques EndGear Damage,” Power TransmissionDesign, March 1995, 37(3), p 23–26

• R. Errichello and J. Muller, “How to Ana-lyze Gear Failures,” Power TransmissionDesign, March 1994, 36(3), p 35–40

CHAPTER 14

Fatigue and Life Prediction

GEARS can fail in many different ways, andexcept for an increase in noise level and vibra-tion, there is often no indication of difficultyuntil total failure occurs. In general, each type offailure leaves characteristic clues on gear teeth,and detailed examination often yields enoughinformation to establish the cause of failure. Thegeneral types of failure modes (in decreasingorder of frequency) include fatigue, impact frac-ture, wear, and stress rupture (Table 1). Theleading causes of failure appear to be tooth-bending fatigue, tooth-bending impact, andabrasive tooth wear.

This chapter summarizes the various kinds ofgear wear and failure and how gear life in ser-vice is estimated. Hopefully, gears are properlydesigned, made of good material, and accu-rately machined so that the life of the gear isadequate for the service intended. The mannerin which gears wear in service and the variouskinds of failure that may occur determine howgear life in service is estimated. In addition, thekinds of flaws in material that may lead to pre-mature gear failure are discussed. Gear life isinfluenced primarily by geometric accuracy,gear-tooth contact conditions, and material con-

dition or flaws. Metallurgical quality is just asimportant as gear-tooth geometric accuracy,and both must be under good control by thosedesigning, making, or inspecting gears.

Gear Tooth Contact

The way in which tooth surfaces of properlyaligned gears make contact with each other isresponsible for the heavy loads that gears areable to carry. In theory, gear teeth make contactalong lines or at points; in service, however,because of elastic deformation of the surfaces ofloaded gear teeth, contact occurs along narrowbands or in small areas. The radius of curvatureof the tooth profile has an effect on the amountof deformation and on the width of the resultingcontact bands. Depending on gear size and load-ing, the width of the contact bands varies fromabout 0.38 mm (0.015 in.) for small, lightlyloaded gears to about 5 mm (0.2 in.) for large,heavily loaded gears.

Gear tooth surfaces are not continuouslyactive. Each part of the tooth surface is in actionfor only short periods of time. This continualshifting of the load to new areas of cool metal andcool oil makes it possible to load gear surfaces tostresses approaching the critical limit of the gearmetal without failure of the lubricating film.

The maximum load that can be carried bygear teeth also depends on the velocity of slid-ing between the surfaces, because the heat gen-erated varies with rate of sliding as well as withpressure. If both pressure and sliding speeds are excessive, the frictional heat developed can cause destruction of tooth surfaces. Thispressure-velocity factor, therefore, has a criticalinfluence on the probability of galling and scor-ing of gear teeth. The permissible value of thiscritical factor is influenced by gear metal, gear

Table 1 Failure modes of gearsFailure mode Type of failure

Fatigue Tooth bending, surface contact (pitting orspalling), rolling contact, thermalfatigue

Impact Tooth bending, tooth shear, toothchipping, case crushing, torsional shear

Wear Abrasive, adhesiveStress rupture Internal, external

In an analysis of more than 1500 studies, the three most common failuremodes, which together account for more than half the failures studied, aretooth-bending fatigue, tooth-bending impact, and abrasive tooth wear. Source:Metals Handbook, 9th ed., Vol 11, Failure Analysis and Prevention, ASMInternational, 1986




design, character of lubricant, and method oflubricant application.

Lubrication is accomplished on gear teethby the formation of two types of oil films. Thereaction film, also known as the boundary lubri-cant, is produced by physical adsorption and/orchemical reaction to form a desired film that issoft and easily sheared but difficult to penetrateor remove from the surface. The elastohydrody-namic film forms dynamically on the gear toothsurface as a function of the surface speed. Thissecondary film is very thin, has a very highshear strength, and is only slightly affected bycompressive loads as long as constant tempera-ture is maintained.

Certain rules about a lubricant should beremembered in designing gearing and analyzingfailures of gears:

• Load is transferred from a gear tooth to itsmating tooth through a pressurized oil film.If not, metal-to-metal contact may be detri-mental.

• Increasing oil viscosity results in a thickeroil film (keeping load, speed, and tempera-ture constant).

• Heat generation cannot be controlled abovea certain maximum viscosity (for a givenoil).

• Breakdown of the oil film will occur whenthe gear tooth surface-equilibrium tempera-ture has reached a specific value.

The scuffing load limit of mating tooth sur-faces is speed dependent. With increasing speed,the load required to be supported by the reactionfilm decreases, while the load that can be sup-ported by the increasing elastohydrodynamicfilm increases. The result is a decreasing scuffingload limit to a certain speed as the reaction filmdecreases; then, as the speed picks up to wherethe elastohydrodynamic film increases, thescuffing load limit increases. This allows an in-crease in overall load-carrying capacity (assum-ing no change in temperature that would changeviscosity).

• At constant speed, surface-equilibrium tem-perature increases as load increases, whichlowers the scuffing load limit of the reactionfilm (surface-equilibrium temperature is at-tained when the heat dissipated from the oilis equal to the heat extracted by the oil).

Damage to and failures of gears can and dooccur as a direct or indirect result of lubricationproblems.

Spur and Bevel Gears. Spur gear teeth arecut straight across the face of the gear blank, andthe mating teeth theoretically meet at a line ofcontact (Fig. 1a) parallel to the shaft. Straightteeth of bevel gears also make contact along aline (Fig. 1b) that, if extended, would passthrough the point of intersection of the two shaftaxes. As teeth on either spur or bevel gears passthrough mesh, the line of contact sweeps acrossthe face of each tooth. On the driving tooth, itstarts at the bottom and finishes at the tip. On thedriven tooth, the line of contact starts at the tipand finishes at the bottom.

Helical, Spiral Bevel, and Hypoid Gears.Gear tooth contact on helical, spiral bevel, andhypoid gears is similar to that developed on astepped spur gear (Fig. 2). Each section, or lami-nation, of the spur gear makes contact with itsmating gear along a straight line; each line,because of the offset between sections, is slight-ly in advance of its adjacent predecessor. Wheninnumerable laminations are combined into asmoothly twisted tooth, the short individual linesof contact blend into a smoothly slanted line(Fig. 1c) that extends from one side of the toothface to the other and sweeps either upward ordownward as the tooth passes through mesh.This slanted-line contact occurs between theteeth of helical gears on parallel shafts, spiralbevel gears, and hypoid gears.

The load pattern is a line contact extending ata bias across the tooth profile, moving from oneend of the contact area to the other end. Underload, this line assumes an elliptical shape andthus distributes the stress over a larger area.Also, the purpose of spiral bevel gearing is torelieve stress concentrations by having morethan one tooth enmeshed at all times.

The greater the angle of the helix or spiral, thegreater the number of teeth that mesh simulta-neously and share the load. With increasedangularity, the length of the slanted contact lineon each tooth is shortened, and shorter but moresteeply slanted lines of contact sweep across thefaces of several teeth simultaneously. The totallength of these lines of contact is greater thanthe length of the single line of contact betweenstraight spur-gear teeth of the same width. Con-sequently, the load on these gears is distributednot only over more than one tooth but also overa greater total length of line of contact. On theother hand, the increased angularity of the teethincreases the axial thrust load and thus increasesthe loading on each tooth. These two factorscounterbalance each other; therefore, if the

Chapter 14: Fatigue and Life Prediction / 295

Fig. 1 Tooth contact lines on a spur gear (a), a bevel gear (b), and a low-angle helical gear (c). Lines on tooth faces of typical teethare lines of contact.

power transmitted is the same, the average unitloading remains about the same.

Helical gears on crossed shafts make toothcontact only at a point. As the teeth pass throughmesh, this point of contact advances from belowthe pitchline of the driving tooth diagonallyacross the face of the tooth to its top, and fromthe top of the driven tooth diagonally across itsface to a point below the pitchline. Even withseveral teeth in mesh simultaneously, this pointcontact does not provide sufficient area to carryan appreciable load. For this reason, helicalgears at angles are usually used to transmitmotion where very little power is involved.

Worm Gears. In a single-enveloping wormgear set, in which the worm is cylindrical inshape, several teeth may be in mesh at the sametime, but only one tooth at a time is fully en-gaged. The point (or points) of contact in thistype of gear set constitutes too small an area tocarry an appreciable load without destruction ofthe metal surface. As a result, single-envelopingworm gear sets are used in applications similar tothose for helical gears on crossed shafts: to trans-mit motion where little power is involved.

Considerable power must be transmitted bycommercial worm gear sets; therefore, the gearsof these sets are throated to provide a greatly

increased area of contact surface. The gear tooththeoretically makes contact with the wormthread along a line curved diagonally across thegear tooth. The exact curve and slant depend ontooth design and on the number of threads onthe worm relative to the number of teeth on thegear. Usually, two or more threads of the wormare in mesh at the same time, and there is aseparate line of contact on each meshing tooth.As meshing proceeds, these lines of contactmove inward on the gear teeth and outward onthe worm threads. To secure smooth operationfrom a gear of this type, the teeth of the gear and sometimes the threads of the worm are usu-ally altered from theoretically correct standardtooth forms. These alterations result in slightlywider bands of contact, thus increasing the load-carrying capacity of the unit. Load-carryingcapacity also depends on the number of teeth insimultaneous contact. Exact tooth design variesfrom one manufacturer to another, and for thisreason, the patterns of contact also vary.

In a double-enveloping worm gear set, theworm is constructed so that it resembles an hour-glass in profile. Such a worm partly envelopesthe gear, and its threads engage the teeth of thegear throughout the entire length of the worm.The teeth of both the worm and the gear have


Fig. 3 An example of gear tooth scuffing. Note radial scratchlines.

straight-sided profiles like those of rack teeth,and in the central plane of the gear, they meshfully along the entire length of the worm.

The exact pattern of contact in double-enveloping (or double-throated) worm gear setsis somewhat controversial and seems to varywith gear design and with method of gear man-ufacture. It is generally agreed, however, thatcontact is entirely by sliding with no rolling andthat radial contact occurs simultaneously overthe full depth of all the worm teeth.

Operating Loads. Gears and gear drivescover the range of power transmission fromfractional-horsepower applications, such ashand tools and kitchen utensils, to applicationsinvolving thousands of horsepower, such asheavy machinery and marine drives. However,neither the horsepower rating nor the size of agear is necessarily indicative of the severity ofthe loading it can withstand. For example, theseverity of tooth loading in the gear train of a186 W (¼ hp) hand drill may exceed that of theloading in a 15 MW (20,000 hp) marine drive.Factors other than horsepower rating and sever-ity of loading can affect gear strength and dura-bility, particularly duration of loading, operat-ing speed, transient loading, and environmentalfactors such as temperature and lubrication.

Gear Tooth Surface Durability and Breakage

Metal gears are normally lubricated with anoil or a grease. Some small, nonmetallic gears

have limited capability to run without lubrica-tion, due to the self-lubricating properties of thematerial.

Scuffing. When metal gears are adequatelylubricated with a clean lubricant, there is very lit-tle abrasive wear of the contacting tooth sur-faces. However, the tooth surface may bequickly damaged by scuffing if (in combinationwith poor surface finish and low-viscosity lubri-cant) the load intensity, temperature, and rub-bing speed are too high. Scuffing consists ofsmall radial tears in the tooth surface. It is mostapt to happen where the tip of one tooth is con-tacting the lower flank of a mating tooth (Fig. 3).

Pitting may occur after some millions orbillions of tooth contacts. In general, pittingalmost never occurs before 10,000 contacts. Pit-ting is a fatigue failure where small cracks formin the tooth surface and then grow to the pointwhere small, round bits of metal break out of thetooth surface (Fig. 4).

Tooth breakage (such as in Fig. 5) is nor-mally the situation where a crack starts in theroot fillet, below the contacting surface, andthen the crack grows such that a whole toothbreaks off in a cantilever-beam-type of failure.In wide-face gears, one end of the tooth maybreak off, leaving the tooth intact for the rest ofthe face width.

Traditionally, the gear designer first deter-mines a pitch diameter and a face width for thepinion that are large enough for the pinion tolast for the required service life with a probabil-ity of failure of no more than 1 in 100. Thisdetermination is based on a possible pittingfatigue failure. It is assumed in the beginningthat the surface finish, the tooth accuracy, the

Fig. 2 Lines of contact on a stepped spur gear. The heavy lineon a tooth face of each gear section represents the

instantaneous line of contact for that section. This offset-contactpattern is typical for helical, spiral bevel, and hypoid gears. Lineson tooth faces are lines of contact.


Fig. 4 Pitted gear teeth. Note micropitting at the pitch line,scattered macropits, and one area of gross pitting near

the left end.

Fig. 5 Misaligned gear has tooth breakage at ends of teeth.

lubrication, and the needed profile and helixmodifications will all be carried out well enoughto avoid any serious risk of scuffing.

Normally, the pinion is more apt to fail in pit-ting than the gear, so the sizing of the piniontends to determine the needed size of the gear.(The gear pitch diameter equals the pinion pitchdiameter multiplied by the ratio. If the gear hasfour times as many teeth as the mating pinion,then the pitch diameter of the gear is four timesgreater than the pinion pitch diameter.)

After the pitch diameter of the pinion hasbeen determined, the size of the teeth are deter-mined by calculations regarding a possible fail-ure in tooth breakage. A broken tooth tends to

be catastrophic to a gear unit, so the designerusually makes the teeth large enough so thatthey are definitely less apt to fail in breakagemode than in a pitting mode. This makes thedesign life of a gear unit primarily dependent onits surface fatigue capacity (pitting resistance)rather than on its cantilever beam capacity(capacity to resist tooth breakage).

Life Determined by Contact Stress

The surface contact stress, Sc, between gearteeth (discussed further in Ref 1 with in-depthpresentations of gear rating calculations andconcepts) may be calculated by a simplified for-mula:

(Eq 1)

where Ck is the geometry factor for durability(see Table 2), K is the index of tooth loading

Sc 1in psi 2 � Ck 1KCd 2 0.5

Table 2 Some typical geometry factors (Ck) fordurabilityNo. of pinion teeth

No. of gear teeth

Standard addendum, ap = 1.000, aG = 1.000,whole depth 2.35 in.

25% long addendum, ap = 1.250, aG = 0.750,whole depth 2.35 in.

Spur gears, 20° pressure angle

25 35 5913 (a)25 50 5985 575625 85 6057 576835 35 5756 (a)35 50 5810 572235 85 5877 572635 275 5925 5732


20 35 5564 537120 50 5660 541920 85 5744 547925 35 5419 (a)25 50 5503 533525 85 5575 538035 35 5262 (a)35 50 5329 526935 85 5407 529835 275 5479 5323

Helical gears, 15° helix angle, 20° normal pressure angle

25 35 4576 (a)25 50 4540 456425 85 4479 453335 35 4516 (a)35 50 4492 449935 85 4419 4469


25 35 4444 (a)25 50 4419 (a)25 85 4383 (a)35 35 4395 (a)35 50 4371 (a)35 85 4335 (a)

(a) 25% long addendum design not used here. ap, pinion addendum; aG, gearaddendum


Table 3 Some typical overall derating factors (Cd)Accuracy level by AGMA

Aspect ratio, d/F 12 or 13 10 or 11 8 or 9 6 or 7

For designs where pinion pitch diameter is about 2 in. (50 mm)

0.25 or less 1.50 1.65 1.80 2.000.50 or less 1.65 1.75 2.00 2.250.75 or less 1.75 2.00 2.25 2.501.0 or less 2.00 2.25 2.50 2.75

For designs where pinion pitch diameter is about 5.0 in. (125 mm)


For designs where pinion pitch diameter is about 12 in. (300 mm)


Note: These derating factors should be considered illustrative only. For a prime mover that is rough running and a driven device that is rough running, the deratingneeds to be more than shown above. Likewise, for a very smooth-running prime mover and a low-inertia, smooth-running driven device, lower derating factors maybe justified. Field experience in vehicles, aircraft, and ships tends to be the best guide for choosing the right derating factor.

severity for pitting (see Eq 2), and Cd is theoverall derating factor for durability (see Table3).

The index of tooth loading for pitting is calledthe “K-factor.” For spur or helical gears, the K-factor is:

(Eq 2)

where Wt is the tangential driving force (inpounds), F is the net face width in contact (ininches), d is the pinion pitch diameter (in inches),and mG is the ratio of gear teeth to pinion teeth.

The tangential driving force is obtained fromthe horsepower being transmitted by the combi-nation of pinion and gear, the speed of the pin-ion in revolutions per minute, and the pitchdiameter of the pinion in inches. Thus:

(Eq 3)

where P is the horsepower transmitted and np isthe speed of the pinion (in rpm).

Example 1: Surface Durability of Gear.To show how the above equations work, con-sider a practical problem of an electric motor(running at a design speed of 1800 rpm) thatdrives a fan at 450 rpm and transmits power at aconstant 30 hp. If the pinion driven by the motorhas 22 teeth at a 15° helix angle and the normaldiametral pitch of the teeth is 10, what are the

Wt �P � 126,050

np � d lb

K �Wt

Fd amG � 1

mGb

calculated K-factor and contact stress when themating gear has a face width 1.0 times the pin-ion pitch diameter? The normal pressure angleis 20°. The tooth design is 25% extra addendumof the pinion and 25% shorter addendum for thegear.

The first step is to obtain the pinion pitchdiameter:

(Eq 4)

where Np is the number of pinion teeth, ψ is thehelix angle, and Pn is the normal diametralpitch. For the problem described above, then:

� 107,380 psi

Sc � 4558 1222.0 � 2.5 2 0.5

K �922.4

2.2776 � 2.28 14.0 � 1 214.0 2 � 222.0

Wt �30 � 126,050

1800 � 2.2776� 922.4 lb

F � 1.0 � 2.2776 � 2.28 in.

d �22

10 cos 115° 2 � 2.2776 in.

d �Np

Pn cos y in.


Fig. 6 Surface durability curve for gear life rating (contact stress vs. cycles) for normal industry quality material (Grade 1 per Ref 2)

Table 2 does not have 22/88 tooth numbers, soin calculating Sc, Ck was determined from Ref 2.

After the contact stress has been calculated, arating curve sheet needs to be used to determinewhat life can be expected. Figure 6 shows typi-cal contact stress values plotted against num-bers of tooth contacts. This curve sheet is drawnfor gearing having these qualifications:

• Material quality: Normal industry quality(Grade 1 per Ref 2)

• Probability of failure: Not over 1 in 100• Lubrication: Full oil film, which is regime

III• Hardness: Both pinion and mating gear at

least as hard as value shown on surface dura-bility figure

Determination of Gear Life. To explainhow gear life is determined, the discussion canbe based on the same sample problem. The cal-culated contact stress was 107,380 psi. FromFig. 6 the following life values are obtained forsteel gears (through hardened):

• 210 HB: 1.1 × 106 cycles• 300 HB: 2.0 × 108 cycles• 60 HRC: over 1.0 × 1010 cycles

The next step is to calculate the number ofpinion cycles for some different lengths of timeat full rated load, where:

Taking some different numbers of hours, thefollowing results are obtained:

Time at rated power, h No. of pinion cycles

500 54 × 106

2,000 216 × 106

20,000 2.16 × 109

Determination of adequate gear life requiressome reasoning. Inexpensive equipment that isused infrequently and is seldom used at fullrated power might be satisfactory if it had onlya 500-hour capability at full rating. The designunder consideration would be quite inadequatefor 500 hours if the teeth were at low hardness,such as 210 HB. However, if the pinion and gearwere at 300 HB hardness, they would haveenough capacity for 500 hours and almostenough for 2000 hours.

At full hardness of 60 HRC, the situationchanges considerably. The calculated lifecapacity is well over 10 billion cycles (on thepinion). Only a little over 2 billion cycles areneeded for a life of 20,000 hours. The gear hasonly one-quarter of the pinion cycles, which isjust a little over 0.5 billion cycles. If the gear

� 1800 � 60 � No. of hours

Cycles � 1rpm 2 � 160 min>h 2 � 1No. of hours 2


Table 4 Situations and concepts of pitting failures in gearsDescription Recommended action

Situation 1

Some micropitting and a few macropits on the pinion.No gear pitting.

Scrap the pinion, even though it is still quite runnable. It may not lastuntil the next scheduled overhaul.

Situation 2

Micropitting and appreciable macropitting (e.g., 3–10% of the tooth surface of the pinion). Almost no pitting on gear.

Scrap the pinion, because metal debris in the oil system is a serioushazard to the bearings. Premature bearing failure may occur at anytime.

Situation 3

Micropitting and considerable macropitting (e.g., 15–40% of the surface). One or more gross pits. Damage to both pinion and gear.

Scrap the gears. Damage to the tooth surface may lead to toothbreakage, starting in a badly pitted location.

Situation 4

Macropitting over 50–100% of the pinion tooth surface. Gross pitting present. Removal of metal thins the teeth and disrupts load sharing between teeth. Gear unit has greatly increased noiseand vibration.

Scrap the gears. Complete failure is imminent. Foundation bolts maybreak. Bearings are probably in the process of failure.

Situation 5

Macropitting all over the teeth. Also considerable gross pitting. Teeth are thinned so much by wear that the tips are becoming sharp like a knife.

Scrap the gears. A thinned tooth may roll over and jam the drive—if itdoesn’t break off first.

hardness is the same as that of the pinion, thegear certainly has adequate capacity.

Derating Factors. In the above calculation,the derating factor (Cd) of 2.50 may seem highbut can be explained. The values given in Table3 are based on an assumption of average condi-tions and a failure from pitting conditions of sit-uation 1, 2, or 3 (see Table 4 and later discus-sions). A derating factor lower than 2.0 mayeven be acceptable for a 2 in. (50 mm) pinion ifthe driving and driven units are very light (lowmass) and run very smoothly. When a low der-ating factor such as 1.5 is used, there is usuallyfairly extensive pitting. If the concept of a “fail-ure” is situation 4 or 5 (Table 4), field experi-ence may show that the gears can survive eventhough the derating is too low for situationssuch as situations 1, 2, and 3 in Table 4.

If a derating factor of 1.50 had been used, thecalculated stress at 10 billion cycles would bereduced by the square root of the change in thederating factor. This works out to (1.50/2.50)0.50

= 0.775. This makes the calculated contactstress drop to 83,220 psi. At this value, athrough-hardened steel at 300 HB has a life ofover 10 billion cycles. This is enough for a lifeof 20,000 hours.

Now consider the variables for the 2.50 der-ating factor. The first of three major factors is aderating factor of 1.4 for typical experience with

industrial fan drives. These run somewhatrough, and gear people evaluate this as a 1.4application factor.

With a face width equal to the pitch diameter,there will normally be some misfit across thewide face. In addition, the accuracy of toothspacing will not be close to perfect. For anindustrial application, the tooth spacing accu-racy is probably AGMA quality level 9. Thisrequires a derating factor of about 1.4 for smallgearing such as a 2 in. (50 mm) pinion.

It is also necessary to consider dynamic over-load due to the masses in the drive system andthe tooth spacing accuracy. In this sample prob-lem, the 2.125 pitch diameter pinion running at1800 rpm has a pitch line velocity of 1073ft/min (327 m/min). This kind of drive at thisspeed could be expected to have a dynamicoverload factor of 1.00/0.80 = 1.25.

The overall derating factor is obtained bymultiplying these three factors such that 1.4 ×1.4 × 1.25 = 2.45 (this is rounded off to 2.50).

For the values shown in Fig. 6, the geometryfactor (Ck) may look quite conservative whencompared to values used in bearing design. Partof this is due to the relatively high component ofsliding in gear tooth contacts. For spur and hel-ical gearing, pure rolling occurs only at the pitchline. Above and below the pitch line there isappreciable sliding. Also, the geometric shape


of bearings is simpler than that of toothed gears.This helps in both quality of fit and quality con-trol of material.

Another factor in comparing rolling elementbearings to gears is probability of failure. Bear-ings are considered somewhat expendable andare generally designed with a probability of fail-ure of 10 in 100 rather than the 1 in 100 that isnormal for gearing. In some cases of expendablegearing, a factor of 10 failures in 100 is used forthe rating curve. If Fig. 6 was redrawn for the 10to 100 probability, all curves shown wouldallow about 17% more stress. The approximatelife for a stress of 107,380 psi (740 MPa) worksout as follows:

Approximate life at probability of failure of:

Hardness, HB 1 out of 100 10 out of 100

210 1.1 million cycles 20 million cycles300 180 million cycles 3.5 billion cycles

Pitting Failure. The degree of risk to beassumed in a gear design is a most importantconsideration. The above results show morethan a 15 times longer life by going from a verylow risk of failure to a still somewhat low risk offailure. If a 10 out of 100 degree of risk was tol-erable, then the gear set being considered wouldhave adequate pitting life for 20,000 hours at300 HB.

The concept and definition for contact stressof pitting failures is another very significant con-sideration. Pitting failure is not easy to define,and a gear designer needs to use judgment basedon experience. In general, a pitted gear tooth willstill run, whereas broken-off gear teeth will sodamage a gear that it is either impossible orimpractical to continue to operate the gear unit.

Table 4 shows five different levels of toothdamage due to pitting that govern whether ornot a pinion and a mating gear have failed bypitting. In aircraft or space vehicle gearing, sit-uation 1 is cause for failure. In long-life turbinegearing, situation 2 is quite apt to be considereda failure. According to the calculated life givenearlier in this chapter, the gear failed when itreached situation 3.

In some factory and farm applications, gearsthat have reached situation 4 are still kept inservice. The cost of replacement and a forgivingenvironment where noise and vibration can betolerated may prompt the gear user to keep run-ning the gears. Situation 5 is the ultimate. If thepinion won’t turn under power or the pinion

does turn and the gear does not turn, there is justno question about the gears having failed.

From what has been discussed so far, themethod used in the gear trade to calculate gearlife should be quite clear. It should be evident,though, that much experience and judgment areneeded to properly decide when a pitted andworn gear should be taken out of service andscrapped.

Although there are good guidelines for eval-uating the things that derate gears, it still takesmuch data and experience to set numerical val-ues that are just right for a particular productapplication. For instance, long-life turbine gear-ing is very expensive, and downtime in rebuild-ing a broken main gear drive may be much moreexpensive than replacing a gear unit. Thismeans that the designer of turbine gearing isvery concerned about having an adequate over-all derating factor and close control over gearmaterial quality. Grade 2 material is often spec-ified rather than grade 1 material. Grade 2 steelis rated to carry about 25% more contact stressthan grade 1 when carburized but only about10% more stress when through hardened.

In the vehicle field (trucks, tractors, and auto-mobiles), gearing is not highly expensive and areplacement gear unit can often be installedwithin a few hours. The designer of the gearsmay use a relatively low overall derating. Thedesigner learns by thousands of similar units inservice how to set the derating factor and how tocontrol geometric quality and material qualityso that adequate gear life is obtained.

The standards of the American Gear Manu-facturers Association (AGMA) give recommen-dations for how to rate many kinds of gears andhow to specify geometric and material quality.AGMA standards define established gearingpractices for the gear trade. In the industrial field,contracts for geared machinery generally spec-ify that the gearing supplied must be in accor-dance with applicable AGMA standards.

The allowable contact stress for gears made ofgrade 1 material (per Ref 2) is drawn for thelubrication condition of regime III (full oil film).Many gears that are small and run at relativelyslow pitch line speeds are in regime II (partial oilfilm) or regime I (wet with oil but with almost noelastohydrodynamic (EHD) oil film thickness).

As of December 1995, there is no nationalstandard for how to rate gears for allowable con-tact stress when they are in regimes II or I.There is much field experience, though, withgears running with an inadequate EHD oil film


thickness. Work is underway to add material toAGMA standards to cover the problem of aninadequate oil film thickness.

Figure 7 shows how the allowable contactstress may change for grade 1 carburized steelgears at 60 HRC. Note the dashed curves forregimes II and I.

Life Determined by Bending Stress

The bending stress of a pinion or a matinggear tooth (Ref 1, 2) may be estimated by a sim-plified formula:

(Eq 5)

where Kt is a geometry factor (see Table 5), Ulis the index of tooth loading severity for break-age (see Eq 6 below), and Kd is the overall der-ating factor for bending stress (see footnote inTable 3). The bending stress derating factor (Kd)is approximately the same as the overall derat-ing factor (Cd) unless there is a wide face width.When the aspect ratio is around 0.25, the Cd forcontact stress and the Kd for bending stress areabout equal. At an aspect ratio of 1.0, Kd may beabout 80% of Cd.

St � KtUlKd

The index of tooth loading for breakage isoften called “unit load.” Its value for spur or hel-ical teeth is:

(Eq 6)

where Wt is the tangential driving force (samevalue as in Eq 3), F is the net face width in con-tact, and Pn is the normal diametral pitch (1/in.).

Pn is the inverse of the tooth size in a planenormal to a helical tooth. The diametral pitch(Pd) is the inverse of the tooth size in a planenormal to the axis of gear. The relation betweenthe two is:

(Eq 7)

The tangential load for tooth strength is thesame quantity as the tangential load used forcontact stress calculations (Eq 3).

The derating factor for strength is sometimestaken as the same value as is used for surfacedurability. In some cases of gears with favorablecontact ratios, there may be justification to use asomewhat lower derating factor for strength.The points of high beam stress are some dis-tance away from the points of maximum contactstress. This tends to allow the beam stress to

Pd � Pn cos 1helix angle, ° 2

Ul �Wt Pn

F

Fig. 7 Regimes of lubrication for carburized gears of normal industry quality material (Grade 1 material, per Ref 2)


spread out more than the contact stress. (In thisbrief chapter it is not practical to show how toreduce the derating factor for the tooth strengthcalculations.) For the sample problem below itis reasonable to use Kd = 2.0. (The pitting derat-ing, Cd, was 2.5.)

Example 2: Rating Gear Life with BendingStress. In Example 1 of this chapter, thenumerical values are Wt = 922.4 lb, Pn = 10, andF = 2.28. For the data just given, the unit loadindex is:

The geometry factor is taken as 1.75 (see Table5). The calculated bending stress becomes:

� 14.159 psi 197.6 MPa 2St � 1.75 � 4045.4 � 2.0

Ul �922.4 � 10

2.28� 4045.4 psi 127.9 MPa 2

The tooth bending stress can now be used todetermine allowable cycles from a rating curve,such as Fig. 8. Figure 8 shows typical bendingstresses plotted against tooth contacts. Thiscurve sheet is drawn for gearing having thesequalifications:

• Material quality: Grade 1• Probability of failure: Not over 1 in 100• Lubrication: Full oil film, which is regime

III• Hardness: Both pinion and mating gear at

least as hard as value shown on bendingstrength figure (Fig. 8)

The expected life of both the pinion and thegear, from a tooth breakage standpoint, can nowbe determined for the calculated stress of 14,159psi (97.6 MPa) for the pinion and a calculatedstress of 14,321 psi (98.7 MPa) for the gear.(The gear has the same unit load as the pinion

Table 5 Some typical geometry factors (Kt) for strengthStandard addendum

ap = 1.000, aG = 1.000, ap = 1.250, aG = 0.750,

whole depth 2.35 whole depth 2.35


25 35 2.72 2.55 2.37 3.0025 50 2.68 2.42 2.33 2.7425 85 2.62 2.22 2.30 2.5435 35 2.50 2.50 2.21 2.9035 50 2.42 2.30 2.18 2.7035 85 2.36 2.15 2.15 2.5435 275 2.20 2.00 2.10 2.45


20 35 2.42 2.16 2.08 2.4220 50 2.38 2.01 2.05 2.2220 85 2.35 1.90 2.03 2.0925 35 2.26 2.10 2.00 2.4025 50 2.23 1.97 1.95 2.2025 85 2.20 1.86 1.91 2.0535 35 2.06 2.06 1.88 2.3435 50 2.02 1.92 1.84 2.1535 85 1.99 1.80 1.80 2.0035 275 1.90 1.70 1.75 1.82


25 35 1.93 1.83 1.74 2.0525 50 1.90 1.76 1.72 1.8825 85 1.87 1.67 1.71 1.7535 35 1.82 1.82 1.68 1.9735 50 1.78 1.73 1.65 1.8235 85 1.75 1.64 1.62 1.73


25 35 1.60 1.52 . . . . . .25 50 1.57 1.47 . . . . . .25 85 1.54 1.40 . . . . . .35 35 1.50 1.50 . . . . . .35 50 1.42 1.42 . . . . . .35 85 1.35 1.34 . . . . . .

25% long addendum

No. of gear teethNo. of pinion teeth


and the same derating factor. However, thegeometry factor for the gear from Ref 1 is 1.77,compared to 1.75 for the pinion.)

Based on Fig. 8, the pinion stress of 14,159psi (97.6 MPa) is well below all the curves. If apinion life of 20,000 hours was desired, thebending stress allowable could be about 23,000psi (158.5 MPa) even for the through-hardened,210 HB steel. This means that with 22 pinionteeth, the “life” of the pinion is determined bypitting and not by tooth breakage.

Suppose the pinion had the same diameter buthad 40 teeth instead of 22 teeth. The bendingstress would increase, because the normaldiametral pitch would be about 18. The deratingwould not change for an increased number ofteeth, and the geometry factor would tend todecrease a small amount. This means that a 40-tooth pinion meshing with a 160-tooth gearwould have a calculated bending stress of about22,300 psi (153.8 MPa).

If the normal diametral pitch was changed to18.18182, the pitch diameters of the pinion andgear would not change with 40 pinion teeth anda 15° helix. The K-factor for pitting would notchange, and the change in the geometry factorfor durability would be a small decrease. Thismeans that it is possible to change numbers ofteeth to adjust bending stress and not have muchchange in the contact stress.

In this sample problem, “life” determined bycontact stress is very short at 210 HB, but it isalmost enough for 2000 hours at 300 HB. Thepinion could have 40 teeth at 300 HB becausethe allowable bending stress is up to 32,000 psi(220 MPa) at 2000 hours (216 × 106 millioncycles). With the bending stress at 24,274 psi(167.4 MPa) there is a modest amount of extramargin in bending strength, but not nearly asmuch as at 22 teeth.

From a practical standpoint, it is quite desir-able to control the life of a gear set and have anappreciable extra margin of bending strength.Having lots of small teeth instead of fewer andlarger teeth is not desirable from two otherstandpoints: in general, parts with fewer teethcost less to make; and larger teeth can standsomewhat more wear.

In summary, this example shows that 22 teethon a pinion is a reasonable design. There is nogood reason to use 40 teeth, even though thebending stress would be allowable.

Gear Tooth Failure by Breakage after Pitting

The preceding section covered tooth break-age by the tensile stress in the root fillet.Another kind of common tooth breakage in

Fig. 8 Bending strength curve for gear life rating of normal industry quality material (Grade 1 per Ref 2)


gearing starts somewhat high on the tooth pro-file rather than in the root fillet. When a gear isdamaged by pitting, a crack can start at a pit,spread lengthwise, and go all the way throughthe tooth. On wider-face-width gears, a triangu-lar piece of tooth often breaks out. This piecemay be as wide as one-third or one-half of theface width. The break may progress as deep asthe root fillet at one end and run out at the out-side diameter at the other end. The “eye” wherethe crack started may be at the pitch line, or itmay be in the lower flank of the tooth.

If a pinion or gear continues in service afteran appreciable part of the tooth is gone, thenow-overloaded remainder of the tooth is likelyto break off. Sometimes, even though severalteeth have portions broken off, the gears con-tinue in service because the increased noise andvibration are not enough to attract attention.Then one or more teeth are completely removedby successive chunks breaking off (see Fig. 9).

In narrow-face-width gears, such as thosewhere the face width is about equal to the toothheight, a break starting at a pit tends to removethe tooth across the whole face width.

The normal calculation of bending stresses isnot useful in designing gears to avoid toothbreakage starting at pits. The logic of this kindof trouble must be considered an incident oftooth breakage caused by pitting.

Gears that are case hardened by carburizingare the most susceptible to this trouble. Gearswith a nitrided case are not quite as susceptiblebecause the nitrided case depths tend to be thin-ner. A pit in a thin case is not quite as great astress riser as a pit in a deep case. To prevent pit-ting altogether, though, deep carburized casedepths may be needed.

Through-hardened gears in the 300 to 400HB range are also quite critical. In general,gears are not used that are around 500 HB. At450 HB and higher, a through-hardened gear isusually so brittle that it will fracture with even asmall amount of surface distress.

The concepts of pitting failure given in Table4 are quite useful in regard to the risk of toothbreakage stemming from pitting. In situation 1,the pitting is relatively minor, so there is verylittle danger of tooth breakage starting at a pit.

In situation 2, there is a moderate risk of somearea on the tooth surface having enough macro-pits to start a tooth breakage crack when the pin-ion or gear has a carburized case. Through-hard-ened parts at 300 HB are not so notch sensitiveand will probably not develop cracks from pits.Through-hardened parts at 210 HB are notnotch sensitive. There is not much risk of cracksfrom pits at this level of hardness.

In situation 3, the much heavier pitting isquite risky for carburized gear teeth and moder-ately risky for through-hardened gears at 300HB. However, through-hardened gears at 210HB do not have much risk.

In some special cases where the pinion is quitehard (e.g., 360 HB) and the gear is much lower inhardness (e.g., 300 HB), there may be such seri-ous ledge wear on the gear due to micro- andmacropitting that a whole layer of metal is wornaway from the gear tooth. This can result in theaddendum of the gear being forced to carry allthe load. This tends to double the stress in thegear root fillet, and gear teeth then break off dueto the greatly increased stress.

Ledge wear that occurs in helical gears over along period of time is not too dangerous if boththe pinion and gear have about the same amountof wear. The big danger of tooth breakage comeswhen one pitted gear has little or no ledge wearand the mating gear has serious ledge wear. Fig-ure 10 shows an example of a gear tooth withledge wear and in danger of breaking. (The pin-ion that mated with this gear had some pitting butessentially no ledge wear.)

In situations 4 and 5, hard gears cannot sur-vive without tooth breakage. Low-hardness

Fig. 9 End of tooth broken because of gross pitting. Notecracks in remaining part of tooth.


gears that run at relatively slow pitch line speedsoften survive for years without tooth breakage,even though the pitting and wear are severe.

In summary, tooth breakage due to pitting isa high risk with hard gears and may not be muchof a risk if the gears are of low hardness and notrunning fast.

Flaws and Gear Life

Metallurgical flaws may seriously reduce thelife of gears. The calculations for the life of gearteeth assume that the material in the gear is notflawed by a mistake in processing the part. If thematerial is grade 1 (normal industrial quality perRef 2) the quality is not as good as for grades 2(extra high quality for high speed, long lifegearing per Ref 2) or 3 (super quality for criticalaerospace gearing per Ref 2), but it is assumedthat the quality is normal for the grade specified.For instance, the microstructure for grade 1 isnot specified to a limit as close as that for grade2. Also, the cleanliness of the steel in grade 1does not have to be as good as the cleanlinessfor grades 2 or 3.

Some of the more common flaws that affectthe life of gear teeth are:

• Case depth for carburized, nitrided, or in-duction-hardened teeth too thin or too thick

• Grinding burns on case-hardened gears• Nonhomogenous structure, voids, hard

spots, soft spots, etc.• Alloy segregation• Core hardness too low near the root diame-

ter or at the middle of the face width• Forging flow lines pronounced and in the

wrong direction

• Quenching cracks• Composition of steel not within specifica-

tion limits

When gears fail prematurely, the normal firststep of an investigator is to make some calcula-tions of gear life to see if the gear unit size waslarge enough for the rated life. If these calcula-tions show that a gear unit rated for somethinglike 10 years of life was indeed large enoughand had the right materials specified, then itbecomes a matter of concern to investigate fac-tors such as lubrication system, behavior ofdriving and driven equipment, operating envi-ronment, and material quality (perhaps someserious metallurgical flaw (or flaws) exist).

Quite often the case depth is not right. Thegear drawing should specify the right case depthfor the midpoint of the tooth flank. Besides themiddle of the tooth, the case depth needs to beright at the lower flank of the tooth. The casedepth at the tip of the tooth is also critical.

The case depth may be right at midheight buttoo thin at the lower flank and root fillet. This isoften caused by inadequate carbon gas penetra-tion between teeth. In large gears, heat soakback after quenching may reduce the hardnessconsiderably. Too much case depth at the toothtip may cause the tooth tips to be so brittle thatthey break off in service. (This has happened offand on in gears used in mining.)

If large, through-hardened gears are quenchedtoo drastically, there may be hidden cracks in thegear body. On the other hand, an inadequatequench may cause the hardness of the gear teethto be below specifications in the middle of theface width or near the root diameter of the teeth.

Case-hardened gears can be ground by sev-eral different methods. There is always a risk of

Fig. 10 Helical gear with serious ledge wear due to micro- and macropitting


grinding too fast or having inadequate coolingat the grinding location. Grinding burns andgrinding cracks must be avoided to get thepotential life out of the gears.

When scrap material is melted to make steel,there is a hazard that something in the melt willproduce a local hard spot or a local soft spot.There may also be stringers of inclusions. Thereis a well-developed art of producing steel ingotsthat can be made into steel billets of uniformgood material for a toothed gear. Good gearsrequire good steel.

When gear parts are forged, the flow lines inthe forging should not be in the wrong directionat critical stress points, such as the root fillet ofa gear tooth or where a thin web meets a thingear rim. Rolled bar stock that is not forged mayhave flow lines in the wrong direction for a crit-ical gear part. Normal gear rating practice isbased on the assumption that the forging orrolling of the stock to make the gear blank isdone right for the configuration of the gear part.

Another flaw to be concerned about is thechemical composition of the steel in the gear.Sometimes mistakes are made and the steel fora gear is taken out of the wrong bin. Through-hardening steels have different compositionsthan case-hardening steels.

Sometimes an improper substitution is made.For example, it quite often happens in world-wide operations that a readily available localsteel is substituted for the specified steel thatwas just right for the rating and method of man-ufacturing used in another country. It is thenquite a shock to have gears failing in a year ortwo that should have lasted for 10 or more years.

Bores and Shafts

Besides proper gear design, geometric accu-racy, and good gear material, associated compo-nents in a gear train can also be important. Thissection briefly reviews some components in thedesign and structure of each gear and/or geartrain that must be considered in conjunctionwith the teeth.

A round bore, closely toleranced andground, may rotate freely around a ground shaftdiameter, rotate tightly against a ground diame-ter by having a press fit, or be the outer race of aneedle bearing that gives freedom of rotation.Each application has unique problems. A groundbore is always subject to tempering, burning, andchecking during the grinding operation. A freelyrotating bore requires a good lubrication film, or

seizing and galling may result. The bore used asa bearing outer race must be as hard as any stan-dard bearing surface and is subject to all condi-tions of rolling contact, such as fatigue, pitting,spalling, and galling. The bore that is press fitonto a shaft is subject to a definite amount of ini-tial tensile stress. Also, any tendency for the boreto slip under the applied rotational forces will setup a unique type of wear between the two sur-faces that leads to a recognizable condition offretting damage.

A spur of a helical round bore gear acting as anidler, or reversal, gear between the input memberand the output member of a gear train has anextremely complicated pattern of stresses. Themost common application is the planet piniongroup in wheel-reduction assemblies or in plan-etary-type speed reducers. Typical stress pat-terns are as follows:

• The tensile and compressive stresses in thebore are due to bending stresses of the gearbeing loaded as a ring.

• The maximum tensile and compressivestresses in the bore increase as the load onthe teeth increases.

• The maximum tensile and compressivestresses in the bore increase as the clearancebetween the bore and the shaft is increased.

• The maximum tensile and compressivestresses in the bore increase as the ratio ofthe size of the bore to the root diameter ofthe teeth is increased.

• During one revolution of the gear underload, the teeth go through one cycle of com-plete reversal of stresses, whereas each ele-ment of the bore experiences two cycles ofreversals.

Three modifications of the round bore alterstress patterns considerably:

• Oil holes that extend into the bore areintended to lubricate the rotating surfaces.Each hole may be a stress raiser that couldbe the source of a fatigue crack.

• Tapered bores are usually expected to beshrink fitted onto a shaft. This sets up a veryhigh concentration of stresses, not onlyalong the ends of the bore but also at thejuncture on the shaft.

• A keyway in the bore also creates a stress-concentration area. A keyway is also re-quired to withstand a very high load that iscontinuous. In fact, the applied load to theside of the keyway is directly proportional tothe ratio of tooth pitchline radius to the


radius of the keyway position. Fatigue fail-ure at this point is common.

Splined Bores. The loads applied to thesplined-bore area are also directly proportionalto the ratio of pitchline radius of the teeth to thepitchline radius of the splines. However, theload is distributed equally onto each spline;therefore, the stress per spline is usually notexcessive. It is possible for an out-of-round con-dition to exist that would concentrate the loadon slightly more than two splines. Also, atapered condition would place all loadings atone end of the splines, which would be detri-mental both to the gear splines and to the shaft.

Heat treating of the splined area must bemonitored closely for quench cracks. Grindingof the face against the end of the splines can alsocause grinding checks to radiate from the cor-ners of the root fillets.

Shafts. The shafts within a gear train, aswell as the shank of a pinion that constitutes ashaft in function, are very important to load-car-rying capacity and load distribution. They arecontinually exposed to torsional loads, both uni-directional and reversing. The less obviousstressed condition that is equally important isbending. Bending stresses can be identified asunidirectional, bidirectional, or rotational.When the type of stress is identified, one canexplore the causes for such a stress.

There can be a number of stresses applied toa shaft that are imposed by parts riding on it. Forexample, helical gears will transmit a bendingstress, as will straight and spiral bevel gears;round bores may be tight enough to cause scor-ing and galling; a splined bore may cause highstress concentration at the end face; runout ingears may cause repeated deflections in bendingof the shaft; and loose bearings may causeexcessive end play and more bending.

ACKNOWLEDGMENT

This chapter was adapted from D.W. Dudley,Fatigue and Life Prediction of Gears, Fatigueand Fracture, Vol 19, ASM Handbook, ASMInternational, 1996, p 345–354

REFERENCES

1. D.W. Dudley, The Handbook of PracticalGear Design, Technomics Publishing Co.,Inc., Lancaster, PA, 1994

2. Fundamental Rating Factors and Calcula-tion Methods for Involute and Helical Gear

Teeth, ANSI/AGMA 2001-C95, AmericanGear Manufacturers Association

SELECTED REFERENCES

Fatigue of Gears

• B. Abersek, J. Flasker, and J. Balic, Theo-retical Model for Fatigue Crack Propaga-tion on Gears, Conf. Proc. Localized Dam-age III: Computer-Aided Assessment andControl, Computational Mechanics Publi-cations, Billerica, MA, 1994, p 63–70

• A.Y. Attia, Fatigue Failure of Gears of Cir-cular-Arc Tooth-Profile, J. Tribol., Vol 112(No. 3), 1990, p 453–459

• G.P. Cavallaro et al., Bending Fatigue andContact Fatigue Characteristics of Carbur-ized Gears, Surf. Coat. Technol., Vol 71(No. 2), 1995, p 182–192

• G. Dalpiaz and U. Meneghetti, MonitoringFatigue Cracks in Gears, Nondestr. Test.Eval. Int., Vol 24 (No. 6), 1991, p 303–306

• J. Flasker and B. Abersek, Determinationof Plastification of Crack Tip of Short andLong Fatigue Crack on Gears, Conf. Proc.Computational Plasticity: Fundamentalsand Applications, Pineridge Press Ltd.,Mumbles, Swansea, U.K., 1992, p1585–1595

• Y. Jia, Analysis and Calculation of FatigueLoading of Machine Tool Gears, Int. J.Fatigue, Vol 13 (No. 6), 1991, p 483–487

• B. Jiang and E.A. Shao, Rapid Method forMeasurement of Rolling Contact FatigueLimit of Case-Hardened Gear Materials,ASTM J. Test. Eval., Vol 18 (No. 5), 1990,p 328–331

• B. Jiang, X. Zheng, and M. Wang, Calcula-tion for Rolling Contact Fatigue Life andStrength of Case-Hardened Gear Materialsby Computer, ASTM J. Test. Eval., Vol 21(No. 1), 1993, p 9–13

• B. Jiang, X. Zheng, and L. Wu, Estimate byFracture Mechanics Theory for RollingContact Fatigue Life and Strength of Case-Hardened Gear Materials with Computer,Eng. Fract. Mech., Vol 39 (No. 5), 1991, p867–874

• G. Mesnard, Super Puma MK II: Rotor andGearbox Fatigue, Conf. Proc. ICAF ’91:Aeronautical Fatigue—Key to Safety andStructural Integrity, Ryoin Co., Tokyo,1991, p 195–215

• M. Nakamura et al., Effects of AlloyingElements and Shot Peening on Fatigue


Strength of Gears, Kobelco Technol. Rev.,No. 16, 1993, p 14–19

• Y. Obata et al., Evaluation of Fatigue CrackGrowth Rate of Carburized Gear byAcoustic Emission Technique, AcousticEmission: Current Practice and FutureDirections, STP 1077, ASTM, 1989, p261–270

• Y. Okada et al., Fatigue Strength Analysisof Carburized Transmission Gears, JSAERev., Vol 11 (No. 3), 1990, p 82–84

• W. Pizzichil, Testing Gear Teeth for Low-Cycle Fatigue and Static Bending Strength,Heat Treating, Vol 24 (No. 2), 1992, p14–20

• H.J. Rose, Vibration Signature and FatigueCrack Growth Analysis of a Gear ToothBending Fatigue Failure, Conf. Proc. Cur-rent Practices and Trends in MechanicalFailure Prevention, Vibration Institute,Willowbrook, IL, p 235–245

• M. Roth and K. Sander, Fatigue Failure ofa Carburized Steel Gear from a HelicopterTransmission, Handbook of Case Historiesin Failure Analysis, Vol 1, ASM Interna-tional, 1992, p 228–230

• G.M. Tanner and J.R. Harty, ContactFatigue Failure of a Bull Gear, Handbookof Case Histories in Failure Analysis, Vol2, ASM International, 1993, p 39–44

• D.P. Townsend, “Improvement in SurfaceFatigue Life of Hardened Gears by High-Intensity Shot Peening,” TM-105678,National Aeronautics and Space Adminis-tration, 1992

• D.P. Townsend and J. Shimski, “Evalua-tion of Advanced Lubricants for AircraftApplications Using Gear Surface FatigueTests,” TM-104336, National Aeronauticsand Space Administration, 1991

• V.I. Tsypak, Fretting Corrosion andFatigue of Gears, Mater. Sci. (Russia), Vol29 (No. 6), 1993, p 680–681

• J.-G. Wang, Z. Feng, and J.-C. Zhou, Effectof the Morphology of Carbides in the Car-burizing Case on the Wear Resistance andthe Contact Fatigue of Gears, J. Mater.Eng. (China), Dec 1989, p 35–40

• T.P. Wilks et al., Conditions Prevailing inthe Carburising Process and Their Effect onthe Fatigue Properties of Carburised Gears,

J. Mater. Process. Technol., Vol 40 (No.1–2), 1994, p 111–125

• J.J. Zakrajsek, D.P. Townsend, and H.J.Decker, An Analysis of Gear Fault Detec-tion Methods as Applied to Pitting FatigueFailure Data, Conf. Proc. The SystemsEngineering Approach to Mechanical Fail-ure Prevention, Vibration Institute, Wil-lowbrook, IL, p 199–208

Gear Durability and Failure

• J.W. Blake and H.S. Cheng, A Surface Pit-ting Life Model for Spur Gears, Part II:Failure Probability Prediction, J. Tribol.,Vol 113 (No. 4), 1991, p 719–724

• R. Gnanamoorthy and K. Gopinath, Sur-face Durability Studies on As-SinteredLow Alloy Steel Gears, Non-FerrousMaterials, Vol 6, Advances in Powder Met-allurgy & Particulate Materials, MetalPowder Industries Federation, 1992, p237–250

• G.M. Goodrich, Failure of Four Cast SteelGear Segments, Handbook of Case Histo-ries in Failure Analysis, Vol 2, ASM Inter-national, 1993, p 45–52

• C. Madhavan and K. Gopinath, SurfaceDurability of Through-Hardened P/MGears, Powder Met. Sci. Technol., Vol 2(No. 4), 1991, p 30–44

• T. Nakatsuji, A. Mori, and Y. Shimotsuma,Pitting Durability of Electrolytically Pol-ished Medium Carbon Steel Gears, Tribol.Trans., Vol 38 (No. 2), 1995, p 223–232

• H.V. Somasundar and R. Krishnamurthy,Surface Durability of HSLA Steel Gears,Conf. Proc. Ninth National Conference onIndustrial Tribology, Central MachineTool Institute, Bangalore, India, 1991, pM87–M95

• Y.L. Su, J.S. Lin, and S.K. Hsieh, The Tri-bological Failure Diagnosis of Spur Gearby an Expert System, Wear, Vol 166 (No.2), 1993, p 187–196

• A. Verma and R.K. Sidhu, Failure Investi-gation of Gears, Tool and Alloy Steels, Vol27 (No. 6), 1993, p 157–160

• K. Wozniak, Worm Gears of IncreasedDurability, Archiwum Budowy Maszyn,Vol 38 (No. 1), 1991, p 5–13

CHAPTER 15

Mechanical Testing

MECHANICAL TESTS are performed toevaluate the durability of gears under load. Oneof the primary uses of gear testing is to generateperformance data, which are used to developdesign-allowable stresses. Design-allowablestresses are used as a guide for determining thesize, geometry, material, manufacturing pro-cess, and process conditions for new designsduring the design process. Gear testing is alsoused to compare the performance of a new attrib-ute or characteristic introduced in the gear to abaseline, which defines the part performancewith the old or existing attributes or characteris-tics. These new attributes or characteristics maybe related to tooth geometry, gear material, man-ufacturing processes, and even process parame-ters used to manufacture the gear. In the aero-space industry, gear testing forms the minimumbasis for accepting a change in these characteris-tics and is usually termed “qualification” of aproposed or recommended change.

Mechanical testing of gears is conductedunder different scenarios. The first scenario istermed rig testing, which is extensively dis-cussed and defined in this chapter. In rig testing,the gear is subjected to simulated loading thatexercises a distinct mode of gear failure. Whilethis simulation may not always be successful fora variety of reasons, data on the resistance of thegear to a distinct mode of failure allow theanalysis of the specific characteristics that needto be altered to change its performance.

After rig testing is complete, it is customary toincorporate the gear into a transmission and sub-ject the transmission to bench testing. In benchtesting, the input and output of the transmissionunder test are simulated using various devicesfor power input and absorption. After bench test-ing, it is not unusual to subject the transmissionto full-scale testing, where the transmission issubjected to controlled but actual operating con-

ditions to determine the performance of the spe-cific gear. Both bench and full-scale testing rep-resent very specific application-oriented testingand are usually carried out by the organizationmanufacturing a specific product. It is obviousthat rig testing, bench testing, and full-scale test-ing represent increasing orders of cost. Conse-quently, in most situations, extensive rig testingis followed by limited bench testing and evenmore limited full-scale testing. While the testingmethods described in this chapter are particu-larly applicable to carburized and hardened steelgears, the described techniques are applicable tothrough-hardened steel and gears fabricatedfrom other materials, with modifications.

Common Modes of Gear Failure

Gear tooth failures occur in two distinct re-gions—the tooth flank and the root fillet. Bothof these types of failures are briefly described inthis section. More detailed information can befound in Chapter 14, “Gear Failure Modes andAnalysis,” and in Ref 1–6.

Failure Modes on Tooth Flanks. In order tounderstand the common modes of failure ontooth flanks, it is important to study the kinemat-ics of a gear mesh, illustrated in Fig. 1 for a pairof spur gears. For the direction of rotationshown, contact starts at the left side of the figureand progresses to the right. Initial contact occurswell below the pitch diameter of the drivingtooth and well above the pitch diameter of thedriven tooth. There is significant sliding alongwith rolling contact at this point. Sliding on thesurface of the driving gear is in the same direc-tion as rolling. As rotation continues, the point ofcontact moves toward the tip of the driving gearand toward the root of the driven gear. Slidingdecreases as the point of contact moves toward




the pitch diameter, reaching zero (pure rolling)at the pitch diameter. As the point of contactmoves above the pitch diameter of the drivinggear, the direction of sliding reverses. At the endof contact, significant sliding again occurs. Testshave shown that sliding in the same direction asrolling (as occurs below the pitch diameter of thedriving gear) has a more severe effect on the sur-face durability of the material.

Failure modes on tooth flanks are caused bythis combination of rolling and sliding. Themore common failure modes are scoring (orscuffing), wear, and pitting.

Failure Modes in Root Fillets. Failure ofthe gear tooth also can occur in the root fillet.This failure is primarily due to bending fatiguebut can be precipitated by sudden overloading(impact). Sudden overloads can be caused by alarge foreign object (e.g., a broken tooth) beingdrawn through the mesh, the driving or drivenshafts suddenly stopping, or sudden loss ofalignment (failure of an adjacent bearing).

Stress Calculations for Test Parameters

Gear-rating standards, such as AmericanNational Standards Institute (ANSI)/American

Gear Manufacturers Association (AGMA)2001-C95 (“Fundamental Rating Factors andCalculation Methods for Involute Spur and Heli-cal Gear Teeth”) and International Organizationfor Standardization (ISO) 6336, base gear per-formance on contact and bending stresses. Nom-inal stresses are determined from first principlesand are then modified to allow for the realities ofmanufactured gears running in actual gearboxes.This modification approximates a reasonableupper limit for the range of stress variation.

ANSI/AGMA 2001-C95 contains factors inthe fundamental stress formulas for contact andbending to address overload, gear dynamics,size, load distribution, surface condition (con-tact only), and rim thickness (bending only).Design-allowable stress numbers are modifiedby further factors that address intended life,operating temperature, reliability, safety factor,and hardness ratio (contact only). It is normalpractice in determining stresses to be reportedwith rig test results to take all of these factors asunity. The intent of rig testing is to compare theeffect of various attributes or characteristics onperformance. Thus, it is reasonable to determinethe actual stress based on a value of unity foreach factor, then determine suitable values forthe factors based on test results.

Fig. 1 Kinematics of a gear mesh

Chapter 15: Mechanical Testing / 313

The factors that are in essence being ignoredby this approach represent real phenomena thatoccur as gears operate. It is critical to addressthis fact in the design of test rigs and in theirday-to-day operation. For example, it is impor-tant to conduct tests in a manner that precludesoverloading; in a set of tests intended to evalu-ate the effect of overloading, only controlledoverloads can be permitted. Most of the otherfactors can be handled in the same manner.However, gear dynamics and load distributionneed to be addressed in a more direct fashionbecause they both can introduce uncontrolledvariation in a set of test results.

Gear dynamics present a problem in deter-mining the proper stress to be related to per-formance. Rating standards provide guidanceon dynamic load variations in normal gear-boxes. Gear test rigs, as described here, load onegearbox against another to keep power require-ments to a minimum. Thus, there are two ormore sets of dynamic variations, plus their inter-actions, to be considered. If the shafts connect-ing the gearboxes are quite rigid, the dynamicloading can be greater than the applied loading,even when precision gears are tested. Owing tothe complexity of the situation, stresses for rigtests are computed making no allowance fordynamics. The fact that the dynamics of geartest rigs are not the same as real machines thatuse gears is a principal reason that bench testingand full-scale testing are required before a givengear design is adopted for critical applications.

The load distribution factor accounts for vari-ations in alignment due to deflections of teeth,gearbox, and so on for variations in axial align-ment of gear teeth, and for variations in loadsharing between teeth. Much of the variation inload distribution can be minimized by straddlemounting test gears between bearings so theiraxes remain parallel under loading, modifyingthe profiles of test gears to optimize load shar-ing and so on. However, concentration of con-tact load at one end of a gear tooth (due to asmall variation in axial alignment) produces abending stress concentration. To avoid this con-dition, one or both test gears can be crowned tokeep the load at the center of the face width. Inthis condition, the load-distribution factor istaken as unity for bending stress, and a suitablefactor is estimated as shown in the followingsection for contact stress. However, crowningadds an additional variable that could affect testrepeatability. It may be more expensive to accu-rately crown (and measure for verification)

these test gears. Many times it may be more fea-sible to use high-accuracy standard test gearsand very stiff (lateral) mounting to ensure uni-form load distribution.

Contact Stress Computations for GearTooth Flank. Contact stresses on the surfacesof gear teeth are determined using Hertz’s solu-tion for the stress between contacting cylinders.The equation for contact stress taken from thissolution, reduced to the simplest form applica-ble to spur gear teeth, is:

(Eq 1)

where the contact force per unit width, P�, is:

(Eq 2)

and

(Eq 3)

where B is the geometry factor, R1 is the radiusof the pinion contact surface at the point ofinterest, and R2 is the radius of the gear contactsurface at the point of interest.

(Eq 4)

where EF is the elasticity factor, E1 is the pinionmodulus of elasticity, υ1 is the pinion Poisson’sratio, E2 is the gear modulus of elasticity, and υ2is the gear Poisson’s ratio. For pinion and gear(both steel), the EF is 2290 in U.S. customaryunits (P� in lb/in., B in in.–1, and stress in psi),and EF is 190.2 in Système International d’Unités (SI) units (P� in N/mm, B in mm–1, andstress in MPa).

The most critical combination of contact loadand sliding in spur gears occurs on the flank ofthe driving gear at the lowest point of contactwith one pair of teeth in mesh (the locationlabeled “lowest single tooth contact” in Fig. 1).The radii of the contact surfaces at this point canbe determined from the corresponding rollangles for the gear and pinion. The radius ofcurvature is the roll angle (in radians) times thebase radius. The radii used in determining thegeometry factor are thus:

(Eq 5)R1 � 1OR2P � BR2

P 2 1>2 �2 � p � BRP

NP

EF � cp a 1 � y21

E1�

1 � y22

E2b d�1>2

B �R1 � R2

R1 � R2

Pinion torque

Pinion base radius � effective face width

Contact stress � 1P¿ � B 2 1>2 � EF


c1 � B � 1p � k � EF � effective face width 2 2

48 � 11 � k 2 � P¿d

1>2

(Eq 6)

where ORP is the pinion outside the radius, BRPis the pinion base radius, NP is the number of pin-ion teeth, OCD is the operating center distance,BRG is the gear base radius, NG is the number ofgear teeth, and OPA is the operating pressureangle, equal to cos–1 (BRP + BGG)/OCD.

The contact stress returned by Eq 1 is a nom-inal stress and assumes uniform distribution ofload. With crowned gears this uniform distribu-tion will not be the case. The contact areabecomes an ellipse, or in most cases, the centerportion of an ellipse, with the highest contactstress at the center of the face width and pro-gressively lower contact stress toward the ends.The proportions of the ellipse can be determinedfrom a more complex form of Hertz’s solutionto the contact stress problem. A second geome-try factor, A, related to the radius of curvaturealong the lead of the gears is needed:

(Eq 7)

where R�1 is the radius of curvature along thepinion lead, R�2 is the radius of curvature alongthe gear lead, and R� is the radius of curvaturealong the lead (only one gear crowned).

The amount of crown is usually a very smallproportion of the face width; thus, the radius ofcurvature is large, and the section that can bemeasured represents an infinitesimal angularsegment of the circle. This geometry makes itdifficult for coordinate measuring machines(CMMs) to determine the crown radius. A use-able crown radius can be determined from leadtraces and Eq 8:

(Eq 8)

The following equations regarding the con-tact ellipse are empirical in nature and assumethat the ratio B/A is appreciably greater than 20,which will be the case with most crowned gears.If this is not the case, a thorough presentation ofHertz’s contact solution, such as Ref 7, shouldbe consulted.

1effective face width 2 28 � 1average drop at ends of effective face 2

crown radius �

A �R1¿ � R2¿R1¿ � R2¿

or A �1

R¿

�2 � p � BRG

NG

R2 � sin1OPA 2 � OCD � 1OR2P � BR2

P 2 1>2 (Eq 9)

where k is the ratio of ellipse minor to majoraxis.

contact stress 1crowned 2 � contact stress �

k � a B

Ab�0.62

(Eq 10)

If the crown radii are small enough in propor-tion to the contact load and effective face width,the contact area will be an ellipse narrower thanthe effective face width. The width of the ellip-tical contact area and the corresponding contactstress for this case can be determined from Eq11, 12, and 13.

(Eq 11)

Width of contact ellipse, EW, is determined by:

(Eq 12)

(Eq 13)

These formulas can compute contact stressesfor rig test specimen gears far higher than wouldbe predicted by the load distribution factors pre-sented in gear-rating standards. The formulasare presented here to permit comparison of per-formance on a stress basis between gears withdiffering crown. Stresses determined in thismanner should be reduced by a typical load dis-tribution factor before being used to developallowable design stresses.

In most cases, there will be variation in con-tact stress between specimen gears in the samelot (and from tooth to tooth on each gear) testedat the same load. The edge break at the ends ofteeth is frequently applied in a manual opera-tion; thus, the effective face width can vary.Crown can vary from tooth to tooth on eachgear. Center distance can vary due to radialrunout in shafts and bearings. The outside diam-eter of gears can vary (as required for manufac-turing tolerance). It is important, therefore, todetermine the mean contact stress and the prob-able range of variance.

contact stress 1crowned 2 �6 � contact force

p � k � EW 2

2 � c 3 � contact force

B � 1p � k � EF 2 2 d1>3

contact force �pinion torque

pinion base radius


Fig. 2 Layout of Lewis parabola for tooth-bending stress cal-culation

load � cos1load angle 2face width

c 6 � h

s2 �tan1load angle 2

sdKf

Bending stress computations for root fil-lets are computed based on the assumption thatthe gear tooth is a cantilever beam with a stressconcentration at its supported end. AGMA rat-ing standards determine the form of the can-tilever beam from the solution presented by W.Lewis (Ref 8) and use a corresponding stressconcentration factor. ISO and Deutsche Indus-trie-Normen (German Industrial Standards)(DIN) use different proportions for the beamand determine the stress concentration factor ina different manner. Only the AGMA approachis discussed here.

Figure 2 shows a spur gear tooth with a pointload applied at the highest point of single-toothcontact. This point of loading corresponds to thehighest bending stress when there is effectiveload sharing between gear teeth. Specimengears used in rig tests should have effective loadsharing, so this is the appropriate point of load-ing for determining bending stress in rig tests.For gears tested in single-tooth bending fatigue,the actual point of loading established by thetest fixture should be used in calculating bend-ing stresses.

The Lewis parabola is drawn from the pointat which the load line intersects the center of thegear tooth and is tangent to the root fillet. Meth-ods used to lay out this parabola depend on howthe root form is generated, the particulars ofwhich are presented in detail elsewhere (Ref 9).The critical height and width are determinedfrom the Lewis parabola as shown in Fig. 2. Theangle between the load line and a normal-to-the-tooth center is termed the load angle (it differs

from the pressure angle at the point of loadingbecause of the thickness of the tooth). The bend-ing stress is thus:

(Eq 14)

where s is the critical width from the Lewisparabola, h is the critical height from the Lewisparabola, and Kf is the stress concentrationfactor:

(Eq 15)

where r is the minimum fillet radius, H is equalto 0.331 – 0.436 × (nominal pressure angle, inradians), L is equal to 0.324 – 0.492 × (nominalpressure angle, in radians), and M is equal to0.261 + 0.545 × (nominal pressure angle, inradians).

Equation 14 is derived from first principlesbut also can be derived from AGMA standardsby taking the forms of relevant formulas perti-nent to spur gears and setting all design factorsat unity. While a similar formula could bedeveloped for helical gears, testing them usuallyrepresents a step between rig testing and benchtesting, and such tests are negotiated betweenthe client and the testing laboratory.

Specimen Characterization

Specimen characterization is a critical part ofany fatigue test program because it enablesmeaningful interpretation of the results. It isimportant to know that the specimens to betested meet specifications, where key parame-ters fall in the specified range, and what the vari-ations are. Characterizations fall into four areas:dimensional, surface finish texture, metallurgi-cal, and residual stress.

Dimensional Characterization. Basic di-mensional checks include size and alignment ofmounting surfaces, size and alignment of testsurfaces relative to mounting surfaces, and sizeand uniformity of edge breaks at the edges oftest surfaces. These checks ensure that the spec-imens will fit into the test rig and either ensuresthat stresses will be consistent or provides datato determine variations.

The important dimensions to check on rollingcontact fatigue (RCF) specimens are diameters

H � a s

rb L a s

hbM


of mounting trunnions and test surface, total indi-cator reading (TIR) test surface-to-mountingtrunnions, and overall length. The importantdimensions to check on the mating load rollersare inside and outside diameters, TIR inside tooutside, crown radius and location of high pointof crown, and thickness. In the case of nonstan-dard specimens where the entire width of the testsurface is intended to make contact, the size anduniformity of the edge break needs to be checked.

The important dimensions to check on gearspecimens fall into the areas of mounting sur-faces, gear functional charts, and other specificfeatures impacting stress. All of the gear speci-mens described in the following sections aremounted on their inside diameter. Thus, insidediameter, length between end faces, and perpen-dicularity of end faces to inside diameter need tobe checked. For specimens with a splined bore,the pitch diameter, or inside diameter if so spec-ified, counts as the inside diameter for alignmentchecks. The gear functional charts are developedwith the gear mounted on the test mounting sur-faces. Typical measurements include lead, pro-file, spacing, index, and runout. Other specificitems to check include diameter over wires, rootdiameter, and size and uniformity of edge breakat tooth ends and along the tip.

Surface Finish/Texture Characterization.It has been standard practice to specify surfacefinish and texture in terms of arithmetic averagesurface roughness (Ra). Because it is possible tomanufacture surfaces with widely varying loadcapacity, all with the same Ra, more informationthan Ra is needed to interpret data. At a minimum,Rz (a measure of “average” peak roughness)should also be measured. A preferable methodwould be to examine surfaces with an opticalinterference system that maps the contour of anarea rather than the traditional line contact. Testsurfaces to be subject to contact fatigue shouldalso be examined at 10× to ensure they are free ofcorrosion, dings, scratches, and so on.

Metallurgical Characterization. Both sur-face hardness and hardness gradients are tomeet specification. For gear specimens, hard-ness should be checked at the tooth half heightand at the root fillet. Details of the microstruc-ture should be characterized at the same loca-tions as hardness. Typical practice has been toprepare and document photomicrographs of theetched structure at 400× to 600×.

Residual Stress Measurement. Residualstresses vary among a lot of parts; therefore,enough measurements should be made to permit

a statistical analysis. Residual stress gradientsprovide more useful information than surfacemeasurements but at a much higher price. Acomplete study should include some residualstress gradient data. Typical practice is to mea-sure surface residual stress at six points per vari-ant and measure the residual stress gradient atone or two of these points. Contact fatigue spec-imens should be measured at the center of thecontact surface. Gear specimens should bemeasured at the tooth half height (or lowestpoint of single-tooth contact) for surface dura-bility tests and at the midpoint of the root filletfor bending strength tests.

Tests Simulating Gear Action

Tests that simulate gear action are the rollingcontact fatigue test, the single-tooth fatigue test,the single-tooth single-overload test, and thesingle-tooth impact test.

Rolling Contact Fatigue (RCF) Test

The RCF test simulates the rolling/slidingaction that occurs in a gear mesh, and dependingon the test parameters employed, it can simulatethe most severe condition in the mesh. Becausethe specimens are cylindrical, this test is the leastexpensive to run in both cost and time. Hence, itis frequently used as a screening test, and itsresults are used to plan further gear testing.

Test Equipment. Figure 3 shows a sche-matic of the rolling/sliding contact fatigue test.The specimen and load rollers are cylindrical.The outside diameter of the load roller is crownedto concentrate the load at the center of contactand eliminate the possibility of concentratedloading at the edge of contact due to misalign-ment. A normal load is applied by air pressure.Phasing gears, attached to the shafts on which thespecimen and load rollers are mounted, controlthe extent of sliding at the specimen/load rollerinterface. The amount of sliding is determined bythe gear ratio and can be fixed at any value (21and 43% are commonly selected), simulating therolling/sliding action at any desired location ongear teeth. This test is primarily intended to eval-uate the resistance of candidate material systemsto surface origin pitting, but other modes of sur-face failure can be studied. The surfaces of thespecimen and load roller are sliding against eachother, with lubrication, under high load. There-fore, some indication of the lubricated wear re-sistance of the material being tested can be


Fig. 3 Schematic of a rolling/sliding contact fatigue (RCF) test

obtained. In addition, the resistance of the mate-rial/surface finish/lubricant system to scuffingcan be studied. Tests are conducted at very highoverload to promote failure in real time; thus, it ispossible to introduce plastic deformation (rip-pling) on the contact surface. With speciallyadapted equipment, these tests can be conductedat different temperatures up to 400 °F. Speci-mens and load rollers can be designed for a vari-ety of testing requirements, depending on theexact material and objective of the test.

Test Procedure. The lubricant stream to thespecimen/load roller interface is aimed at thedischarge side of the mesh (to cool the surfacesafter contact). The lubricant flow rate is adjusted(typically to about 2 L/min, or as specified for theproject), with the lubricant at test temperature.

Alignment of the specimen and load roller ischecked as each test is set up. One method oftenused is to coat the surface of the load roller witha thin layer of layout blue and ensure that con-tact occurs uniformly at the center of the loadroller. Before the start of testing at load, a break-in run is typically conducted. This procedure isaccomplished by running the machine for 10min at each of a series of increasing loads up tothe full test load. The intent of the break-in runis to gently polish away asperities on the con-tacting surfaces that might cause scuffing (i.e.,

localized scoring), burnishing, or wear to occurunder full load.

Tests are stopped periodically, and the con-tacting surfaces of the specimen and load rollerare inspected for signs of surface distress. Thediameter at the center of the specimen is alsomeasured to provide an indication of wear. Theformation of large, progressing pits produces astrong vibration signal, which, in turn, shutsdown the test. Lubricant temperature, lubricantpressure, and air pressure (to apply the contactload) are also monitored, and the test is stoppedif irregularities are detected.

The results of contact fatigue tests exhibitmore scatter than is typical with other fatiguetests. One gage of scatter is the Weibull slope, ameasure of the increase in rate of failure withincreasing life. For many fatigue tests, a Weibullslope of six or more is typical. A Weibull slopeof six can be roughly translated into practicalterms as follows. If 20 samples were randomlyselected from a large group of theoretically iden-tical parts and tested to failure under identicalconditions, the longest test would, on the aver-age, last about twice as long as the shortest. Forcontact fatigue testing with current ultracleansteels, a Weibull slope of 1.5 is typical. In thisexample, if the Weibull slope were 1.5, thelongest of the 20 tests would last approximately


Table 1 Example of rolling/sliding contact fatigue test dataLubricant, automatic transmission fluid. Bulk temperature, 90 °C (194 °F). Filter, 10 mm (nominal). Test speed, 1330 rpm. Phasinggear set, 16 tooth/56 tooth. Slide/roll ratio, 43%. Contact stress, 400 ksi. Load, 3000 lb.

Test duration

Test No. Specimen No. 106 cycles h Specimen Load roller λ(b) Wear(c), in. Wear rate(d) Comments

1.173 14.7 13.5 3.83 10-9/LR 1 1.603 20.2 8.5 . . . 0.58 0.0002 12 Surface origin pitting8 10-11/LR 5 7.332 92.3 9.3 . . . 0.56 0.0001 1.4 Surface origin pitting12 10-4/LR 13 7.565 95.3 . . . 5.0 0.57 0.0008 12 Surface origin pitting. Severe

exfoliation and wear atcenter of wear track

18 10-2/LR 17 5.267 66.3 9.0 6.8 0.51 0.0002 3.8 Surface origin pitting22 10-3/LR 22 6.322 79.7 . . . 5.0 0.56 0.0003 4.7 Surface origin pitting

(a) Ra, arithmetic average surface roughness measured in axial direction. μin. (b) λ, ratio of elastohydrodynamic film thickness to composite surface roughness. In caseswhere surface roughness was not measured for a particular specimen or load roller. λ is based on average surface roughness for group. (c) Diametral wear (i.e., changein diameter) on specimen. (d) Change in diameter, in. × 10–5/cycles × 106

Ra(a)

20 times as long as the shortest. The impact ontest programs is that many tests have to be con-ducted to develop enough data to make statisti-cally meaningful comparisons. The minimumnumber of tests with each variant (at each load)to enable reasonable comparisons has typicallybeen considered to be six. With six tests for eachof two variants and Weibull slopes of 1.5, theG50 life of one variant would have to be twicethat of the other to conclude that it is better. If thecomparison were made on the basis of G10 life,the ratio would have to be 5 to 1.

Test Results. An example set of data, repre-sentative of the results of rolling/sliding contactfatigue testing, is shown in Table 1. In addition tospecimen identification, load, and life to failure,other information is reported to aid in the inter-pretation of results. Several test parameters canbe varied as needed; thus, the actual values are re-ported with the results. These parameters includelubricant, lubricant bulk temperature, nominalfilter size, test speed, and phasing gear set/slideratio. Also reported for each test are data regard-ing surface roughness, ratio of elastohydrody-namic lubricant film thickness to compositeroughness, wear, and wear rate. A Weibull statis-tical analysis of this set of results is shown graph-ically in Fig. 4. Comparisons between variantsare made on either a G10 life or a G50 life basis.

Single-Tooth Fatigue (STF) Test

The STF test is used to generate a statisticallysignificant quantity of bending fatigue data at acomparatively low price. Teeth are tested one ata time with a fixed loading point, allowing thegeneration of bending fatigue data at compara-tively high cycles without risk of losing tests toother modes of failure. Another cost-saving

measure is that four or more tests can be con-ducted with each gear specimen.

Test Equipment. A gear is placed in a fix-ture so that one tooth at a time can be loadedwhile another tooth supports the reaction. Thetest is usually done in an electrohydraulic, ser-vocontrolled universal test machine. The pri-mary object of this test is to determine fatigueproperties in bending. However, the same setupcan be used to determine single overload prop-erties (ultimate bending strength) as well. Fre-quently, enough teeth are tested to develop astress-cycles diagram to define the bendingfatigue characteristics of the material system.

Several arrangements for loading can be con-sidered. One fixture arrangement is shown inFig. 5. This illustration shows the Boeing flex-ural design, which appears to have found favorwith the aerospace sector. This fixture isdesigned for a 32 tooth, 5.333 diametral pitch(DP). 8 mm (⅜ in.) face width spur gear with sev-eral teeth removed to provide access to test andreaction teeth. The gear is rigidly supported on ashaft. Load is applied through a carbide blockcontacting the test tooth at the highest point ofsingle-tooth contact. The loading block is held inthe specified orientation to the gear by a flexuralloading arm. This flexural design ensures accu-rate loading of the gear tooth with minimalmigration of the point of loading. Reaction iscarried through a block contacting the reactiontooth at the lowest point of single-tooth contact.Load is cycled from the specified test load to aminimum load high enough to keep the slack inthe system taken up (usually 10% of the testload). While most testing is conducted at 20 Hz,other frequencies also are possible. The fatiguetest machine is instrumented to monitor instanta-neous loads and tooth deflections. Changes in


Fig. 4 Weibull analysis with RCF test data

Fig. 5 Flexure arm single-tooth fatigue (STF) test fixture Fig. 6 SAE division 33 single-tooth fatigue (STF) test fixture

monitor catastrophic tooth failure. Typicalfatigue load capacity of such types of equipmentis in the range of 10 to 20 kips, although higherloads, up to 110 kips, can be used for single over-load tests.

A second fixture arrangement (Fig. 6) appearsto have found favor with many other industrysegments. This fixture utilizes a 34 tooth, 6 DP,25 mm (1 in.) face width spur gear and is deriveddirectly from the Society of Automotive Engi-neers (SAE) Division 33 STF fixture. Fatiguetest loads up to about 15 kips are feasible withthis fixture, and single overload tests up to about50 kips can be accommodated. These STF fix-tures are compact enough to be immersed inheated fluid; thus, fatigue testing can be con-ducted at elevated temperatures (up to 400 °F).

Test Procedure. Special concern must betaken with regard to safety in conducting theSTF test (in addition to general lab safety pro-cedures). Setting up the test requires moving thehydraulic load ram while lining up the fixture,bypassing safety features, such as a light curtainto stop the machine, and so on, and considerablecaution needs to be exercised during setup. Peri-odic calibration of the test fixture is importantbecause there are many closely fitted parts thatcan wear and change the bending stress in spec-imen gears. A calibration gear is made from astandard specimen with strain gages fit at keypoints in the root fillets. This calibration gear isinstalled in the fixture and loaded to set loadsperiodically to ensure consistent loading. Ifspecimens for a specific test program differfrom the standard design established for the fix-ture, one of these specimens should also be fit-

compliance can be used for monitoring crack ini-tiation and propagation in the root fillet region.In addition, a crack wire can be incorporated to


Lif

e, c

ycle

s�

106

0.26

3

0.15

2

0.32

4

0.27

0

0.91

8

Run

out

Run

out

Run

out

0.52

1

0.46

1

Run

out

Run

out

Run

out

0.55

7

0.29

9

Run

out

0.22

0

0.78

3

Run

out

Run

out

Run

out

0.20

9

0.31

0

0.42

5

Gea

r/to

oth

2/1

4/1

6/1

2/2

4/2

6/2

2/3

4/3

6/3

2/4

4/4

6/4

2/5

4/5

6/5

2/6

4/6

6/6

2/7

2/8

4/7

2/9

2/10 6/7

Load 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

9,000 lb X

8,500 lb X X X X

8,000 lb X X O X

7,500 lb X O X O O

7,000 lb X O O

6,500 lb O O

Load 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Searching tests Modified staircase test sequence

Table 2 Results from a typical set of gear single-tooth fatigue tests showing overall testingsequence, including modified staircase (“up and down”) testsLegend: X, failure; O, runout.Specimen serial numbers 2, 4, and 6. Specimens cut from bar stock, hobbed roots. R, loading; R = 0.1. Frequency, 25 Hz

Finite life and confirmation tests

4/8

4/9

6/8

6/9

29 Failure rate28272625

. . .

. . .

100%X X X

0.16

5

0.23

2

25 26 27 28 29 Failure rate

9,500 lb

10,000 lb

6.000 lb

X

X

X

O

O

. . .

0%

25%

50%

80%

100%

0.10

5

0.12

8

X O

ted with strain gages, and calibrations should beconducted with both gears. Typical calibrationintervals are from every six to every thirty tests,or any time the fixture is cleaned and repaired.

Other set-up items that can affect test resultsare mounting of the fixture on the universal teststand, tuning of the test-stand controller, andtest frequency. If the SAE type fixture is used, itis important to ensure that the fixture floatsfreely on an oil film before starting each test.Other fixture designs can be bolted to the ma-chine base, provided proper alignment betweenthe load ram and loading point on the load armis maintained. The feedback control should betuned to suit test fixture and specimen compli-ance. Some systems do this automatically eachtime the machine is turned on; with others; thistuning may have to be done manually. At a min-imum, tuning should be verified as often as fix-ture calibration. Some systems provide a featureto automatically adjust tuning as compliancechanges. This feature should be turned off whenrunning STF tests—a significant change incompliance is proof of failure. The maximumfrequency for STF testing is limited by thecapacity of the system to maintain a satisfactoryload waveform. An inability to maintain peakson the unload side of the wave at the specifiedvalue is a sign of testing at too high a frequency.All of the tests for a given project should be con-

ducted at the same frequency, which is usuallyset at slightly less than the maximum for thehighest anticipated load.

The other procedural item that can affect testresults is the method used to detect failure andstop the test (and stop counting cycles). All sys-tems can be set up to stop if the load goes out ofthe specified range. This deviation will happenwhen compliance changes, usually as a result ofa crack in the root fillet. Many systems incorpo-rate a linear variable differential transformerand can be set up to stop if the load ram movesbeyond the specified range (also an indication oftooth failure). A limit switch can be set to tripwhen the load ram moves too far. Other failuredetection devices, such as a crack wire bondednear the root fillet so that it will break when thetooth cracks, or an ultrasonic system to detectcracking, can be used to stop the test. At leasttwo of these methods should be employed toensure that the machine stops cycling load whenthe tooth breaks. If a computer is used to controlloading during tests, one of the failure detectionsystems should be connected directly to the uni-versal test-stand controller to guarantee that themachine stops if the computer crashes.

Test Results. Table 2 summarizes resultsfrom a typical set of STF tests. Testing was con-ducted in three phases. Initial searching testswere conducted to establish loads that would


Fig. 7 Load cycles diagram constructed from STF data. See Table 2 for load-cycles relationship for data

result in failure in reasonable time. A “modifiedstaircase sequence” of tests was conducted todevelop data at a series of loads representingzero to 100% failure. Further tests were con-ducted to fill in the stress cycles relationship.Searching tests are started at a high load toensure starting with a failure, then stepped downuntil the tooth survives the specified number ofcycles (here, 5 million cycles has been selectedas a run-out limit). The modified staircasesequence is conducted by testing three speci-men gears in sequence. If the tested tooth breaksbefore the specified limit, the next test is con-ducted one load step lower. If it does not breakby the specified limit, the next test is conductedone load step higher. After the modified stair-case sequence is completed, additional tests areconducted to ensure that all the specimen gearsare tested at the lowest load. More tests are con-ducted to develop enough data for Weibullanalysis at two loads resulting in 100% failure.

The load-cycles diagram shown in Fig. 7 wasdeveloped from the data in Table 2. Results at9000 and 8500 lb were analyzed via Weibull sta-tistical analyses (similar to that shown in Fig. 4)to determine lives to 10, 50, and 90% failure. Thefailure rates at 5 million cycles for loads from6500 to 8500 lb were analyzed using normalprobability concepts to determine 10, 50, and90% failure loads. The curves labeled G10, G50,and G90 were then fit visually using the results

of these analyses as a guide. Results are reportedin terms of load versus cycles, and load can beconverted to stress using the method discussedpreviously. Comparisons can be made betweengroups of gears with the same geometry on aload-cycles basis or between gears with differ-ing geometry on a stress-cycles basis. Whenconverting to stress for comparison with runninggear data, consideration must be given to the dif-ferent stress ranges applied to STF gears andrunning gears. Also, consideration must begiven to the statistical difference between four,eight, or more data points from a single STFspecimen gear compared with one data pointfrom a running gear specimen set.

Single-Tooth Single-Overload and Impact Testing

The single-tooth impact test is used to inves-tigate impact strength of gear steels. Impactstrength is an important property for steels to beused in high-speed gear drives or transmissionsfor off-highway equipment, which can be sub-jected to significant shock loading. It has beensuggested that fatigue strength can be related toimpact strength; however, results of tests to sup-port this suggestion have been mixed.

Single overload tests are used to investigatethe ultimate strength of gear materials. The re-sults are useful in selecting loads for fatigue


Fig. 8 Test area of an impact test tower

tests and in constructing allowable stress-rangediagrams (e.g., for use in comparing STF resultswith bending fatigue data developed from run-ning gear tests).

Test Equipment. Figure 8 shows a closeupof the test area of a 4.5 m (15 ft) drop tower forsingle-tooth impact testing. A single-toothfatigue test fixture, without loading block, loadarm, and so on, is placed on a load cell andarranged so that the striking surface of the dropweight hits the load point on the test gear tooth.Stops are provided to prevent the forces requiredto stop the drop weight after the test tooth frac-tures passing through the load cell. A high-speeddigital oscilloscope captures the signal from theload cell.

Single-tooth, single-overload tests are ac-complished with the same equipment used inSTF testing. The only change is that a high-speed digital oscilloscope captures the signalfrom the single event.

Test Procedure. The single-tooth fatiguetest fixture, without loading block, loading arm,and so on, is placed on a load cell and installedunder the drop weight. The striking surface onthe drop weight is adjusted to the correct angle tostrike the test tooth at the load point. This point isverified by coating the tooth with a thin layer oflayout blue and allowing the drop weight assem-bly to contact the tooth statically. The digital

oscilloscope is set up to record a single eventusing a change in signal as a trigger. Usuallythree to six tests per variant are conducted.

For single-overload tests, the STF fixture isinstalled in the universal test stand as for fatiguetesting, and a preload is applied. For the SAEfixture, 1800 kg (4000 lb) is used, and for otherfixtures the load should be high enough to takethe slack out of the system. The function gener-ator is set up to ramp up the load to break thetooth in approximately 30 s for slow bend testsand in approximately 0.050 s for fast bend tests.One slow bend and three fast bend tests usuallyare conducted per variant.

Test Results. A load deflection trace for asingle-tooth impact test is shown in Fig. 9.Results from fast and slow bend tests are simi-lar. This trace shows load increasing linearlywith deflection up to 5900 kg (13,000 lb), thenincreasing at a slower rate until tooth breakageat 9000 kg (20,000 lb). This result is typical formany materials and is possibly related to theonset of plastic flow prior to fracture. Based onthis, the stress corresponding to the change inslope of the load deflection (or load time) tracecorresponds to the ultimate bending strength ofthe material at the critical point in the case.Maximum load, or energy required to break thetooth, represents the strength of the core ratherthan the strength of the case.


Fig. 10 Gear failure map Fig. 11 Schematic of a power (re-) circulating (PC) test rig

Fig. 9 Load deflection trace from single-tooth impact test

Gear Power-Circulating (PC), or Four-Square, Tests

A gear failure map is shown in Fig. 10. Thismap indicates that by varying load and speed,failure by any of several different modes can beinduced. Thus, PC gear tests can be used to eval-uate bending fatigue strength, surface durabilitywith regard to pitting, or scoring resistance. Alimiting factor is that tests targeted at one of thefailure modes may have to be terminatedbecause of failure by another mode. For exam-ple, bending fatigue tests conducted at a compar-atively low load, targeting failure in several mil-lion cycles, may have to be terminated due topitting failure. Consequently, PC gear testing ismore expensive than the tests simulating gearaction previously discussed. It is, however, lessexpensive than bench testing, and several stan-dard specimen designs are available to allowtests targeted at particular failure modes.

Test Equipment. A test and a torque-reversing gear set are mounted at opposite endsof the test bed. One shaft connects the test andtorque-reversion pinions, and another connectsthe torque-reversing and test gears. One gear-box is loaded against the other by twisting theshafts to lock in torque. This rig is known as apower (re-) circulating, or four-square, test rigand is schematically illustrated in Fig. 11. Thelocked-in torque, which is fixed at various val-ues to create the required tooth load, can be gen-erated mechanically or hydraulically. The entireloaded arrangement is driven by an electricmotor at the required speed, and the motor needonly supply the friction losses. Significant trans-mitted power can be simulated in this systemwith comparatively little power input. Datafrom these tests can be directly translated fordesign use.

In a four-square test rig, the tooth accuracy ofthe torque-reversing gears, and their transmis-sion error, has a significant impact on the dy-namic loads on the test-gear pair. These dynamicloads due to torque reversing gear inaccuracycan be further amplified or attenuated by thelongitudinal and torsional frequency responsecharacteristics of the four-square-test rig. Thisintensification is of particular significance inhigh-speed testing where operating frequencieswill be close to or at torsional and/or longitudinalnatural frequencies of the four-square system.However, high-accuracy torque-reversing gearsare expensive. Consequently, the PC test rigs canbe classified into two categories. The first cate-gory of PC test rigs have low power, operate atlow speeds, and generally have AGMA qualityclass Q9 or Q10 gears in the torque-reversing


Fig. 12 Low-speed (4 in. center distance) PC test rig

gearbox that are quite adequate for many indus-try segments. The second category of PC test rigsoperate at high power, high speed, and incorpo-rate high-accuracy torque-reversing gears thatare essential for gear testing in certain industrysegments, such as the aerospace industry. Test-ing costs associated with each of the two cate-gories of test rigs are significantly different.

The low-speed PC test rig illustrated in Fig.12 nominally operate at 900 rpm but can beadapted to operate at 1500 rpm. The standardcenter distance is 100 mm (4 in.), which can bemodified if necessary, although there are somecosts associated with doing so. These test rigscan simulate the transmission of up to 100 hpwhen driven with a 3 hp motor. Load is appliedvia a mechanical loading arm and locked in witha special coupling that can be set at any angle.Thus, load cannot be varied as the rig is running.Depending on specimen design, contact stressesof up to 450 ksi at the lowest point of single-tooth contact and bending stresses up to 160 ksican be generated. Splash lubrication is standard,and spray lubrication to either side of the meshcan be provided. These rigs can be adapted toconduct scoring tests.

Figure 13 shows a PC test rig with a 155 mm(6 in.) center distance that can operate up to 8000rpm and simulate the transmission of up to 1400hp. This test rig has two test gearboxes so thattwo pairs of gears can be tested simultaneously.

In programs to evaluate materials for aerospacegearing, runout can be set as high as 400 millioncycles for surface durability tests, making theproject a lengthy exercise. In this case, obtainingtwo data points in one run can be a significantbenefit. Figure 14 shows another PC test rig witha 90 mm (3.5 in.) center distance, capable ofoperating at 10,000 rpm and simulating trans-mission of up to 700 hp. Torque-reversing gearsin these high-power rigs are in AGMA qualityclass Q13 and Q14. Load is applied via a servo-controlled hydraulic system and can be varied asrequired during tests. Torque is monitored con-tinuously by a noncontact torque cell. This mon-itoring permits interpretation of test results inlight of the actual load signature. Based on inputlubricating oil temperature and load, surfacedurability (pitting), bending, and scoring testscan be conducted on these PC test rigs. Spraylubrication, to either side of the mesh, is stan-dard; oil-mist lubrication can be provided.

Test Procedures for Surface Durability(Pitting) and Root Strength (Bending) Test-ing. One or both gears in the specimen set arecoated with a thin layer of layout blue prior toinstallation in the test machine. After the gearsare installed, they are run briefly at low loadwith room-temperature lubricant to determinethe contact pattern. The low-speed test rigsallow some alignment adjustment to optimizecontact pattern. The specimen mountings in the


Fig. 14 High-speed (3.5 in. center distance) PC test rig

Fig. 13 High-speed (6 in. center distance) PC test rig


high-speed test rigs are rigid, so the only rem-edy for nonuniform contact is to change speci-men gear sets.

A break-in run is generally conducted beforethe start of the test run. On the low-speedmachines this run is accomplished by applyingone-half of the test load and running for ½ h attest speed starting with room-temperature lubri-cant. The friction of the meshing gears warmsthe lubricant to near test temperature in this time.On the high-speed machines, load and speed areincreased in a set pattern to accomplish break-in.As described previously, break-in is expected toincrease the life of the gears. Thus, all specimenstested in a given project should be broken inusing the same method. For root strength (bend-ing fatigue) tests, break-in may not affect bend-ing fatigue life but may delay the onset of pittinglong enough to allow the gear to fail in bending.

In general, the main difference in surfacedurability (pitting) and root strength (bending)tests is the load. Most of the standard specimengear sets are designed to allow surface durabil-ity testing at loads high enough to produce fail-ure in less than 10 million cycles. Root strengthtests, therefore, have to be conducted at loadshigh enough to produce failure in less than 1 million cycles to avoid surface durability fail-ures. Thus, unless specially designed specimensare tested, the results of this test can only becompared to the lower-life portion of the stress-cycles relationship developed in the STF test.

Surface durability gear tests have similarproblems with scatter as those previously de-scribed for RCF tests. However, each specimengear has 18 or more teeth; therefore, the result ofa single PC surface durability test represents thelowest performance of 18 or more items tested.This statistical difference causes the results ofPC surface durability tests to exhibit less scatterthan those of RCF tests, and Weibull slopes aregenerally three or higher. Six tests are still gen-erally conducted with each variant at each load,the reduced scatter being used to allow morestatistically reliable comparison of the resultsrather than to reduce the number of tests. A sim-ilar statistical difference exists between theresults of STF tests and PC bending tests, andthis difference must be considered when com-paring STF and PC bending results.

Test Results. The end point of a surface-durability test may be somewhat ambiguous.Several points in the development of surfaceorigin pitting may be considered failure. Testgear teeth are also subject to wear and localized

scoring, both of which can affect the appearanceof the contact surface in ways similar to some ofthe stages of pitting development. A compositefailure criterion has to be adopted that specifiesthe level of damage in each of these categoriesthat constitutes failure. A typical failure crite-rion for pitting is one pit 4 mm (0.16 in.) wideor several smaller pits with slightly greater totalarea. Typical failure criteria for micropitting ismicropitting over half of the contact width of allthe teeth and for wear, a loss of 12 μm (0.0005in.) at any point on the profile.

A test program evaluating bending and sur-face durability performance of candidate mate-rials would include 24 tests with each material.Six tests would be conducted at each of twoloads intended to result in bending failure; thebalance of the tests would be conducted at twoloads intended to result in pitting failure. Theresults of tests at each of the four loads are ana-lyzed with Weibull statistical analysis (as illus-trated in Fig. 4). A load-cycles diagram is thenconstructed showing loads corresponding to 10,50, and 90% failures at various lives for bothbending and surface durability. Comparisonsare made on the basis of life to 50% (or 10%)failures at a given load, or the load correspon-ding to 50% failures at a given life. It is usefulto construct a stress-cycles diagram (determin-ing contact stress as described here) to comparesurface durability results obtained from speci-mens having differing crown.

Test Procedures for Scoring (or Scuffing)Testing. Scoring is typically most severe in thededendum of the driving gear (at the start of con-tact) and at the tip of the driven gear. Therefore,to facilitate observation of scoring, the gears andloading are set up so that the specimen is thedriven gear. Scoring is more probable at highspeed, high load, and/or high-lubricant tempera-ture. Because of this probability, the test machineis set up to run at high speed and high-lubricanttemperature. Resistance to scoring is then mea-sured by the load that will precipitate scoring.Load is increased in comparatively small stepsuntil scoring starts. Because small variations inlead or crown can produce as much variation inunit loading at the most heavily loaded area asone or more load steps, specimens used for scor-ing should be those with the most consistentgeometry that can be selected from the lot to min-imize scatter. Gear alignment should be adjusted,if possible, to obtain the best contact pattern.

Break-in is a particularly critical part of thistest. Therefore, all specimens should be broken


in using an identical process, and control speci-mens should be included in the project testmatrix to benchmark the results for comparisonwith prior tests. Typically, break-in is started atlow load in room-temperature oil and run-in oneto four load steps lasting 20,000 to 50,000 load-ing cycles each. The lubricant temperature isallowed to slowly rise due to the friction of themeshing gears during break-in. The condition ofthe lubricant also can affect the outcome of thetest; thus, lubricant should be changed prior tothe start of each test.

Test Results. After break-in, the surfaceroughness (Ra) is measured in the axial directionat the tips of several teeth on the specimen gear,and the surface condition is documented. Theload is increased, and the lubricant temperatureis raised to test temperature. The gear set is run20,000 to 50,000 loading cycles for each loadstep. After each load step, surface roughnessand surface condition are examined and re-corded. The appearance of score marks, or anabrupt increase in surface roughness, indicatesscoring failure. Typically, three tests are con-ducted per variant. Comparisons between vari-ants are made on the basis of the load that pre-cipitates scoring. Contact stress consideredalone has little influence on scoring; conse-quently, comparisons made on the basis of con-tact stress may be misleading.

ACKNOWLEDGMENT

This chapter was adapted from D.R. McPher-son and S.B. Rao, Mechanical Testing of Gears,Mechanical Testing and Evaluation, Vol 8,ASM Handbook, ASM International, 2000, p861–872

REFERENCES

1. E.E. Shipley, “Failure Modes in Gears,”presented at Forum on Gear Manufactureand Performance, 19 Oct 1973 (Detroit),American Society of Mechanical Engineers

2. D.W. Dudley, Gear Wear, Wear ControlHandbook, M. Peterson and W. Winer, Ed.,American Society of Mechanical Engi-neers, 1980

3. G. Niemann and H. Winter, Getriebeschä-den und Abhilfe, Entwicklungstendenzen,Maschinen-elemente, Vol 2, 2nd ed.,Springer-Verlag (Berlin), 1983

4. “Appearance of Gear Teeth—Terminologyof Wear and Failure,” ANSI/AGMA 1010-E95, American National Standards Insti-tute/American Gear Manufacturers Associ-ation

5. R. Errichello, Friction, Lubrication, andWear of Gears, Friction, Lubrication, andWear Technology, Vol 18, ASM Handbook,ASM International, 1992, p 535–545

6. L. Alban, Systematic Analysis of Gear Fail-ures, American Society for Metals, 1985

7. A.P. Boresi and O.M. Sidebottom, Ad-vanced Mechanics of Materials, 4th ed.,John Wiley & Sons, 1985

8. W. Lewis, Investigation of the Strength ofGear Teeth, Proc. Eng. Club, Philadelphia,PA, 1893

9. “Information Sheet: Geometry Factors forDetermining the Pitting Resistance andBending Strength of Spur, Helical, andHerringbone Gear Teeth,” AGMA 908-B89 (R1995), American Gear Manufactur-ers Association, 1995

SELECTED REFERENCES

• C.W. Bowen, Review of Gear TestingMethods, Gear Manufacture and Perfor-mance, American Society for Metals, 1974,p 137–162

• D.H. Breen, “Physical and Analytical Mod-eling of Contact Fatigue Pits fromRolling/Sliding Tests,” Technical Paper87-FTM-8, American Gear ManufacturersAssociation, 1987

• L. Flamand, D. Berthe, and M. Godet, Sim-ulation of Hertizian Contacts Found in SpurGears With a High Performance DiskMachine, Trans. ASME, Vol 102, Jan,1981, p 204

• D. Medlin, G. Krauss, D.K. Matlock, K.Burris, and M. Slane, “Comparison of Sin-gle Gear Tooth and Cantilever BeamFatigue Testing of Carburized Steel,”Technical Paper 950212, SAE Interna-tional, 1995

• M.B. Slane, R. Buenneke, C. Dunham, M.Semenek, M. Shea, and J. Tripp, “GearSingle Tooth Bending Fatigue,” TechnicalPaper 821042, SAE International, 1982

• M.N. Webster and C.J.J. Norbart, AnExperimental Investigation of MicropittingUsing a Roller Disk Machine, STLE Trib.Trans., Vol 38, 1995, p 883

Index

AAbrasive water jet machining, 15Abrasive wear. see also Wear

caused by, 24prevention of, 25

Acrylonitrile-butadiene-styrene (ABS), 80Active profile, defined, 2(F)Addendum, 1(F), 2Adhesive wear, 23–24. see also Wear

prevention guidelines, 24Aerospace Material Specification (AMS), specifications

frequently applied to gear steels, 189–190Almen intensity, defined, 61American Gear Manufactures Association (AGMA), 2Annealing

intercritical, heating above Ac1, 16overview, 155–156subcritical, heating to just below Ac1, 16–17supercritical (full annealing) heating above Ac3, 16

Antiscuff additives, 26, 31, 32extreme-pressure (EP) antiscuff additives, 25

Atmospheric furnaces, 165Auger electron spectroscopy, 53

auger electron spectra from case fracture surfaces of car-burized 8620 steel, 54(F)

Austempered ductile irons, 70. see also Ductile cast ironAustenitic grain size and fatigue, 56–60(F)

BBacklash, 2, 3(F)Base circle, 1(F), 2Basic applied stresses, 9–12

basic stresses applied to gear teeth, 9(F)helical gear, 10(F)helical gear, side thrust secondary stresses, 10(F)hypoid gear, 11spur gear, 9–10spur gear, stress areas on basic spur tooth, 10(F)straight bevel gear, 10–11

Bending fatigue testingaxial fatigue testing, 49cantilever bend specimen evolved from the Brugger

specimen, 50(F)data presentation and analysis, 47–48

example of typical S-N plots for a series of carburizedalloy steels, 49(F)

location of maximum stress on cantilever bend speci-men, 50(F)

mean stress and stress ratio, defined, 49–50results of strain-based bending fatigue testing of uncar-

burized and carburized 4027 steel, 50(F)specimen design, 48–49testing of actual machine components, 50–51Typical allowable-stress-range diagram, 50(F)

Bevel gears, 6(F)applications, 9gear selection, 9grinding, 120–121(F)machining methods, 92–98(F), 101–103minimum tolerance capabilities for bevel P/M gears,

144(T)spiral bevel gears, 6, 7(F)straight bevel gear, stresses applied to, 10–11straight bevel gears, 6, 7(F)template machining, 92–93, 94(F)zero bevel gears, 6–7(F)

Blok’s contact temperature theory (scuffing), 28–29Blok’s flash temperature equation, 28–29Bottom land, 2, 2(F)

defined, 1(F)Breather vents (gearboxes), 24Brinell (hardness range), 47(F), 156(T), 157, 229(T)Broaching, defined, 14. see also Gear cutting; Internal

gearsBronzes

aluminum bronzes, 72–73(T)compositions and properties of cast gear bronzes, 73(T)compositions and properties of wrought gear bronzes,

73(T)manganese bronzes, 72, 73(T)silicon bronzes, 73(T)tin bronzes, 72, 73(T)

CCarbonitriding

applicable steels and applications, 246depth of case, 246distortion, 247




Carbonitriding (continued)hardenability of case, 246(F)overview, 245–246(F)quenching and tempering, 247(T)

Carburized gearsshot peening of, 208–211(F)wear resistance, 23

Carburized steelsbend ductility transition curves for carburized and hard-

ened steels, 64(F)bending fatigue strength, 46–47bending fatigue testing, 47–48example of typical S-N plots for a series of carburized

alloy steels, 49(F)fatigue fracture in gas-carburized and modified 4320

steel, 51(F)fracture toughness data, 66fracture toughness in carburized steels as a function

below the surface, 67(F)fracture toughness results for carburized SAE 4320

bending fatigue specimens, 52(T)hot hardness, defined, 63hot hardness of three carburized steels, 63(F)impact fracture strength, 64–66(F)improved elevated temperature performance, 66(T)improvements in rolling contact fatigue life, 62(F)intergranular cracking, 51–52(F), 55microstructural features, 63results of strain-based bending fatigue testing of uncar-

burized and carburized 4027 steel, 50(F)rolling contact fatigue, defined, 62S-N curves determined by bending fatigue of carburized

SAE 8219 steel, 56(F)stages of fatigue and fracture, 51–53(F,T)subzero cooling and fatigue, 59–60(F,T)test specimen used by Cameron for fatigue, bend, and

impact fracture tests, 65(F)testing of actual machine components, 50–51toughness, measuring, 64wear resistance, 62–63

Carburizing, 163–226(F,T)AMS 2304, 190atmosphere carburizing characteristics, 217–218blank design for uniform hardness of wide face width

gears, 198–200(F)bulk temperature, defined, 29–30carbon content and case properties, 175carburizing methods, 41–42carburizing methods, advantages/limitations, 42–43carburizing steels, 41–43carburizing temperature, 164–165(F)case depth at tooth tips, 180(T)case depth of tooth, 175–176case study: property comparisons of a steel gear

processed by atmosphere and vacuum carburizing,219–225(F,T)

cleanliness standards (AGMA), 190cold treatment, 169comparison of atmosphere and vacuum carburizing,

164(F), 217, 218(T)

copper plating of a gear to control case depth at toothtip, 185–186, 187(T)

core hardness of gear teeth, 181(F)core hardness vs. maximum bending strength,

181–182(F,T)costs, vs. case depth, tolerance and special features,

212(F)determination of case depth-shear stress theory,

177–179(F)direct quenching, 166–167dumb-bell shaped pinion, controlling distortion of, 198effect of carburizing processes on surface carbon,

182–183(F)effect of common alloying elements on hardness and

hardenability, 172–174effective case depth of high-alloy steel gears,

176–177(F)furnaces and equipment for gas carburizing, 165–166gas carburizing: processing and equipment,

163–164(F)grain size and case depth, 180–181(T)grain size and core hardness, 182(F)hardness and hardenability, 170–175(F)hardness and hardenability, determining, 170–172(F)heat treat cracks at tooth edges, 200–201(F)heat treat distortion of carburized and hardened gears,

188–189high-temperature vacuum carburizing, 216–217(T)highest point of single-tooth contact (HPSTC), 177Jominy, or end-quench, test for hardenability, 170,

172(F), 174(F)long slender pinions, 198(F)lowest point of single-tooth contact (LPSTC), 177material and heat treat process factors, 189–190(F)measurement of case depth, 176(F)measurement of gear distortion, 193mechanics of heat treat distortion, 189microstructure of carburized cases, 183–184(T), 185(F),

186(F)overview, 163pinion shaft with threads, 199(F), 200(F)preheating of gears prior to loading into furnace, 196problems associated with, 184–185, 187(F)quality of steel and its effect on distortion, 189quenching and hardening, overview, 166recarburizing, 169recommendations to minimize distortion, 193–196(F)recommended total case depth for low-alloy steel gears,

180(T)reheating of carburized gears and quenching, 167retained austenite and its effect on gear performance,

186–188(F)selection of gear steel by hardenability, 174–175(F,T)selection of materials for carburized gears, 169–170(T)stock removal and tooth surface hardness, 202–203(F)surface hardness variations after quenching, 167–168surface oxidation effect, to be avoided, 182tempering of carburized and quenched gears,

168–169(F)tip and edge radii, 186, 187(T)



Index / 331

total case depth(F), 179vacuum carburizing, 212–216(F,T)vacuum carburizing characteristics, 218–219vacuum-melted vs. air-melted alloy steels, 191–192(T)VAR materials permit saving costs, 192–193

Case hardening, 17, 158Cast irons

austempered ductile iron structure, 71(F)cost and machinability, 69ductile cast iron (spheroidal-graphite (SG) cast iron),

69–70(F,T)ductile cast irons, minimum mechanical property

requirements for, 70(T)gray iron, 68–69mechanical property requirements of austempered duc-

tile iron, 72(T)minimum hardness and tensile strength requirements,

69(T)spheroidal graphite, 69(F)strength and ductility ranges of as-cast and heat-treated

ductile irons, 71(F)Cast steels

gear rack segment made from cast ASTM A 148 Grade120–95 alloy steel, 68(F)

properties of cast carbon and low-alloy steels, 68(T)steel casting process, 67–68(F,T)

Castingcold chamber die casting process, 131defined, 14investment casting process, 131overview, 129(T)sand casting, 130shell molding process, 130–131(F)

Center distance, 2Circular pitch, 1(F), 2Circular thickness, 1(F), 2Computer-aided design and manufacturing

(CAD/CAM), 135Computer numerical control milling and hobbing

machines (CNC), 15, 113–114Crossed-helical gears, 8(F)

DDiametral pitch (DP), 2, 3(F), 4(T)Distortion

distortion characteristics of some gear materials,196–197(T)

distortion derating factor (DDF), defined, 204grinding of distorted gears, 201–202(F)grinding stock allowance on tooth flanks to compensate

for distortion, 201improvement in gear design to control heat treat distor-

tion, 197–201(F)Double helical gears. see Herringbone gearsDuctile cast iron

ductile cast iron (spheroidal-graphite (SG) cast iron),69–70(F,T)

ductile cast irons, minimum mechanical propertyrequirements for, 70(T)

machinability of commonly used gear steels, 48(T)strength and ductility ranges of as-cast and heat-treated

ductile irons, 71(F)

EElastohydrodynamic (EHD) lubrication

Blok’s contact temperature theory (scuffing), 28–29Fatigue failures, 261load sharing factor, 28mean coefficient of friction equation, 29minimum film thickness, equation, 28plot of absolute viscosity vs. bulk temperature for min-

eral oil lubricants, 29(F)plot of load-sharing factors for unmodified and modified

tooth profiles, 28(F)plot of pressure-viscosity coefficient vs. bulk tempera-

ture for mineral oil gear lubricants, 30(F)regions of contact between mating gear teeth, 27(F)scuffing temperature, 30–31scuffing temperatures for synthetic lubricants used with

carburized gears, 31(T)semiwidth of the Hertzian contact band, defined as, 29thermal contact coefficient, 29welding factor for selected gear steels, 31(F)

Electrical discharge machining (EDM), 15Energy-dispersive x-ray spectroscope (EDS), metallur-

gical examination of fragmented tooth, 235Ethylene vinyl acetate (EVA), 80

FFace gears, 7–8(F)

terminology used with face gears, 7(F)Face hob cutting, 94–95(F)Face mill cutting, 94Face width, 1(F), 2Fatigue

austenitic grain size and fatigue, 56–57(F)detrimental effects of subzero cooling, 60(F)intergranular fracture and fatigue, 53–55(F)retained austenite and fatigue, 58–59rolling contact fatigue, 62, 268(F), 269(F), 269–270(F)stages of fatigue and fracture, 51–62(F,T)subcase fatigue (case crushing), 266–267(F)subzero cooling and fatigue, 59–60(F,T)surface oxidation and fatigue, 57–58(F)thermal fatigue, 271, 272(F)

Fatigue failuresbending fatigue, 258–260(F)contact fatigue, 260–262, 263(T)contact fatigue terminology, 263(T)macropitting, 262–265overview, 257–258photoelastic study of mating teeth, 259(F)subcase fatigue, 262subsurface-origin pitting, 261–262surface-origin pitting, 261tooth-bending fatigue failure, 258(F), 259(F), 260(F)

Ferrous and nonferrous alloys, 39–76(F,T)



Fillers (plastic gears), 79Fillet radius, 2, 2(F)Finishing, 122–126(F)

grinding to produce a surface finish, 122honing, 122–124(F)lapping of gears, 124–125(F)overview, 89–90plastic gears, 82shaving, 89–90superfinishing processes, 125–126(F)surface roughness values produced by common manu-

facturing/production methods, 125(F)Weibull plot of surface fatigue tests, superfinished gears,

126(F)Flame hardening

applicable materials, 254(T)equipment, 253–254gases used for flame hardening, 254overview, 253

Fluidized bed furnaces, 166Forging

closed-die forging, 133(F)computer-aided design and manufacturing (CAD/CAM),

135defined, 15high-energy rate forging, 133–134high-energy rate forging, automotive flywheel, 134(F)near-net shape quality gears, 135–137(F)near-net shape quality gears, fatigue data for, 135(F)overview, 133precision forging, 135–137(F)typical gear forgings, 134–135(F)

Formingcold drawing and extrusion, 132fine blanking (fine-edge blanking), 132gear rolling, 132–133(F)stamping, metalworking technique, 131–132(T)

Furnacesatmospheric, 165, 167atmospheric vs. vacuum, 217–218(F,T)a batch-graphic integral oil quench vacuum furnace,

216(F)carburizing furnace, 196check list for setting up a furnace, 196a continuous ceramic vacuum carburizing furnace,

215(F)endothermic carburizing furnace, 183fluidized bed furnace, 166load arrangement in the furnace, 195, 196(F)types of, 217vacuum, 165, 179, 214–216(F), 218(T), 220

GGear blank, defined, 2Gear blanks, improvement in gear design to control

heat treat distortion, 197–201(F)Gear cutters, 78(F)

construction materials, 106–107G-Trac gear generator, 107(F)hobbing speed, 107–109

nominal feeds for hobbing, 108–109(T), 110–111(T),112–113(T)

shaping speed, 109, 110–111(T)speeds for interlocking and face mill cutters,

112–113(T)Tangear generator, 104–106, 107(F)

Gear cutting. see also Machiningbevel gears, 92–98(F)broaching, 90–91(F)CNC machines, 113–114CNC machines , four types of gashers, 114(F)comparison of steels for gear cutting, 113cutting fluids, 111–113Cyclex method, 94face hob cutting, 94–95(F)face mill cutting machines, 94(F)formate and helixform methods, 93–94(F)gear shaping, 92(F)hobbing, 91(F). see also Hobbinginterlocking cutters (completing generators), 95–96(F)milling, 90(F), 92overview, 89, 89(F)planing generator, 97–98planing generator, components of, 97(F)rack cutting, 92Revacycle generating process, 96(F)shear cutting, 91(F)spiral bevel gears, 102straight bevel gears, 102template machining, 92–93(F)two-tool generators, 96–97(F)

Gear, defined, 2Gear distortion, measurement of, 193Gear failure analysis, 276–290(F,T)

ANSI/AGMA 2000 Appendix D, contact pattern tests,280

Conducting the Failure Analysis, 277–283determining the failure mode, 282document your observations, 281endplay and backlash, inspect, 280examples of gear failure analysis, 283–290(F,T)external examination, inspect and photograph, 279form and test your conclusions, 283gather gear geometry, 281–282gear tooth patterns, observe, 279–280gearbox mounting alignment, measure and check for

twist, 280gearboxes, remove, transport, store, disassemble,

280–281inspect components, before and after cleaning, 281inspect in situ, 279loaded contact patterns, photograph, 280minimum number of days needed for inspection, 282no-load contact patterns, paint and transfer, 280prepare the failure analysis report, 283preparing for the inspection, 277–278select specimens for laboratory tests, 282

Gear failure modes, 257–276(F,T)classification of gear failure modes, 21(T), 257fatigue failures, 257–262(F,T)gear failure modes proposed by Alban, 258(T)




gear failure nomenclature recommended by the AGMA,258(T)

impact, 271–273stress ruptures, 276wear, 273–275(F)

Gear failure, reasons forfailure modes of gears, 293(T)gear tooth contact, 293–294gear tooth failure by breakage after pitting, 300(T),

304–306(F)helical, spiral bevel, and hypoid gears, 294–295(F),

296(F)Hertzian fatigue, 21(T). see also Hertzian fatigueledge wear, 305lubrication problems, 294operating loads, 296pitting, 296, 297(F)scuffing, 296spur and bevel gears, 294, 295(F)tooth breakage, 296–297(F)worm gears, 295–296

Gear inspectiongear inspection terms, 148–149mechanical testing, 149P/M gears, 148–149part drawing, what to include, 148spur tooth strength test, 149(F)surface durability (Rockwell hardness), 149

Gear lifecommon flaws that affect gear life, 306–307determined by surface contact stress, formula, 297(T),

297–298(T)Example: Surface Durability of Gear, 298–303(F,T)Example: Rating Gear Life with Bending Stress,

303–304(F,T)round bores, and how they affect gear life, 307–308shafts, stresses affecting gear life, 308splined bores, and how they affect gear life, 308

Gear lubricantsapplication methods, 33–35Case history: Failure of a 24-unit speed-increaser gear-

box, 35–37probability of wear-related surface distress, 34(F)selection of gear lubricant viscosity, 33

Gear lubrication systemspressure-fed systems, 34–35recommended values of constant c based on oil flow and

gear mesh specifications, 35(T)splash lubrication systems, 34

Gear manufacturingalternative or nontraditional methods, 15automated gear-checking machines, 15–16(F)carbonitriding, 17. see also Carbonitridingcarburizing, 17. see also Carburizingcase hardening, 17casting, forming and forging processes, 14–15(F)examples of gear manufacturing processes, 13(F)heat treating, 14(F), 16–18inspection process, 15–16(F)metal removing processes, 13–14(F,T)nitriding, 17–18. see also Nitriding

through hardening (direct hardening), 17–18. see alsoThrough-hardening

Gear materialsadditional nonferrous alloys used for gears, 74classified into two groups, 39–45overview, 12–13plastics, 77–88(F,T)recommended steels for various applications and gear

types, 12(T)selection guidelines, 13

Gear nomenclature, 1–5(F,T)Gear pinion, 2, 4(F)Gear power-circulating (PC) or four square, tests

gear failure map, 323(F)low-speed PC test rig, 324(F)overview, 323schematic of a power (re-) circulating (PC) test rig,

323(F)test equipment, 323–324, 325(F)

Gear quality numbers (AGMA gear quality numbers),2–3

Gear rating standards, 312–313Gear ratio, 3Gear rolling, defined, 14Gear selection, 8–9

selection guidelines, 13Gear steels

additional nonferrous alloys used for gears, 74austenitic grain size and fatigue, 56–57(F)bending strength and bend ductility, 63–66(F,T)bronzes, 72–73(T)cast irons (gray irons and ductile cast irons),

68–70(F,T)cast steels, 67–68(F,T)copper-base alloys used for gearing, 73–74gear steel requirements, 44–45high-speed tool steels, 71hot-work tool steels (group H steels), 71inclusions and fatigue, 55–56(F)intergranular fracture and fatigue, 53–55(F)maraging steels, 71–72powder forged nickel steels, 71processing characteristics (hardenability and machin-

ability), 45–46(F,T)residual stresses, shot peening, and fatigue, 60–62(F)sintered steels, 70stages of fatigue and fracture, 51–55(F,T)stainless steels, 71subzero cooling and fatigue, 59–60(F,T)surface oxidation and fatigue, 57–58(F)yellow brass, 73–74, 141(T)

Gear tooth failure modes, 21basic failure modes of gear teeth, 21(T)

Gear tooth vernier calipers, 15Gear tribology, 19–38(F,T)

defined, 19and lubrication, 21–38(F,T)nomenclature and units required to calculate Eq 1 to

24, 20(T)overview, 19

Gear wear. see Wear

Index / 333



GearboxCase history: Failure of a 24-unit speed-increaser gear-

box, 35–37(F)run-in recommendation, 23, 25

GearsAGMA 1012-F90, Gear nomenclature, Definitions of

Term and Symbols, 2bevel gears, 6(F). see also Bevel gearscrossed-helical gears, 8, 8(F)face gears, 7–8(F)helical gears, 5(F), 5–6. see also Helical gearshypoid gears, 7(F), 8. see also Hypoid gearsinternal gears, 6, 6(F). see also Internal gearsmanufacturing gears, 129–137(F,T)overview, 1plastics, 77–88(F,T)spiral bevel gear, 11. see also Bevel gearsspiroid gears, 8, 8(F)spur gears, 4(F), 5, 5(F). see also Spur gearsstrength, 11–12(F)that operate on intersecting shafts, 6–8(F)that operate on nonparallel and on intersecting shafts,

7(F), 8, 8(F)that operate on parallel shafts, 5–6(F)types, 5–8(T)worm gear sets, 8, 8(F)

Gearsets, run-in recommendation, 23, 25–26Generation grinding

cup-shaped wheels, 118dish-shaped wheels, 118–119(F,T)rack-tooth worm wheels, 119–120(F)straight wheels, 118

Grinding, 114–122(F,T)advantages and disadvantages, 115bevel gears, 120–121(F)correcting for distortion in heat treating, 117defined, 14effects on grinding carburized and hardened gears,

205–206Example: Grinding die-quenched gears, 117(F)Example: Grinding spiral bevel gears with a cup-shaped

wheel, 121, 122(F)form grinding, 117–118(F)gear grind burn identification, 206(F)gear teeth of various diametral pitch, 116(F)generated gears, 121generation grinding, 118–120(F,T)infeed, influenced by pitch of gear, 116–117inspection and limited acceptance criteria of grind

burns, 206–207(F)multi-piece loads, 116nongenerated (formed) gears, 121overview, 114–115, 222–223plastic gears, 82to produce a surface finish, 122stock allowance, 115–116(F)Waguri grinding method for nongenerated spiral bevel

and hypoid gears, 121(F)wheel specifications; types of wheels, 116wheel surface speeds, 116

Grinding fluids, 121–122

HHardenability

defined, 45hardenability characteristics of commonly used gear

steels, 46(T)maximum attainable hardness, 45. see also Carburizing

Hardness callout, minimum range, 157Heat treating, 16–18

prehardening processes, 16–17typical gear manufacturing costs, 14(F)

Helical gears, 5(F), 5–6external helical gears, uses for, 9gear selection, 9hobbing, 99–100honing of helical gear teeth, 123(F)milling, 99minimum tolerance capabilities for helical P/M gears,

144(T)shaping, 100

Helix angle, 3Herringbone gears (double helical gears), 6(F)

end milling, shaping and hobbing, 100milling, 90

Hertzian fatiguegear tooth failure, contributing to, 21(T)micropitting, 22–23. see also Micropittingpitting, 22. see also Pittingprevention of pitting, 22

Highest point of single-tooth contact (HPSTC), 177Hobbing

CNC gear hobbing machine, 115(F)defined, 14helical gears, 99–100herringbone gears, 100hobbing machines, available capacities, 114hobbing of a spur gear, 91(F)hobbing speed, 107–109large gears, 102nominal feeds for hobbing, 108–109(T), 110–111(T),

112–113(T)overview, 91recommended tolerances in terms of AGMA quality

numbers for manufacturing processes, 129vs. shaping, 99spur gears, 98, 99worms, 101

Honingapplicability, 123–124constant-pressure method, 123defined, 14honing of helical gear teeth, 123(F)microhoning, 123(F), 124schematic representation of honing, 123(F)tools used in honing gear teeth, 123zero-backlash method, 123

Hypoid gears, 7(F), 8applications, 9face mill cutting, 94, 95(F)formate cutting and helixform cutting, 93–94(F)gear selection, 9




prone to scuffing, 32setup for lapping of hypoid gears, 125(F)stresses applied to, 11

IImpact (gear failure mode)

tooth-bending impact, 271–272tooth chipping, 272–273(F)tooth shear, 272, 273(F)

Impact modifiers (for plastics), 80Induction and flame hardening. see also Flame harden-

ing; Induction hardeningcomparison of flame- and induction-hardening

processes, 249(T)overview, 249

Induction hardening, 249–253(F,T)applicable materials, 250core hardness of tooth and fatigue strength, 252current frequency vs. case depth, 251(T)dual-frequency process, 253effective case depth, 252(F)hardening patterns, 250–251hardening patterns, variations in, 250(F)heating with induction, 251overview, 249–250preheat treatment, 250problems associated with induction hardening,

252–253(F)quenching, 251(F)recommended depth of hardness in root region for

induction hardened teeth, 251(T)residual compressive stress distribution, 254(F)surface hardness and case depth, 251–252tempering, 251

Injection molding, defined, 14–15Internal gears, 6(F)

broaching, 90(F), 100shaping, 101shear cutting, 91(F), 100–101

Involute gear tooth, 3, 4(F)Ion (plasma) nitriding

distortion, 244(T)hardness and case depth, 243(F,T)improved case property, 243–244overview, 241–242results after ion nitriding of common materials, 242(T)time and case depth, 242–243(F)white layer, removing, 242

JJern Konntoret (JK) chart, for determining the inclu-

sion in steel, 192(F)Jominy, or end-quench, test for hardenability, 45, 170,

172(F), 174(F)

KKevlar (agamid) fibers, 79–80Knit lines, 87

LLapping, 124–125(F)

defined, 14lapping media, 124(F)lapping plate, 124processing techniques, 124–125setup for lapping of hypoid gears, 125(F)

Lapping plate, defined, 124Laser machining

advantage/disadvantages, 15computerized-numerically-controlled (CNC) machines,

15Lewis parabola, 315(F)Load pattern, defined, 294Lowest point of single-tooth contact (LPSTC), 177Lubricants

grease, 31oil, 31. see also Oil lubricant applicationsopen-gear lubricants, 31solid lubricants, 31synthetic lubricants, 31–32

LubricationElastohydrodynamic (EHD) lubrication, 27–31lubricant selection, 31–32. see also Lubricantsselection of gear lubricant viscosity, 33

Lubrication regimesoverview, 19schematic showing three lubrication regimes, 20(F)

Lubrication-related failure, overview, 21–23Lubrication terminology, 19–21(F)

boundary lubrication, 20Elastohydrodynamic (EHD) lubrication (EHD), 19–20fluid-film lubrication (thick-film lubrication), 19–20schematic showing three lubrication regimes, 20(F)solid lubrication, 20thin-film lubrication, 20

MMAAP (methylacetylene propadiene), 254Machinability

criteria for making machinability judgments, 45–46cutting speed for one-hour tool life vs. Brinell hardness

of various gears, 47(F)defined, 45machinability of commonly used gear steels, 48(T)

Machining, 89–114(F,T)bevel gears, 92–98(F)broaching, 90–91(F)gear shaping, 92(F)for gears other than bevel gears, 90–92(F)hobbing, 91(F)large gears, 102–103milling, 90(F)plastic gears, 82rack cutting, 92selection of machining process, 98shear cutting, 91(F)

Macropittingdefined, 262, 263(F)

Index / 335



Macropitting (continued)overview, 262–263(T)subsurface-origin macropitting, 263–264surface-origin macropitting, 264–265(F)

Magnetic particle test, cleanliness test, aircraftindustry, 191

Manufacturing gears, 129–137(F,T)tolerances in terms of AGMA quality numbers for various

gear manufacturing processes, 129(T)

Maraging steels, 71–72Martensitic transformation, predicting, 169Mechanical testing, 311–328(F,T)

bending stress computations for root fillets, 315(F)common modes of gear failures, 311contact stress computations for gear tooth flank,

313–315dimensional characterization, 315–316failure modes in root fillets, 312failure modes on tooth flanks, 311–312(F)metallurgical characterization, 316overview, 311residual stress management, 316rolling contact fatigue (RCF) test, 316–318(F)single-tooth fatigue (STF) test, 318–321single-tooth single-overload and impact testing,

321–322(F)specimen characterization, a critical part of any fatigue

test program, 315stress calculations for test parameters, 312–315surface finish/texture characterization, 316test procedures for scoring (or scuffing) testing,

326–327test procedures for surface durability (pitting) and root

strength (bending) test, 324–326test procedures for surface durability (pitting) and root

strength (bending) testing, 319(F)Metal removal processes, 4(T), 13–14(F,T)

examples of gear manufacturing processes, 13(F)Methacrylate-butadiene-styrene (MBS), 80Microexamination, cleanliness test, 191–192Micropitting

appearing as “frosting”, 23gray staining (Japanese reference), 23Hertzian fatigue, 21(T), 22–23overview, 265–266(F)preventing, 23scanning electron microscopy (SEM) (determining

fatigue process), 23Milling, defined, 14

NNear-net shape gears, 135–137(F)

five basic configurations, 136–137precision forged near-net shape gears, 136(F)specifications for spiral bevel, straight bevel and spur

gears, 136–137Nitrided gears, wear resistance, 23Nitrided steels, resistance to scuffing, 27

Nitriding, 227–244(F,T)bending-fatigue life of nitrided gears, 238–239case depth in nitriding, 228, 229(T)Case history: Fatigue failure of nitrided gears,

234–238(F)chemical compositions of nitriding steels commonly

used in gears, 228(T)controlled nitriding, advantages of, 241(F)controlled nitriding, how it works, 240core hardness, 181(F), 229distortion in nitriding, 239(T)effective case depth and total case depth, 228gas nitriding applications, 239gas nitriding costs, 239–240(F)gas nitriding process, 227–228general recommendations for nitriding gears, 231–232ion nitriding, 241–244(F,T)microstructure of nitrided cases and cores, 232, 233(F)nitriding cycle time, 228, 229(F)nitriding potential, defined, 240overload and fatigue damage of nitrided gears,

232–234(F)overview, 227recommended tip and edge radii of teeth, 229, 230(T)surface hardness, taken in Rockwell 15-N scale, 229(T)white layer in nitrided gears, 229–231(F,T)

Nitriding steels, 43–44(T)applications, 43chemical compositions of Nitralloy gear steels, 44(T)overview, 43

Nonferrous alloys, 72–74(T)additional nonferrous alloys used for gears, 74

Normal section, 2(F), 3Normalizing

defined, 156overview, 17

OOil lubricant applications

critical applications, calculate with Blok’s equation (Eq 1), 32

rust and oxidation inhibited (R&O) mineral oils, 32spur, helical, and bevel gears essentially the same, 32worm gears, 32–33

PPhysical vapor deposition (PVD), 274–275Pinion rods, defined, 132Pitch circle, 1(F), 3, 4(F)Pitch cylinder, defined, 5Pitch diameter, 3Pitch line, 3, 4(F)Pitch point, 4, 4(F)Pitch radius, 1(F), 4Pitting

contributing to gear failure, 297(F)defined, 22distortion derating factor (DDF), defined, 204




equation for pitting life in terms of stress cycles,203–204

gear tooth failure by breakage after pitting, 304–306Hertzian fatigue, 22initiation of, 267–269(F)prevention of, 22spall, formation of, 22subsurface-origin pitting, 261–262surface-origin pitting, 261

Plastic gear manufacture, 82–88(F)AGMA quality levels, 83gates and runners, 86–87hot runner injection mold, 87(F)injection mold design, 86, 86(F)injection molding, 82–86injection molding compounds, 83–84injection molding machines, 84–86(F)knit lines, 87material shrinkage (volumetric shrinkage), 87mold cooling, 87mold materials, 88mold venting, 87–88part removal, 87

Plastic gears, 77–88(F,T)additives (reduce cost or property improvement),

79–80advantages and limitations, 77comparing to metal, 78–79overview, 77thermoplastics, 78, 80–81thermosets, 78, 81–82typical stress-strain curve for an engineering metal,

78(F)typical stress-strain curve for an engineering plastic,

79(F)viscoelastic, defined, 79

Polishing wear, 25and extreme-pressure (EP) antiscuff additives, 25prevention of, 25

Polytetrafluoroethylene (PTFE or Teflon), 80Powder metallurgy (P/M) gears

bevel and face gears, 143combination gears, 143compaction tooling for compound gear, 145(F)design guidelines, 146–147(F)Example: Drive gear for mailhandling machine,

149–150(F)Example: Transfer gears for postage meter counting

applications, 150–151(F)Example: Eccentric gear, 151(F)Example: Fourth reduction gears, 151(F)Example: Powder forged internal ring gear, 152(F)examples of gear design, 142(F), 143(F), 144(F)gear design and tooling, overview, 144–145gear inspection terms, 148–149gear performance, 147(F)helical gears, 142–143quality control and inspection, 148–149selecting gear materials, 147–148spur gears, most common type P/M gear, 142

tolerances of P/M gears, determining, 143–144(F)tolerances of single pressed and sintered gears, 145(T)

Powder metallurgy (P/M) processing, 139–154(F,T)advantages and limitations, 141capabilities and limitations, overview, 140–141commonly used metal powder grades, 141(T)defined, 14material requirements for P/M pump gear applications,

139(T)overview, 139–140P/M gear production process, 140(F)P/M manufacturing methods, 140(F)P/M materials have both macro- and microhardness, 149

Pressure angle, 1(F), 4Pressure-fed lubrication systems, guidelines for flow,

pressure, jet size and number, 35

QQuench embrittlement, defined, 53

RRack, 4(F), 5(F)Racks, milling and shaping, 101Reciprocating-screw injection molding machine,

84–86(F)Reinforcements (plastic gears)

carbon fibers, 79impact modifiers, 80Kevlar (agamid) fibers, 79–80lubricants, 80

Revacycle cutting method, 96(F), 102Rolling contact fatigue (RCF) test

test equipment, 316–318(F)test procedure, 317–318(F)test results, 318, 319(F)

Root circle, 1(F), 5Run-in recommendation, 23, 25Rust and oxidation inhibited (R&O) mineral oils, 32

SScanning electron microscopy (SEM), 23

examination of a tooth segment, 235Scoring. see ScuffingScuffing

antiscuff films, use of, 26basic mechanism of, 26Blok’s contact temperature theory (scuffing), 28–29contributing to gear failure, 297(F)controlled by the total contact temperature, 26defined, 21, 25graphical representation of rolling velocities of pinion

(vr1) and gear (vr2) in relation to sliding velocity,27(F)

is a lubrication failure, 275–276, 277(F)overview, 25–26predicting, 26preventing, 26–27

Index / 337



Scuffing (continued)scuffing temperature, defined, 30–31scuffing temperatures for synthetic lubricants used with

carburized gears, 31(T)symptoms, 25test procedures for scoring (or scuffing) testing,

326–327welding factor for selected gear steels, 31(F)

Shaping, defined, 14Shaving

cutting speeds and feeds, 104, 105–106(T)defined, 14operating principles, 103shaving cutters, 103–104(F)shaving methods, 104spur and helical gears, 103–104(F)

Shear stress, 10Shot peening

compressive stress at and below the surface after shotpeening, 211(F)

coverage, 210–211dual peening, 224(F)overview, 208–209(F), 222, 222(F)principle of shot peening, 208(F)residual stress, 211residual stresses, shot peening, and fatigue, 61–62(F)shot intensity, 209–210shot peening intensity control, 210(F)shot peening specification, 211type of shot and shot size, 209typical gear tooth surface profile after shot peening,

211(F)Single-tooth fatigue (STF) test

test equipment, 318–319(F)test procedure, 319–320test results, 320–321(F,T)

Single-tooth single-overload and impact testingoverview, 321–322test area of an impact test tower, 322(F)test equipment, 322test procedure, 322test results, 322, 323(F)

Sintered steels, 70density range for P/M steel consolidation methods,

140(T)material requirements for P/M pump gear applications,

139(T)tolerances of single pressed and sintered gears, 145(T)

Skiving, defined, 14Spall, formation of, 22Spalling, 62, 270–271(F), 272(F)Spheroidal-graphite (SG) cast iron. see Ductile cast

ironSpiroid gears, 8, 8(F)Spur gears, 4(F), 5, 5(F)

applications, 9form grinding, 117–118(F)form milling, 90(F), 98–99gear selection, 9hobbing, 99, 100

minimum tolerance capabilities for spur P/M gears,144(T)

shaping, 99shear cutting, 99spur tooth strength test, 149(F)

Stainless steels, as gear material, 71Stamping, defined, 14Strength

maximum tensile and shear stress orientation, 11(F)overview, 11–12(F)

Stress, basic stresses applied to gear teeth, 9(F)Stress relieving, overview, 17Stress ruptures, internal and external ruptures, 276,

278(F)Subzero cooling, 59–60(F,T)Surface-hardening steels, 40–44(T)

carburizing steels, 41–43. see also Carburizinggeneral properties, 40nitriding steels, 43–44(T). see also Nitriding steelsselection factors, 40–41

Surface oxidation effect, to be avoided, 182

TTest procedures for scoring (or scuffing) testing

test procedure, 326–327test results, 327

Test procedures for surface durability (pitting) androot strength (bending) testing

test procedure, 324–326test results, 319(F), 326

Thermal stress, 189Thermoplastic gear materials, 80–81(F,T)

acetal polymers, 80, 83(F), 83(T), 84(F)additional thermoplastics used for gears, 80–81applications, 80nylons, 80, 81(T), 82(T), 83(F)

Thermoset gear materialslaminated phenolic, 82phenolics, 82polymides, 81–82

Through-hardened gears, wear resistance, 23Through-hardening

annealing, 155–156approximate relation between hardness-test scales,

156(T)Case history: Design and manufacture of a rack,

158–162(F,T)distortion of through-hardened gears, 157–158(T)hardness measurement, 157normalizing and annealing, 156normalizing and tempering, 156overview, 155quench and temper, 156through-hardened gear design, 157typical Brinell hardness ranges of gears after through

hardening, 156(T)Through-hardening steels, overview, 44Titanium alloys used for gears, 74Tool steels, 12, 71




Tooth thickness, 1(F), 5Top land, 1(F), 2(F)Transformation stress, 189Transverse section, 2(F), 5

VVacuum carburizing

a batch-graphic integral oil quench vacuum furnace,216(F)

boost step, 213a continuous ceramic vacuum carburizing furnace,

215(F)diffusion step, 213furnace design, 214–216heat and soak step, 213oil quenching step, 214(F)overview, 212process overview, 213

Vacuum furnaces, 165–166Vacuum induction melting followed by vacuum arc

remelting (VIM/VAR), 39VAR steels, 190, 191, 193Volumetric shrinkage, 87

WWaguri method, 121(F)Wear

abrasion, 24–25abrasive wear, 273–274(F)adhesive wear, 23–24, 274, 275(F), 276(F)

nitrided gears, 23polishing wear, 25run-in time of new gearsets, 23scuffing, 23, 25–27. see also Scuffingscuffing–severe adhesive wear, 23wear resistance coatings, 274–275

Weibull, plot of surface fatigue tests, 126(F)White layer

in nitrided gears, 229–231(F,T)removing, 242

Winter and Weiss, 37Worm gear sets, 8

double-enveloping gear set, 8(F)Worm gears

applications, 9gear selection, 9

Worms, milling, hobbing, shaping machining methods,98(F), 101, 101(F)

Wrought gear steelscompositions of surface hardening steels, 40(T)compositions of through-hardening steels, 41(T)mechanical properties of selected gear steels, 42(T)overview, 39

YYellow brass, 73–74, 141(T)

ZZerol gears

face mill cutting, 94, 95(F)

Index / 339



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