Analysis of a Split-Path Gear Train with Fluid-Film Bearings Analysis of a Split-Path Gear Train...

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  • Analysis of a Split-Path Gear Train with

    Fluid-Film Bearings

    by

    Andrew V. Wolff

    Thesis submitted to the faculty of the

    Virginia Polytechnic Institute and State University

    In partial fulfillment of the requirements for the degree of

    Master of Science

    in

    Mechanical Engineering

    Committee Members: R. Gordon Kirk, Chair

    Charles Reinholtz Daniel J. Inman

    May 6, 2004 Blacksburg, VA

    Keywords: helical, gearbox, split path, split torque

    Copyright 2004

  • Analysis of a Split-Path Gear Train with

    Fluid-Film Bearings

    Andrew Wolff, M.S.

    Virginia Polytechnic Institute and State University, 2004

    Advisor: R. Gordon Kirk

    (Abstract)

    In the current literature, split path gear trains are analyzed for use in helicopter

    transmissions and marine gearboxes. The goal in these systems is to equalize the

    torque in each path as much as possible. There are other gear trains where the

    operator intends to hold the torque split unevenly. This allows for control over the

    gearbox bearing loading which in turn has a direct effect on bearing stiffness and

    damping characteristics. Having control over these characteristics is a benefit to a

    designer or operator concerned with suppressing machine vibration.

    This thesis presents an analytical method for analyzing the torque in split path gear

    trains. A computer program was developed that computes the bearing loads in

    various gearbox arrangements using the torque information gathered by the analytical

    method. A case study is presented that demonstrates the significance of the analytical

    method in troubleshooting an industrial gearbox that has excessive vibration.

  • iii

    To my father,

    Dr. David A. Wolff,

    and my mother,

    Dr. Linda D. Wolff

  • iv

    Acknowledgements

    I would like to thank my advisor, Dr. Gordon Kirk, for his guidance throughout my

    graduate work at Virginia Polytechnic Institute and State University. I appreciate the

    invitation to conduct rotor dynamics research after attending his class on the topic. I

    would also like to extend my thanks to Dr. Charles Reinholtz and Dr. Daniel J.

    Inman as members of my advisory committee.

    Finally I would like to thank my parents and Jen for their support and love

    throughout my academic career. It has been rewarding and exciting sharing the

    graduate student experience with Jen.

  • v

    Table of Contents

    page

    Abstract ii

    Dedication iii Acknowledgements iv List of Figures vii List of Tables ix Nomenclature x

    Chapter 1 Introduction 1

    1.1 Literature Review................................................................... 2 1.2 Research Objectives................................................................ 4 Chapter 2 Bearing Loads in a Gearbox 5

    2.1 Introduction............................................................................ 5 2.2 Concepts and Definitions..................................................... 5 2.3 Visual Basic.NET Code ...................................................... 10 Chapter 3 Split Path Gear Trains 16

    3.1 Introduction ........................................................................... 16 3.2 Concepts and Definitions .................................................... 16 3.3 Analytical Model .................................................................... 21 3.4 Computer Program Split Path Calculation ....................... 28

    Chapter 4 Case Study: CRF Test Stand 33

    4.1 Introduction ........................................................................... 33 4.2 Analytical Model Comparison ............................................. 41

    Chapter 5 Conclusions and Recommendations 50

    5.1 Conclusions ............................................................................ 50 5.2 Recommendations ................................................................. 51

  • vi

    Table of Contents (continued) page References 53

    Appendix A -- Gear Layout 1 Code Segment 54 Appendix B -- Gear Layout 2 Code Segment 58

    Appendix C -- Bearing Profile Plotting Program 65

    Vita 67

  • vii

    List of Figures

    page

    2.1 Helical Gear Nomenclature ....................................................................... 7

    2.2 Helical Gear Mesh Force Components .................................................. 8

    2.3 Helical Gear Axial Force Directions ..................................................... 9

    2.4 Gear Layout Option Screen ..................................................................... 10

    2.5 Force Vector Diagram for Gear Layout 1 ............................................. 11

    2.6 Bearing Location Input Screen for Gear Layout 1 ................................ 12

    2.7 Shaft Mass Input Screen for Gear Layout 1 .......................................... 13

    2.8 Gear Parameter Input Screen for Gear Layout 1 ................................. 14

    2.9 Bearing Loads Results Screen for Gear Layout 1 .................................. 15

    3.1 Split Path Gear Train – Front View ......................................................... 18

    3.2 Split Path Gear Train – Top View .......................................................... 19

    3.3 Conceptual Plot of Split Path Torque .................................................... 20

    3.4 Split Path Torque – Each torque path has identical stiffness .............. 26

    3.5 Split Path Torque – Path B has greater stiffness than path A ............ 27

    3.6 Split Path Torque – Path A has greater stiffness than path B ............ 27

    3.7 Bearing and Gear Arrangement for Gear Layout 2 ............................... 28

    3.8 Force Vector Diagrams for Gear Layout 2 ............................................. 29

    3.9 Bearing Location Input Screen for Gear Layout 2 ................................ 30

    3.10 Gear Parameter Input Screen for Gear Layout 2 ................................. 31

    3.11 Bearing Loads Result Screen for Gear Layout 2 .................................... 32

    4.1 CRF Test Stand Gear Train ...................................................................... 34

    4.2 High Speed Pinion Shaft DyRoBeS Model ............................................ 36

    4.3 Multiple Station Forced Response with estimated bearing loading ...... 36

    4.4 High Speed Pinion Shaft Bearing Profile ................................................. 38

    4.5 Matlab plot used to match measured bearing profile ........................... 40

    4.6 Torque split plot using the CRF gear train parameters ........................ 44

  • viii

    List of Figures (continued)

    page

    4.7 Torque Split in Path B as a Function of Clocking Angle –

    CRF gear train parameters ........................................................................... 45

    4.8 Torque in Each Path using as a Function of Clocking Angle –

    CRF gear train parameters .......................................................................... 45

    4.9 BePerf Bearing Diagram Updated with Correct Loading Vector ........ 46

    4.10 Multiple Station Forced Response – 10,000 HP ..................................... 47

    4.11 3D Forced Response – 10,000 HP – 0.56 Torque Split ......................... 47

    4.12 Sensitivity Plot – Changes in Support Stiffness ....................................... 48

    4.13 Sensitivity Plot -- Changes in Torque Splits ............................................ 49

  • ix

    List of Tables

    page

    4.1 Comparison Between DyRoBeS and VT-FAST Software ..................... 35

    4.2 BePerf Approximate and Improved Bearing Properties ........................ 41

    4.3 Stiffness Factors in each Path of the CRF test stand .............................. 42

    4.4 Bearing Support Stiffness Sensitivity ......................................................... 49

    4.5 Bearing Load Sensitivity ............................................................................... 49

  • x

    Nomenclature

    ac = pt = transverse circular pitch

    ae = pn = normal circular pitch

    Cb = Bearing clearance

    Cp = Lobe radial clearance

    Cxx = Bearing damping in the x-direction

    D = Bearing inner diameter

    Fa = Helical gear axial force component

    Fn = Helical gear transmission force

    Fr = Helical gear radial force component

    Ft = Helical gear tangential force component

    GR = gear reduction ratio of the input pinion and compound shaft gear

    kA = torsional stiffness of path A

    kB = torsional stiffness of path B

    Kxx = Bearing stiffness in the x-direction

    L = Bearing length

    L/D = Length to Diameter ratio