A N A M E R I C A N N A T I O N A L S T A N D A R D

ASME B5.50-2009[Revision of ASME B5.50-1994 (R2003)]

7/24 Taper Tool to Spindle Connection for Automatic Tool Change

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Date of Issuance: December 11, 2009

This Standard will be revised when the Society approves the issuance of a new edition. There willbe no addenda or written interpretations of the requirements of this Standard issued to this edition.

Periodically, certain actions of the ASME B5 Committee may be published as Cases. Cases arepublished on the ASME Web site under the Committee Pages at http://cstools.asme.org as they areissued.

ASME is the registered trademark of The American Society of Mechanical Engineers.

This code or standard was developed under procedures accredited as meeting the criteria for American NationalStandards. The Standards Committee that approved the code or standard was balanced to assure that individuals fromcompetent and concerned interests have had an opportunity to participate. The proposed code or standard was madeavailable for public review and comment that provides an opportunity for additional public input from industry, academia,regulatory agencies, and the public-at-large.

ASME does not “approve,” “rate,” or “endorse” any item, construction, proprietary device, or activity.ASME does not take any position with respect to the validity of any patent rights asserted in connection with any

items mentioned in this document, and does not undertake to insure anyone utilizing a standard against liability forinfringement of any applicable letters patent, nor assume any such liability. Users of a code or standard are expresslyadvised that determination of the validity of any such patent rights, and the risk of infringement of such rights, isentirely their own responsibility.

Participation by federal agency representative(s) or person(s) affiliated with industry is not to be interpreted asgovernment or industry endorsement of this code or standard.

ASME accepts responsibility for only those interpretations of this document issued in accordance with the establishedASME procedures and policies, which precludes the issuance of interpretations by individuals.

No part of this document may be reproduced in any form,in an electronic retrieval system or otherwise,

without the prior written permission of the publisher.

The American Society of Mechanical EngineersThree Park Avenue, New York, NY 10016-5990

Copyright © 2009 byTHE AMERICAN SOCIETY OF MECHANICAL ENGINEERS

All rights reservedPrinted in U.S.A.

CONTENTS

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivCommittee Roster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vCorrespondence With the B5 Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Essential Dimensions for 7/24 Taper Toolholder Shank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 Essential Dimensions for Retention Knobs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

4 Essential Dimensions for 7/24 Taper Spindle Sockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Figure1 Optional Face-Mount Holes, 7/24 Taper Spindle Socket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Tables1 Essential Dimensions of Basic Toolholder Shanks for Machining Centers With

Automatic Tool Changers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Essential Dimensions of Retention Knobs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Essential Dimensions of 7/24 Taper Spindle Socket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Nonmandatory AppendicesA Useful Technical Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9B Excerpt From ISO 1947:1973, System of Cone Tolerances for Conical Workpieces

From C p 1:3 to 1:500 and Lengths From 6 to 630 mm . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

iii

FOREWORD

The Aerospace Industries Association (AIA) developed, in cooperation with machine toolbuilders and users, standards of toolholder shanks and retention knobs for machining centerswith automatic tool changers. AIA/NAS 970 was first published in 1964. The objective of thisstandardization effort was to reduce the large number of already existing tool shank configurationsand to prevent the creation of new ones. The toolholder shanks made by different machine toolbuilders varied in the methods and in dimensional details of the gripping by the transfer mecha-nism and retention in the machine tool spindle. The resulting lack of interchangeability createdproblems of maintaining large toolholder inventories. The AIA standard covered a series ofstraight and tapered shank toolholders, but the standard never found wide acceptance; one ofthe reasons given for this was that standardization attempted too “early in the art” would havestifled innovation and development of better tool shanks for machining centers.

During the intervening years, almost every machine tool builder continued to develop theirown, often proprietary and very ingenious, toolholder shank configurations for their machiningcenters. This resulted in an almost unbearable economic situation, where one user had to maintainno less than 28 noninterchangeable tool shank configurations to operate their machining centers,supplied by the various machine tool builders. These 28 different tool shank configurations shouldbe multiplied by the number of basic sizes to get an understanding of the resulting tool inventoryproblem.

A major user of machining centers decided to end this situation and developed a tool shankfor machining centers. Several major machine tool builders, toolholder manufacturers, and usersof machining centers were approached to discuss and confirm the need and practicality of theirproposed design, and consider it as a basis for an American National Standard. A technicalcommittee (TC 45) of American National Standards Committee (ANSC) B5, Group C, was dele-gated to study the proposed tool shank and prepare drafts for an American National Standard.

A standard was developed and published in November of 1978, as ANSI B5.50-1978. Thetechnical committee followed the policy to establish new standards in SI units, and it was hopedthat ISO would adopt a common worldwide metric standard.

After a number of meetings and recommendations, the ISO put forward a recommendationthat would create more than one standard, which would lead to confusion by the addition of anumber of national metric standards.

TC 45 of ANSC B5, Group C therefore recommended that the 1978 edition of the standard berevised and replaced with a new inch standard to reflect usage in this country.

This Standard specifies the dimensions of toolholder shanks, retention knobs, and sockets, anduseful related technical information for machine tool spindles having 7/24 tapers intended forautomatic tool changing.

Dimension M (Table 1) has been revised to allow for greater manufacturing flexibility.Prior to this Standard, there were no applicable standards specifying dimensions and tolerances

for tool sockets to match the tool shanks in ASME B5.50-1994.Suggestions for improvement of this Standard are welcome. They should be sent to The

American Society of Mechanical Engineers, Secretary, B5 Standards Committee, Three ParkAvenue, New York, NY 10016-5990.

This revision was approved as an American National Standard on March 31, 2009.

iv

ASME B5 COMMITTEEMachine Tools — Components, Elements,

Performance, and Equipment(The following is the roster of the Committee at the time of approval of this Standard.)

STANDARDS COMMITTEE OFFICERS

C. T. Wax, ChairC. J. Gomez, Secretary

STANDARDS COMMITTEE PERSONNEL

J. A. Babinski, Contributing Member, Danaher MotionA. M. Bratkovich, The Association for Manufacturing TechnologyJ. B. Bryan, Honorary Member, ConsultantH. Cooper, Honorary Member, ConsultantD. A. Felinski, The Association for Manufacturing TechnologyC. J. Gomez, The American Society of Mechanical EngineersK. J. Koroncey, General MotorsC. D. Lovett, ConsultantD. Mancini, Edmunds GagesJ. A. Soons, National Institute of Standards and TechnologyR. C. Spooner, Powerhold, Inc.D. Springhorn, Diebold Goldring Tooling, USAC. T. Wax, Consultant

TECHNICAL COMMITTEE 45 — SPINDLE NOSES ANDTOOL SHANKS FOR MACHINING CENTERS

D. Springhorn, Chair, Diebold Goldring Tooling, USAJ. Burley, Vice Chair, BIG Kaiser Precision Tool, Inc.D. W. Berling, OdawaraD. G. Hartman, Parlec, Inc.G. S. Hobbs, Advanced Machine and Engineering Co.K. Hoffmann, Ingersoll Machine ToolsC. Koehn, Stotz USAR. Laube, Hydra-Lock Corp.D. Mancini, Edmunds GagesE. I. Rivin, Wayne State UniversityO. Sandkuehler, Bilz Tool Co., Inc.S. G. Wallace, The Boeing Co.C. T. Wax, ConsultantH. M. Whalley, The George Whalley Co.C. Xie, Centrix Precision, Inc.

CORRESPONDENCE WITH THE B5 COMMITTEE

General. ASME standards are developed and maintained with the intent to represent theconsensus of concerned interests. As such, users of this Standard may interact with the Committeeby proposing revisions and attending Committee meetings. Correspondence should beaddressed to:

Secretary, B5 Standards CommitteeThe American Society of Mechanical EngineersThree Park AvenueNew York, NY 10016-5990http://go.asme.org/Inquiry

Proposing Revisions. Revisions are made periodically to the Standard to incorporate changesthat appear necessary or desirable, as demonstrated by the experience gained from the applicationof the Standard. Approved revisions will be published periodically.

The Committee welcomes proposals for revisions to this Standard. Such proposals should beas specific as possible, citing the paragraph number(s), the proposed wording, and a detaileddescription of the reasons for the proposal, including any pertinent documentation.

Proposing a Case. Cases may be issued for the purpose of providing alternative rules whenjustified, to permit early implementation of an approved revision when the need is urgent, or toprovide rules not covered by existing provisions. Cases are effective immediately upon ASMEapproval and shall be posted on the ASME Committee Web page.

Requests for Cases shall provide a Statement of Need and Background Information. The requestshould identify the standard, the paragraph, figure, or table number(s), and be written as aQuestion and Reply in the same format as existing Cases. Request for Cases should also indicatethe applicable edition(s) of the standard to which the proposed Case applies.

Attending Committee Meetings. The B5 Standards Committee regularly holds meetings, whichare open to the public. Persons wishing to attend any meeting should contact the Secretary ofthe B5 Standards Committee.

vi

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ASME B5.50-2009

7/24 TAPER TOOL TO SPINDLE CONNECTION FOR AUTOMATICTOOL CHANGE

1 GENERAL

1.1 Scope

This Standard pertains to the standardization of basictoolholder shank, retention knob, and socket assembliesfor numerically controlled machining centers with auto-matic tool changers. The requirements contained hereinare intended to provide toolholder interchangeabilitybetween machining centers with automatic tool chang-ers of various types. This Standard is the inch solutionfor basic toolholder shank, retention knob, and socketassemblies. This design specifies an interchangeableretention knob with a 45-deg clamping surface.

Section 2 of this Standard specifies the dimensionsand tolerances of toolholder shanks having 7/24 tapersintended for automatic tool change. These are intendedfor use with the corresponding basic retention knob andspindle sockets specified in sections 3 and 4 (see Table 1).

Section 3 contains information for standardization ofretention knobs for use with the 7/24 connection systemdescribed herein (see Table 2).

Section 4 specifies the dimensions and tolerances ofspindle sockets, drive keys, and key seats for machinetool spindles having 7/24 tapers intended for automatictool change (see Table 3 and Fig. 1). These are intendedfor use with the corresponding basic toolholder shankand retention knob specified in sections 2 and 3.

1.2 Noninterchangeability

Tool shanks conforming to ASME B5.18-1972 andASME B5.40-1977 are not interchangeable with toolshanks established in this Standard. Tool shanks con-forming to ISO 7388-1:1983 and retention knobISO 7388-2:1984 types “A” and “B” are not interchange-able with this Standard. This also applies to additionalshank and knob designs that are in the draft stageswithin the ISO standards development system. Accord-ingly, the reader should note the warning statementincluded with the retention knob specifications shownin Table 2.

Some incompatibility with existing automatic toolchange arms may arise from dimension M (Table 1).

1.3 Classification

This Standard covers a basic toolholder shank withan “inch” threaded retention knob with 45-deg clampingsurface that is applicable to general-purpose machining

1

centers where loading and exchange of toolholders isaccomplished by automatic means. The termgeneral purpose is intended to differentiate betweenmachine designs for unusually high accuracy require-ments or designs intended to function with exception-ally high spindle rotational speeds coupled with higheraxis feed rates, such as is normally found in high-speedmachining. Tool shanks made to this Standard may beused with a variety of proprietary retention and/orflange locking systems.

1.4 Definitions

Terms relevant to this Standard and its applicationare as follows:

automatic tool changer (ATC): mechanism for the transferof the toolholder between a storage feature and the spin-dle or nonrotating socket.

balance: when the mass centerline and rotational center-line of a rotor are coincident.

basic cone: geometrically ideal conical surface that isgiven by its geometrical dimensions. These are a basiccone diameter, the basic cone length, and the basic rateof taper, or the basic cone angle.

basic toolholder shank: unit that fits directly into the spin-dle or nonrotating socket of the machine and has provi-sion for automatic tool change.

coolant hole: passage through the center of the retentionknob that allows through-the-spindle coolant to pass.This hole also permits access to a tool set height adjust-ment screw if so equipped.

drive key: device intended to assist in delivery of thedriving torque from the spindle nose to the tool.

effective case: depth within a metal part, measured fromthe part’s surface, where the minimum required hard-ness is present.

retention knob: member of the toolholder retention sys-tem that provides a coupling point between the tool-holder taper and the spindle drawbar.

spindle: component assembly of the machine tool, thefunction of which is to accept the basic toolholder shank.

spindle nose: the part of a spindle into which the toolshank is accepted.

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ASME B5.50-2009

Fig. 1 Optional Face-Mount Holes, 7/24 Taper Spindle Socket

CC

BB

Section D–D

-A-

AA

D

D

45 deg

0.006 A0.008

Taper sizes 30, 40, and 45Taper sizes 50 and 60 A

tool angular orientation: mechanical feature to positionand retain the basic toolholder shank in a specific angu-lar relationship to the spindle or nonrotating socket.

tool shank: the part of a tool which mates with the taperin the spindle nose.

1.5 References

1.5.1 The following is a list of publications refer-enced in this Standard.

ASME B5.18-1972, Spindle Noses and Tool Shanks forMilling Machines

ASME B5.40-1977, Spindle Noses and Tool Shanks forHorizontal Boring Machines

ASME Y14.5-2009, Dimensioning and TolerancingPublisher: The American Society of Mechanical

Engineers (ASME), Three Park Avenue, New York,NY 10016-5990; Order Department: 22 Law Drive, Box2300, Fairfield, NJ 07007-2300 (www.asme.org)

ISO 1940-1:2003, Mechanical vibration — Balance qual-ity requirements for rotors in a constant (rigid) state —Part 1: Specification and verification of balancetolerances

ISO 1940-2:1997, Mechanical vibration — Balance qual-ity requirements of rigid rotors — Part 2: Balanceerrors

ISO 1947:1973 (withdrawn), System of cone tolerancesfor conical workpieces from C p 1:3 to 1:500 andlengths from 6 to 630 mm

ISO 7388-1:2007, Tool shanks with 7/24 taper for auto-matic tool changers — Part 1: Dimensions and desig-nation of shanks of forms A, AD, AF, U, UD and UF

2

ISO 7388-2:2007, Tool shanks with 7/24 taper for auto-matic tool changers — Part 2: Dimensions and desig-nation of shanks of forms J, JD and JF

Publisher: International Organization forStandardization (ISO), 1 ch. de la Voie-Creuse, postale56, CH-1211 Gene ve 20, Switzerland/Suisse(www.iso.org). Copies of ISO documents may beobtained from the American National StandardsInstitute (ANSI), 25 West 43rd Street, New York, NY10036 (www.ansi.org).

1.5.2 The following documents are not referencedin this Standard but are relevant to the subject and maybe of interest to the user of this Standard.

ASME B5.10-1994, Machine Tapers (Self Holding andSteep Taper Series)

ISO 9270:1992, 7/24 tapers for tool shanks for automaticchanging — Tapers for spindle noses

2 ESSENTIAL DIMENSIONS FOR 7/24 TAPERTOOLHOLDER SHANK

See Table 1.

3 ESSENTIAL DIMENSIONS FOR RETENTIONKNOBS

See Table 2.

4 ESSENTIAL DIMENSIONS FOR 7/24 TAPERSPINDLE SOCKETS

4.1 DimensionsSee Table 3.

4.2 Optional Face-Mount HolesSee Table 3 and Fig. 1.

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ASME B5.50-2009

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ASME B5.50-2009

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ASME B5.50-2009

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ASME B5.50-2009

NONMANDATORY APPENDIX AUSEFUL TECHNICAL INFORMATION

A-1 GENERAL

This Nonmandatory Appendix is intended to provideinformative content pertaining to the use of the 7/24taper spindle-to-toolholder connection. These are gen-eral recommendations which if followed should max-imize performance and minimize maintenancedifficulties. Nominal operational values for 7/24 tapertoolholder shanks are shown in Table A-1. All of thiscontent is derived from decades of practical experiencewith the subject toolholder interface in aerospace, auto-motive, and general machine shop practice. Items toconsider when specifying either the toolholder or spin-dle side of the interface are

(a) age, condition, and service requirements of themachine tool

(b) the ability to either maintain toolholder interfaceintegrity or repair and replace worn-out equipment

(c) updated training for machinists and programmers(d) the knowledge of your machine tool supplier on

the subjects of machining dynamics, allowable machin-ing forces, and maintenance of drawbar mechanisms

(e) the degree to which a given spindle taper can bereground without exceeding the depth of the hard-ened case

The cone tolerance system as historically describedby ISO 1947 is presented to the extent that it pertainsto this Standard (see Nonmandatory Appendix B).

A-2 DRAWBAR FORCES

7/24 taper tool to spindle connections require suffi-cient force pulling on the retention knob to achieve thefollowing operational characteristics. These characteris-tics are directly affected by the amount of pulling forceand, because of this, performance characteristics of thetoolholder-to-spindle connection will change if drawbarforce changes. At tool change, the drawbar pull forceelastically deforms the mating tapers until enough sur-face area contact is made to distribute point contactforces and seat the taper. The performance characteris-tics affected by drawbar pull force are

(a) positional accuracy and stability of the machinetool

(b) resistance to torque-induced slippage at thetoolholder–spindle interface

9

(c) resistance to pulling out (unseating the taper) dur-ing heavy cuts

(d) vibration characteristics of the machining system(e) resistance to damage between mating tapers

NOTE: A poor taper fit will degrade any or all of the aboveperformance characteristics regardless of drawbar pull force.

A-3 BALANCE REQUIREMENTS

Balance should not be pursued to unnecessarily highquality levels. For additional information, see ISO 1940-1and ISO 1940-2.

A-4 REFERENCES AND INFORMATION

A-4.1 Care of the Tool-to-Spindle Connection

In order to guarantee the minimum runout error anda long spindle and toolholder life, special care must betaken to keep this area clean. The person loading andunloading tools from the machine should visuallyinspect each toolholder for wear and signs of corrosion.

Below is a description of each item involved in theprocess.

A-4.1.1 Spindle. The spindle nose must be keptclean and free from deposits of any kind. Depending onthe application, the user must establish regular cleaningintervals. Occasionally, a special taper cleaner (commer-cially available from tool manufacturers) should be usedto clean the seating surfaces. A high-resolution indicatorcan be used to measure the taper runout. If the runoutis excessive, the spindle may need repair. A runout testarbor can be used to check the runout at a certain dis-tance from the spindle nose.

A-4.1.2 Toolholder Care. Toolholders must bereplaced when the taper starts to wear or when excessivecorrosion is noted. Minor blemishes can be repaired witha stone or crocus cloth. Occasionally, the runout of thecutting tool seat should be checked with an indicatoron the machine. Toolholders that will not be used forsome time should be treated with a rust preventative.

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ASME B5.50-2009

Table A-1 Nominal Operational Values for 7/24 Taper Toolholder Shanks

MaximumRetention Knob Maximum Operational Rotational

Taper Installation Suggested Drawbar Bending Moment at Speed,Standard Torque, ft-lb Pull Force, lb Gage Line, in.-lb rpm

30 8 1,200 1,800 14,00040 30 2,300 3,450 10,00045 50 4,000 6,000 8,00050 75 5,000 7,500 6,00060 120 13,000 19,500 3,600

GENERAL NOTE: Higher rotational speeds may be obtained by optimizing balance level and interfacecone tolerances, and minimizing tool assembly projection.

A-4.1.3 Drawbar Care. The drawbar gripper posi-tion must be set according to the manufacturer’s specifi-cations, and should be checked frequently and adjustedif necessary. A pull-force gage can be used to determinethe drawbar condition. A low pull force will cause exces-sive wear to toolholder and spindle nose and must beavoided. If low pull force is detected or suspected, thedrawbar may require maintenance.

10

A-4.1.4 Tool Magazine. The tool magazine must bekept clean and free from chips. The magazine must beable to handle the toolholder and present it to themachine with sufficient accuracy that the holder willseat properly in the spindle after clamping. Grippersthat allow excessive looseness/sag of the holder must bereplaced or, alternatively, tools exceeding the magazinecapacity must be loaded manually.

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ASME B5.50-2009

NONMANDATORY APPENDIX BEXCERPT FROM ISO 1947:1973, SYSTEM OF CONE

TOLERANCES FOR CONICAL WORKPIECES FROM C p 1:3 TO1:500 AND LENGTHS FROM 6 TO 630 mm

© International Organization for Standardization (ISO). This material is reproduced from ISO 1947:1973 with permission of the AmericanNational Standards Institute on behalf of ISO. ISO 1947:1973 was withdrawn by ISO on August 17, 1995 and can no longer be consideredan approved ISO standard. No part of this material may be copied or reproduced in any form, electronic retrieval system, or otherwise ormade available on the Internet, a public network, by satellite, or otherwise without the prior written consent of the American National StandardsInstitute, 25 West 43rd Street, New York, NY 10036.

NOTE: This excerpt from ISO 1947:1973 and the standards refer-enced within are nonbinding to ASME B5.50. Content is shown toclarify the derivation of angular tolerance (AT) grades only. Notolerance system is endorsed nor encoded by inclusion herein.Portions of the original ISO 1947:1973 are omitted for clarity.

B-1 SCOPE AND FIELD OF APPLICATION

This international Standard specifies a cone tolerancesystem which applies to rigid conical workpieces forwhich the length of the generator can be considered aspractically equal to the basic cone length; this appliesin the case of cones having a rate of taper C p 1:3 to1:500.1

For dimensioning and tolerancing cones on drawings,see ISO 3040, Technical drawings — Dimensions andtolerancing cones.2

For general information on tolerances of form and ofposition, see ISO/R 1101, Tolerances of form and ofposition — Part I: Generalities, symbols, indications ondrawings.

B-2 BASIS OF THE SYSTEM

B-2.1 Types of Cone Tolerance

The following four types of tolerance provide the basisof the cone tolerance system:

(a) cone diameter tolerance, TD, valid for all conediameters within the cone length, L.

(b) cone angle tolerance, AT, given in angular or lineardimensions (AT� or ATD).

1 For cones of 1:3 up to 1:500, the length of the generator andthe cone length may be regarded as equal, since these lengths givedifferences in cone angle tolerances of less than 2%.

2 At present at the stage of draft.

11

(c) cone form tolerance, TF (tolerances for thestraightness of the generator and for the roundness ofthe section).

(d) cone section diameter tolerance, TDS, given for thecone diameter in a defined section. It is valid for thecone diameter of this section only.

B-2.2 Cone Diameter Tolerance, Cone AngleTolerance, and Cone Form Tolerance

Normal cases will be handled by application of thecone diameter tolerance, TD, only. It includes the twotolerances of the types in paras. B-2.1(b) and (c). Thismeans that the deviations of these two types may, inprinciple, utilize the whole tolerance space given by thecone diameter tolerance, TD (see Fig. B-1). In case ofstronger requirements, the cone angle tolerance and thecone form tolerance may be reduced within the conediameter tolerance, TD, by means of supplementaryinstructions. In this case, likewise, no point on the conicalsurface is permitted to lie outside the limit cones’ givenTD. In practice, all types of tolerance generally exist atthe same time and, as far as normal cases are concerned,each tolerance may occupy a part of the cone diametertolerance, TD, only in such a way that no point on theconical surface lies outside the tolerance space. In otherwords, no point on the conical surface is permitted tolie outside the limit cones.

B-2.3 Cone Section Diameter Tolerance

If for functional reasons the cone diameter toleranceis required in a defined section, then the cone diametertolerance, TDS [para. B-2.1(d)], must be indicated. In thiscase, it is also necessary to indicate the cone angle toler-ance. If general tolerances for the cone angle are speci-fied, e.g., in an international document, and if it isreferred to this tolerance, then it is not necessary toindicate special cone angle tolerances.

ASME B5.50-2009

B-3 DEFINITIONS

B-3.1 Definitions Relating to Geometry of Cones

cone: a conical surface or a conical workpiece (seeFig. B-2), defined by its geometrical dimensions. In theabsence of any indication concerning the geometricalform, cone is understood to mean a straight circularcone or truncated cone.

conical surface: a surface of revolution which is formedby rotating a straight line (generator) around an axiswith the straight line intersecting this axis at the apex(see Fig. B-2). The parts of this infinite conical surfaceare also known as conical surfaces or cones. Similarly,“cone” is also the abbreviated designation of a trun-cated cone.

conical workpiece: a workpiece or portion of a workpiece,the main part of which is a conical surface (see Figs. B-3and B-4).

external cone: a cone which limits the outside form of aconical feature of a workpiece (see Figs. B-3 and B-5).

internal cone: a cone which limits the inside form of aconical feature of a workpiece (see Figs. B-4 and B-5).

basic cone: the geometrically ideal conical surface whichis given by its geometrical dimensions. These are either

(a) a basic cone diameter, the basic cone length, andthe basic rate of taper or the basic cone angle, or

(b) two basic cone diameters and the basic cone length(see Fig. B-6)

actual cone: that cone the conical surface of which hasbeen found by measurement (see Fig. B-7).

limit cones: the geometrically ideal coaxial surfaces, hav-ing the same basic cone angle, which result from thebasic cone and the cone diameter tolerances. The differ-ence between the largest and the smallest cone diametersis the same in all sections normal to the cone axis (seeFig. B-8). The surfaces of the limit cones may be madeto coincide by axial displacement.

generator: the line of intersection of the conical surfacewith a section in the axial plane (see Figs. B-2 and B-5).

B-3.2 Definitions Relating to Sizes on Cones

cone diameter: the distance between two parallel linestangent to the intersection of the circular conical surfacewith a plane normal to the cone axis.

basic cone diameters are as follows (see Fig. B-6):(a) the largest cone diameter, D, or(b) the smallest cone diameter, d, or(c) the cone diameter, d, at a place determined by its

position in the axial direction

actual cone diameter, da: the distance between two parallellines tangent to the intersection of the surface of theactual cone with a defined plane normal to the cone axis(see Fig. B-7).

12

limit cone diameters: the diameters of the limit cones ineach section in a plane normal to the axis (see Fig. B-8).

basic cone length, L: the distance in the axial directionbetween two limiting ends of a cone (see Figs. B-5 andB-6).

basic cone angle, �: the angle formed by the two genera-tors of the basic cone in a section in the axial plane (seeFig. B-9).

limit cone angles: the largest and the smallest cone anglesresulting from the basic cone angle, cu, and the d positionand magnitude of the cone angle tolerance (seeFig. B-10).

cone generating angle, �/2: the angle contained between agenerator and the cone axis (see Fig. B-9). The generatingangle is equal to half the basic cone angle, �.

rate of taper, C: the ratio of the difference between thecone diameters, D and d, to the cone length, L

C pD − d

Lp 2 tan

�2

The rate of taper is often indicated by the expressions1:x or 1/x and “Cone 1:x” for short. For example,C p 1:20 means that a diameter difference, D − d, of1 mm occurs an axial distance, L, of 20 mm between thecone diameters, D and d.

B-3.3 Definitions Relating to Cone Tolerances

cone tolerance system: a system containing the cone diam-eter tolerances, the cone angle tolerances, and the toler-ances on the cone form of the generator and thecircumferential line of the section normal to the coneaxis.

cone diameter tolerance, TD: the difference between thelargest and smallest permissible cone diameters in anysection, i.e., between the limit cones (see Fig. B-8).

cone angle tolerance, AT:3 the difference between the larg-est and smallest permissible cone angles (see Figs. B-10and B-11).

cone form tolerances, TF

tolerance on the straightness of the generator: the distancebetween two parallel, straight lines between which theactual generator must lie (see Fig. B-8). The actual valuefor the error on straightness is taken as the distancebetween two parallel straight lines touching the actualgenerator, and so placed that the distance between themis a minimum.

tolerance on the roundness of the section: the distancebetween two coplanar concentric circles in a section nor-mal to the axis between which the actual cone sectionmust be situated (see Fig. B-12). The actual value for theerror on roundness is taken as the distance between two

3 AT p angle tolerance.

ASME B5.50-2009

coplanar concentric circles which touch the actual lineof any section normal to the axis.

cone section diameter tolerance, TDS: the difference betweenthe largest and smallest permissible cone diameters ina defined section (see Fig. B-13).

B-3.4 Definitions Relating to Actual Cone Angles

actual cone angle: in any axial plane section, the anglebetween the two pairs of parallel straight lines thatenclose the form errors of the two generators in such away that the maximum distance between them is theleast possible value (see Fig. B-14). For a given cone,there is not only one actual cone angle; for cones havingdeviations of roundness, the actual cone angle will bedifferent in different axial planes (see �1 and �2 inFig. B-14).

average actual cone angle: the arithmetical average valueof the actual cone angle measured in accordance withthe definition above in several equally distributed axialplane sections. Amongst the axial planes chosen, one atleast shall cover the greatest deviation of roundness fromthe circle line of the cone diameter.

B-3.5 Definition Relating to Cone Tolerance Space

cone tolerance space: for the conical surface, the spacebetween the two limit cones. Cone tolerance spaceincludes all the tolerances referred to in para. B-3.3. Itmay be represented by tolerance zones in two planesections (see Figs. B-8 and B-12).

B-3.6 Definitions Relating to Cone Tolerance Zones

cone diameter tolerance zone: in a graphic representation,that zone, lying in the plane section of the cone axis,which is limited by the limit cones. The total toleranceszone is represented in Figs. B-8 and B-12 by the hatchedportions that also indicate the cone tolerance space. Itincludes the tolerances for the cone diameter, the coneangle, the roundness, and the straightness that canoccupy the whole cone tolerance zone. In general, eachof these particular deviations occupies a part of the conediameter tolerance zone only.

tolerance zone for the cone angle: a fan-shaped zone withinthe limit cone angles. The inclination of the limit conescan be indicated by plus, minus, or plus/minus for thecone angle tolerances (see Fig. B-15). For the indicationof plus/minus, the values can be different.

tolerance zone for the straightness of the generator: in agraphic representation, that zone (band), situated in anyaxial plane section and disposed on each side of thecone axis, which is determined by the form tolerance ofthe generators (see Fig. B-8). As this zone is smaller thanthat referred to in the above definition of cone diametertolerance zone, it only applies if the tolerance on thestraightness of the generator is reduced with respect tothe cone diameter tolerance zone. The actual generator

13

has to be situated anywhere within a tolerance zonegiven by the tolerance for the straightness.

tolerance zone for the roundness of the section: in a graphicrepresentation, the zone lying in a section normal to thecone axis and formed by concentric circles (see Fig. B-12).As this zone is narrower than that referred to in theabove definition of cone diameter tolerance zone, it onlyapplies if the tolerance for the roundness of the sectionis reduced with respect to the cone diameter tolerancezone. The contour has to be situated anywhere withina tolerance zone given by the tolerance for the roundnessof the section.

cone section diameter tolerance zone: the tolerance zone forthe cone diameter in a defined section. It appears in thatcase if the cone diameter tolerance is indicated for afixed diameter only.

B-4 CONE DIAMETER TOLERANCE, TD

In general, the choice of the cone diameter tolerance,TD, is based on the large cone diameter, D. It is selectedfrom the ISO standard IT tolerances and applies overthe whole of the cone length, L. If it is not required toindicate smaller tolerances of angle and form, a conediameter tolerance, TD, given on the drawing, appliesalso to the angle and form deviations. It should be bornein mind, however, that in this case all workpieces thatconform to Figs. B-11 and B-16 must be accepted. Thesymbols of the ISO tolerances system shall be used toindicate the cone diameter tolerances referred to thecorresponding cone diameter. If the conical surface ofthe conical workpiece concerned is not intended for acone fit, the tolerance positions, JS and js, should bechosen for preference, e.g., 40js10.

B-5 CONE ANGLE TOLERANCE, AT

B-5.1 Cone Angle Tolerance Resulting From the ConeDiameter Tolerance, TD

The actual cone angle lies within the cone diametertolerance zone in case of absence of any special indica-tion of cone angle tolerances. The cone angles, �max and�min (see Fig. B-11), are thus the limit cone anglesresulting from the cone diameter tolerance, TD. Conse-quently, in this case, the actual cone angle is permittedto be disposed with respect to the basic cone angle, �,from +�� to −�� (for values of ��, see Table B-1).

B-5.2 Fixed Cone Angle Tolerance

If the cone angle tolerance has to be smaller than thatgiven by the cone diameter tolerance, it is necessaryto establish the cone angle limits. For the cone angletolerances, the deviations must be indicated by plus,minus, or plus/minus, e.g., +AT, −AT, ±AT/2. For theindication of plus/minus, the values can be different.

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ASME B5.50-2009

B-6 CONE FORM TOLERANCES, TF

Cone form tolerances comprise the tolerances on(a) the straightness of the generator (see Fig. B-8)(b) the roundness of the cone section (see Fig. B-12)Cone form tolerances shall be especially indicated (in

micrometers) if they must be smaller than half of thecone diameter tolerance.

B-7 CONE SECTION DIAMETER TOLERANCE, TDS

If the cone diameter tolerance should be reducedlocally and should be given for a defined section only, forfunctional or manufacturing reasons, the cone diametertolerance must be indicated for this section only.

B-8 TABLE OF CONE ANGLE TOLERANCES

As the cone angle tolerances, AT, have different func-tions, they are stepped in grades represented by num-bers, e.g., AT5. They are expressed in microradians(�rad)4 for AT�, or in micrometers (�m) for ATD, calcu-lated from the constant AT value within a range of conelengths. ATD is valid normal to the axis5 in the form ofa diameter difference. It must be smaller with respectto the cone diameter tolerance, TD. Taking account ofthe units (micrometers, microradians), the followingrelationship exists (see also Fig. B-17):

ATD p AT� � L

The grade numbers for IT (diameter) and AT (angle)tolerances are chosen in such a way that the same num-bers correspond to approximately the same difficulties

4 1 �rad p an angle producing an arc of length 1 �m at a radialdistance of 1 m. 5 �rad p 1 in. (1 sec); 300 �rad p 1 ft (1 min).

5 The measurement normal to the cone axis is regarded as equiva-lent to the theoretical correct measurement normal to the generator,as the difference of the measured AT0 values is only 2% even fora cone 1:3.

14

of manufacture. No direct relation is given, however,because the IT values are stepped in accordance withthe diameter of cylindrical workpieces, whereas the ATvalues are stepped in accordance with the cone length, L.

The ratio for the cone angle tolerances from one ATgrade to the next higher grade is 1.6. It is necessary torelate the cone angle tolerance, AT, to the cone length,L, because the longer the length of cone, the better theangle may be met. The cone lengths, L, from 6 mm to630 mm are divided into ten ranges with a stepped ratioof 1.6.

The AT� values decrease from one range of length tothe next higher range by a step of 0.8, which correspondsto the experimental relationship

AT� ~1

�L

As the AT� values are held constant in a cone lengthrange, it is the corresponding ATD values that vary. Theyare given for the limits of the ranges of lengths andincrease from one length range to the next with a ratioof 1.25.

Figure B-17 shows the largest and smallest values forATD resulting from the largest (Lmax) and smallest (Lmin)basic lengths of a length range at a constant AT� value.

No relationship is provided for between the coneangle tolerance and the cone diameter because of lackof experience (see Fig. B-18). The introduction of sucha relationship will be made in the future if sufficientexperience is available. In the case of conical workpieceswith large cone diameter, it is left to the user to selecta higher AT grade than that used for conical workpiecesof small diameter.

If finer or coarser angle tolerances are necessary, theyshall be calculated by division or multiplication by 1.6from the AT1 and AT12 values, respectively. The finer ATgrades shall be designated AT0, AT01.

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ASME B5.50-2009

Fig. B-1 Cone Diameter Tolerance Space Formed by the Cone Diameter Tolerance

Dm

inT D

/

Dm

ax

2

Fig. B-2 Cone

Generator

Conical surface and conical workpiece

Fig. B-3 Conical Workpiece, External Cone

15

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ASME B5.50-2009

Fig. B-4 Conical Workpiece, Internal Cone

Fig. B-5 General Definitions

De

Limit edges

Cone axis

Conical surface and generator

Face

Basic point

FaceExternal cone

Cone length, Le

Cone length, Li

Internal cone

Di

Limit edges

Fig. B-6 Basic Cone

dx

X

L

d D

16

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ASME B5.50-2009

Fig. B-7 Actual Cone

da

da

Fig. B-8 Limit Cones, Cone Diameter, Tolerance Zone, and Straightness of the Generator Tolerance Zone

dmax dmin

Dm

in

Actual cone

Limit cones

Form tolerance zone of the generator

Cone diameter tolerance zone

Tolerance on the straightness

Dm

ax

L

TD /2

Fig. B-9 Angles on Cones

L

d

Basic cone

Generating angle

Basic angle

D

/2

17

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ASME B5.50-2009

Fig. B-10 Limit Cone Angles

αmaxαmin

ATα /2

Fig. B-11 Admissible Limit Cone Angles Resulting From the Cone Diameter Tolerance

Dm

in

Dm

ax

T D/2

Fig. B-12 Cone Diameter Tolerance Zone and Roundness Tolerance Zone

Cone diameter tolerance zone

Tolerance on the roundness

Actual cone

Form tolerance zone of the section

TD /2

18

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ASME B5.50-2009

Fig. B-13 Cone Section Diameter Tolerance, TDS, and Cone Angle Tolerance, AT

Dm

ax

Defined section [Note (1)]

Dx

Defined section [Note (2)]D

min

Defined section [Note (3)]

T DS

/2T D

S/2

T DS

/2

AT/2

AT/2

AT/2

NOTES:(1) The actual cone diameter in the defined section has the maximum permissible size of the cone diameter.(2) The actual cone diameter in the defined section lies between the limit sizes of the cone diameter.(3) The actual cone diameter in the defined section has the minimum size of the cone diameter.

Fig. B-14 Actual Cone Angles

2

2

2

2

1

1

1

1

19

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ASME B5.50-2009

Fig. B-15 Position of the Cone Angle Within the Cone Diameter Tolerance Zone

(a)

AT/2 AT/2 AT/2

AT/2

(b) (c)

Fig. B-16 Admissible Cone Form Deviation Resulting From the Cone Diameter Tolerance

Dm

in

Dm

ax

T D/2

Fig. B-17 Variation of ATD Within a Range of Cone Length With the Limits of the Length Range,L1 and L2

at L

2

at L

1

L2

L1

AT D

/2

AT /2

AT D

/2

20

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ASME B5.50-2009

Fig. B-18 Cone Angle Tolerance, AT� , of a Cone Defined by Its Measuring Diameter and the LongitudinalDimensions of Which Are Defined Themselves From the Position of the Measuring Plane

D

Table B-1 Table of Cone Angle Tolerances

Range ofAT4 AT3Cone Length, L,

mm AT� AT�

Over Up to �rad sec ATD, �m �rad sec ATD, �m

6 10 200 41 1.3 to 2 125 26 0.8 to 01.310 16 160 33 1.6 to 2.5 100 21 1 to 1.616 25 125 26 2 to 3.2 80 16 1.3 to 225 40 100 21 2.5 to 4 63 13 1.6 to 2.540 63 80 16 3.2 to 5 50 10 2 to 3.2

63 100 63 13 4 to 6.3 40 8 2.5 to 4100 160 50 10 5 to 8 31.5 6 3.2 to 5160 250 40 8 6.3 to 10 25 5 4 to 6.3250 400 31.5 6 8 to 12.5 20 4 5 to 8400 630 25 5 10 to 16 16 3 6.3 to 10

21

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ASME B5.50-2009

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