AGMA 2002-C16-2016 Tooth Thickness and Backlash Measurement of Cylindrical Involute Gearing.pdf

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1、ANSI/AGMA 2002-C16ANSI/AGMA 2002-C16 (Revision of ANSI/AGMA 2002-B88) American National Standard Tooth Thickness and Backlash Measurement of Cylindrical Involute Gearing AMERICAN NATIONAL STANDARD ANSI/AGMA 2002-C16 AGMA 2016 All rights reserved i Tooth Thickness and Backlash Measurement of Cylindri

2、cal Involute Gearing ANSI/AGMA 2002-C16 Revision of ANSI/AGMA 2002-B88 Approval of an American National Standard requires verification by ANSI that the requirements for due process, consensus and other criteria for approval have been met by the standards developer. Consensus is established when, in

3、the judgment of the ANSI Board of Standards Review, substantial agreement has been reached by directly and materially affected interests. Substantial agreement means much more than a simple majority, but not necessarily unanimity. Consensus requires that all views and objections be considered, and t

4、hat a concerted effort be made toward their resolution. The use of American National Standards is completely voluntary; their existence does not in any respect preclude anyone, whether he has approved the standards or not, from manufacturing, marketing, purchasing or using products, processes or pro

5、cedures not conforming to the standards. The American National Standards Institute does not develop standards and will in no circumstances give an interpretation of any American National Standard. Moreover, no person shall have the right or authority to issue an interpretation of an American Nationa

6、l Standard in the name of the American National Standards Institute. Requests for interpretation of this standard should be addressed to the American Gear Manufacturers Association. CAUTION NOTICE: AGMA technical publications are subject to constant improvement, revision or withdrawal as dictated by

7、 experience. Any person who refers to any AGMA Technical Publication should be sure that the publication is the latest available from the Association on the subject matter. Tables or other self-supporting sections may be referenced. Citations should read: See ANSI/AGMA 2002-C16, Tooth Thickness and

8、Backlash Measurement of Cylindrical Involute Gearing, published by the American Gear Manufacturers Association, 1001 N. Fairfax Street, Suite 500, Alexandria, Virginia 22314, http:/www.agma.org. Approved May 3, 2016 ABSTRACT This standard establishes the procedures for determining the specification

9、limits for tooth thickness of external and internal cylindrical involute gearing. It includes equations and calculation procedures for the commonly used measuring methods. A specific tooth thickness specification limit can be established from the design thickness or from another tooth thickness meas

10、urement. The procedures can be used with an established design tooth thickness, or with actual tooth thickness dimensions. The effect of tooth geometric quality variations on tooth thickness dimensions is discussed. Calculations for backlash are included, and are based on the specified tooth thickne

11、ss, center distance, and tolerances. Published by American Gear Manufacturers Association 1001 N. Fairfax Street, Suite 500, Alexandria, Virginia 22314 Copyright 2016 by American Gear Manufacturers Association All rights reserved. No part of this publication may be reproduced in any form, in an elec

12、tronic retrieval system or otherwise, without prior written permission of the publisher. Printed in the United States of America ISBN: 978-1-55589-056-8 American National Standard AMERICAN NATIONAL STANDARD ANSI/AGMA 2002-C16 AGMA 2016 All rights reserved ii Contents Foreword iv 1 Scope 1 1.1 Measur

13、ement methods included in standard 1 1.2 Types of gears. 1 1.3 Dimensional and material limitations 1 1.4 Exclusions . 1 2 Normative references 2 3 Symbols and terminology 2 3.1 Symbols . 2 3.2 Definitions 8 4 Application. 11 4.1 General 11 4.2 Datum surfaces and the datum axis . 11 4.3 Gear tooth t

14、hickness specification systems 12 4.4 Gear tooth thickness measurement methods . 13 4.5 Reporting of gear tooth thickness . 14 4.6 Measurement diameter versus contact diameter 14 4.7 Gear geometry calculations 15 5 Measurement by pitch or index . 19 5.1 Principle of measurement . 19 5.2 Underlying a

15、ssumptions and limitations 19 5.3 Advantages and disadvantages 19 5.4 Selection of measurement diameter . 20 5.5 Tooth thickness from index measurement 20 6 Measurement with a master gear on a double flank tester . 20 6.1 Principle of measurement . 20 6.2 Underlying assumptions and limitations 22 6.

16、3 Advantages and disadvantages 23 6.4 Master gear design considerations . 23 6.5 Tight mesh center distance limits 25 6.6 Test radius limits from tight mesh center distance limits 28 6.7 Functional normal circular tooth thickness from double flank test results. 28 7 Measurement with a master gear on

17、 a single flank tester 29 7.1 Principle of measurement . 29 7.2 Underlying assumptions and limitations 29 7.3 Advantages and disadvantages 30 7.4 Master gear design considerations . 30 7.5 Functional circular tooth thickness from single flank test results 30 8 Span measurement . 30 8.1 Principle of

18、measurement . 30 8.2 Underlying assumptions and limitations 32 8.3 Advantages and disadvantages 32 8.4 Number of teeth or tooth spaces spanned 33 8.5 Span measurement limits 35 8.6 Angle of rock . 36 8.7 Tooth thickness from span measurement . 37 9 Measurement over or between balls or pins . 37 9.1

19、Principle of measurement . 37 9.2 Underlying assumptions and limitations 38 9.3 Advantages and disadvantages 39 9.4 Selection of the ball or pin diameter 40 9.5 Calculations with specified ball or pin diameter 46 9.6 Measurement over one ball or pin 47 9.7 Measurement over two balls or pins . 49 9.8

20、 Free pin measurement over two pins on a helical gear with an odd number of teeth 51 9.9 Transverse measurement over two pins on a helical gear with an odd number of teeth . 53 9.10 Transverse plane measurement method over three balls or pins . 54 9.11 Axial plane measurement over three pins on a he

21、lical gear or cylindrical worm 56 AMERICAN NATIONAL STANDARD ANSI/AGMA 2002-C16 AGMA 2016 All rights reserved iii 10 Measurement with measuring blocks . 57 10.1 Principle of measurement . 57 10.2 Underlying assumptions and limitations 58 10.3 Advantages and disadvantages 58 10.4 Measuring block sets

22、 59 10.5 Block measurement limits . 59 10.6 Tooth thickness from block measurements 60 11 Chordal measurement 60 11.1 General 60 11.2 Measurements with a gear tooth caliper (in the normal plane) . 60 11.3 Chordal measurement with an optical device (in the transverse plane) . 65 11.4 Chordal measurem

23、ent with a coordinate measurement machine (CMM) 69 12 Backlash in gear meshes 69 12.1 General 69 12.2 Factors that influence backlash . 70 12.3 Backlash in the functional system . 70 12.4 Backlash in the nominal system 72 12.5 Other potential influences on backlash . 75 12.6 Ways to express backlash

24、 75 12.7 Variations in backlash . 77 Annexes Annex A Tooth thickness measurement using analytical machines . 78 Annex B Establishing tooth thickness specifications in the nominal system 80 Annex C Establishing tooth thickness specifications in the functional system . 82 Annex D Calculation method fo

25、r the inverse involute function . 84 Annex E Example calculations 85 Annex F Acknowledgements 144 Annex G Bibliography . 146 Figures Figure 1 External gear normal circular, chordal and base tooth thickness . 8 Figure 2 Relationship of tooth thickness tolerance to total composite tolerance . 11 Figur

26、e 3 General arrangement of a double flank tester . 20 Figure 4 A double flank tester in tight mesh. 21 Figure 5 Sample double flank test report . 21 Figure 6 Tight mesh center distance limits for an external gear 27 Figure 7 Span measurement using a disc micrometer 31 Figure 8 Span measurement geome

27、try for external spur gears 31 Figure 9 Span measurement of helical gears 32 Figure 10 Tooth thickness measurement over pins . 37 Figure 11 Rack nomenclature 45 Figure 12 Measurement over one ball or pin for external and internal gears 48 Figure 13 Measurement over two balls or pins for external and

28、 internal gears . 50 Figure 14 Measurement using transverse plane method for three balls or pins, external gear 55 Figure 15 Measurement using transverse plane method for three balls or pins, internal gear . 55 Figure 16 Measurement over three pins using the axial plane three pin method on a helical

29、 gear 56 Figure 17 Measurement over three pins using the axial plane three pin method on a cylindrical worm . 56 Figure 18 Measurement with measuring blocks for even and odd numbers of teeth 58 Figure 19 Female block 59 Figure 20 Male block 59 Figure 21 Chordal tooth thickness measurement using a ge

30、ar tooth caliper 61 Figure 22 Chordal tooth thickness in plane of measurement 61 Figure 23 Transverse chordal dimension . 66 Figure 24 Backlash in a spur gear mesh . 69 Tables Table 1 Symbols and terms . 2 Table 2 Tooth thickness specification system and corresponding measurement methods 13 Table 3

31、Gear deviations that can affect tooth thickness measurement . 14 Table 4 Ball or pin measurement usage 38AMERICAN NATIONAL STANDARD ANSI/AGMA 2002-C16 AGMA 2016 All rights reserved iv Foreword The foreword, footnotes and annexes, if any, in this standard are provided for informational purposes only

32、and are not to be construed as a part of AGMA Standard 2002-C16, Tooth Thickness and Backlash Measurement of Cylindrical Involute Gearing. This Standard presents calculation procedures for determining tooth thickness dimensions of external and internal cylindrical involute gearing. It supersedes AGM

33、A 231.52, Inspection Pin Measurement Tables for Involute Spur Gears. This Standard has been prepared to consolidate previously published AGMA tooth thickness information, to add more information on internal and helical gears and to add details on more measurement methods. Previous AGMA publications

34、have presented this information in tabular form, calculated for 1 DP and standard tooth proportions, with adjustment factors for nonstandard conditions. This Standard is arranged for direct calculation of the desired results, to eliminate the intermediate calculation steps and interpolation previous

35、ly required. The study of tooth thickness and backlash has been a major interest of gear technicians throughout the history of the industry. In the last fifty years, many clarifications and contributions have been made by Buckingham, Candee, Leming, Vogel, Wildhaber and others. Their work is consoli

36、dated here, without further attribution, and the work of more recent contributors is added where it improves the presentation. In this edition of ANSI/AGMA 2002-C16, the concept of functional tooth thickness has been broadened, and the treatment of the effects of tooth profile, pitch, lead, and runo

37、ut deviations on tooth thickness dimensions has changed. This edition uses a direct calculation of measured tooth thickness from a nominal circular tooth thickness, and a clear distinction is made between measurement methods for nominal and functional tooth thickness. A section on the calculation of

38、 backlash was added, and the effects of tolerances are included in the calculation of backlash. As a result of these changes, the title of this standard has been revised to reflect the new content. An annex was added to provide sample calculations. The first draft of ANSI/AGMA 2002-C16 was created i

39、n June 2013. It was approved by the membership in March 2016 and as an American National Standard on May 3, 2016. Suggestions for improvement of this standard will be welcome. They may be submitted to techagma.org. AMERICAN NATIONAL STANDARD ANSI/AGMA 2002-C16 AGMA 2016 All rights reserved v PERSONN

40、EL of the AGMA Gear Accuracy Committee Chairman: Steven A. Lindley . Rexnord Gear Group Vice Chairman: John M. Rinaldo . Atlas Copco Comptec LLC ACTIVE MEMBERS M.Cowan Gleason Metrology Systems Corporation M. Crossman Caterpillar, Inc. R. Frazer University of Newcastle-Upon-Tyne, Design Unit D. Hepk

41、er . Great Lakes Industry, Inc. E. Lawson. Gleason Metrology Systems Corporation R. Layland Precision Gage Company A. March . Hunting Dearborn Inc. M. May The Gleason Works E. Reiter . Web Gear Services Ltd. K. Terry . Triumph Gear Systems AGMA 2016 All rights reserved 1 AMERICAN NATIONAL STANDARD A

42、NSI/AGMA 2002-C16 American National Standard Tooth Thickness and Backlash Measurement of Cylindrical Involute Gearing 1 Scope This standard establishes the calculation procedures for determining specification limits for external and internal cylindrical involute gearing when the desired tooth thickn

43、ess is known. This standard also shows the relationships between backlash and the tooth thickness, center distance, and tooth deviations in a pinion and gear mesh. 1.1 Measurement methods included in standard Equations and procedures are included for the following tooth thickness measuring methods:

44、- measurement by pitch or index; - measurement with a master gear on a double flank tester; - measurement with a master gear on a single flank tester; - span measurement; - measurement over or between balls or pins; - measurement with measuring blocks; - chordal measurement. 1.2 Types of gears This

45、standard applies to the following types of gears: - external and internal involute spur gears; - external and internal parallel axis involute helical gears; - involute worms and other crossed-axis helical gears; - spur and helical racks; - involute sector gears, spur, and helical. 1.3 Dimensional an

46、d material limitations The equations in this standard apply to gears of all sizes and materials, and to all manufacturing methods. However, practical considerations and availability of test equipment can preclude the use of some methods on some sizes of gears. Some methods may not be appropriate for

47、 compliant materials if the use of the tooth thickness measuring tools and techniques result in deformation of the gear teeth. 1.4 Exclusions The determination of design tooth thickness for a given application is beyond the scope of this standard. AMERICAN NATIONAL STANDARD ANSI/AGMA 2002-C16 AGMA 2

48、016 All rights reserved 2 2 Normative references The following documents contain provisions which, through reference in this text, constitute provisions of this American National Standard. At the time of publication, the editions were valid. All standards are subject to revision and parties to agree

49、ments based on this standard are encouraged to investigate the possibility of applying the most recent editions of the standards indicated below. ANSI/AGMA 1012-G05, Gear Nomenclature, Definitions of Terms with Symbols 3 Symbols and terminology 3.1 Symbols The symbols used in this standard are as shown in Table 1. The symbols and terms referenced in footnote 1 as “Input variable“ should be measured, known, or determined by the designer. Methods to calculate these input variables are beyond the scope of thi