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ANSI/AGMA2005-D03

ANSI/AGMA 2005-D03Revision of

ANSI/AGMA 2005--C96)

AMERICAN NATIONAL STANDARD

Design Manual for Bevel Gears

ii

Design Manual for Bevel GearsANSI/AGMA 2005--D03[Revision of ANSI/AGMA 2005--C96]

Approval of an American National Standard requires verification by ANSI that the require-ments for due process, consensus, and other criteria for approval have been met by thestandards developer.

Consensus is established when, in the judgment of the ANSI Board of Standards Review,substantial agreement has been reached by directly and materially affected interests.Substantial agreement meansmuchmore than a simplemajority, but not necessarily una-nimity. Consensus requires that all views and objections be considered, and that aconcerted effort be made toward their resolution.

The use of American National Standards is completely voluntary; their existence does notin any respect preclude anyone, whether he has approved the standards or not, frommanufacturing, marketing, purchasing, or using products, processes, or procedures notconforming to the standards.

The American National Standards Institute does not develop standards and will in nocircumstances give an interpretation of any American National Standard. Moreover, noperson shall have the right or authority to issue an interpretation of an American NationalStandard in the name of the AmericanNational Standards Institute. Requests for interpre-tation of this standard should be addressed to the American Gear ManufacturersAssociation.

CAUTION NOTICE: AGMA technical publications are subject to constant improvement,revision, or withdrawal as dictated by experience. Any person who refers to any AGMATechnical Publication should be sure that the publication is the latest available from theAssociation on the subject matter.

[Tables or other self--supporting sections may be referenced. Citations should read: SeeANSI/AGMA2005--D03,DesignManual for Bevel Gears, published by the AmericanGearManufacturers Association, 500 Montgomery Street, Suite 350, Alexandria, Virginia22314, http://www.agma.org.]

Approved ________________________

ABSTRACTThis manual provides the standards for the design of straight bevel, zerol bevel, spiral bevel and hypoid gears,along with information on the fabrication, inspection and mounting of these gears. Topics include preliminarydesign parameters, blank design including standard taper, uniform depth, duplex taper and tilted root so thatGleason, Klingelnberg and Oerlikon machine tools are covered. Also included are drawing format, inspection,materials, lubrication, mountings and assembly.

Published by

American Gear Manufacturers Association500 Montgomery Street, Suite 350, Alexandria, Virginia 22314

Copyright 2003 by American Gear Manufacturers AssociationAll rights reserved.

No part of this publication may be reproduced in any form, in an electronicretrieval system or otherwise, without prior written permission of the publisher.

Printed in the United States of America

ISBN: 1--55589--818--1

AmericanNationalStandard

iii

ContentsPage

Foreword vi. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 Scope 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 References 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 Symbols, terms and definitions 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 General design considerations 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 Preliminary design 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 Tooth geometry and cutting considerations 17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 Gear tooth design 22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8 Rating 32. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 Blank considerations 32. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 Tolerance requirements 37. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 Drawing format for bevel gears 42. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12 Bevel gear inspection 42. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 Materials and heat treatment 49. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14 Lubrication 50. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 Design of bevel gear mountings 53. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 Assembly 57. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Tables

1 Symbols and terms 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 Material factors 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 Suggested minimum numbers of pinion teeth (spiral bevels and hypoids) 14. . . .4 Suggested depth factor, k1 23. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 Mean addendum factor, c1 23. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 Sum of dedendum angles, Σδ 23. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 Dedendum angles, δP and δG 24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8 Minimum normal backlash allowance (measured at the outer cone) 25. . . . . . . .9 Straight, zerol and spiral bevel formulas 25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 Hypoid design formulas 27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 Face angle and back angle distance tolerances 37. . . . . . . . . . . . . . . . . . . . . . . . .12 Suggested tolerances for bore or shank diameter 38. . . . . . . . . . . . . . . . . . . . . . . .13 Suggested tolerances for outside diameter, crown to back, face angle

and back angle 39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14 Suggested normal backlash tolerance at tightest point of mesh 41. . . . . . . . . . . .15 Drawing format basic outline for bevel gears 43. . . . . . . . . . . . . . . . . . . . . . . . . . . .16 Example of E, P and G values 47. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 Typical oil flows per gear mesh 53. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18 Typical oil jet location 53. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19 Load face 54. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

iv

Figures

1 Bevel gear nomenclature -- axial plane 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 Bevel gear nomenclature -- mean section (A--A in figure 1) 3. . . . . . . . . . . . . . . . .3 Hypoid nomenclature 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 Straight bevel 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 Spiral bevel 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 Zerol bevel 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 Hypoid 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8 Pinion pitch diameter versus pinion torque -- pitting resistance 11. . . . . . . . . . . . .9 Pinion pitch diameter versus pinion torque -- bending strength 11. . . . . . . . . . . . .10 Suggested number of teeth in pinion for spiral bevel and hypoid gears

(non--automotive) 13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 Suggested number of teeth in pinion for straight bevel and zerol bevel

gears 13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12 Hypoid direction of offset 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 Face width of spiral bevel gears operating at 90 degree shaft angle 15. . . . . . . .14 Face contact ratio for spiral bevel gears 16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 Bevel gear tooth tapers 18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 Root line tilt 18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 Bevel gear depthwise tapers 19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18 Tooth tip chamfering on the pinion 19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19 Angle modification required because of extension in pinion shaft 20. . . . . . . . . . .20 Geometry of face hobbing process 21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21 Circular thickness factor, k3 24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22 Recommended proportioning of the blank 33. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 Tooth backing 33. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 Webless miter gear -- counterbored type 33. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25 Suggested locating surfaces 34. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 Shank type pinion with tapped hole 34. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 Shank type pinion with external threads 34. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28 Spline mounting 35. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 Typical bevel ring gears mounted on hubs 35. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 Method of centering counterbored--type gear on gear center 36. . . . . . . . . . . . . .31 Method of mounting gear when thrust is inward 36. . . . . . . . . . . . . . . . . . . . . . . . . .32 Use of bolt with castellated nut 36. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33 Example of required cutter clearance 36. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34 Method 1 for specifying blank tolerances on bevel gears 37. . . . . . . . . . . . . . . . . .35 Method 2 for specifying blank tolerances on bevel gears 38. . . . . . . . . . . . . . . . . .36 Typical light load contact patterns 40. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 Desired tooth contact pattern under full load 41. . . . . . . . . . . . . . . . . . . . . . . . . . . .38 Tooth contact patterns 45. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39 Explanation of E and P movements 47. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40 Toe/heel contact nomenclature 47. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41 Single flank inspection chart 48. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42 Housing tolerances 54. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43 Direction of rotation 55. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v

Figures (concluded)

44 Resultant gear tooth forces 56. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45 Typical straddle mounting for both members 57. . . . . . . . . . . . . . . . . . . . . . . . . . . .46 Typical overhung mounting 57. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47 Typical gear marking 58. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48 Measurement of normal backlash 59. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 Hypoid pinion mounting gage 60. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50 Pinion setup gage for angular bevel gears 60. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51 Photograph of pinion setup gage 61. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 Mounted bevel gears 61. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 Gears shown in figure 52 61. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 Typical assembly 62. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 Shimming procedure for bevel pinion with 90° shaft angle 62. . . . . . . . . . . . . . . . .56 Vertical sub--assembly 63. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 Housing--vertical mounting distance 63. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58 Horizontal sub--assembly 64. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 Housing--horizontal mounting distance 64. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 Shimming procedure for bevel pinion with other than 90° shaft angle 65. . . . . . .61 Angular bevel gear box housing mounting distance measurements

and calculations 65. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 Positioning of bevel gears 66. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63 Bevel gear backlash, normal and transverse 66. . . . . . . . . . . . . . . . . . . . . . . . . . . .64 Axial movement per 0.001 inch change in backlash 67. . . . . . . . . . . . . . . . . . . . . .

Annexes

A Bevel gear sample calculations 69. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B Hypoid gear sample calculations 73. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .C Machine tool vendor data 81. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .D Hypoid geometry 83. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .E Tabulation of bevel and hypoid gear tolerances 85. . . . . . . . . . . . . . . . . . . . . . . . . .F Loaded tooth contact patterns 91. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .G Bibliography 93. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vi

Foreword

[The foreword, footnotes, and appendices, if any, are provided for information purposesonly and should not be construed as a part of ANSI/AGMA 2005--D03, Design Manual forBevel Gears.]

Because of the widespread use of bevel gearing in industry and because of the manyspecial problems associated with this type of gearing, it was felt there was a need fortechnical information relating to this field of gearing, which would provide the designers withuseful information. A committee of bevel gear experts was asked to develop a DesignManual for Bevel Gearing.

The first draft of the Design Manual for Bevel Gears was prepared by the Bevel GearingCommittee in March, 1962. The Committee completed and approved the manual inNovember, 1964. It was approved by the AGMAMembership by letter ballot as of February,1965.

The Bevel Gearing Committee believed that they could best serve the Association and theusers of AGMAStandards by consolidating the engineering design information for all formsof bevel gearing into one document. This task was undertaken in 1982 and this revisionincludes design information for straight bevel, spiral bevel, and hypoid gearing. Thestandard included the pertinent data from, and superseded the following standards:

AGMA 202.03 1965, System for ZEROL Bevel GearsAGMA 208.03 1979, System for Straight Bevel GearsAGMA 209.04 1982, System for Spiral Bevel GearsAGMA 330.01 1972, Design Manual for Bevel Gears

The standard was revised in 1994 to include all currently used hypoid design methods,refine some calculations, expand the section on lubrication and update all sections with thelatest material. At the same time the clauses concerning ratings were edited so as not toconflict with AGMA 2003--A86, Rating the Pitting Resistance and Bending Strength ofGenerated Straight Bevel, Zerol Bevel and Spiral Bevel Gear Teeth. ANSI/AGMA2005--C96 was approved by the AGMAmembership in October 1994 and by the AmericanNational Standard Institute as a National Standard on October 8, 1996.

This edition, ANSI/AGMA 2005--D03, was to revise and edit clause 7.14, Table 10, and theAnnex B example for hypoid gear design, only.

ANSI/AGMA 2005--D03 was approved by the AGMAmembership on July 10, 2003 and bythe American National Standards Institute as a National Standard on__________________.

AGMA Standards are subject to constant improvement, revision, or withdrawal as dictatedby experience. Any personwho refers to anAGMA technical publication should be sure thatthe publication is the latest available from the Association on the subject matter.

Suggestions for improvement of this standard will be welcome. They should be sent to theAmericanGearManufacturers Association, 500Montgomery Street, Suite 350, Alexandria,Virginia 22314.

vii

PERSONNEL of the AGMA Bevel Gearing Committee

Chairman: R. F. Wasilewski Arrow Gear Company. . . . . . . . . . . . . . . . . . . . . .Vice Chairman: G. Lian Amarillo Gear Company. . . . . . . . . . . . . . . . . . . . . . . . .

ACTIVE MEMBERS

R. Green R7 Group. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .J. Kolonko Falk Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T.J. Krenzer Consultant (Gleason). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P.A. McNamara Caterpillar, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .K. Miller Dana Spicer Off Highway Products. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ASSOCIATE MEMBERS

J. Anno Xtek, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .J.L. Arvin Arrow Gear Company. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .D.L. Borden D.L. Borden, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B. Casilla G&N Rubicon Gear, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .S. Chachakis New England Engineering & Gear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .J. Chakraborty Dana Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .M.R. Chaplin Contour Hardening, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R.J. Ciszak Euclid--Hitachi Technical Center. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A.S. Cohen Entranes y Maquinaria Arco, S.A.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .S. Curtis Curtis Machine Company, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R.L. Errichello GEARTECH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .L. Faure C.M.D.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .G.G. Rey Instituto Superior Politecnico. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .L.L. Haas Rolls--Royce Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .H. Hagiwara Nippon Gear Company, Ltd.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .J. Harrison Metal Improvement Company. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .J.M. Hawkins Rolls--Royce Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .G. Henriot Consultant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .M. Hirt Renk AG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .D. Hlavac Milwaukee Electric Tool Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T.K. Ho General Motors Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .L.Z. Jaskiewicz Warsaw University of Technology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .K.T. Jones Boeing Commercial Airplane Group. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A. Kubo Kyoto University. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .R.R. Kuhr Enplas USA, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .O.A. LaBath Gear Consulting Services of Cincinnati, LLC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .E. Masa ATA Gears, Ltd.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .W.R. McVea Gear Consultant, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .W.J. Michaels Consultant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A.G. Milburn Milburn Engineering, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .C.H. Myers Mack Trucks, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .D. Palmer Brad Foote Gear Works, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .J.A. Pennell University of Newcastle--Upon--Tyne. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .W.P. Pizzichill, Jr. Rockwell Automation/Dodge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .V.Z. Rychlinski Brad Foote Gear Works, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .C.D. Schultz Pittsburgh Gear Company. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .D.H. Senkfor Precision Gear Company. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Y. Sharma Rockwell Automation/Dodge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .M.J. Shebelski Northstar Aerospace -- Chicago. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .D.F. Smith Solar Turbines, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .L.J. Smith Consultant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .L. Spiers Emerson Power Transmission Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A.A. Swiglo Alion Science and Technology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .K. Taliaferro Rockwell Automation/Dodge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .D. Townsend Townsend Engineering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .H.J. Trapp Klingelnberg Sohn GmbH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .F.C. Uherek Flender Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .J. Wittrock Falk Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .S.M. Yamada ArvinMeritor Automative. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .M. Ziegler Joy Mining Machinery. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1 AGMA 2003 ---- All rights reserved

ANSI/AGMA 2005--D03AMERICAN NATIONAL STANDARD

American National Standard --

Design Manual for BevelGears

1 Scope

This standard contains information for the design,fabrication, inspection and mounting of bevel gears.

The term bevel gears is used tomean straight, spiral,zerol bevel and hypoid gear designs. If the textpertains to one or more but not all, the specific formsare identified.

The manufacturing process of forming the desiredtooth form is not intended to imply any specificprocess, but rather to be general in nature andapplicable to all methods of manufacture.

Precision finish, as used in this standard, refers to amachine finishing operation which includes grinding,skiving, and hard cut finishing. However, thecommon form of finishing known as lapping isspecifically excluded as a form of precision finishing.

Users should determine the cutting methodsavailable from their gear manufacturer prior toproceeding. Cutting systems used by bevel gearmanufacturers are heavily dependent upon the typeof machine tool that will be used.

This standard is intended for use by an experiencedgear designer capable of selecting reasonablevalues for the factors based on his knowledge andbackground. It is not intended for use by theengineering public at large.

2 References

The following documents contain provisions which,through reference in this text, constitute provisions ofthe standard. All publications are subject to revision,and the users of this manual are encouraged toinvestigate the possibility of applying themost recenteditions of the publications listed.

AGMA 390.03a -- 1980, Gear Handbook -- GearClassification, Materials and Measuring Methodsfor Bevel, Hypoid, Fine Pitch Wormgearing andRacks Only as Unassembled Gears.

ANSI/AGMA 1010--E95, Appearance of Gear Teeth-- Terminology of Wear and Failure.

ANSI/AGMA 1012--F90, Gear Nomenclature,Definitions of Terms with Symbols.

ANSI/AGMA 2003--B97, Rating The Pitting Resis-tance And Bending Strength Of Generated StraightBevel, Zerol Bevel and Spiral Bevel Gear Teeth.

ANSI/AGMA 2004--B89, Gear Materials and HeatTreatment Manual.

ANSI/AGMA9005--E02, Industrial Gear Lubricants.

3 Symbols, terms and definitions

The symbols, terms, and definitions used in thisstandard are, wherever possible, consistent withother approved AGMA documents. It is known,because of certain limitations, that some symbols,their titles, and their definitions, as used in thisdocument, are different than in similar literaturepertaining to spur and helical gearing.

Bevel gear nomenclature used throughout thisstandard is illustrated in figure 1, the axial section ofa bevel gear, and in figure 2, the mean transversesection. Hypoid nomenclature is illustrated in figure3.

3.1 Symbols

Table 1 is a list of the symbols used in this standard,along with the associated terms. The “Where firstused” column gives the clause or equation numberwhere the particular symbol is first used.

3.2 Definition of terms

addendum of gear, mean, aG: The height by whichthe gear tooth projects above the pitch cone at themean cone distance.

addendum of pinion, mean, aP: The height bywhich the pinion tooth projects above the pitch coneat the mean cone distance.

ANSI/AGMA 2005--D03 AMERICAN NATIONAL STANDARD


AGear

Pinion

C

D

E

F

GH

I

J

L

Q

R

T U

A

A

SO

N

M

K

B

PV

A Back angle H Face angle P Pitch angle

B Back cone angle I Face width Q Pitch cone apex

C Back cone distance J Front angle R Pitch cone apex to crown

D Clearance K Mean cone distance S Pitch diameter

E Crown point L Midface T Root angle

F Crown to back M Mounting distance U Shaft angle

G Dedendum angle N Outer cone distance V Equivalent pitch radius

O Outside diameter

NOTE: See figure 2 for mean transverse section, A--A.

Figure 1 -- Bevel gear nomenclature -- axial plane



Clearance

Chordalthickness

Chordaladdendum

Workingdepth

Wholedepth

Addendum

Dedendum

Circularpitch

Circularthickness

Pitchcircle

Backlash

Pitchpoint

Equivalentpitch radius

Figure 2 -- Bevel gear nomenclature -- mean section (A-A in figure 1)

A Face apex beyond crossing point

B Root apex beyond crossing point

C Pitch apex beyond crossing point

N D Crown to crossing point

E Front crown to crossing point

BF Outside diameter

AM G Pitch diameter

F H Shaft angle

J Root angle

L

K Face angle of blank

DE

L L Face widthD

R

M Pinion offset

C

RN Mounting distance

C

K P Pitch angle

H

J

L D R Outer cone distance

G

JP

N

F

NOTE:1. Apex beyond centerline of mate(positive values)2. Apex before centerline of mate(negative values)

Figure 3 -- Hypoid nomenclature



addendum of gear, mean normal chordal, acG:The height from the top of the gear tooth to the chordsubtending the circular thickness arc at the meancone distance in a plane normal to the tooth trace.

addendum of pinion, mean normal chordal, acP:The height from the top of the pinion tooth to thechord subtending the circular thickness arc at themean cone distance in a plane normal to the toothtrace.

back angle distance, LBG, LBP: The distance fromthe intersection of the gear axis and the mountingsurface to a back cone element, for gear and pinionrespectively.

backlash allowance, outer normal, B: Theamount by which the tooth thicknesses are reducedto provide the necessary backlash in assembly. It isspecified at the outer cone distance.

commercial quality: Those gears that are cutunder process control to an accuracy level of AGMAQ7 to Q9.

control gear: The adopted term for bevel gearing inplace of the term, master gear, which implies a gearwith all tooth specifications held to close tolerances.However, the term master gear is frequently used.

crown to back, LXG, LXP: The perpendiculardistance from the mounting surface to the intersec-tion of a face cone element with a back coneelement, for gear and pinion respectively.

cutter radius, rc: The nominal radius of the facetype cutter or cup--shaped grinding wheel that isused to cut or grind the spiral bevel teeth.

dedendum angles, duplex sum of, ΣδD: The sumof dedendum angles for duplex taper.

dedendum angles, sum of, Σδ: The sum of thepinion and gear dedendum angles.

dedendum angles, standard sum of, ΣδS: Thesum of dedendum angles for standard taper.

dedendum angles, tilted root line sum of, ΣδT:The sum of dedendum angles for tilted root linetaper.

dedendum angles, uniform depth sum of, ΣδU:The sum of dedendum angles for uniform depth.

dedendum of gear, mean, bG: The depth of thetooth space of the gear below the pitch cone at themean cone distance.

dedendum of pinion, mean, bP: The depth of thetooth space of the pinion below the pitch cone at themean cone distance.

depth, mean whole, hm: The tooth depth at meancone distance.

depth,meanworking, h: Thedepth of engagementof two gears at mean cone distance.

direction of rotation: Determined by an observerviewing the gear from the back looking toward thepitch apex.

face angle distance, LFG, LFP: The distance fromthe intersection of the gear axis and the mountingsurface to a face cone element, for gear and pinionrespectively.

face width, F: The length of the teeth measuredalong a pitch cone element.

factor, mean addendum, c1: Apportions the meanworking depth between gear and pinion meanaddendums. The gear mean addendum is equal toc1 times the mean working depth.

mean radius of curvature, Ã: The radius ofcurvature of the tooth surface in the lengthwisedirection at the mean cone distance.

number of blade groups,NS: The number of bladegroups contained in the circumference of the cuttingtool.

number of teeth in gear, N: The number of teethcontained in the whole circumference of the gearpitch cone.

number of teeth in pinion, n: The number of teethcontained in the whole circumference of the pinionpitch cone.

pitch, mean circular, pm: The distance along thepitch circle at the mean cone distance betweencorresponding profiles of adjacent teeth.

ratio, equivalent 90 degree,m90: The gear ratio ofa pair of 90 degree shaft angle bevel gears whoseequivalent numbers of teeth are equal to theequivalent numbers of teeth in the angular bevel pair.

symmetrical rack proportions: The tooth thick-ness proportions when the gear and mating pinionhave a common basic rack.

tooth thickness of gear, mean normal chordal,Tnc: The chordal thickness of the gear tooth at themean cone distance in a plane normal to the toothtrace.



tooth thickness of gear, mean normal circular,Tn: The length of arc on the pitch cone between thetwo sides of the gear tooth at themean cone distancein the plane normal to the tooth trace.

tooth thickness of pinion, mean normal chordal,tnc: The chordal thickness of the pinion tooth at themean cone distance in a plane normal to the tooth

trace.

tooth thickness of pinion, mean normal circular,tn: The length of arc on the pitch cone between thetwo sides of the pinion tooth at the mean conedistance in the plane normal to the tooth trace.

tooth trace: The curve of the tooth on the pitchsurface.

Table 1 -- Symbols and terms

Symbol Terms UnitsWhere

first usedAiG Gear inner cone distance in (mm) Eq. 14Am Mean cone distance in (mm) Eq. 3AmG Gear mean cone distance in (mm) Eq. 5AmP Pinion mean cone distance in (mm) 7.14Ao Outer cone distance in (mm) Eq. 3AoG Gear outer cone distance in (mm) 7.7aG Gear mean addendum in (mm) 7.8acG Gear mean chordal addendum in (mm) 7.12acP Pinion mean chordal addendum in (mm) 7.12aoG Gear outer addendum in (mm) 7.13aoP Pinion outer addendum in (mm) 7.13aP Pinion mean addendum in (mm) 7.13B Outer normal backlash allowance in (mm) 7.11Bn Normal backlash in (mm) 16.4Bt Transverse backlash in (mm) 16.4bG Gear mean dedendum in (mm) 7.7boG Gear outer dedendum in (mm) 7.13boP Pinion outer dedendum in (mm) 7.13bP Pinion mean dedendum in (mm) 7.7biP Pinion inner dedendum in (mm) Eq. 22bilP Pinion limit inner dedendum in (mm) Eq. 21CM Material factor -- -- 5.1.3.5c Clearance in (mm) 7.5c1 Mean addendum factor -- -- 7.6D Outer gear pitch diameter in (mm) Eq. 4Dm Gear mean pitch diameter in (mm) 7.13Do Gear outside diameter in (mm) 7.13d Outer pinion pitch diameter in (mm) Eq. 2di Reference hypoid pinion pitch diameter in (mm) Eq. 2dm Pinion mean pitch diameter in (mm) 7.13do Pinion outside diameter in (mm) 7.13E Hypoid offset in (mm) Eq. 2F Net face width in (mm) Eq. 3FiP Pinion face width from calculating point to inside in (mm) 7.14FP Pinion face width in (mm) 7.14FoP Pinion face width from calculating point to outside in (mm) 7.14Go Pinion face apex beyond crossing point in (mm) 7.14GR Pinion root apex beyond crossing point in (mm) 7.14

(continued)



Table 1 (continued)


first usedh Mean working depth in (mm) 7.4hk Outer working depth in (mm) 7.13hm Mean whole depth in (mm) 7.13ht Outer whole depth in (mm) 7.13htG Gear whole depth in (mm) 7.14htP Pinion whole depth in (mm) 7.14K1 Approximate hypoid dimension factor -- -- 7.14k1 Depth factor -- -- 7.4k2 Clearance factor -- -- 7.5k3 Circular thickness factor -- -- 7.10LBG Gear back angle distance in (mm) Eq. 42LBP Pinion back angle distance in (mm) Eq. 41LFG Gear face angle distance in (mm) Eq. 40LFP Pinion face angle distance in (mm) Eq. 39LXG Gear crown to back in (mm) Eq. 40LXP Pinion crown to back in (mm) Eq. 39met Outer transverse module (mm) Eq. 3MmF Face contact ratio -- -- Eq. 3mG Gear ratio -- -- Eq. 2m90 Equivalent 90° ratio -- -- 7.6N Number of gear teeth -- -- Eq. 4NS Number of blade groups -- -- Eq. 7Nc Number of crown gear teeth -- -- Eq. 6n Number of pinion teeth -- -- Eq. 4nP Pinion speed rpm Eq. 1P Power hp (kW) Eq. 1Pd Outer transverse diametral pitch in--1 Eq. 3Pdm Mean diametral pitch in--1 7.13pm Mean circular pitch in (mm) 7.13Q Intermediate variable in (mm) 7.13R Gear mean pitch radius in (mm) 7.14RiG Gear inside pitch radius in (mm) Eq. 28RP Mean pinion radius in (mm) 7.14RiP Inner pinion radius in (mm) Eq. 35R2P Approximate pinion mean radius in (mm) 7.14rc Cutter radius in (mm) Eq. 5rc1 Limit curvature radius in (mm) 7.14S1 Crown gear to cutter center distance in (mm) Eq. 9TG Torque transmitted by the gear lb in (Nm) Eq. 44Tn Gear mean normal circular tooth thickness in (mm) 7.10Tnc Gear mean normal chordal tooth thickness in (mm) 7.12TP Pinion torque lb in (Nm) Eq. 1tn Pinion mean normal circular tooth thickness in (mm) 7.10tnc Pinion mean normal chordal tooth thickness in (mm) 7.12Vap Accumulated pitch variation in (mm) 10.2

(continued)



Table 1 (continued)


first usedVK Kinematic viscosity centistokes Eq. 43Vp max Maximum pitch variation in (mm) 10.2Wr Radial force lb (N) Eq. 48Wt Tangential force lb (N) Eq. 46WtG Tangential force at mean diameter of gear lb (N) Eq. 44WtP Tangential force at mean diameter of pinion lb (N) Eq. 45Wx Axial force lb (N) Eq. 46Xo Gear pitch cone apex to crown in (mm) 7.13xi Pinion front crown to crossing point in (mm) 7.14xo Pinion pitch cone apex to crown in (mm) 7.13Z Gear pitch apex beyond crossing point in (mm) 7.14ZG Crossing point to mean point along gear axis in (mm) 7.14ZiP Crossing point to inside point along pinion axis in (mm) Eq. 29Zo Gear face apex beyond crossing point in (mm) 7.14ZR Gear root apex beyond crossing point in (mm) 7.14αG Gear addendum angle deg (rad) 7.14αP Pinion addendum angle deg (rad) 7.14Γ Gear pitch angle deg (rad) Eq. 6Γi Approximate gear pitch angle deg (rad) 7.14Γo Gear face angle deg (rad) 7.9ΓR Gear root angle deg (rad) 7.13γ Pinion pitch angle deg (rad) Eq. 12γi Pinion inside pitch angle deg (rad) Eq. 31γo Pinion face angle deg (rad) 7.9γR Pinion root angle deg (rad) 7.13γ2 Intermediate pinion pitch angle deg (rad) 7.14∆ Iteration factor -- -- 7.14∆B Total change in backlash in (mm) Eq. 50∆BG Change of backlash for gear in (mm) Eq. 50∆Bi Increment along pinion axis from calculating point to inside in (mm) 7.14∆Bo Increment along pinion axis from calculating point to outside in (mm) 7.14∆BP Change of backlash for pinion in (mm) Eq. 50∆Fi Gear face width from point to inside in (mm) 7.14∆Fo Gear face width from point to outside in (mm) 7.14∆FoP Pinion face width increment in (mm) 7.14∆G Axial movement of gear in (mm) Eq. 54∆K Increment in hypoid dimension factor -- -- 7.14∆P Axial movement of pinion in (mm) Eq. 53∆RP Pinion mean radius increment in (mm) 7.14∆RP/R Ratio of pinion mean radius increment to gear mean pitch radius -- -- 7.14∆Σ Shaft angle departure from 90° deg (rad) 7.14∆t Thickness change in (mm) 7.10δG Gear dedendum angle deg (rad) 7.8δP Pinion dedendum angle deg (rad) 7.8εi Pinion offset angle in axial plane at inside deg (rad) 7.14

(continued)



Table 1 (concluded)


first usedε′2i Pinion offset angle in pitch plane at inside deg (rad) 7.14εo Pinion offset angle in face plane deg (rad) 7.14εR Pinion offset angle in root plane deg (rad) 7.14ε1 Pinion offset angle in axial plane deg (rad) 7.14ε′1 Pinion offset angle in pitch plane deg (rad) 7.14ε2 Intermediate pinion offset angle in axial plane deg (rad) 7.14ε′2 Intermediate pinion offset angle in pitch plane deg (rad) 7.14ζo Auxiliary angle for calculating pinion offset angle in face plane deg (rad) 7.14ζR Auxiliary angle for calculating pinion offset angle in root plane deg (rad) 7.14η Gear offset angle at axial plane deg (rad) 7.14ηo Intermediate angle deg (rad) 7.13ηi Gear offset angle at inside deg (rad) Eq. 34η1 Second auxiliary angle deg (rad) Eq. 10λ First auxiliary angle deg (rad) Eq. 8λ′ Angle between the projection of pinion axis into pitch plane and

the pitch elementdeg (rad) 7.14

ν Lead angle of cutter deg (rad) Eq. 7νt Pitch line velocity ft/min (m/s) Eq. 43Ã Lengthwise tooth mean radius of curvature in (mm) Eq. 11Σ Shaft angle deg (rad) 7.13Σδ Sum of dedendum angles deg (rad) 7.7ΣδD Sum of dedendum angles for duplex taper deg (rad) Eq. 5ΣδS Sum of dedendum angles for standard taper deg (rad) 6.1.1ΣδT Sum of dedendum angles for tilted root line taper deg (rad) 6.1.4ΣδU Sum of dedendum angles for uniform depth taper deg (rad) 6.1.2Ô Normal pressure angle at pitch surface deg (rad) Eq. 5Ôo Limit pressure angle deg (rad) 7.14ÔTi Inner transverse pressure angle deg (rad) Eq. 20Ô1 Pressure angle on concave side of pinion deg (rad) 7.14Ô2 Pressure angle on convex side of pinion deg (rad) 7.14ψ Mean spiral angle at pitch surface deg (rad) Eq. 3ψG Gear spiral angle deg (rad) 7.14ψiG Inner gear spiral angle deg (rad) Eq. 15ψiP Inner pinion spiral angle deg (rad) Eq. 33ψo Outer spiral angle deg (rad) 7.13ψoG Outer gear spiral angle deg (rad) 7.14ψoP Desired pinion spiral angle deg (rad) 7.14ψP Pinion mean spiral angle deg (rad) Eq. 4ψ2P Intermediate pinion mean spiral angle deg (rad) 7.14

4 General design considerations

It is important in any general design employing gearsto first make a study of all the conditions under whichthe gears must operate. This includes the antici-pated loads and speeds and any special operatingconditions which may affect the design of the gears.

4.1 Types of bevel gears

Bevel gears are suitable for transmitting powerbetween shafts at practically any angle or speed.However, the particular type of gear best suited for aspecific application is dependent upon themountings, available space, and operatingconditions.



4.1.1 Straight bevels

Straight bevel gears (see figure 4) are the simplestform of bevel gears. Contact on the driven gearbegins at the top of the tooth and progresses towardthe root. They have teeth which are straight andtapered which, if extended inward, would intersect ina common point at the axis.

Figure 4 -- Straight bevel

4.1.2 Spiral bevels

Spiral bevel gears (see figure 5) have curved obliqueteeth on which contact begins at one end of the toothand progresses smoothly to the other end. Theymesh with contact similar to straight bevels but asthe result of additional overlapping tooth action, themotion will be transmitted more smoothly than bystraight bevel or zerol bevel gears. This reducesnoise and vibration especially noticeable at highspeeds. Spiral bevel gears can also have their toothsurfaces precision finished.

Figure 5 -- Spiral bevel

4.1.3 Zerol bevels

Zerol bevel gears (see figure 6) as well as otherspiral bevel gears with zero spiral angle have curvedteeth which are in the same general direction asstraight bevel teeth. They produce the same thrustloads on the bearings and can be used in the samemounting, have smooth operating characteristics,and are manufactured on the same machines asspiral bevel gears. Zerol bevels can also have theirtooth surfaces precision finished. Gears with spiral

angles less than 10 degrees are sometimes referredto by the name zerol.

Figure 6 -- Zerol bevel

4.1.4 Hypoids

Hypoid gears (see figure 7) are similar to spiral bevelgears except that the pinion axis is offset above orbelow the gear axis. If there is sufficient offset, theshafts may pass one another, and a compactstraddle mounting can be used on the gear andpinion. Hypoid gears can also have their toothsurfaces precision finished.

Figure 7 -- Hypoid

4.2 Ratios

Bevel gears may be used for both speed reducingand speed increasing drives. The required ratiomust be determined by the designer from the giveninput speed and required output speed. For powerdrives the ratio in bevel and hypoid gears may be aslow as 1 but should not exceed approximately 10.High ratio hypoids from 10 to approximately 20 havefound considerable usage in machine tool designwhere precision gears are required. In speedincreasing applications, the ratio should not exceed5.

4.3 Loading

In determining the conditions of loading, considera-tion should be given to the following:

-- The power rating of the prime mover, itsoverload potential and the uniformity of its outputtorque;



-- The output loading. This includes the normaloutput load, peak loads and their duration, and thepossibility of stalling or severe loading atinfrequent intervals;

-- Inertia loads arising from acceleration ordeceleration.

From this analysis, a basic design load for the gearscan be selected together with suitable factors to giveprotection for expected intermittent overloads, de-sired life expectancy, and safety. A knowledge ofloading is also important in the design of themounting and lubrication.

4.4 Speed

The speed or speeds at which a gear set will operatemust be known to determine the inertia loads and thevelocity factor which makes allowances for thedynamic load increment in the rating formulas.Speed is also a factor in selecting the type of gears,the accuracy requirements, the design of themounting, and the type of lubrication.

Straight bevel gears are suggested for peripheralspeeds up to 1000 ft/min (5 m/s) where maximumsmoothness and quietness are not of prime impor-tance. Zerol bevel gears are used for peripheralspeeds up to 8000 ft/min (40 m/s) and run smootherand quieter than straight bevel gears. Spiral beveland hypoid gears provide the ultimate in smoothnessand quietness and are suggested for peripheralspeeds up to 8000 ft/min (40 m/s). When peripheralspeeds in excess of 8000 ft/min (40 m/s) areencountered, precision finished gears should beused.

4.5 Accuracy requirements

In deciding upon the accuracy required in a set ofgears, it should be kept in mind that the greater theaccuracy the higher the cost. The optimum istherefore the lowest degree of accuracy which willfulfill the requirements of the application. In general,the higher the speed at which a pair of gears mustrun, the higher the required accuracy, so that noiseand dynamic loading will not be excessive. Thereare applications where a precise control of motion isrequired so that the gears must have a high degreeof accuracy regardless of the speed at which theyoperate.

4.6 Space limitations

Space limitations, which may be due to fixedmounting distance, external interference, or particu-lar location, must be considered. Space limitationsmay determine the type of gearing required, the ratiolimitation, or both.

4.7 Special operating considerations

Consideration must be given to any special oradverse operating conditions which may exist in agiven design such as one or more of the following:

-- high ambient temperature;

-- presence of corrosive elements;

-- abnormal dust or abrasive atmosphere;

-- extreme repetitive shock or reversing loads;

-- operating under variable alignment;

-- gearing exposed to weather;

-- special noise level requirement;

-- gears in inaccessible location;

-- inadequate lubrication and cooling.

The above influences are typical and not intended tobe all inclusive.

5 Preliminary design

5.1 Load considerations

5.1.1 Estimated load

In most gear applications, the load is not constant.Therefore, the torque load will vary. To obtain valuesof the operating torque load, the designer should usethe value of the power and speed at which theexpected operating cycle of the driven apparatus willperform.

In the case where peak loads are present, the totalduration of the peak loads is important. If the totalduration exceeds ten million cycles during the totalexpected life of the gear, use the value of this peakload for estimating the gear size. If the total durationof the peak loads is less than ten million cycles, startwith one half the value of this peak load or the valueof the highest sustained load, whichever is greater.

When peak loads are involved, a more detailedanalysis is usually required to complete the design.Refer to ANSI/AGMA 2003--B97, annex B.

5.1.2 Torque

Pinion torque is a convenient criterion for approxi-mate rating of bevel gears, requiring conversionfrom power to torque by the relation:

...(1)TP=63 000 P

nP

...(1M)TP=9550 PnP

where

TP is pinion torque, lb in (Nm) (see 5.1.1);

P is power, hp (kW);



nP is pinion speed, rpm.

5.1.3 Estimated pinion size

The accompanying charts, figures 8 and 9, relate thesize of commercial quality spiral bevel pinions to

pinion torque. The charts are for 90 degree shaftangle design. For other than 90 degree shaft angledesigns, the preliminary estimate is less accurateand may require additional adjustments based onthe rating calculations.

2:14:1

10:1

1:1

10 100 1000 10 000 100 000 1 000 000

100

10

1

0.1

Pinion torque, lb in

1.13 11.3 113 1130 11 300 113 0002540

254

25.4

2.54

Pinionpitchdiam

eter,in

Pinionpitchdiam

eter,m

m

Pinion torque, Nm

Gear ratio Nn

Figure 8 -- Pinion pitch diameter versus pinion torque -- pitting resistance

10 100 1000 10 000 100 000 1 000 000

100

10

1

0.1

1.13 11.3 113 1130 11 300 113 0002540

254

25.4

2.54

Pinion torque, lb in

2:14:110:1

1:1

Pinionpitchdiam

eter,in

Pinionpitchdiam

eter,m

m

Pinion torque, Nm

Gear ratio Nn

Figure 9 -- Pinion pitch diameter versus pinion torque -- bending strength



5.1.3.1 Spiral bevels

For spiral bevel gears of case hardened steel, thepinion diameter is given by figures 8 and 9. Followvertically from pinion torque value to desired gearratio, then follow horizontally to pinion pitchdiameter. See annex A for examples.

5.1.3.2 Straight and zerol bevels

Straight bevel and zerol bevel gears will be some-what larger than spiral bevels. The values of pinionpitch diameter obtained from figures 8 and 9 are tobe multiplied by 1.3 for zerol bevel gears and 1.2 forstraight bevel gears. The larger diameter for thezerol bevel gears is due to a face width limitation.

5.1.3.3 Hypoids

In the hypoid case, the pinion pitch diameter, asselected from the chart, is the equivalent piniondiameter. The reference hypoid pinion pitchdiameter, di, is given by:

...(2)di= d − EmG

where

d is pinion pitch diameter, from figure 8 orfigure 9, whichever is larger, in (mm);

E is hypoid offset, in (mm);

mG is gear ratio.

The actual pinion pitch diameter will be establishedin the blank calculations. See annex B for anexample calculation.

5.1.3.4 Precision finished gears

When gears are precision finished, the load carryingcapacity will be increased. The initial pinion size is

based on both pitting resistance and bendingstrength. Based on pitting resistance, the piniondiameter, as given by figure 8 or as calculated byequation 2, is to be multiplied by 0.80. Based onbending strength, the pinion diameter is given byfigure 9 or is calculated by equation 2. From thesetwo values, choose the larger pinion diameter.

5.1.3.5 Material factor, CM

For materials other than case hardened steel at 55minimum HRC, the pinion diameter as given byfigure 8 or as calculated by equation 2, is to bemultiplied by the material factor given in table 2.

5.1.3.6 Statically loaded gears

Statically loaded gears should be designed forbending strength rather than pitting resistance. Forstatically loaded gears which are subject to vibration,the pinion diameter, as given by figure 9 or ascalculated by equation 2, is to be multiplied by 0.70.For statically loaded gears which are not subject tovibration, the pinion diameter, as given by figure 9 oras calculated by equation 2, is to be multiplied by0.60.

5.2 Numbers of teeth

Although the selection of the numbers of teeth maybe made in any arbitrary manner, experience hasindicated that for general work, the numbers of teethselected from figures 10 and 11 will give goodresults. Figure 10 is for spiral bevel and hypoid gearsand figure 11 is for straight bevel and zerol bevelgears. These charts give the suggested number ofteeth in the pinion.

Table 2 -- Material factors

Gear set materialsGear material and hardness Pinion material and hardness Material

Material Hardness Material HardnessMaterialfactor, CM

Case hardened steel 58 HRC min Case hardened steel 60 HRC min 0.85Case hardened steel 55 HRC min Case hardened steel 55 HRC min 1.00Flame hardened steel 50 HRC min Case hardened steel 55 HRC min 1.05Flame hardened steel 50 HRC min Flame hardened steel 375--425 HB 1.05Oil hardened steel 375--425 HB Oil hardened steel 55 HRC min 1.20Heat treated steel 250--300 HB Case hardened steel 55 HRC min 1.45Heat treated steel 210--245 HB Case hardened steel 55 HRC min 1.45Cast iron ---- Case hardened steel 50 HRC min 1.95Cast iron ---- Flame hardened steel 160--200 HB 2.00Cast iron ---- Annealed steel ---- 2.10Cast iron ---- Cast iron ---- 3.10



Pinion pitch diameter, d, in

Ratio

1:1

2:1

3:14:1

6:1

10:1

51 102 152 203 254 305

Approximatenumberofteeth,

Pinion pitch diameter, d, mm

nSpiralbevelpinion

Spiral bevel gears35° spiral angle

0

10

20

30

40

2 40 6 8 10 12

Figure 10 -- Suggested number of teeth in pinion for spiral bevel and hypoid gears(non--automotive)

Pinion pitch diameter, d, in

Ratio

1:1

2:13:14:16:1

10:1

51 102 152 203 254 305

Approximatenumberofteeth,

Pinion pitch diameter, d, mm

nStraightorzerolbevelpinion

Straight andzerol bevel gears

0

10

20

30

40

2 40 6 8 10 12

Figure 11 -- Suggested number of teeth in pinion for straight bevel and zerol bevel gears

The number of teeth in the mating gear will bedetermined by the gear ratio. When the gears are tobe lapped, the numbers of teeth in the pinion andmating gear should have no common factor.

Straight bevel gears are designed with 12 teeth andhigher. Zerol bevel gears are designed with 13 teethand higher. This limitation is based on achieving anacceptable contact ratio without undercut.

Spiral bevel and hypoid gears can be designed withfewer numbers of teeth because the additionaloverlap resulting from oblique teeth allows the teethto be stubbed to avoid undercut and still maintain anacceptable contact ratio. The three dimensionaleffectmust be considered in that the tooth character-istics at the inner end of the teethmust be used in theanalysis of undercut. In later clauses suggested



pressure angles, tooth depth, and addendum pro-portions will minimize the possibility of undercut. Anundercut check should be made to verify thatundercut does not exist. Table 3 gives suggestedminimumpinion numbers of teeth for spiral bevel andhypoid gears.

5.3 Hypoid offset

The pinion offset is designated as being above orbelow the center line of the gear. The direction ofoffset is determined by looking at the gear set withthe pinion to the right. In figure 12, (a) and (b)illustrate the below center position and (c) and (d)illustrate the above center position.

It is strongly suggested that a left hand spiral on thepinion be used when the offset is below centerlineand a right hand spiral pinion be usedwhen the offsetis above centerline. Cases where hand of spiral and

direction of offset are not as defined are beyond thescope of this standard.

Table 3 -- Suggested minimum numbers ofpinion teeth (spiral bevels and hypoids)

Approximate ratioMinimum numbersof pinion teeth

1.00 -- 1.50 131.50 -- 1.75 121.75 -- 2.00 112.00 -- 2.50 102.50 -- 3.00 93.00 -- 3.50 93.50 -- 4.00 94.00 -- 4.50 84.50 -- 5.00 75.00 -- 6.00 66.00 -- 7.50 57.50 -- 10.0 5

Below center LH pinion RH gear

Above center RH pinion LH gear

Figure 12 -- Hypoid direction of offset



In general, due to lengthwise sliding, the offsetshould not exceed 25 percent of the gear pitchdiameter and for heavy duty applications, the offsetshould be limited to 12.5 percent of the gear pitchdiameter.

5.4 Face width

For shaft angles less than 90 degrees, a face widthlarger than given in figure 13 can be used. For shaftangles greater than 90 degrees, a face width smallerthan given in figure 13 should be used. Generally,the face width should not exceed 30 percent of thecone distance or 10/Pd (10 met) whichever is less.Figure 13 face widths are based on 30 percent of theouter cone distance. For zerol bevel gears, the facewidth given by figure 13 should be multiplied by 0.83and should not exceed 25 percent of the conedistance. For shaft angles substantially less than 90degrees, care should be exercised to ensure that theratio of face width to pinion pitch diameter does notbecome excessive.

In the case of a hypoid, follow the above face widthguidelines for the gear. The hypoid pinion face widthis generally greater than the face width of the gear.Its calculation can be found in table 10.

5.5 Diametral pitch

The diametral pitch may be obtained by dividing thenumber of teeth in the gear by the gear pitch

diameter. Since tooling for bevel gears is notstandardized according to pitch, it is not necessarythat the diametral pitch be an integer.

5.6 Spiral angle

Common design practice suggests that the spiralangle be selected to give a face contact ratio ofapproximately 2.00. For high speed applicationsand maximum smoothness and quietness, facecontact ratios greater than 2.00 are suggested, butface contact ratios less than 2.0 are allowed.

5.6.1 Spiral bevels

The following equation for face contact ratio,mF, maybe used to select spiral angle:

mF=AoAm

Pd F tanψπ ...(3)

mF=AoAm

F tan ψmet π

...(3M)

where

Ao is outer cone distance, in (mm);

Am is mean cone distance, in (mm);

Pd is outer transverse diametral pitch, in--1;

F is net face width, in (mm);

ψ is mean spiral angle at pitch surface;

met is outer transverse module, mm.

Pinion pitch diameter, in0 2 4 6 8 10 12

1

3

2

4

5

6

7

8

9 229

203

178

152

127

102

76

51

25

51 102 152 203 254 3050

Facewidth,in

Pinion pitch diameter, mm

Facewidth,m

m

mG = 10:1

mG = 1:1

mG = 2:1

mG = 3:1

mG = 4:1

mG = 5:1

mG = 6:1

Figure 13 -- Face width of spiral bevel gears operating at 90 degree shaft angle



Figure 14 may be used to assist in the selection ofspiral angle when the face width is 30 percent of theouter cone distance.

5.6.2 Hypoids

For hypoid sets, the pinion spiral angle is calculatedby the following formula:

ψP= 25+ 5 Nn + 90 ED

...(4)

where

ψP is pinion mean spiral angle;N is number of gear teeth;n is number of pinion teeth;D is outer gear pitch diameter, in (mm).

The gear spiral angle depends on the hypoidgeometry and is calculated as part of the hypoidformulas in clause 7.

5.7 Pressure angle

The most commonly used pressure angle for bevelgears is 20 degrees. The pressure angle affects the

gear design in a number of ways. Lower pressureangles increase the transverse contact ratio, reducethe axial and separating forces and increase thetoplands and slot widths. Lower pressure anglesalso increase the risk of undercut. The opposites aretrue for higher pressure angles. The effect ofpressure angle on bending strength is complex. Theincreased slot widths produced by lower pressureangles allow the use of larger fillet radii. This, alongwith the increased contact ratio, increases bendingstrength. However, the thickness at the root of thetooth is decreased which reduces the bendingstrength. Generally, lower pressure angles increasethe bending stress but reduce the contact stress.Based on the requirements of the application, theengineer may decide to choose higher or lowerpressure angles. The following sections suggestpressure angles to avoid undercut based on toothnumbers.

1.0 1.5 2.0 2.5 3.0Face contact ratio (mF)

3.0

2.5

2.0

1.5

1.0

Spiral angle (ψ)10° 15° 20° 25° 30° 35° 40° 45°2 50°

3

4

5

6

7

8

9

10

11

13

12

14

0.5

FacewidthXDiametralpitch

Facewidth

Module

(F/m

)et(F

P)

d

mF = (0.3885 tan ψ -- 0.0171 tan3 ψ) F PdBased on F

Ao= 0.3

÷

Figure 14 -- Face contact ratio for spiral bevel gears



5.7.1 Straight bevels

To avoid undercut, use a pressure angle of 20degrees or higher for pinions with 14 to 16 teeth and25 degrees for pinions with 12 or 13 teeth.

5.7.2 Zerol bevels

On zerol bevels, 22.5 degree and 25 degreepressure angles are used for low tooth numbers,high ratios, or both to prevent undercut. Use a 22.5degree pressure angle for pinions with 14 to 16 teethand a 25 degree pressure angle for pinions with 13teeth.

5.7.3 Spiral bevels

To avoid undercut, use a 20 degree pressure angleor higher for pinions with 12 or fewer teeth.

5.7.4 Hypoids

On hypoid sets the pressure angle is unbalanced onopposite sides of the gear teeth in order to produceequal contact conditions on the two sides. For thisreason average pressure angle is specified onhypoids. In addition to 20 degree, an 18 degreepressure angle is used for light duty drives and 22.5degree and 25 degree pressure angles are used forheavy duty drives. To avoid undercut, use anaverage pressure angle of 20 degrees or higher forpinions with 12 or fewer teeth.

5.8 Hand of spiral

The hand of spiral should be selected to give an axialthrust that tends tomove both the gear and pinion outof mesh when operating in the predominant workingdirection.

Often, the mounting conditions will dictate the handof spiral to be selected. For spiral bevel and hypoidgears, both members should be held against axialmovement in both directions.

5.8.1 Spiral bevels

To avoid the loss of backlash, the hand of spiral forspiral bevels should be selected to give an axialthrust that tends tomove the pinion out ofmesh. Seeclause 15.

5.8.2 Hypoids

For hypoids, the hand of spiral depends on thedirection of the offset. See 5.3 for details.

5.9 Shaft angle

The shaft angle is determined by the application.

5.10 Preliminary gear size

Once the preliminary gear size is determined asexplained above, the tooth proportions of the gears

should be established and the resulting designshould be checked for bending strength and pittingresistance. See clause 8.

6 Tooth geometry and cuttingconsiderations

This clause presents a method of calculating gearblank and tooth dimensions for bevel gears in whichthe teeth are machined by a facemill cutter, face hobcutter, a planing tool, or a cup--shaped grindingwheel. Bevel gear geometry is a function of thecutting method used. For this reason, it is importantthat the user of this manual be familiar with thecuttingmethods used by the gearmanufacturer. Thefollowing section is provided to familiarize the userwith this interdependence.

6.1 Tooth taper

Bevel gear tooth design involves some considera-tion of tooth taper because the amount of taperaffects the final tooth proportions and the size andshape of the blank.

It is advisable to define the following interrelatedbasic types of tapers: (These are illustrated in figure15 in which straight bevel teeth are shown forsimplicity.)

-- Depth taper refers to the change in toothdepth along the face measured perpendicular tothe pitch cone;

-- Point width taper (frequently called slot widthtaper) refers to the change in the point widthformed by a V--shaped cutting tool of nominalpressure angle, whose sides are tangent to thetwo sides of the tooth space and whose top istangent to the root cone, along the face;

-- Space width taper refers to the change in thespace width along the face. It is generallymeasured in the pitch plane;

-- Thickness taper refers to the change in tooththickness along the face. It is generally measuredin the pitch plane.

The taper of primary consideration for production isthe point width taper. The width of the slot at itsnarrowest point determines the point width of thecutting tool and limits the edge radius that can beplaced on the cutter blade.

The taper which directly affects the blank is the depthtaper through its effect on the dedendum angle,which is used in the calculation of the face angle ofthe mating member.



Depth

Space width

Thickness

Pointwidth

Figure 15 -- Bevel gear tooth tapers

The point width taper depends upon the lengthwisecurvature and the dedendum angle. It can bechanged by varying the depth taper; i.e., by tilting theroot line as illustrated in figure 16 in which theconcept is simplified by illustrating straight bevelteeth. In spiral bevel and hypoid gears, the amountby which the root line is tilted is further dependentupon a number of geometric characteristics includ-ing the cutter radius. This relationship is discussedmore thoroughly in 6.1.3.

The root line is generally tilted about the mean pointin order to maintain the desired working depth at the

mean section of the tooth.

6.1.1 Standard depth

Standard depth pertains to the configuration wherethe depth changes in proportion to the cone distanceat any particular section of the tooth. If the root line ofsuch a tooth is extended, it intersects the axis at thepitch cone apex, as illustrated in figure 17. The sumof the dedendum angles of pinion and gear forstandard depthwise taper, ΣδS, does not depend oncutter radius.

Most straight bevel gears are designed withstandard taper.

Pitch cone apex

Pitch cone apex

Figure 16 -- Root line tilt



mean wholedepth

mean wholedepth

mean wholedepth

Standard depth taper

Uniform depth

Duplex and tilted root line taper

meanaddendum

meandedendum

meanaddendum

meanaddendum

meandedendum

meandedendum

Figure 17 -- Bevel gear depthwise tapers6.1.2 Uniform depth

Uniform depth is the configuration where the toothdepth remains constant along the face width regard-less of cutter radius. In this case, the root line isparallel to an element of the face cone, as illustratedin figure 17. The sum of the dedendum angles ofpinion and gear for uniform depth taper, ΣδU, equalszero.

For the uniform depth tooth, the cutter radius, rc,should be greater than AmG sin ψ, but not more than1.5 times this value. This approximation of length-wise involute curvature, in conjunction with theuniform depth, holds the variation along the facewidth in normal circular thickness on the pinion andgear to a minimum.

If narrow inner toplands occur on the pinion, a smalltooth tip chamfer may be provided (see figure 18).

Face width

Length ofchamfer

Angle of chamferFigure 18 -- Tooth tip chamfering on the pinion

6.1.3 Duplex depth taper

This taper represents a tilt of the root line such thatthe slot width is constant while maintaining theproper space width taper. The point width taper iszero on both members.



The formula for the sum of the dedendum angles is:

...(5)ΣδD=

90Pd Ao tanÔ cosψ

1 − AmGsin ψrc

...(5M)ΣδD=

met 90Ao tan Ô cos ψ

1 − AmGsin ψrc

where

ΣδD is sum of the dedendum angles for duplextaper;

Ô is normal pressure angle at pitch surface;

AmG is gear mean cone distance, in (mm);

rc is cutter radius, in (mm).

A brief study of this formula indicates that the cutterradius, rc, has a significant effect on the amount bywhich the root line is tilted. For a given design, thefollowing tendencies should be noted:

-- A large cutter radius increases the sum of thededendum angles. If the radius is too large, theresultant depthwise taper could adversely affectthe depth of the teeth at either end; i.e., tooshallow at inner end for proper tooth contact, andtoo deep at the outer end which can causeundercut and narrow toplands. Therefore, thecutter radius should not be too large and an upperlimit of rc approximately equal to AmG is sug-gested;

-- A small cutter radius decreases the sum ofthe dedendum angles. In fact, if rc equalsAmG sin ψ, the sum of the dedendum angles

becomes zero which results in uniform depthteeth. If rc is less than AmG sin ψ, reversedepthwise taper would exist and the teeth wouldbe deeper at the inner end than at the outer. Inorder to avoid excessive depth (undercut andnarrow toplands) at the inner end, a minimumvalue of rc equal to 1.1 AmG sin ψ, is suggested.

NOTE: For gears cut with a planing tool, the cuttercenter is considered to be at infinity and root lines arenot tilted. Standard taper is the norm for gearsproduced in this manner.

6.1.4 Tilted root line taper (TRL)

This taper is an intermediate one in which the rootline is tilted about the mean point. In this case, theslot width of the gear member is constant along thetooth length and any point width taper is on the pinionmember.

For the TRL case, where the root line is tilted topermit finishing the gear in one operation, theamount of tilt is somewhat arbitrary but should fallwithin the following guidelines:

-- The sum of the dedendum angles of bothpinion and gear for tilted root line depthwise taper,ΣδT, should not exceed 1.3 times the sum of thededendum angles of the standard depthwisetaper, ΣδS, nor should it exceed the sum of thededendum angles for duplex depthwise taper,ΣδD;

-- In practice, the smaller of the values, 1.3 ΣδSor ΣδD, is used.

Meanpitch

diam

eter

Mean pitch diameter

Dedendum anglemodification

γ

Γ

Figure 19 -- Angle modification required because of extension in pinion shaft



6.2 Dedendum angle modifications

To avoid cutter interference with a hub or shoulder,the gear and pinion root line can be rotated about themean point as shown in figure 19. The dedendumangle can be modified within a maximum suggestedrange of --5 to +5 degrees.

6.3 Mean radius of curvature

Two types of cutting processes are used in theindustry. In the process which will be referred to asthe facemilling process, the cradle axis and theworkaxis roll together in a timed relationship. In theprocess which will be referred to as the face hobbingprocess, the cradle axis, work axis andcutter axis rolltogether in a timed relationship.

With the face milling process, the mean radius oftooth curvature is equal to the cutter radius.

With the face hobbing process, the curve in thelengthwise direction of the tooth is an extendedepicycloid and is a function of the relative rollbetween the workpiece and the cutter. It issomewhat smaller than the cutter radius. Thefollowing set of formulas are used to calculate themean radius of tooth curvature (see figure 20). Sincein the hypoid case the mean radius of curvature is afunction of both the cutting process and the hypoidgeometry, the calculation of this value for hypoids ispart of the hypoid dimension calculations.

Number of crown gear teeth

...(6)Nc= Nsin Γ

where

Nc is number of crown gear teeth;

Γ is gear pitch angle.

Lead angle of cutter

...(7)sin ν=AmG NSrc Nc

cosψ

where

ν is lead angle of cutter;

NS is number of blade groups.

First auxiliary angle

λ = 90° -- ψ + ν ...(8)

where

λ is the first auxiliary angle.

Center distance: crown gear to cutter

...(9)S1= A2mG+ r2c − 2 AmG rc cos λwhere

S1 is crown gear to cutter center distance.

Second auxiliary angle

...(10)cosη1=AmG cos ψS1 Nc

Nc+ NS

where

η1 is the second auxiliary angle.

S1

Cutter center

Toothsurface

Center ofcurvature

λ

Crowngear center

ν

ψψ

rc

AmG

η1

Figure 20 -- Geometry of face hobbing process



Lengthwise tooth mean radius of curvature

...(11)

Ã= AmG cosψtanψ+ tan η11+ tan ν tanψ+ tan η1

where

ρ is the lengthwise tooth mean radius ofcurvature.

ρ is used in the hypoid design formulas and theundercut check formulas (see 7.14 and 7.15,respectively).

6.4 Cutter radius

Most curved tooth bevel gears are manufacturedwith face cutters. The selection of the cutter radiusdepends on the cutting system used. A list ofnominal cutter radii is contained in annex C.

6.5 Hypoid design

An infinite number of pitch surfaces exist for anyhypoid pair. The two practical design proceduresused in the industry will be referred to as Method 1and Method 2.

In Method 1, the pitch surfaces are selected suchthat the hypoid radius of curvature matches thecutter radius of curvature at the mean point for gearsto be manufactured by the face milling process andmatches the mean epicycloidal curvature at themean point for gears cut by the face hobbingprocess.

Method 2 is amethod for designing gears to be cut bythe face hobbing process. In this case the gear pitchapex, pinion pitch apex, and cutter center lie on astraight line.

Designations, Method 1 and Method 2, direct theuser through the hypoid calculations in table 10.Annex C provides a guide as when to use eachmethod.

7 Gear tooth design

Each of the following clauses refers to a pertinentvariable in the calculations. The variable, its symbol,and a discussion are provided.

NOTE: When making metric calculations, thediametral pitch, in millimeters, should be used. Whenmakingmetric drawings, the transversemodule, ratherthan the diametral pitch should be specified. Thetransverse module is the inverse of the diametral pitchin consistent units.

7.1 Pitch diameter, d and D

The preliminary pinion pitch diameter was specifiedin 5.1 to suit the requirements of the application. Thiswas used to establish the diametral pitch of the gearset which is now used to calculate the gear pitchdiameter. The actual pinion pitch diameter for thehypoid case depends on the hypoid geometry and isestablished in the calculations.

7.2 Pitch angle, γ and Γ

For the common case where the shaft angle is 90degrees, the formulas for pitch angle are simplifiedas follows:

...(12)γ= arctan nN

...(13)Γ= arctanNnwhere

γ is pinion pitch angle.

For hypoid sets and bevel sets with shaft anglesother than 90 degrees, the pitch angles are estab-lished as part of the calculations.

CAUTION: If the pinion pitch angle is less than 10degrees, or the gear pitch angle exceeds 85 degrees,the machine set--up should be checked to be certainthat no interference of machine components exists.

NOTE: If the gear pitch angle equals or exceeds 90degrees, it will be necessary to form cut the gear.

7.3 Mean cone distance, Am

The mean cone distance is of special significance inbevel gearing because the calculations for machinesettings, bending strength, and pitting resistance aremade at midface.

For hypoid gear sets themean cone distances for thepinion and gear are not equal.

7.4 Mean working depth, h

The depth calculation is made at midface to assureproper depth of contact at this section of the tooth forany depthwise taper. Normally a depth factor, k1, of2.000 is used to calculatemeanworking depth, h, butit can be varied to suit design and other require-ments. Table 4 gives suggested depth factors basedon pinion tooth numbers.

7.5 Clearance, c

While the clearance is constant along the entirelength of the tooth, the calculation is made atmidface. Normally the value of 0.125 is used for theclearance factor, k2, but it can be varied to suit thedesign and other requirements.



Table 4 -- Suggested depth factor, k1

Type of gear Depthfactor

Pinion toothnumbers

Straight bevel 2.000 12 and higherSpiral bevel 2.000

1.9951.9751.9401.8951.8351.765

12 and higher11109876

Zerol bevel 2.000 13 and higherHypoid 2.000

1.9501.9001.8501.8001.750

11 and higher109876

NOTE: During the manufacturing of fine pitch gearing,Pd =20 (met =1.27) and finer, 0.002 inch (0.051mm)maybe added to the clearance of the teeth which are to befinished in a secondary machining operation. This0.002 inch (0.051 mm) should not be included in thecalculations.

7.6 Mean addendum factor, c1

This factor apportions the working depth betweenthe pinion and gear addendums. The pinionaddendum is longer than the gear addendum,except when the numbers of teeth are equal. Longeraddendums are used on the pinion to avoid under-cut. Suggested values for c1 are found in table 5.Other values based on sliding velocity, topland orpoint width limits, or matching strength between twomembers, can be used.

7.7 Sum of dedendum angles, Σδ

The sum of the dedendum angles is a calculatedvalue that is established by the depthwise taperwhich is chosen in accordance with the cutting

method. See clause 6. The formulas for calculatingthis value are listed in table 6.

7.8 Dedendum angles, δP and δG

For all bevel gears, except hypoids, the sum of thededendum angles is apportioned between the pinionand gear using the formulas in table 7. The desireddepthwise taper dictates which formulas are to beused when determining the dedendum angles ofeach member.

For hypoid gears, the pinion dedendum angle iscalculated independently in 7.14 and only the geardedendum angle is determined from table 7.

7.9 Face angle of blank, γo and Γo

The face angle of the blank is made parallel to theroot angle of the mating member as shown in figures1 and 3. This increases bending strength byproviding uniform clearance along the tooth andallows the use of large edge radii on the cutting tools,without causing fillet interference at the inner end ofthe tooth, thus increasing strength.

Table 5 -- Mean addendum factor, c1

Type ofgear

Meanaddendum factor

Piniontooth

numbersStraightbevel

0.210 + 0.290/m902 12 andhigher

Spiral beveland hypoid

0.210

0.2100.1750.1450.1300.1100.100

+

++++++

0.290/m902

0.280/m9020.260/m9020.235/m9020.195/m9020.160/m9020.115 /m902

12 andhigher11109876

Zerol bevel 0.210 + 0.290/m902 13 andhigher

Table 6 -- Sum of dedendum angles, Σδ

Depthwise taper Sum of dedendum angles (degrees)

Standard ΣδS= arctan bPAmG+ arctan bGAmG

Uniform depth ΣδU= 0

Duplex ΣδD= 90.0Pd AoG tan Ô cos ψ

1 − AmG sinψrc

ΣδD= met 90.0AoG tan Ô cos ψ

1 − AmG sin ψrc (M)

TRL ΣδT= ΣδD or 1.3 ΣδS , whichever is smaller



Table 7 -- Dedendum angles, δP and δG

Depthwisetaper

Dedendum angles(degrees)

StandardδP= arctan bPAmG

δG= ΣδS − δP

Uniform depth δP= δG= 0Duplex

δP= ΣδDaGh

δG= ΣδD − δPTRL

δP= ΣδTaGh

δG= ΣδT − δP

7.10 Mean normal circular thickness, tn and Tn

The mean normal circular thickness is calculated atmidface. Values of k3 based on equal stress arefound by using the graph in figure 21. Other values ofk3 may be used if a different strength balance isdesired.

7.11 Outer normal backlash allowance, B

The concept of backlash is complex. Backlash isnecessary in order to compensate for the build up oftolerances at assembly. It exists only when a pair ofgears is in engagement.

Backlash is used in this clause in the calculation oftooth thickness. Suggested minimum values aregiven in table 8. It will be noted that the backlashallowance is inversely proportional to the diametralpitch. Two ranges of values are given: one for AGMAQuality Numbers 4 through 9, the other for AGMAQuality Numbers 10 through 13 per AGMA 390.03a.

If the user desires greater amounts of backlash onNumbers 10 through 13 gear pairs, larger valuesmay be specified. However, it may not be practical toreduce the backlash values in Numbers 4 through 9gears due to the larger runout and larger toothaccuracy tolerances.

The calculations are made at the mean conedistance to provide a measurement with the use of atooth vernier caliper. The mean cone distance hasbeen chosen as the point of measurement for thereasons specified in 7.3.

Ratio mG = N/n1 2 3 4 5 6 7

10

15

20

2530354045500.300

0.250

0.200

0.150

0.100

0.050

0

Thickness change

Number of teeth in pinion

∆t=k3 cosψPdm

Circularthicknessfactor,k 3

k3 = -- 0.088 + 0.092mG -- 0.004mG2 + 0.0016 (n -- 30)(mG -- 1)

Figure 21 -- Circular thickness factor, k3



Table 8 -- Minimum normal backlash allowance (measured at the outer cone)

Allowance in inches Allowance in millimetersAGMA Quality number AGMA Quality number

Diametralpitch

4through

9

10through

13

Transversemodule

4through

9

10through

131.00 to 1.25 0.032 0.024 25.00 to 20.00 0.81 0.611.25 to 1.50 0.027 0.020 20.00 to 16.00 0.69 0.511.50 to 2.00 0.020 0.015 16.00 to 12.00 0.51 0.382.00 to 2.50 0.016 0.012 12.00 to 10.00 0.41 0.302.50 to 3.00 0.013 0.010 10.00 to 8.00 0.33 0.253.00 to 4.00 0.010 0.008 8.00 to 6.00 0.25 0.204.00 to 5.00 0.008 0.006 6.00 to 5.00 0.20 0.155.00 to 6.00 0.006 0.005 5.00 to 4.00 0.15 0.136.00 to 8.00 0.005 0.004 4.00 to 3.00 0.13 0.108.00 to 10.00 0.004 0.003 3.00 to 2.50 0.10 0.0810.00 to 12.00 0.003 0.002 2.50 to 2.00 0.08 0.0512.00 to 16.00 0.003 0.002 2.00 to 1.50 0.08 0.0516.00 to 20.00 0.002 0.001 1.50 to 1.25 0.05 0.0320.00 to 25.00 0.002 0.001 1.25 to 1.00 0.05 0.03

7.12 Mean normal chordal thickness, tnc and Tnc,and mean chordal addendum, acP and acG

These are twobasic dimensions usedwhenmeasur-ing the tooth sizes of the initial or sample pair of bevelgears.

7.13 Straight, zerol and spiral bevel designformulas

The formulas in table 9 are used to calculate theblank and tooth dimensions for bevel gears.

Table 9 -- Straight, zerol and spiral bevel formulas

Item Pinion Both pinion and gear Gear

Pitch diameter d= nPd

D= NPd

(metric) d= n met D= N met

Pitch angle γ= arctan sinΣNn + cosΣ Γ= Σ− γ

Outer cone distance Ao= 0.5Dsin Γ

Mean cone distance Am= Ao− 0.5FDepth factor k1 (See table 4)

Mean working depth h=k1PdAmAo cosψ

(metric) h= k1 met AmAo cosψClearance factor k2 (See 7.5)

Clearance c= k2h

Mean whole depth hm= h+ c

Equivalent 90° ratio m90=Nncos γcosΓ

Mean addendum factor c1 (See table 5)

Mean circular pitch pm= πPdAmAo

(continued)



Table 9 (continued)


Mean circular pitch(metric) pm= π met AmAo

Mean addendum aP= h− aG aG= c1h

Mean dedendum bP= hm− aP bG= hm− aGSum of dedendum

anglesΣδ (See table 6)

Dedendum angle δP (See table 7) δG (See table 7)

Face angle γo= γ+ δG Γo= Γ+ δPRoot angle γR= γ− δP ΓR= Γ− δGOuter addendum aoP= aP+ 0.5F tan δG aoG= aG+ 0.5F tan δPOuter dedendum boP= bP+ 0.5F tan δP boG= bG+ 0.5F tan δGOuter working depth hk= aoP+ aoGOuter whole depth ht= aoP+ boPOutside diameter do= d+ 2aoP cos γ Do= D+ 2aoG cosΓ

Pitch cone apex tocrown xo= Ao cos γ− aoP sin γ Xo= Ao cos Γ− aoG sinΓ

Mean diametral pitch Pdm= Pd AoAmMean pitch diameter dm= n

PdmDm= N

PdmThickness factor k3 (See figure 21)

Mean normal circularthickness theoreticalwithout backlash

tn= pm cosψ− Tn Tn=(0.5pm cosψ)− aP− aG tanÔ−k3 cosψPdm

Outer normal backlashallowance

B (See table 8)

Outer spiral angle (facemilling) sinψo=

2Amrc sinψ− A2m+ A2o2Aorc

Outer spiral angle (facehobbing) Nc= N

sin Γ

sin ν=AmNsrcNc

cosψ

λ= 90°–ψ+ ν

S1= A2m+ r2c− 2Am rc cos λ

Q=S1

1+ NsNc

cos ηo=A2o+ S21− r2c

2AoS1

tanψo=Ao−Q cos ηo

Q sin ηo

Mean normal chordalthickness Tnc= Tn− T3n

6D2m− 0.5B

AmAo

cosÔcosψcosψo

tnc= tn− t3n6d2m− 0.5B

AmAo

cosÔcosψcosψo

Mean chordaladdendum acP= aP+ 0.25

t2n cos γdm

acG= aG+ 0.25T2n cosΓDm



7.14 Hypoid design formulas

The formulas in table 10 are used to calculate theblank and tooth dimensions for hypoids. Annex Dcontains further information and diagrams of the

hypoid geometry. All face milling designs useMethod 1. Depending on manufacturer, facehobbed designs use Method 1 or Method 2. In usingtable 10 formulas, the user needs to exercise carerelative to which formulas apply to the various cases.

Table 10 -- Hypoid design formulas


Pitch diameter D= NPd

(metric) D= NmetGear ratio mG=

Nn

Desired pinion spiralangle

ψoP= ψP

Shaft angle departurefrom 90° ∆Σ= Σ− 90

Approximate gear pitchangle

tan Γi=mG(cos∆Σ)

1.21− mG sin∆Σ

Gear mean pitch radius R=D− F sin Γi

2Approximate pinion

offset angle in pitchplane

sin ε′2i=E sinΓi

R

Approximate hypoiddimension factor

K1= tanψoP sin ε′2i+ cos ε′2i

Approximate pinionmean radius R2P=

RK1mG

Start of iterationFirst trial

Gear offset angle inaxial plane

tan η= ER tan Γi cos∆Σ− sin∆Σ + R2P

Second trialIntermediate pinion

offset angle in axialplane

sin ε2=E− R2P sin η

R

Intermediate pinionpitch angle tan γ2=

sin ηtan ε2 cos∆Σ

+ tan∆Σ cos η

Intermediate pinionoffset angle in pitchplane

sin ε′2=sin ε2 cos∆Σ

cos γ2

Intermediate pinionmean spiral angle tanψ2P=

K1− cos ε′2sin ε′2

Increment in hypoiddimension factor ∆K= sin ε′2tanψoP− tanψ2P

Ratio of pinion meanradius increment togear mean pitchradius

∆RPR = ∆K

mG

Pinion offset angle inaxial plane sin ε1= sin ε2−

∆RPR sin η

Pinion pitch angle tan γ=sin η

tan ε1 cos∆Σ+ tan∆Σ cos η

Pinion offset angle inpitch plane sin ε′1=

sin ε1 cos∆Σcos γ

(continued)



Table 10 (continued)


Spiral angle tanψP=K1+ ∆K− cos ε′1

sin ε′1ψG= ψP− ε′1

Gear pitch angle tan Γ=sin ε1

tan η cos∆Σ+ cos ε1 tan∆Σ

Mean cone distance AmG=R

sinΓ

Pinion mean radiusincrement

∆RP= ∆RPR RMean cone distance AmP=

R2P+ ∆RPsin γ

Mean pinion radius RP= AmP sin γ

Limit pressure angle (− tanÔo)=tan γ tanΓcos ε′1AmP sinψP− AmG sinψG

AmP tan γ+ AmG tanΓ

Nc= Nsin Γ

sin ν=AmGNsrcNc

cosψG

λ= 90° − ψG+ ν

Meantooth

Face Hobbing S1= A2mG+ r2c− 2AmGrc cos λtoothcurvature

g

cos η1=AmG cosψG

S1Nc(Nc+ Ns)

Ã= AmG cosψGtanψG+ tan η11+ tan ν tanψG+ tan η1

Face Milling Ã= rc

Iteration

Method 1

Hypoid radiusof curvature(Face milling or

Calculate the following

rc1=secÔo tanψP− tanψG

(− tanÔo) tanψPAmP tanγ+

tanψGAmG tanΓ+ 1

AmP cosψP− 1

AmG cosψGIterationfactor

(Face milling orface hobbing) ∆= Ãrc1− 1Method 2(Face hobbing rc cosψG− ν n cosψG sin ε′1

Calculate the following

(Face hobbingonly)

∆=rc cosψG− ν

AmG sinΓ− rc sin Γ sinψG− ν−

n cosψG sin ε 1N cosψP sin γ− n cosψG cos ε′1

Testing for convergenceChange η until |∆|≤ 0.001

End of iteration

Pressure angle concave Ô1= Ô+ Ôo Ô2= Ô− Ôo

Pressure angle convex Ô2= Ô− Ôo Ô1= Ô+ Ôo

Crossing point to meanpoint along gear axis

ZG= AmP tan γ sinΓ−E tan∆Σtan ε1

Gear pitch apex beyondcrossing point Z= R

tanΓ− ZG

Outer cone distanceAoG=

0.5Dsin Γ

(continued)




Item Pinion Both pinion and gear GearGear face width from

calculation point tooutside

∆Fo= AoG− AmG

Equivalent 90° ratio m90= sinΣ− cosΣtan(Σ− Γ)

cos γ cos ηcos Γ

Depth factor k1 (See table 4)Mean addendum factor c1 (See table 5)

Mean working depth h=2k1R cosψG

NMean addendum aP= h− aG aG= c1h

Clearance factor k2 (See 7.5)

Mean dedendum bP= bG+ aG− aP bG= h1+ k2− c1Clearance c= k2h

Mean whole depth hm= aG+ bGSum of dedendum

angles Σδ (See table 6)

Dedendum angle δG (See table 7)

Addendum angle αG= Σδ− δGOuter addendum aoG= aG+ ∆Fo sinαGOuter dedendum boG= bG+ ∆Fo sin δGGear whole depth htG= aoG+ boGOuter working depth hk= htG− c

Root angle ΓR= Γ− δGFace angle Γo= Γ+ αGGear outside diameter Do= 2aoG cos Γ+D

Gear crown to crossingpoint

Xo= ZG+ ∆Fo cosΓ− aoG sin Γ

Root apex beyondcrossing point ZR= Z+

AmG sin δG− bGsin ΓR

Face apex beyondcrossing point Zo= Z−

AmG sinαG− aGsinΓo

Auxiliary angle forcalculating pinionoffset angle in rootplane

tan ζR=E tan∆Σ cosΓR

AmG cos δG− Z cosΓR

Auxiliary angle forcalculating pinionoffset angle in faceplane

tan ζo=E tan∆Σ cosΓo

AmG cosαG− Z cos Γo

Pinion offset angle plusauxiliary angle inroot plane

sinεR+ ζR =E cos ζR sin ΓR

AmG cos δG− Z cosΓR

Pinion offset angle plusauxiliary angle inface plane

sin(εo+ ζo)=E cos ζo sinΓo

AmG cos αG− Z cosΓo

Face angle sin γo= sin∆Σ sinΓR+ cos∆Σ cosΓR cos εRRoot angle sin γR= sin∆Σ sinΓo+ cos∆Σ cosΓo cos εoFace apex beyond

crossing point Go=E sin εR cosΓR− ZR sinΓR− c

sin γo

(continued)




Item Pinion Both pinion and gear GearRoot apex beyond

crossing point GR=E sin εo cosΓo− Zo sin Γo− c

sin γRAddendum angle αP= γo− γDedendum angle δP= γ− γRAngle between

projection of pinionaxis into pitch planeand pitch element

tan λ′ =sin ε′1 cos Γ

mG cos γ+ cosΓ cos ε′1

Gear face width fromcalculating point toinside

∆Fi= FG− ∆Fo

Pinion face widthincrement ∆FoP= h sin εR1− 1

mG

Pinion face width froma calculating point tooutside

FoP=∆Fo cos λ′cosε′1− λ′

Pinion face width fromcalculating point toinside

FiP=∆Fi cos λ′

cosε′1− λ′Increment along pinion

axis from calculatingpoint to outside

∆Bo=FoP cos γocosαP

+ ∆FoP− bG− c sin γ

Increment along pinionaxis from calculatingpoint to inside

∆Bi=FiP cos γocosαP

+ ∆FoP+ bG− c sin γ

Crown to crossing point xo= Etan ε1 cos∆Σ

− RP tan γ+ ∆Bo

Front crown to crossingpoint

xi=E

tan ε1 cos∆Σ− RP tan γ− ∆Bi

Whole depth, pinion htP=(xo+ Go) sin γo− γR

cos γo − sin γR GR−GoOutside diameter do= 2 tan γo(xo+Go)

Face width FP=xo− xicos γo

Mean circular pitch pm= πPdAmGAoG

Mean diametral pitch Pdm= PdAoGAmG

Thickness factor k3 (See figure 21)Mean pitch diameter dm= 2AmP sin γ Dm= 2AmG sinΓ

Pitch diameter d= 2AmP+ 0.5FP sin γMean normal circular

tooth thickness,theoretical withoutbacklash

tn= pm cosψ− Tn Tn= 0.5pm cosψG− aP− aG tanÔ−k3 cosψGPdm


B (See table 8)

Outer gear spiral angleface milling sinψoG=

2AmGrc sinψG− A2mG+ A2oG2AoGrc

(continued)



Table 10 (concluded)


Outer gear spiral angleface hobbing

Q=S1

1+ NsNc

cos ηo=A2oG+ S21− r2c

2AoG S1

tanψoG=AoG− Q cos ηo

Q sin ηo

Mean normal chordaltooth thickness tnc= tn− t3n

6d2m−0.5B

AmGAoG

cosÔcosψGcosψoG

Tnc= Tn− T3n

6D2m−0.5B

AmGAoG

cosÔcosψGcosψoG

Mean chordal

addendum acP= aP+0.25t2n cos γ

dmacG= aG+

0.25T2n cos ΓDm

7.15 Undercut check

Tooth numbers, pressure angles, tooth depths andaddendum proportions were chosen to avoid under-cut. However, due to the combination of the threedimensional geometry and various tooth tapers, anundercut check should be made at the inner end ofthe pinion teeth and on low shaft angle generatedgear teeth. The following formulas can be used tocalculate the limit inner dedendum. If this value isless than the inner dedendum of the design,undercut will result and the design should bemodified.

7.15.1 Bevels (excluding hypoids)

Inner cone distance

AiG = Am -- 0.5F ...(14)

Inner gear spiral angle (straight bevel)

ψiG = 0 ...(15)

Inner gear spiral angle -- face milling

...(16)sinψiG=2Am rc sinψ − A2m+ A2iG

2AiG rc

Inner gear spiral angle -- face hobbing

Q=S1

1+ NsNc

...(17)

cosηi=A2iG+ S21 − r2c

2AiG S1...(18)

tanψiG=AiG − Q cos ηi

Q sin ηi...(19)

Inner transverse pressure angle

...(20)tanÔTi=tanÔcosψiG

Limit inner dedendum

bilP = AiG tan γ sin2 ÔTi ...(21)Inner dedendum

biP = bP -- 0.5F tan δP ...(22)7.15.2 Hypoids

Inner gear cone distance

AiG = AmG -- 0.5F ...(23)Inner gear spiral angle -- face milling

...(24)sinψiG=2AmG rc sinψG − A2mG+ A2iG

2AiG rcInner gear spiral angle -- face hobbing

Q=S1

1+ NsNc

...(25)

cosηi=A2iG+ S21 − r2c

2AiG S1...(26)

tanψiG=AiG − Q cosηi

Q sin ηi...(27)

Gear inside pitch radius

RiG = AiG sin Γ ...(28)Crossing point to inside point along gear axis

ZiP = ZP -- 0.5F cos Γ ...(29)Pinion inner offset angle in axial plane

...(30)sin εi=E

RiG+ ZiP ctn Γ

Pinion inside pitch angle

sin γi = cos Γ cos εi ...(31)Pinion offset angle in pitch plane at inner end

...(32)sin ε′i=sin εicos γi



Inner pinion spiral angle

ψiP = ψiG + ε′i ...(33)

Gear offset angle at inside

sin ηi = tan εi tan γi ...(34)

Inner pinion radius

...(35)RiP=ZiPcos ηi

Inner pinion transverse pressure angle

...(36)tanÔTi=tan(Ô+ Ôo)cosψiP

Limit inner dedendum

...(37)bilP=RiPcos γi

sin2ÔTi

Pinion inner dedendum

biP = bP -- FiP tan δP ...(38)

8 Rating

8.1 Introduction

Determining the approximate size of a pair of bevelgears to carry a specified torque rating can easily bedone by the method described in clause 5. Thisavoids an extensive trial--and--error technique andenables the designer to proceed quickly into moredetailed calculations which will complete the designinsofar as the transmitted torque is concerned.Additional rating criteria for bending strength andpitting resistance must also be considered. Thelatest accepted method for appraising the bendingstrength and pitting resistance of bevel gear teeth isstated fully in ANSI/AGMA 2003--B97, Rating thePitting Resistance and Bending Strength of Gener-ated Straight Bevel, Zerol Bevel, and Spiral BevelGear Teeth.

8.2 Bending strength

Bending strength as a criterion of bevel gearcapacity can be defined as the ability of the gear setto withstand repeated or continued operation underdesign load without the fracture of the teeth byfatigue in bending. It is a function of the bending(tensile) stresses in a cantilever beam and is directlyproportional to the applied tooth load. It also involvesthe fatigue strength of the gear materials and theshape of the teeth. Therefore, either the pinion or thegear could be the limiting member of the set.

8.3 Pitting resistance

Pitting resistance as a criterion of bevel and hypoidgear capacity can be defined as the ability of the gearset to withstand repeated or continued operationunder design load without suffering destructivepitting of the tooth surfaces. The experienced gearengineer recognizes that moderate, non--destruc-tive pitting of the tooth surfaces occurs in manycases during the early stages of operation, espe-cially on non--hardened or through hardened gears.In these cases, the pitting ceases to progress afterthe asperities have been removed by the initialoperation. This process, called initial pitting, has nosignificant effect on gear life. Destructive pitting,although attributable in principle to the same phe-nomena, progresses widely enough to destroy thegeometry of the tooth surfaces and ultimately leadsto failure. The distinction between initial anddestructive pitting is defined more thoroughly inANSI/AGMA 1010--E95, Appearance of Gear Teeth-- Terminology of Wear and Failure.

Pitting is a function of several factors; the mostsignificant is Hertzian contact (compressivestresses) between the twomating tooth surfaces andis proportional to the square root of the applied toothload. The ability of bevel and hypoid gear teeth towithstand repeated surface contact under loadwithout destructive pitting involves the resistance ofthe gear materials to fatigue under contact stresses.Because the teeth of the smaller gear of the pairreceive more stress cycles per unit time, the smallergear is usually the limiting element of the pair. Insome cases the smaller gear is made harder than itsmate, to increase its surface durability so that thelimiting capacity may exist in either element.

9 Blank considerations

The quality of any finished gear is dependent on thedesign and accuracy of the gear blank. A number ofimportant factors which affect cost, as well asperformance, must be considered.

Bores, hubs, and other locating surfaces must be inproper proportion to the gear diameter and pitch.Small bores, thin webs, and any condition thatresults in excessive overhang and deflection shouldbe avoided.

9.1 Clamping surface

Nearly all bored--type bevel gears are held bymeansof a clamp plate at the front face of the hub when the



teeth are being cut; therefore, the blank shouldincorporate a suitable surface for this purpose asshown in figure 22.

Clampingsurfaceprovided

No surfaceprovided forclamping

Not recommended

Recommended

Figure 22 -- Recommended proportioning ofthe blank

9.2 Tooth backing

Sufficient thickness of metal should be providedunder the roots of gear teeth to give proper supportfor the teeth. It is suggested that the minimumamount of metal under the teeth should not be lessthan the whole depth of the tooth. Highly stressed

gears may require additional backing. This metaldepth should be maintained under the small ends ofthe teeth as well as under the middle (see figure 23).In addition, onwebless--type ring gears theminimumstock between the bottom of the tap drill hole and thegear root line should be one--third the tooth depth.

Tooth backing

Figure 23 -- Tooth backing

9.3 Load direction

A gear blank should be designed to avoid excessivelocalized stresses and serious deflections withinitself. For heavily stressed gears, a preliminaryanalysis of the direction and magnitude of the forcesis helpful in the design of both the gear and themounting. Where possible, the direction of the webshould coincide with the direction of the resultanttooth load in an axial section. Gear sections shouldbe designed in such a way that the tooth load will bedirected through the section as shown in figure 24.

9.4 Locating surface

The back of the gears should be designed with alocating surface of generous size. This surfaceshould be machined or ground square with the boreand is used both for locating the gear axially inassembly and for holding it when the teeth are cut.The front clamping surface must, of course, be flatand parallel to the back surface. A flat and parallelsurface also provides a convenient inspectionsurface after installation.

Loaddirection

Figure 24 -- Webless miter gear -- counterbored type



9.5 Auxiliary locating surface

Gears with a comparatively large ratio of pitchdiameter to hub diameter, greater than 2.5 to 1,should have an auxiliary locating surface behind theteeth as shown in figure 25. A similar surface shouldalso be used for thin--webbed gears where there isdanger of blank distortion or vibration from cuttingforces.

9.6 Solid shanks

When gears with solid shanks are made in large

quantities, a collet chuck is usually used. For smallquantities, the gears should be provided with atapped hole or external threads at the end of theshank to hold the gear securely in the chuck whilecutting the teeth, see figures 26 and 27.

9.7 Flanged hub

Whether the gear is mounted on a flanged hub or ismade integral with the hub, the supporting flangeshould be of sufficient section size to preventdeflections in the direction of the gear axis at themesh point.

Suggested locating surfaces

Figure 25 -- Suggested locating surfaces

Figure 26 -- Shank type pinion with tapped hole

Centers should be as large as possible and should be relieved as shown

Figure 27 -- Shank type pinion with external threads



The web preferably should be made conical withoutribbing to permit rough machining of the blanks forobtaining better balance, to eliminate oil churningwhen dip lubrication is used, and to lessen thedanger of stress concentration being set up withinthe castings.

9.8 Splined bores

In mounting gears with splined bores, a pilotingdiameter is suggested to reduce eccentricity.Hardened gears with straight--sided splines in thebore should be piloted in assembly by the bore orminor diameter of the splines, which must be groundconcentric with the teeth after hardening. Unhard-ened gears with straight--sided splines should bepiloted in assembly by the major diameter of thesplines. In either case, the finish machining of theblank, cutting of teeth, and the soft testing should beperformedwith the gear centered on the arbor by thebore, which has beenmachined truewith the splines.

Figure 28 shows a gear with a cylindrical fit at eachend of the bore, the splines being used for drivingonly. This type of fit is particularly applicable foraircraft gears which often use involute splines with afull fillet radius on the major diameter. This design isan excellent solution, particularly when the splineshave to be hardened, because fitting on the sides ofthe splines is extremely difficult when size changesand distortion take place during heat treatment.

Involute splines generally fit on the side of the splineonly. When gears are hardened it may be necessaryto resort to lapping or grinding of splines, or to

selective assembly, or both. Even when the splinesare shaped after hardening, it is difficult to obtain theaccuracy of fit and the concentricity desired forprecision gears. Precision finishing the teeth of thegear on involute splined arbors after the splines havebeen shaped results in considerable improvement,but even then different degrees of eccentricity will beobtained by shifting the gear to different positions ona splined arbor or shaft.

Since heat treatment may introduce distortion andout of round conditions in the splines which cannotbe corrected, it is important that the splines be of nogreater length than is actually required for loadtransmission. Splines should be located as near thegear teeth as possible on blanks with long hubs.

9.9 Ring--type designs

The most common ring--type designs are (as shownin figure 29):

Figure 28 -- Spline mounting

(A) Webless type ring gear

(B) Counterbored type ring gear

(C) Web type ring gearFigure 29 -- Typical bevel ring gears mounted on hubs



-- webless;

-- counterbored;

-- web.

Of these, the bolted--on webless ring design shownin figure 29(A) is best for hardened gears larger thanseven inches in diameter. These relatively largehardened gears usually are made in ring shape andsubsequently mounted on a hub or center, becausethe ring form can be more effectively hardened inquenching dies.

The fit of the gear on its centering hub should eitherbe a size--to--size fit or a slight interference fit. Thesegears should be mounted on the centering hub asshown in figures 30 and 31, or with through bolts asshown in figure 32. Several methods of lockingscrews and nuts in place are indicated in theillustrations. The method shown in figure 31 can beused for mounting gears which will operate with aninward thrust only. Designs where gear loadsincrease screw or bolt tension should be avoided.

Center gear on one ofthese surfaces

Figure 30 -- Method of centeringcounterbored--type gear on gear center

Thrustdirection

Load on inside face ofweb in this case; other-wise not recommended

Figure 31 -- Method of mounting gear whenthrust is inward

Center gear on one ofthese surfaces

Figure 32 -- Use of bolt with castellated nut

9.10 Dowels

On reversing or vibrating installations separatedowel drives may be used. The use of dowels orbody fitted bolts has been found unnecessary inmost automotive and industrial drives. When bolts orcap screws are drawn tightly, the friction of the ringgear mounting surface prevents bolt shear. Hard-ened gears smaller than seven inches in diametermay be of conventional design with integral hubs.

9.11 Hub projections

All hub projections, front or rear, which extend abovethe root line, as shown in figure 33, should beeliminated.

Root line

Blank turned offfor cutter clearance

Cutter

Figure 33 -- Example of required cutterclearance



10 Tolerance requirements

Bevel gears are manufactured to suit many engi-neering applications. In order to satisfy these needsproperly, it is necessary to analyze the conditionsunder which these gears must operate. Reasonablemanufacturing tolerances must then be establishedto insure that the gears will perform satisfactorily inthe application.

10.1 Gear blank dimensions and tolerances

In dimensioning bevel gear blanks, it is necessary tospecify properly the items important to the function-ing of the teeth. There are two acceptedmethods forspecifying gear blank tolerances, both of which aregiven below.

10.1.1 Method 1

This method can be used easily and accurately oneither the gear blanks or the finished gears. Items tobe checked include:

-- face angle distance;

-- back angle distance;

-- bore or shank diameter.

The face angle distance and back angle distance areobtained in the following manner:

Face angle distances

LFP = 0.5 do cos γo + LXP sin γo ...(39)LFG = 0.5 Do cos Γo + LXG sin Γo ...(40)

where

LFP is pinion face angle distance, in (mm);

LXP is pinion crown to back, in (mm);

LFG is gear face angle distance, in (mm);

LXG is gear crown to back, in (mm).

Back angle distances

...(41)LBP=

LFP −LXPsinγ

tan γ

...(42)LBG=

LFG −LXGsinΓ

tanΓ

where

LBP is pinion back angle distance, in (mm);

LBG is gear back angle distance, in (mm).

Figure 34 showsMethod 1 for dimensioning the gearblanks when this method of specifying tolerances isto be followed.

Tables 11 and 12 give suggested tolerances for facedistance, back angle distance and bore or shankdiameter.

X.XXXX.XXX

PitchapexFace

apex

Back angledistance

Outside diameter (ref.)

Crown toback (ref.)

Face angledistance

X.XXXX.XXX

Figure 34 -- Method 1 for specifying blanktolerances on bevel gears

Table 11 -- Face angle and back angle distancetolerances

Tolerances, in (mm)

Diametral pitch DistanceDiametral pitch(module) Face angle Back angle

2.5 and coarser +0.000 +0.005--0.005 --0.005

(10 and coarser) (+0.00) (+0.13)(--0.13) (--0.13)

2.5 to 20 +0.000 +0.004--0.004 --0.004

(10 to 1.25) (+0.00) (+0.10)(--0.10) (--0.10)

20 to 50 +0.000 +0.003--0.004 --0.003

(1.25 to 0.5) (+0.00) (+0.08)(--0.10) (--0.08)

50 to 80 +0.000 +0.002--0.003 --0.002

(0.5 to 0.3) (+0.00) (+0.05)(--0.08) (--0.05)

80 and finer +0.0000 +0.001--0.001 --0.001

(0.3 and finer) (+0.00) (+0.03)(--0.03) (--0.03)



Table 12 -- Suggested tolerances for bore or shank diameter

Suggested tolerance, in (mm)

Nominal locating boreor shank diameter

Quality numbers12 & 13

Quality numbers10 & 11

Quality numbers6 thru 9or shank diameter

inches (mm) Shank Bore Shank Bore Shank BoreUp to 1 (25) +0.0000 +0.0002 +0.0000 +0.0005 +0.000 +0.001

--0.0002 --0.0000 --0.0005 --0.0000 --0.001 --0.000(+0.000) (+0.005) (+0.000) (+0.013) (+0.00) (+0.03)(--0.005) (--0.000) (--0.013) (--0.000) (--0.03) (--0.00)

1 to 4 +0.0000 +0.0003 +0.0000 +0.0005 +0.000 +0.001(25 to 100) --0.0003 --0.0000 --0.0005 --0.0000 --0.001 --0.000

(+0.000) (+0.008) (+0.000) +(0.013) (+0.00) (+0.03)(--0.008) (--0.000) (--0.013) (--0.000) (--0.03) (--0.00)

4 to 10 +0.0000 +0.0005 +0.0000 +0.0010 +0.000 +0.002(100 to 250) --0.0005 --0.0000 --0.0010 --0.0000 --0.002 --0.000

(+0.000) (+0.013) (+0.000) (+0.025) (+0.00) (+0.05)(--0.013) (--0.000) (--0.025) (--0.000) (--0.05) (--0.00)

10 to 20 +0.0000 +0.0010 +0.000 +0.003(250 to 500) --0.0010 --0.0000 --0.003 --0.000

(+0.000) (+0.025) (+0.00) (+0.08)(--0.025) (--0.000) (--0.08) (--0.00)

20 (500) and larger +0.0000 +0.0020 +0.000 +0.004--0.0020 --0.0000 --0.004 --0.000(+0.000) (+0.050) (+0.00) (+0.10)(--0.050) (--0.000) (--0.10) (--0.00)

10.1.2 Method 2

This method is not as applicable as Method 1because it cannot readily be used on finished gears.Since it is common practice to include a radius or flaton the crown diameter, the crown point, which is thebasic reference point, is lost. Items to be checkedinclude:

-- outside diameter;

-- crown to back, or mounting surface;

-- face angle;


Figure 35 shows the suggested method for dimen-sioning the gear blanks when this method oftolerancing is to be employed. Tables 12 and 13 givesuggested tolerances for bore or shank diameter,outside diameter, crown to back, face angle, andback angle.

10.1.3 Drawing specifications for blanks

Values for inspected blank parameters should bespecified on the drawings. Some of these featuresare as follows:

-- face angle;

-- back angle;

-- outside diameter;

-- crown to back, or mounting surface;


These latter dimensions are used in place of the faceangle distance and back angle distance for settingup certain commercial blank--checking equipment.

Crownto back

Back angle

Faceapex

Face angleXX_XX°XX_XX°

XX_XX°XX_XX°

X.XXXX.XXX

Outside diameter X.XXXX.XXX

Pitchapex

Figure 35 -- Method 2 for specifying blanktolerances on bevel gears



Table 13 -- Suggested tolerances for outside diameter, crown to back, face angle and back angle

Diametral pitch( d l )

Tolerance, in (mm) Tolerance, minutesp(module) Outside diameter1) Crown to back1) Face angle Back angle

2.5 (10) and coarser +0.000 +0.000 +8 +15--0.010 --0.004 --0 --15(+0.00) (+0.00)(--0.30) (--0.10)

2.5 to 20 +0.000 +0.000 +8 +15(10 to 1.25) --0.005 --0.003 --0 --15

(+0.00) (+0.00)(--0.13) (--0.08)

20 to 50 +0.000 +0.000 +15 +30(1.25 to .5) --0.004 --0.002 --0 --30

(+0.00) (+0.00)(--0.10) (--0.05)

50 to 80 +0.000 +0.000 +30 +60(0.5 to 0.3) --0.003 --0.001 --0 --60

(+0.00) (+0.00)(--0.08) (--0.03)

80 (0.3) and finer +0.000 +0.000 +40 +60--0.002 --0.001 --0 --60(0.00) (+0.00)(--0.05) (--0.03)

NOTE:1) Outside diameter and crown to back dimensions can only be inspected on parts which have no radius on the crownof the blank. Usually the inspection is performed prior to rounding the crown.

10.2 Accuracies of tooth components

In setting tolerances for bevel tooth components, thefollowing parameters are used:

-- maximum pitch variation, Vpmax;

-- accumulated pitch variation, Vap.

10.2.1 Maximum pitch variation

Maximum pitch variation is the largest plus or minusdifference between the actual measured pitch ofadjacent teeth and the theoretical pitch.

10.2.2 Accumulated pitch variation

Accumulated pitch variation is equal to the algebraicdifference between the maximum and minimumvalues obtained from the summation of successivepitch variation values.

10.2.3 AGMA quality number tolerances

Annex E is a tabulation of maximum pitch variationand accumulative pitch variation tolerances for eachAGMA Quality Number of coarse and fine pitchgearing.

10.2.4 Composite variations (double flank)

Double flank composite measurements and testsare not meaningful in defining bevel gear quality.

10.2.5 Profile variation

Profile variation is the difference between the actualtooth profile and a specified tooth profile. Deliberateprofile modifications are introduced in the cutting orprecision finishing process in order to insure adjus-tability during assembly, and to achieve the desiredcontact pattern under load.

10.3 Tooth contact patterns

The position and the size of the tooth contact patternis an important contributor to bevel gear quality.Depending on the amount of load applied to bevelgears, deflections occur, and changes appear in thetooth contact pattern. It is desirable to modify thetooth contact pattern in the generating operation toallow for stresses which are present under operatingconditions.



The location of the tooth contact pattern is directlyaffected by the relative position of the members inassembly. Any deviation from the proper contactpattern indicates the nature of the error. The toothcontact pattern is that portion of the gear toothsurface which actually makes contact with its mate.It can readily be observed by painting the teeth with amarking compound and running the gear for a fewseconds under a light load.

10.3.1 Typical contact pattern

Typical tooth contact patterns under a light load forcommercial quality gears in rigid mountings areshown in figure 36. Note that the contact extendsalong approximately one--half the tooth length and isnearer the toe of the tooth than the heel. In addition,the contact is relieved slightly along the flank and thetop of the profile.

b) Typical range of spiral andhypoid bevel contact patterns

a) Typical straight and zerolbevel contact patterns

Figure 36 -- Typical light load contact patterns

Figure 37 indicates the desired contact patternsunder full load. As shown in this sketch, the contact

pattern should have a slight relief at the ends, andalong the flank and top of the tooth profile. Generally,



the tooth contact pattern should utilize virtually thetotal tooth length, without having concentration at theend or tops of the teeth of either member.

80--85% idealized coverage of lengthwisetooth surface -- relief at top and edges, no

concentrations

Figure 37 -- Desired tooth contact patternunder full load

10.3.2 Need for position control

Complete control of the localized tooth contactpattern under load at assembly is essential. Itcontributes to smooth quiet running qualities of bevelgears while in operation. Lack of control may causethe pattern to concentrate dangerously near the toeor heel of the tooth.

Gears cut on older machines, where no lengthwiselocalization is possible, should have contact patternscorrectly placed so that full tooth contact exists at fullload.

10.3.3 Deflection tests

The amount and the position of the localized toothcontact pattern should be determined to suit thespecific requirements of the gear and pinion applica-tion. Deflection tests should be made on heavily

loaded gears, to determine the precise amount andposition of the tooth bearing pattern in themanufacturing stage.

10.3.4 Drawing specifications

Upon completion of the deflection test and theresultant final development of the proper toothbearing, two sketches of the desired tooth contactpattern may be shown on the gear and pinion print.One should show the contact pattern required formanufacturing; the other should show the finalpattern required under normal running conditions atassembly.

10.4 Backlash

Bevel gear sets should be manufactured andassembled to have a definite amount of backlash,which varies according to pitch and operatingconditions. Backlash is necessary for safe opera-tion. If gears are set too tightly, they will be noisy,wear excessively, and possibly score on the toothsurfaces, or even break.

Backlash is obtained during manufacture by control-ling the tooth thickness. Themanner of providing thisbacklash is dependent upon the strength balancerequired betweengear and pinion, and themethod ofmanufacturing the gear teeth.

Minimum backlash allowance for use in calculatingtooth thicknesses is given in table 8. The suggestednormal backlash tolerances for assembled gears areshown in table 14. In many instances, these limitswill require modifications to suit the special condi-tions of operation. It may be necessary to allowsmaller limits for precision instruments and finerpitch gears.

Table 14 -- Suggested normal backlash tolerance at tightest point of mesh

Outer normal backlash

Diametralpitch Module

AGMA quality numbers 4through 9

inches (mm)

AGMA quality numbers 10through 13

inches (mm)1.00 to 1.25 (25.00 to 20.00) 0.032 -- 0.046 (0.81 -- 1.17) 0.024 -- 0.030 (0.61 -- 0.76)1.25 to 1.50 (20.00 to 16.00) 0.027 -- 0.040 (0.69 -- 1.07) 0.020 -- 0.025 (0.51 -- 0.66)1.50 to 2.00 (16.00 to 12.00) 0.020 -- 0.032 (0.51 -- 0.81) 0.015 -- 0.020 (0.38 -- 0.51)2.00 to 2.50 (12.00 to 10.00) 0.016 -- 0.026 (0.41 -- 0.66) 0.012 -- 0.016 (0.30 -- 0.41)2.50 to 3.00 (10.00 to 8.00) 0.013 -- 0.022 (0.33 -- 0.56) 0.010 -- 0.013 (0.25 -- 0.33)3.00 to 4.00 (8.00 to 6.00) 0.010 -- 0.018 (0.25 -- 0.46) 0.008 -- 0.011 (0.20 -- 0.28)4.00 to 5.00 (6.00 to 5.00) 0.008 -- 0.016 (0.20 -- 0.41) 0.006 -- 0.008 (0.15 -- 0.20)5.00 to 6.00 (5.00 to 4.00) 0.006 -- 0.013 (0.15 -- 0.33) 0.005 -- 0.007 (0.13 -- 0.18)6.00 to 8.00 (4.00 to 3.00) 0.005 -- 0.010 (0.13 -- 0.25) 0.004 -- 0.006 (0.10 -- 0.15)8.00 to 10.00 (3.00 to 2.50) 0.004 -- 0.008 (0.10 -- 0.20) 0.003 -- 0.005 (0.08 -- 0.13)10.00 to 12.00 (2.50 to 2.00) 0.003 -- 0.005 (0.08 -- 0.13) 0.002 -- 0.004 (0.05 -- 0.10)12.00 to 16.00 (2.00 to 1.50) 0.003 -- 0.005 (0.08 -- 0.13) 0.002 -- 0.004 (0.05 -- 0.10)16.00 to 20.00 (1.50 to 1.25) 0.002 -- 0.004 (0.05 -- 0.10) 0.001 -- 0.002 (0.03 -- 0.05)20.00 to 25.00 (1.25 to 1.00) 0.002 -- 0.003 (0.05 -- 0.08) 0.001 -- 0.002 (0.03 -- 0.05)



The amount of backlash at other than the tightestpoint in mesh depends on the quality of the gears.

10.5 Surface finish

The surface finish of cut bevel gears made withcertain steels, or different cutting methods, can reada value of 130microinches (3.3microns); however, itmay be possible to achieve 60 microinches (1.5microns). Careful lapping on hardened gears mayfurther improve surface finish. This reading isobtained by checking the surface across the lay ofthe finish. Proper control of cutter sharpening isessential to hold a fine finish on cut gears.

Precision finished bevel gears are usually producedwith a finish of 20 to 30 microinches (0.50 to 0.76microns). Finer finishes may be obtained.

10.6 Tolerance class selection

The selection of the proper tolerance class isdependent upon the requirements of the gearapplication. High speed gears require closer toler-ances. However, this does not imply that theselection of the tolerance class should be judged byspeed alone. When gears are required for indexingmechanisms, or for high precision units, closetolerances are also required.

11 Drawing format for bevel gears

Table 15 is provided as a general guide for a drawingformat for all bevel gears. Certain items may bedeleted when not applicable. It is frequentlydesirable to include a sketch or note indicating thetooth contact pattern required at a specified lightload. Although table 15 shows decimal degrees,angles may be expressed in degrees, minutes andseconds.

12 Bevel gear inspection

Gears are inspected to determine if they are incompliance with drawing specifications. There aremany levels of inspection which range from a casualvisual inspection through complex measuring tech-niques. The amount of effort that should beexpended upon the inspection of a gear should beara direct relationship to the service that the gear is toperform. The drawing should indicate the level ofinspection required. This is accomplished by thecompleteness with which the gear is described bydimensions, tolerances, and notes and themagnitude of the individual tolerances.

12.1 Visual inspection

The simplest type of inspection is a visual inspectionfor major defects such as missing teeth, burrs, ornicks.

12.2 Gear blank inspection

The basic purpose of inspecting bevel gear blanks isto determine if further work should be applied to theblanks. In general, the bore, the mounting surfacesand the surfaces that become the toplands are themost important details that should be checked.

12.2.1 Bore inspection

The bore (or journals) should be inspected todetermine if a proper fit on the shaft or in the bearingswill be possible at assembly.

12.2.2 Mounting surface inspection

The interface between mounting surfaces should beflat and perpendicular to the reference diameter.

Gear blanksmay be checked by techniques employ-ing surface plates, sine bars, and surface gages, orthey may be checked by highly automatic equip-ment. Certain features such as face and back coneposition on smaller size gears can be convenientlychecked by optical techniques.

Gear blank checkers are available with indicatingdevices which move along an element of the gearblank surface. Thus, to inspect the face cone angleand position, the indicating device is moved along aline parallel to an element of the face cone. Toinspect runout of the face cone at any point along thesurface, the gear blank is turned about its axis underthe indicator. In the same manner, other surfacessuch as the back cone can be inspected. Thus, allparts of the surface are inspected.

These checkers make use of theoretical lines andpoints. The bore andmounting surfaces are used asreferences rather than specific points on the gearblank.

12.2.3 Face cone inspection

The face cone of the bevel gear blank provides thetoplands of the teeth. The amount of clearancebetween the tips of the teeth and the roots of themating teeth is a function of the position of the facecone along the axis of the blank. The position andslope of the face cone must be established as beingwithin drawing limits to assure that sufficient stockexists to produce full depth teeth, and yet not extendso close to the mating gear as to interfere with the



teeth of the mating gear. The slope is critical, since itgoverns clearance or interference at each end of theteeth. Also, since the face of the blank is frequently

used as a holding surface during the quenchingoperation on hardened gears, both the slope andface runout are critical.

Table 15 -- Drawing format basic outline for bevel gears

Bevel gear dataSuggested number of decimalplaces (where applicable)Bevel gear datainches (mm)

Basic specificationsNumber of teethDiametral pitch (transverse module)Pitch diameterOuter cone distancePressure angleShaft anglePitch angleMean spiral angleHand of spiralAddendum (theoretical)Whole depthFace angleRoot angle (ref.)Circular thickness (ref.)Cutter specificationsNumber of teeth in mating gearMating gear part number

For hypoids these additional values are to be includedPinion offsetPitch apex beyond crossing pointFace apex beyond crossing pointRoot apex beyond crossing point

XXXXX.XXXXX.XXXXXX.XXXXXX.XXXX°XX.XXXX°XX.XXXX°XX.XXXX°RH or LH.XXXX.XXXX

XX.XXXX°XX.XXXX°.XXXX

XXX(Dwg. no.)

XX.XXXXXX.XXXXXX.XXXXXX.XXXX

XX.XXXX.XXXXX.XXX

.XXX

.XXX

.XXX

XX.XXXXX.XXXXX.XXXXX.XXX

Metallurgical dataMaterialHeat treatmentDepth of case1) (specify method of measure)Surface hardnessCore hardness1) (specify location of HRC)

Operating dataDriving member isDirection of rotation (looking at back)Speed range (rpm)Power transmitted at ____rpm

Pinion or gearCW or CCW

Inspection dataAGMA Quality numberAccumulated pitch variation2)Allowable pitch variation2)Mean normal chordal addendumMean normal chordal tooth thicknessOuter backlash with mate/control gear at specified mountingdistance (at tightest point of mesh)

NormalTransverse

Test loadTooth contact pattern length under test loadIdeal tooth contact pattern (gear) Drive

Coast

XX.XXXX.XXXX.XXXX.XXXX

.XXX to .XXX

.XXX to .XXX

X.XX to X.XX

.XXX

.XXX

.XXX

.XXX

.XX to .XX

.XX to .XX

XX.X to XX.X

NOTES:1) Specify for surface hardened gears.2) Applies when individual tooth element check is desired.



12.3 Individual tooth element checks

This type of gear inspection is an attempt todetermine the accuracy of each of themajor featuresof the teeth. In theory, each element is measuredwithout reference to the others, but in practice,several factors have some influence on the itembeing measured.

In order to avoid misunderstanding, it is desirable tospecify the surfaces to be used to locate the gear andthe area of the surface to be examined. All individualtooth element checks attempt to establish theposition of the teeth relative to each other and to thecenter of the shaft and the mounting surface of thegear. Thus, the essential features to be specified ona gear are the surfaces fromwhich the teeth are to betested.

12.3.1 Concentricity and spacing inspection

The most accurate method for making concentricityand spacing checks is to use a fixture with aprecision index spindle. A single probe reads toothposition variations on each tooth as the part isindexed from tooth--to--tooth. The use of a proximityprobe can further improve accuracy by reducingvariations due to surface finish. From this data,accumulated pitch variation and spacing variationsare determined.

A second method, which requires a simple fixtureconsisting of an arbor on which the gear can bemounted and turned along with two probes, is lessaccurate (see AGMA 390.03a). The probes, whenmaking a concentricity check, are located to contacttwo teeth which are approximately 180 degreesapart. One probe is fixed. The other probe isarranged to move tangent to the pitch cone with anindicator that indicates the movement required tobring the probe to the tooth surface. The measure-ment is repeated for all teeth on the gear blank. Thechange between the smallest and the largestreadings is a value which is two times runout.

The same fixture described in the above paragraphcan be used to measure tooth spacing variations. Inthis case the probes are located so as to contact thesame points on adjacent teeth. Differences betweenreadings of successive pairs of teeth on the gear aschecked around the gear are interpreted as spacingvariations. Readings from this check can bemathematically manipulated to give pitch variationand accumulated pitch variation. However, becauseof the quality of measurements due to surface

irregularities, the resulting answers can beinaccurate.

12.3.2 Tooth thickness inspection

The tooth thickness of bevel gears is critical in that itdetermines the backlash in themesh and, to a limitedextent, the strength of the teeth. Tooth thicknessvariation can also be an important factor in the noisecharacteristics of a bevel gear set.

There are three generally recognized types of tooththickness:

-- the dimensional tooth thickness asmeasuredby a thickness gage or vernier caliper;

-- the functional tooth thickness as seen by amating gear;

-- the dimensional tooth thickness asmeasuredby a CMM.

The customary way to specify tooth thickness is byindicating a chordal tooth thickness and a chordaladdendum. If the tooth thickness measurement isnot at the pitch cone, the term “chordal addendum” isdropped and replaced with “chordal height” (seeANSI/AGMA 1012--F90 for further information).These dimensions are usually specified at the meannormal section of the teeth. They are subject toposition of the face cone and the back cone, and thedetermination of the mean normal section.

Tooth thickness can also be evaluated by meshingtwo gears together at their proper mounting dis-tances and noting the backlash present. Sincevariations in tooth profile, spiral angle, and spacingall affect actual backlash, the thicknessmeasured bythis method will usually be more than that measuredby the chordal technique. Thus, it is called thefunctional tooth thickness.

12.3.3 Tooth flank inspection

Coordinate measuring machines are used to checktooth flanks by two methods. The first methodinvolves measuring a control gear and storing thedata. Manufactured gears are then measured andcompared to the control gear data. Deviations in thedirection of the tooth surface normals are calculatedand plotted as output. The second method is similarto the first, except that the control gear data isreplaced with theoretical gear data.

12.4 Tooth contact inspection

Two commonly used inspection methods for toothcontact are tooth contact pattern evaluation and theE, P and G check. Contact pattern position,



smoothness of operation, adjustability, and runoutare evaluated by these methods.

12.4.1 Tooth contact evaluation

Tooth contact inspection is made in a test machinearranged with two spindles that can be set at thecorrect shaft angle, mounting distances, and offset.The gear to be inspected is mounted on one spindleand the mating gear or a control gear is mounted onthe other spindle.

The tooth contact is evaluated by coating the teethwith a gear marking compound and running thegears under a light load for a short period of time.Areas where the compound is worn off shows thetooth contact pattern.

The operator evaluates the contact pattern withregard to position and area, based on the specifiedtooth contact pattern.

The sketches in figure 38 illustrate various toothcontact patterns on the pinion tooth. A left handpinion is used throughout, but the contacts arerepresentative of those on right hand pinions as wellas straight bevel pinions. All contact patterns exceptfigure 38(B) represent contacts under light load.

When an incorrect contact pattern is observed atassembly, either the gears have been incorrectlymanufactured or they are incorrectly mounted. Thecause of the error can be readily determined byrunning the gears in a testing machine.

(A) Central toe contact (B) Desired contact under full load

(C) Toe contact (D) Heel contact (E) Cross contact

(F) Low contact (G) High contact (H) Lame contact

(I) Wide contact (J) Narrow contact (K) Bridged (profile) con-tact

(L) Long (full length) contact (M) Short contact (N) Bridged (lengthwise) con-tact

(O) Bias in (P) Bias out

Regardless of the hand of spiral on the pinion, “bias in” will always run from the flank at the toe to the top at theheel on the convex side, and from the top at the toe to the flank at the heel on the concave side.

Figure 38 -- Tooth contact patterns



The incorrect conditions described in 12.4.1.6through 12.4.1.15 are a result of manufacturingproblems and are not correctable at assembly. Theycan only be corrected by changing the gear manu-facturing, cutting tool specifications or adding sec-ondary finishing. The specific changes depend onthe manufacturing methods.

12.4.1.1 Toe contact

When the contact pattern is concentrated at the toeon both sides of the tooth, as shown in figure 38(C),the shaft angle is too large or the root angle setting ofone member was too small during manufacture.

12.4.1.2 Heel contact

When the contact pattern is concentrated at the heelon both sides of the tooth, as shown in figure 38(D),the shaft angle is too small or the root angle setting ofone member was too large during manufacture.

12.4.1.3 Cross contact

The cross contact patterns, as shown in figure 38(E),result when the bevel gears are not accuratelylocated in the correct planes in mounting, when theoffset is not correct during manufacture or when thedistance between the machine axis and the cuttingaxis is incorrect during manufacture.

12.4.1.4 Low contact

When the contact pattern is too low on the profile ofthe pinion, as shown in figure 38(F), the pinion is toofar from the center of the gear. The pinion may havebeen manufactured or assembled with too great amounting distance. The correction for this conditionis obtained by decreasing the pinion mountingdistance.

12.4.1.5 High contact

When the contact is too high on the profile of thepinion, as shown in figure 38(G), the pinion is toonear the center of the gear. The pinion may havebeen manufactured or assembled with too small amounting distance. The correction for this conditionis obtained by increasing the pinion mountingdistance.

12.4.1.6 Lame contact

The contact pattern shown in figure 38(H) is too lowonone side of the tooth and too high on the other sideof the tooth.

12.4.1.7 Wide contact

The contact pattern shown in figure 38(I) is too wide.

12.4.1.8 Narrow contact

The contact pattern shown in figure 38(J) is toonarrow.

12.4.1.9 Bridged (profile) contact

The contact pattern shown in figure 38(K) is bridgedwith a heavier concentration at the flank and at thetop of the tooth.

12.4.1.10 Long contact

The length of the contact pattern in figure 38(L) isextended to full length of the face width.

12.4.1.11 Short contact

The contact pattern shown in figure 38(M) is tooshort.

12.4.1.12 Bridged (lengthwise) contact

The contact pattern shown in figure 38(N) is bridgedin the lengthwise direction with heavierconcentrations at the toe and at the heel.

12.4.1.13 Bias--in contact

The contact patterns shown in figure 38(O) rundiagonally from the flank at the toe to the top at theheel on the convex side, and from the top at the toe tothe flank at the heel on the concave side.

12.4.1.14 Bias--out contact

The contact patterns shown in figure 38(P) rundiagonally from the top at the toe to the flank at theheel on the convex side and from the flank at the toeto the top at the heel on the concave side.

12.4.1.15 Contact runout

Runout is characterized by the tooth pattern shiftingprogressively around the gear from heel to toe andtoe to heel.

12.4.2 The E, P and G check

The E, P and G check is a method for measuring theamount and direction of the vertical, E, and axial, P,displacements of the pinion, from its standardposition, to obtain a tooth contact in the middle of thetooth profile, at the extreme toe, and at the extremeheel of the tooth. Interpretation of the data obtainedfrom this check provides an indication of the shape ofthe actual profiles, and provides a practical way ofaccurately measuring the amount of relative vertical



displacement from the specified mounting positionwhich the gears can withstand without causing loadconcentrations at the ends of the teeth.

Gear axial displacement, G, is generally only used tomaintain backlash. In most gear sets it does notsignificantly affect the tooth contact pattern.

The E and P adjustments have traditionally beenreferred to as V and H respectively.

The readings for all dials on the testing machinemaybe considered as zero readings when the gears aremounted in their specified mounting positions. Allhorizontal and vertical movements are measuredfrom these zero positions. The following rules willdetermine the correct signs to be used with thesemovements.

-- Increase pinion mounting distance = (+)plus P

-- Decrease pinion mounting distance = (--)minus P

-- Pinion axis lower with reference to the gearaxis = (+) plus E

-- Pinion axis raised with reference to the gearaxis = (--) minus E. See figure 39.

VerticalMovement

HorizontalMovement

-- +P

--

+E

Figure 39 -- Explanation of E and P movements

In table 16, the columns entitled “Reading at toe”,“Reading at heel”, and “Total movement toe to heel”,constitute the E and P check. See figure 40. It isoccasionally very desirable to determine the verticaland horizontal settings necessary to place the toothcontact in the center of the tooth profile at theextreme toe and extreme heel. The total movementbetween the toe and heel readings is obtained bysubtracting the heel reading from the toe readingsalgebraically. This is illustrated in the followingexample.

Toe Heel

Toe Heel

Toe contact

Heel contact

Figure 40 -- Toe/heel contact nomenclature

Referring to table 16, the line entitled “Verticalmovement” gives the relative displacement from thecentral position to the toe, (in the example +0.010 in)from the central position to the heel, (in the example--0.018 in) and from the toe to the heel, (in theexample 0.028 in). This last value, “Total movementfrom the toe to heel” is a measure of the bearinglength in terms of displacement, and is sometimesreferred to as a “____ length” (in this example “28length”).

Table 16 -- Example of E, P and G values

Movement Reading at toe Reading at heelTotal movement

toe to heelVertical, E +0.010 in (0.25 mm) --0.018 in (0.46 mm) 0.028 in (0.71 mm)

Horizontal, P --0.014 in (0.36 mm) +0.020 in (0.51 mm) 0.034 in (0.87 mm)

Gear axial, G 0.000 in (mm) 0.000 in (mm) 0.000 in (mm)

Total vertical movement = (+0.010) -- (--0.018) = + 0.028 inTotal horizontal movement = (--0.014) -- (+0.020) = -- 0.034 inThe algebraic signs of these totals are ignored since the magnitude of these quantities is the item of interest.



When the total vertical movement of the E and Pcheck is too large, it indicates that the tooth bearingis too short and therefore, the load will be concen-trated on too small an area of the tooth surface,thereby causing danger of excessive wear. Whenthe total vertical movement is too small, it indicatesthat the tooth bearing is too long and hence, thegears will lack sufficient adjustability to compensatefor mounting deflections, which may lead to loadconcentration at the ends of the teeth.

12.4.3 Smoothness of operation

Smoothness of operation may be evaluated simulta-neously with the contact pattern inspection or as aseparate test. With a non--instrumented machine,the operator subjectively judges the noise qualitybased on his past experience.

12.5 Backlash measurement

Normal backlash is measured with a dial indicator,with the stem mounted perpendicular to the toothsurface at the heel of the tooth at or near the pitchline. It is measured by rotating the gear back andforth while holding the pinion solidly against rotation.

Backlash in the plane of rotation is obtained bydividing the normal backlash by the cosine of theouter spiral angle and the cosine of the pressureangle (see figure 63). It is sometimes necessary tocheck backlash by means of a boom arrangementattached to the gear shaft. Thismethod is often usedfor the fine pitch gears and gives a direct reading ofbacklash in the plane of rotation. The indicator

reading is taken at a position approximately equal tothe pitch radius of the gear. See figure 64.

12.6 Single flank inspection

Single flank inspection is done on a special type ofmachine. The gears roll together in their propernominal position with backlash and one flank incontact. Encoders which measure rotational motionare attached to each shaft. The data from theencoders is processed in an instrument that showsthe motion variation of the driven gear relative to itstheoretical angular position as it is being driven bythematingmember. This data can be directly relatedto profile variation, maximum pitch variation, accu-mulated pitch variation and local high spot variation(burrs). See figure 41.

12.7 Metallurgical inspection

In addition to the inspection for the geometricfeatures of gears, the metallurgical features are alsoinspected. These inspections include:

-- etching techniques for detecting grindingdistress;

-- metallographic techniques for determiningcase depth and case, and core hardness;

-- spectrographic analysis for materialchemistry;

-- magnetic and ultrasonic particle inspectionfor detection of subsurface flaws.

Appropriately sized and shaped test coupons of thegear material are frequently evaluated to establishboth the quality of the material and the care withwhich the gears were heat treated.

Totaltransmissionvariation

BurrAdjacentpitch

variationEffectiveprofilevariation

Tooth to toothtransmissionvariation

Accumulatedpitch variation

Figure 41 -- Single flank inspection chart



13 Materials and heat treatment

The quality of materials and methods of heattreatment required are governed by the application.Care should be taken to choose the proper materialfor each application in order to obtain the load andlife values that are desired. Heat treatment is usuallyneeded to develop the necessary hardness,strength, and wear resistance.

Forgings, castings, and bar stock can be useddepending on the requirements to be met. Theyshould be free from seams, cracks, folds, orunacceptable microstructures.

For an in depth discussion of materials and heattreatment, refer to ANSI/AGMA 2004--B89 andANSI/AGMA 2003--B97.

13.1 Steel

13.1.1 Non--heat treated

Steels that are not heat treated may be used wherethe service conditions will permit.

13.1.2 Through hardened

Through hardened steels are used when mediumwear resistance and load carrying capacity aredesired. The selection of the particular type of steeldepends on the properties required. The harden-ability and section size are the usual basis forselection.

The following steels are some of those used,beginning with the steel of lowest hardenability: AISI1045, 1144, 4640, 4140, 4150, 4340 and 4350.

Through hardened gears should be tempered at thehighest temperature that will produce the desiredstrength and hardness and provide maximum reliefof hardening stresses.

13.1.3 Surface hardened

13.1.3.1 Carburized

Carburized and hardened gears are used when highwear resistance and load carrying capacity arerequired. Carburized steels used in gears normallyhave a carbon content of 0.10 to 0.25 percent andshould have sufficient alloy content to allow harden-ing of the section sizes that are used. Selection of aparticular steel depends on its properties. Common-ly used steels are: AISI 4620 and 8620; if higher corehardness is required, AISI 4320, 4820 or 9310 canbe used.

Carburized gears should be specified as follows:

-- effective depth to 50 HRC equivalent ofcarburized case after finishing operations;

-- surface hardness;

-- core hardness at center of tooth at rootdiameter;

-- maximum case carbon content (optional).

Gears should be quenched from a temperaturewhich will ensure a minimum amount of retainedaustenite.

13.1.3.2 Nitrided

Nitrided steels are used in applications which requirehigh wear resistance with minimum distortion in heattreating and where shallow case depths are allow-able. The commonly used steels are: AISI 4140,4150, and 4340. If extreme hardness and wearresistance are required, the Nitralloy steels can beused. Care should be exercised in using Nitralloysteels since they produce hard, relatively shallowcases. To achieve the desired results in the nitridingoperation, all material should be hardened andtempered above the nitriding temperature prior tofinish machining. Sharp corners should be avoidedon external surfaces.

Specifications for nitrided gears should include: totaldepth of nitrided case after finishing operations,surface hardness, and core hardness.

To reduce distortion in the nitriding operation, it isgood practice to stress relieve parts after the roughmachining operation. This should be carried out at atemperature about 50°F (28° C) above the tempera-ture of the nitriding operation and 50°F (28°C) belowthe tempering temperature used for hardening andtempering.

The nitriding operation should be performed in amanner that will result in a minimum white layer toavoid pitting or spalling. In critical cases, the whitelayer can be removed by grinding or chemicaletching.

13.1.3.3 Induction hardened

Induction hardening is used on bevel gears havingcomplicated sections where localized hardeningwith little distortion is desired. In certain cases, it isalso used where it is more economical than furnacehardening. Both alloy and carbon steels in the 0.40to 0.55 percent carbon range can be hardened bymeans of induction heating.



13.1.3.4 Flame hardened

Flame hardening is used on bevel gears that are toolarge or too costly to harden by other methods. Thismethod is also used in some cases for reducingdistortion.

All types of hardenable steel, cast iron and mostductile irons are suitable for flame hardening.Carbon content for steel is normally in the range of0.40 to 0.55 percent.

13.2 Cast iron

Cast iron is used in place of non--heat treated steelwhere good wear resistance combined with excel-lent machinability is required. Complicated blankshapes can be cast more easily from iron than theycan be produced bymachining frombars or forgings.

Usually cast iron gears are not hardened. Whenrequired, furnace hardening is used for throughhardening. Induction or flame hardening can beused when localized hardening is desirable.

13.3 Ductile (nodular) iron

Ductile iron can be through hardened or surfacehardened.

13.4 Bronze

Bronze materials are used when corrosionresistance or non--magnetic properties are required.

13.5 Non--metallic

Some non--metallic materials offer advantageswhen loads are light and operating temperaturespermit.

Selection and specifications for these materialsshould be based upon the requirements of theapplication.

14 Lubrication

The principles suggested for the lubrication of bevelgears in operation are similar to those followed in thelubrication of spur and helical gears. The lubricationin these applications has a dual function:

-- to prevent metal to metal contact;

-- to carry away the heat generated by friction intooth engagement.

To fulfill these functions, each tooth surface mustcarry a film of lubricant when it enters into engage-

ment with a mating tooth, and there must besufficient volume of lubricant to absorb and dissipatethe heat generated by friction, without excessivetemperature rise.

14.1 Selection of lubricants

The type of lubricant used in a gearbox is oftendetermined by factors independent of the gears.

14.1.1 Environment

The operating environment must be carefully con-sidered when selecting the lubrication system of agearbox. The ambient temperature is the mostcommon consideration. Temperature is covered in14.2.1.2. Contamination is a common factor, but isfrequently overlooked. Some applications, such asmining, papermills, textile mills, and printing pressesproduce large amounts of abrasive dust. Thismaterial can seriously affect the operation of gears ifit contaminates the lubricant. A circulating oil systemwith proper filtration is a common solution forcontamination.

14.1.2 Maintenance

The type of maintenance a product will receive canrestrict the type of lubrication systems available tothe gearbox designer. In situations where lubricantscan be easily checked and replaced, the selectionscan be numerous. Natural oils and greases arecommon selections. Frequently the gears areplaced in an application where maintenance isdifficult or impossible, such as sealed for lifeconsumer appliances. Here the designer maychoose synthetic oils, greases or self lubricatingmaterials. Frequently the designer has to increasethe amount of lubricant and component sizes tocompensate for the wear they will experience due tothe less than desirable lubrication conditions.

14.1.3 Application

The application for the gear system may dictate thetype of lubricants available to the designer. Certainindustries have a predetermined selection of lubri-cant. A common example would be a food process-ing plant. The lubricant selection may be limited toproducts that would not be harmful to the foodprocessed should contamination occur. Medicalprocesses have similar restrictions. Aircraft andmilitary lubricants must be selected from those thathave passed rigorous tests and qualifications.Spacecraft and satellite applications can not containmaterials that will produce gasses in a vacuum.



14.1.4 Internal components

Gears do not operate totally by themselves. Theydepend on bearings, seals, clutches and sometimesother components to perform their intended func-tions. The selection of lubricants is frequentlyconstrained by the other components in the system.A typical example is the automotive engine. Thelubricant is tailored to the combustion part of theengine, yet must lubricate the gears and bearings aswell. The gear designer may have to select the gearmaterial, heat treatment, surface finish, or geometryspecifically for the systems required lubricant.

14.1.5 Cooling requirements

One of the two primary functions of a lubricant is tocarry away heat. Most high speed drives require oilto properly remove the heat generated duringoperation. Several methods can be used to removeheat. The simplest is allowing the gearbox housingto dissipate the heat. This requires that the housingis large enough to allow the heat to dissipate at leastas fast as it is produced. Frequently external coolingis required. This may be accomplished by the use offans or a heat exchanger. The determination of theheat flow in a gearbox is beyond the scope of thisstandard.

14.2 Types of lubricants

Numerous types of lubricants are available to thedesigner. Oil is the most versatile and popular.Grease is the second most popular. Other materialscan also be used.

14.2.1 Oil

Oil is by far the most frequently used lubricant forgears. The properties of oil can be changed bychanging its viscosity or by the addition of chemicaladditives. It can be produced from natural hydrocar-bons or by synthetics. The proper selection of oilvaries drastically with application. There is nouniversal gear oil. Oil selected for one applicationcould be disastrous in another. See ANSI/AGMA9005--E02, Industrial Gear Lubrication.

14.2.1.1 Viscosity

Apart from the formulation of the lubricant, viscosityis the most significant property requiring specifica-tion. Usually, viscosity is selected for the gear meshhaving the heaviest load and lowest speed amongthose served by the same lubricant.

When straight mineral oils are used, the viscositymay be selected by the following:

...(43)VK=7000v0.5t

...(43M)VK=35.56v0.5t

where

VK is kinematic viscosity, centistokes;

vt is pitchline velocity, ft/min (m/s).If v is less than 500 ft/min (2.5 m/s), use 500ft/min (2.5 m/s).

The above equations provide a guide. While thenearest viscosity grade given in ANSI/AGMA9005--E02 is usually selected, satisfactory perform-ance may be obtained with a viscosity level onegrade higher or lower than indicated.

14.2.1.2 High/low temperature

The ambient operating temperature for a gearboxhas amajor effect on its lubricant selection. Devicesoperating in arctic regionsmay be required to start attemperatures of --65°F (--55°C). Devices operatingnear heat sources may easily see temperaturesabove 400°F (205°C). Some applications, such asan aircraft engine gearbox, can be exposed to bothhigh and low temperature extremes.

Typical lubricants do not operate over wide ranges oftemperature. Low temperatures may retard theability of oil to pour, and thereby prevent anycirculation of the lubricant. High temperatures willdecrease an oil’s viscosity andmay cause a lubricantto chemically breakdown, rendering it useless.

14.2.1.3 Viscosity index improver

The viscosity of oil changes with temperature.Higher temperatures lower the viscosity. Viscosityindex improvers tend to reduce the rate of change ofviscosity with temperature.

14.2.1.4 Pour depressants

Natural petroleum products have a cold temperaturepour limit. Frequently, applications require the lubri-cant to be fluid at a lower temperature. This pourpoint can be lowered by additives. Synthetic lubri-cants have a much lower pour point without anyadditives and are generally more expensive.

14.2.1.5 Oxidation inhibitor

Petroleum products react with oxygen. Thesereactions reduce the performance of the lubricant



and form by--products. These reactions are acceler-ated by temperature. Oxidation inhibitors retardthese reactions.

14.2.1.6 Corrosive inhibitors

Chemical additives can reduce the corrosion offerrous and nonferrous metals in the gearbox.These metals may include bearing cages, tubing, aswell as the gears and bearings. Most gearboxesabsorb some water and as a result require additivesto reduce the formation of rust.

14.2.1.7 Antifoam additives

Foam is an unstable mixture of liquid and gas. Itspresence is undesirable in a gearbox. It can act asan insulator, restricting cooling. It can also enter theoil pump and disturb the flow. Foaming is usually theresult of a fault in the lubrication system such aschurning or improper oil level. Additives can reducethe tendency of oil to foam under these conditions.

14.2.1.8 Extreme pressure additives

Extreme pressure additives react with the surface ofthe gear tooth to form a protective barrier. Theyincrease surface load capacity and increase scoringresistance. They are particularly useful under thehigh sliding conditions found with hypoid gears.They react with the tooth surface when the contactpressures raise the local temperatures. The addi-tives used to provide this protectionmight be harmfulto other components in the system.

14.2.2 Grease

Grease is a mixture of a base oil and a thickeningagent. The thickening agent, usually ametallic soap,is used to control consistency. The consistency canvary from a solid to a thin semi--fluid. Since the baseoil provides all lubrication, the discussion regardingoil also applies to grease.

Grease is frequently selected as a lubricant in anattempt to avoid leakage problems. Since greasedoes not flow as readily as oil, seals are not ascritical. The oil does tend to separate from thethickener with time, so care must be taken if minorleaks cannot be tolerated.

Grease is also frequently used as an initial lube forself--lubricating gears.

At high speeds, gears will cut a channel through astanding reservoir of grease and throw off anyremaining grease from the gear. The semi--fluid

consistency prevents the grease from flowing backto fill the channel. Poor heat transfer characteristicscombine with the flow limitations to reduce the loadcapacity of the gearbox. For these reasons, the useof grease should be restricted to low speedapplications, below 1000 ft/min (5 m/s).

14.2.3 Dry lubricants

Dry lubricants refer to coatings applied to the geartooth surface and are not intended to be replenished.They may include molybdenum disulfide (MoS2),graphite or organic materials such aspolytetrafluoroethylene (PTFE or Teflon). The useof these materials is highly desirable from a designstandpoint, but actually quite limited in practice.They essentially provide a wear surface between theteeth. They cannot provide cooling, which is oftenthe primary lubricant requirement. Because of this,dry lubricants are not normally used for anythingother than lightly loaded applications.

14.2.4 Self lubricating

The use of polymer compounds (plastics), hasbecome quite popular. They are light in weight, canbe molded into final shape and include some limitedself lubrication. They suffer from some of the sameproblems as dry lubricants. That is, they can notdissipate heat or carry a heavy load. They alsodeflect more than metal gears. Even though thematerial is self lubricating, an initial coating of greaseor oil will greatly improve the break--in of selflubricating materials. Care must be exercised in theselection of lubricants applied to these materials toprevent undesirable chemical reactions.

14.3 Scuffing (scoring)

Scuffing is defined as the localized damage causedby the occurrence of solid--phase welding betweensliding surfaces. It is accompanied by the transfer ofmetal from one surface to another due to weldingand tearing, and may occur at any sliding and rollingcontact where the oil film is too thin to separate thesurfaces.

The analysis of scuffing in bevel gears is not welldefined. It is beyond the scope of this standard.

14.4 Application of lubricant

Regardless of the type of lubricant selected, properoperation requires that an adequate quantity isapplied. The methods used to insure the applicationof that quantity varies with the type of lubricant.



14.4.1 Quantity required

The amount of lubricant is dependent on severalfactors. Table 17 may be used when oil is theselected lubricant. A minimum of 0.5 gal/min perinch (1.9 l/min per 25mm) of face width is suggestedregardless of the power transmitted.

14.4.2 Method of application

Splash lubrication and pressure jets are the typicalmeans of applying oil. Splash lubrication is theprocess of allowing a rotating component, usually agear, to dip into the oil. Centrifugal forces fling the oilaround inside the gearbox. Oil may also cling to thegear, carrying it into mesh. Increasing the oil level tobring more oil into contact with the rotating compo-nent can be detrimental. The additional oil can leadto churning and hence increased temperatures,foaming and a loss of efficiency. The use of splashlubrication is usually confined to slow speed drivesand may require some experimentation for properoperation.

In pressure feed systems, oil is forced throughorifices, called jets, to the gear teeth near themeshing point. The jets should be positioned with atleast one jet per inch (25 mm) of face width. Highspeed gears can act as air pumps and deflect the oilcoming from the jets. The position of the jets andpressure must be adjusted to assure that the meshreceives oil. Pressures at the jet can range from 25to 50 lb/in2 (0.17 to 0.34 N/mm2) depending on theflow rate and the gear speed.

Table 18 is frequently used for the location of oil jetsin pressure feed systems.

15 Design of bevel gear mountings

To ensure the proper operation of bevel gears thesame care that goes into the design of the bevel gearblanks and gear elements should be exercised in thedesign of the mountings.

Table 17 -- Typical oil flows per gear mesh

hp/gpmFl T i l kW

l∕min Flow

conditionTypicaltemp rise

Comments

400 (80) Copious 50°F(28°C)

General industry

800 (160) Adequate <75°F(42°C)

Typical aviation

1200 (235) Lean <100°F(56°C)

Lightweight, high efficient aviation, unusual conditions

1600 (315) Starvation >100°F(56°C)

Not recommended

Table 18 -- Typical oil jet location

Pitch line velocityft/min (m/s)

Jet location Comments

3000 (15) None Properly designed splash is adequate3000 -- 5000 (15 -- 25) Into mesh Lubrication is primary; cooling is secondary; splash with

adequate baffles and channels may also work5000 -- 12 000 (25 -- 60) Out--of--mesh

or into meshCooling is the primary function; sufficient oil adheres toteeth to lubricate the contact

12 000 -- 20 000 (60 -- 100) Out--of mesh Cooling is by far the dominant need; copious flow onout--of--mesh side required

>20 000 (100) Into mesh andout of mesh

Low flow should be provided on into--mesh side forlubrication, and high flow should be provided to out--of--mesh side for cooling



The gear and pinion mountings must be designed togive adequate support to the gears for all loadconditions to which the gears may be subjected.Each member of spiral bevel and hypoid gear setsshould be held against axial movement in bothdirections. Bevel gears can accommodate reason-able displacements and misalignment without detri-ment to tooth action. Excessive misalignmentreduces the load capacity with consequent danger ofsurface failure and tooth breakage.

Suggested housing tolerances are shown in figure42.

The suggested allowable deflections under highestsustained loads has been determined to be:

-- The gear and pinion axes should not separatemore than 0.003 in (0.08 mm);

-- The pinion should not move axially more than0.003 in (0.08 mm) in either direction;

-- The gear should not move axially more than0.003 in (0.08 mm) in either direction on miters ornear miters, or more than 0.010 in (0.25 mm)away from the pinion for higher ratios.

The above limits are for gears from 6 in (152 mm) to15 in (380 mm) diameter. Somewhat narrowerdeflections are used for smaller diameter gears andsomewhat higher deflections are used for largerdiameter gears. Somewhat greater deflectionvalues are allowable in a static condition. Bearingend play is not considered in this discussion.

15.1 Analysis of forces

The gear tooth forces are tangential, axial and radial.The axial and radial forces are dependent on thecurvature of the loaded tooth face. Use table 19 todetermine the load face.

Offset

Offset

Bevel gear Hypoid gears

Shaft angle toleranceShaft angle + 0° 2’

-- 0° 0’

Size range Bevel gear axes shouldintersect within:

Hypoid offset dimensionshould be within:

Gears up to 12 in (300 mm) diameter + 0.001 in (0.03 mm) + 0.001 in (0.03 mm)Gears 12 in (300 mm) to 24 in (600 mm) diameter + 0.002 in (0.05 mm) + 0.002 in (0.05 mm)Gears 24 in (600 mm) to 36 in (900 mm) diameter + 0.003 in (0.08 mm) + 0.003 in (0.08 mm)

Figure 42 -- Housing tolerances

Table 19 -- Load face

Pinion hand Rotation of driverLoad facePinion hand

of spiralRotation of driver

Driver DrivenRight Clockwise Convex Concave

Counterclockwise Concave ConvexLeft Clockwise Concave Convex

Counterclockwise Convex Concave



The equations to calculate the above forces arepresented below.

15.1.1 Tangential

The tangential forces on a bevel gear (member withlarger number of teeth) is given by:

...(44)WtG=2TGDm

where

WtG is tangential force at mean diameter on thegear, lb (N);

TG is torque transmitted by the gear, lb in (Nm).

The tangential force on themating pinion is given by:

...(45)WtP=WtG cosψPcosψG

=2TPdm

where

WtP is tangential force at mean diameter on thepinion, lb (N).

15.1.2 Axial

The values of axial force, Wx, on bevel gears aregiven in the following formulas. The symbols in theformulas represent the values (e.g., tangential force,spiral angle, pitch angle, and pressure angle) for thegear or pinion member under consideration:

For a concave load face:

...(46)Wx=Wtcosψ

tanÔ sin γ+ sinψ cos γ

For a convex load face:

...(47)Wx=Wtcosψ

tanÔ sin γ− sinψ cos γ

where

Wx is axial force, lb (N);

Wt is tangential force, lb (N);

Ô is normal pressure angle. This is thepressure angle on the loaded side of thetooth (depending upon direction of rotation);

γ is pitch angle of pinion or gear on bevelgears.

A positive sign (+) indicates direction of thrust isaway from pitch apex.

A negative sign (--) indicates direction of thrust istoward pitch apex.

15.1.3 Radial

The values of radial force, Wr, on bevel gears aregiven in the following formulas. When using theformulas the tangential force, spiral angle, pitchangle, and pressure angle of the correspondingmember must be used:

For a concave load face:

...(48)Wr=Wtcosψ

tanÔ cos γ − sinψ sin γ

For a convex load face

...(49)Wr=Wtcosψ

tanÔ cos γ+ sinψ sin γ

where

Wr is radial force, lb (N).

A positive sign (+) indicates direction of force is awayfrom the mating member. This is commonly calledthe separating force.

A negative sign (--) indicates direction of force istoward the mating member. This is commonly calledthe attracting force.

15.2 Direction of forces

The direction of forces is determined by the hand ofthe spiral and the direction of rotation. The directionof rotation is determined by viewing towards the gearor pinion apex as seen in figure 43.

Figure 43 -- Direction of rotation

The resultant forces in the axial plane are shown infigure 44.

In figure 44(A), the forces are due either to aright--hand gear being driven counterclockwise ordriving clockwise, or to a left--hand gear being drivenclockwise or driving counterclockwise.

In figure 44(B), the forces are due either to aright--hand gear being driven clockwise or driving



counterclockwise, or to a left--hand gear being drivencounterclockwise or driving clockwise.

In figure 44(C), the forces are due either to aleft--hand pinion driving clockwise or being drivencounterclockwise, or to a right--hand pinion driving

counterclockwise or being driven clockwise.

In figure 44(D), the forces are due either to aleft--hand pinion driving counterclockwise or beingdriven clockwise, or to a right--hand pinion drivingclockwise or being driven counterclockwise.

A. Convex load face on gear

C. Concave load face on pinion

Separating force

Tangential force

Tangential force

B. Concave load face on gear

D. Convex load face on pinion

Tangential force

Tangential force

Axial force

Separating force

Attracting

Axial force

Figure 44 -- Resultant gear tooth forces



15.3 Types of mountings

The preferred design of a bevel gearbox providesstraddle mounting for both gear and pinion, and thisarrangement is generally used for industrial andother heavily loaded applications. When it is notfeasible to use this arrangement, themember havingthe higher radial load should be straddle mounted.Overhung mountings may be required due to gearbox space limitations.

Figures 45 and 46 show typical mountingarrangements.

Ideally, the bevel gear mountings should be of gooddesign with adequate rigidity. For the situation

where the gear can move axially due to the internalclearance of the bearing, the gear should be locatedin its normal running positionwhen the load pattern ischecked.

16 Assembly

The quality that is designed andmanufactured into aset of bevel gears can only be achieved by thecorrect mounting of the gears at assembly. To becorrectly mounted, each gear and its pinion must belocated axially at a position that will provide the toothcontact pattern and backlash specified on thedrawing. For additional guidance refer to ANSI/AGMA 2008--C01.

Figure 45 -- Typical straddle mounting for both members

Figure 46 -- Typical overhung mounting



16.1 Proper assembly

It is important that gears be assembled carefully tomeet the mounting pattern specifications. Gearsassembled with an improper mounting will wearexcessively, operate noisily, scuff, and possiblybreak.

Generally, the only adjustments the assembler cancontrol are those which axially position the pinionmember and the gear member at assembly. Incertain designs the assembler is not provided withmeans of shimming or other methods for positivelylocating the axial positions of the members. Theassemblies resulting from such designs will beaffected by maximum tolerance accumulations andin many cases will not exhibit a good tooth contactpattern.

When mounting distances are marked on the gears,and when provisions are made for shimming, theassembler should shim to achieve these mountingdistances. These adjustments eliminate the effectsof axial tolerance accumulations in both the gears

and mountings. Shimming cannot correct for shaftangle errors or offset errors.

16.2 Markings

Before installing a set of bevel gears, examine andunderstand all the markings on the parts and on anytags which may be attached. If no markings appearon the gears, the necessary information must beobtained from design specifications (see figure 47).

16.2.1 Mounting distance

The mounting distance is usually shown as “MD”followed by the actual dimension.

16.2.2 Backlash

The minimum amount of total backlash of a pair ofbevel gears is measured at the tightest point ofmeshwith a dial indicator or bevel gear testing machine(see figure 48). This value is usually marked on thegearmember. The amount of backlash is denoted bythe markings, for example B/L .006. Unless other-wise specified, backlash (B/L) is assumed to benormal backlash and cannot be measured in theplane of rotation.

Figure 47 -- Typical gear marking



Figure 48 -- Measurement of normal backlash

16.2.3 Matched teeth

Some bevel gears are lapped in sets to improve theiroperation. These gear sets, especially those havingtooth counts with a common factor, have markedteeth to assure proper assembly engagement. Atassembly, a tooth marked with an “X” on onemember must be engaged between two teethmarked with an “X” on the mating member. It is alsoimportant when checking backlash to rotate the setof gears to a position where the marked teeth areengaged.

16.2.4 Set number

While the teeth of bevel gears are manufactured toclose tolerances, slight characteristic tooth formchanges do occur from gear to gear, due to tool wearin manufacturing and distortion in heat treating. Inmost cases, a gear and pinion are operated under alight load in a bevel gear test machine, and sets areselected for a predetermined tooth contact pattern.Therefore, it is important to mark a serial number oneach member of a set of gears to assure matchedidentification; for example, set number 4. Gearswhich are identified by such a number should alwaysbe assembled with the correct mate.

16.2.5 Part number

Most gears are identified by a part number. It usuallyappears in an area away from themarking previouslymentioned.

16.2.6 Other markings

Other markings may appear which do not affect theassembly procedure. Among these are manufactur-er’s trademark, material identification, gagedistance, head distance, date of manufacture, andinspector’s or operator’s symbol. Manufacturer’sinstructions should be provided to explain themarkings.

16.3 Positioning the gear

The same procedure should be used for positioningthe gear member. When the gear mounting distanceis not marked, its correct axial position is determinedat the point where the proper backlash is measuredat the tightest point of mesh between the matingmembers.

16.3.1 Positioning the pinion by setup gage

The correct mounting distance can be determinedusing a gage assembled in the housing in place ofthe pinion. A mounting gage used to locate a hypoidpinion is shown on figure 49. This mounting gage isgenerally made shorter than the gaging distance toprovide space for using feeler gages when assem-bling the pinions. A similar gaging method wouldapply to the gear member when the shaft angle is 90degrees.

For ease of assembly, it may be necessary to mountthe pinion or gear member from a front locatingsurface. The thickness of the gear blank issubtracted from the conventional mounting distanceto obtain the more convenient locating surface. Seefigure 49.

A setup gage used for locating the pinion of a bevelset on other than 90 degree shaft angle designs isshown in figures 50 and 51. This setup gage is usedfor assembling the gears shown in figures 52 and 53.In this gage, a spring loaded shaft bears against aconical surface ground on the gaging members. Adirect reading between the gaging surfaces deter-mines the thickness of the spacing collar necessaryto position each member properly.

16.3.2 Positioning the pinion by measurements

Another method for positioning the pinion accuratelyis by direct measurement of all components thataffect its location.



Mountingdistance

Set to mountingdistance withgaging blocksor feelers

Gagingdistance

Less feelerthickness

Figure 49 -- Hypoid pinion mounting gage

Gagingsurfaces

Thickness ofspacing collar

Thickness ofspacing collar

GagingSurfaces

Figure 50 -- Pinion setup gage for angular bevel gears



Figure 51 -- Photograph of pinion setup gage

Figure 52 -- Mounted bevel gears

16.3.2.1 90 degree measurement

A typical assembly procedure for mounting a pinionwith a 90 degree shaft angle is shown in figure 54.The upper portion shows the measurements neces-sary to determine the distance from the pinionmounting face of the housing to the center line of the

gear axis. The lower portion shows the measure-ments and calculations necessary to determine theshim thickness required to position the pinion. Inorder to minimize any possible accumulation oferrors in measurements, the least number of meas-urements necessary to calculate the shim should bemade. For example, for the gear box shown in figure55, detailed measurements are shown in figures 56through 59. Care must be taken to assure that thebearings are seated as they would be under normaloperating conditions.

Figure 53 -- Gears shown in figure 52

16.3.2.2 Angular assembly

A typical assembly procedure for mounting a pinionhaving a shaft angle other than 90 degrees is shownin figure 60. When the shaft angle is other than 90degrees, the distance from the pinion mounting faceof the housing to the crossing point is not easilymeasured. This dimension can, however, easily beobtained during the machining of the housing andeither the actual dimension or the deviation from themean can be marked on the housing. A method tocalculate themounting distance is illustrated in figure61. With this dimension available, the necessaryshim is determined in a manner similar to a pinionhaving a 90 degree shaft angle.

An analogous procedure is used to assemble thegear member.



X

1/2

DIM* DIM DIM

M.D.Marked on pinion

Shim

1

DIA 1

2

C

DIM B

Gearaxis

A D E

Pinionaxis

B 2+1= 1/2

D+A= M.D. + +C E

Shim = -- DIM BCXTypical example

M.D. = 1.798 DIA 1 = 3.422 C = 3.476

+ DIM A = 0.578 -- B = 3.399

+ DIM D = 0.517 1/2 1 = 1.711 Shim X = 0.077

+ DIM E = 0.583 + 2 = 1.688

C = 3.476 B = 3.399

NOTE: DIM taken between inner and outer race with axial bearing clearance removed.A

Figure 54 -- Typical assembly

M.D.

Shim Shim

M.D.

Figure 55 -- Shimming procedure for bevel pinion with 90° shaft angle



MDa

ma

Shimhere

Wp

MDp

MDa = MDp -- Wp + ma

Figure 56 -- Vertical sub--assembly

VMD

Bore

SurfaceShim = MDa -- VMD

Figure 57 -- Housing--vertical mounting distance



MDa = MDg -- Wg + ma

MDa

ma

Wg

MDg

HsgC

L

Figure 58 -- Horizontal sub--assembly

Bore

HMD

Surface SHIM = MDa -- HMD

Figure 59 -- Housing--horizontal mounting distance



Gearaxis

SHIM

Pinionaxis

M.D.

DIM Markedon housing

DIM* DIM DIM

Marked on pinionA D E

BX

C

D+A= M.D. + +C E CShim = -- DIM BXTypical exampleTypical example

M.D. = 3.305 C = 4.980

+ DIM A = 0.579 -- DIM B = 4.882

+ DIM D = 0.513 Shim X = 0.098

+ DIM E = 0.583= 4.980

NOTE: DIM taken between inner and outer race with axial bearing clearance removed.A

Figure 60 -- Shimming procedure for bevel pinion with other than 90° shaft angle

Z F

XY

D

1. Measure Di, Gi, Ei b = Ball DiameterD = Di -- b

3. a = X + Y

G= Gi+ b2

E= Ei+ b2

2. GD= sinX ED= sinZ= sinY

4. F= D2 – E25.MDH2=

Fsin a

6.MDH1=MDH2 – Gcos a

Housing mountingdistance 1, MDH2

Ei

Gi

Housing mountingdistance 2, MDH2

b

a

G

MDH1

E

MDH2

aDi

Figure 61 -- Angular bevel gear box housing mounting distance measurements and calculations



16.3.3 Positioning by flush surfaces

In the cases where measurement of mountingdistance is difficult, flush surface may be ground onthe back cone faces (back angles) of the gear andpinion when in correct position in the testingmachine. When the gears are assembled they mustbe positioned so that the ground areas on the backcone surface are flush (see figure 62).

16.4 Backlash

Normal backlash of a pair of bevel gears ismeasuredwith a dial indicator. The stem of the indicator shouldbe mounted perpendicular to the gear tooth surfaceat the extreme heel. Backlash is then measured byrotating the gear member back and forth, makingcertain that the pinion member is held motionless,see figure 48. The backlashmeasured at the tightestpoint of mesh or at the matched teeth should be heldwithin the values in table 14, if not specified.

To calculate backlash in the plane of rotation, dividethe normal backlash by the product of the cosine ofthe outer spiral angle and the cosine of the pressureangle as specified, see figure 63. Figure 62 -- Positioning of bevel gears

Gearpitchradius

φ

Bt Transverse backlashmeasured at the pitch radiusof gear or pinion

ψo

Bt Transversebacklash

Bn Normal backlash (normalto the tooth surface)

Pinionpitchradius

Bn φ

Bncos Bt=

BncosÔ cosψo

ψo= arcsin2Am rc sinψ – A2m+ A2o

2Aorc

Bn = Normal backlashBt = Transverse backlash (plane

of rotation)ψo = Outer spiral angle

Bt Transversebacklash

ψo

Figure 63 -- Bevel gear backlash, normal and transverse



If the backlash does not fall within the recommendedlimits, one of the following procedures may be useddepending on the original method of assembly.

16.4.1 Adjusting backlash when at mountingdistance

If the pinion and gear are assembled to the markedmounting distance, and the required backlash is notobtained, the individual components should bethoroughly evaluated to determine the cause.

16.4.2 Adjusting backlash when gears are flushground

If the pinion and gear were assembled so that theback cone angles are flush, it will be necessary forthe axial position of both members to be adjusted tosatisfy backlash requirements.

16.5 Amount of axial movement for change inbacklash

The amount of axial movement for either pinion orgear member necessary to obtain a change inbacklash may be determined by the graph in figure64, or by the following formulas:

...(50)∆B= ∆BG+ ∆BP

...(51)∆BG=∆ B Nn+ N

...(52)∆BP=∆ B nn+ N

...(53)∆P=∆BP

2 tanÔ sin γ

...(54)∆G=∆BG

2 tanÔ sinΓ

where

∆B is total change in backlash;

∆BP is change in backlash for pinion;

∆BG is change in backlash for gear;

∆P is axial movement of pinion;

∆G is axial movement of gear.

NOTE: These formulas do not apply to hypoid gearing.For higher ratios the effect of pinion axial movement onbacklash is small.

16.6 Endplay

If either member of a pair of bevel gears isassembled with allowance for bearing end play andnot held to a fixed position, it will be necessary tocheck for minimum backlash when the floatingmember is moved axially to its foremost positiontoward the crossing point.

Ô = 14 1/2°

Ô = 20°Ô = 22 1/2°Ô = 25°

90

80

70

60

50

40

30

20

10

00.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.011

0.025 0.051 0.076 0.102 0.127 0.153 0.178 0.203 0.229 0.254 0.279

Pitchangle(degrees)

Axial movement

Axial movement per 0.025 mm change in backlash

Figure 64 -- Axial movement per 0.001 inch change in backlash



Annex A(informative)

Bevel gear sample calculations

[This annex is provided for informational purposes only, and should not be construed as a part of ANSI/AGMA 2005--D03,Design Manual for Bevel Gears.]

A.1 Sample bevel gear set

The example in table A.1 is included to assist usersin the selection, design, cutting method, rating,inspection, heat treatment and mounting of a

hypothetical gear set. The numbers which precedemany of the terms are included to assist users byidentifying that portion of the standard where thatinformation is presented. These calculations are inconventional U.S. units.

Table A.1 -- Calculation example

Standard ItemSelection or calculationStandard

clause ItemPinion Both pinion and gear Gear

4 General designconsiderations

4.1 Type Spiral bevel4.2 Ratio Approximately 2.75 to 14.4 Speed Pinion: 1750 rpm4.5 Accuracy requirement AGMA class Q115 Preliminary design5.1 Load considerations5.1.1 Peak loads Load for 95% of time:

Pnormal = 25 hpLoad for 5% of time:Pmax = 40 hp

Expected life: 10 yrs.Cycles at peak load:1.09¢ 108 cyclestherefore P = 40 hp

5.1.2 Torque TP = 1440 lb in5.1.3 Estimated pinion size d = 2.500 in, based on fig 85.2 Numbers of teeth5.2.1 Pinion number of teeth n = 14 based on fig 105.2.2 Gear number of teeth N = 39, therefore

mG = 39/14 = 2.786 andD = 6.965 in

5.4 Face width F = 1.000 in based on fig 135.5 Diametral pitch Pd = 5.6005.6 Spiral angle Assume ψ = 35°

mF = 1.48 acceptable5.7 Pressure angle Assume Ô = 20°5.8 Hand of spiral Left hand Right hand5.9 Shaft angle Σ = 90°6 Cutting methods6.1 Tooth taper Duplex depth taper6.3 Mean radius of

curvatureFace--milling process

ρ = rc6.4 Cutter radius rc = 4.50 in7 Gear tooth design

(continued)



Table A.1 (continued)



7.13 Spiral bevel designFormulasPitch diameter d = 2.500 in D = 6.965 inPitch angle γ = 19.747° Γ = 70.253°Outer cone distance Ao = 3.700 inMean cone distance Am = 3.200 inDepth factor k1 = 2.000Mean working depth h = 0.253 inClearance factor k2 = 0.125Clearance c = 0.032 inMean whole depth hm = 0.285 inEquivalent 90° ratio m90 = 2.786Mean addendum factor c1 = 0.247Mean circular pitch pm = 0.485 inMean addendum aP = 0.191 in aG = 0.062 inMean dedendum bP = 0.094 in bG = 0.223 inSum of dedendumangles

ΣδD = 8.626°

Dedendum angle δP = 2.114° δG = 6.512°Face angle γo = 25.259° Γo = 72.367°Root angle γR = 17.633° ΓR = 63.741°Outer addendum aoP = 0.248 in aoG = 0.080 inOuter dedendum boP = 0.112 in boG = 0.280 inOuter working depth hk = 0.328 inOuter whole depth ht = 0.360 inOutside diameter do = 2.967 in Do = 7.019 inPitch cone apex tocrown

xo = 3.399 in Xo = 1.175 in

Mean diametral pitch Pdm = 6.475Mean pitch diameter dm = 2.162 in Dm = 6.023 inThickness factor k3 = 0.090Mean normal circularthickness

tn = 0.257 in Tn = 0.140 in


B = 0.005 in

Outer spiral angle ψoG = 36.846°Mean normal chordalthickness

tnc = 0.254 in Tnc = 0.138 in

Mean chordaladdendum

acP = 0.197 in acG = 0.062 in

7.15 Undercut check7.15.1 Bevels excluding hypoid

gearsInner cone distance AiG = 2.700 inInner gear spiral angle ψiG = 33.945°Inner transverse pressureangle

ÔTi = 23.689°

Limit inner dedendum bilP = 0.156 inInner dedendum biP = 0.075 in, therefore no

undercut problem

(continued)



Table A.1 (concluded)



10 Tolerance requirements10.1 Gear blank dimensions and

tolerancesFace angle tolerance +0.000 to --0.004 inBack angle tolerance +0.004 to --0.004 inPinion shank (2.5 indiameter) tolerance

+0.0000 to --0.0005 in

Gear bore tolerance (3.0in diameter)

+0.0005 to --0.0000 in

Outside diametertolerance

+0.000 to --0.005 in

Crown to back tolerance +0.000 to --0.003 inFace angle tolerance +08’ to --00’Back angle tolerance +15’ to --15’

10.2 Accuracies of toothcomponents (annex D)Maximum pitch variation 0.0004 in 0.0004 inAccumulated pitchvariation

0.0012 in 0.0013 in

10.3 Tooth contact patternPosition Central toeProfile Slight relief top and flankLength 1/2 Tooth length (light

load)10.4 Backlash

Normal backlash atassembly

0.005 to 0.007 in

10.5 Surface finishCut 60 m inLapped 35 m in

13 Materials and heattreatment (see ANSI/AGMA2003--B97 and 2004--B89)

14 Lubricant (see ANSI/AGMA9005--E02)

15.1 Analysis of forces15.1.1 Tangential, Wt 1332 lb 1332 lb15.1.2 Axial, Wx

Left hand spiral, pinionPinion drive CCW --678 lb 872 lbPinion drive CW 1078 lb 242 lb

15.1.3 Radial, WrLeft hand spiral, pinionPinion drive CCW 872 lb --678 lbPinion drive CW 242 lb 1078 lb



Annex B(informative)

Hypoid gear sample calculations

[This annex is provided for informational purposes only and should not be construed as a part of ANSI/AGMA 2005--D03,Design Manual for Bevel Gears.]

B.1 Sample hypoid gear set

This example is included to assist users in theselection, design, cutting method, rating, inspection,heat treatment and mounting of a hypothetical gear

set. The numbers which precede many of the termsare included to assist users by identifying that portionof the standard where that information is presented.These calculations are in conventional U.S. units.

Table B.1 -- Calculation example



4 General design consider-ations

4.1 Type Hypoid 1.500” offsetrequired

4.2 Ratio Approximately 4 to 14.4 Speed Pinion 1200 rpm

clockwise4.5 Accuracy requirement AGMA class Q115 Preliminary design5.1 Load considerations5.1.1 Peak loads exceed 10 million cycles5.1.2 Torque TP = 5000 lb in P = 95 hp5.1.3 Estimated gear size

Estimated pinion diameter dii = 3.000 in based onfig 8

Estimated pinion diameter di = 2.633 in hypoidmodification

Estimated gear size D = 10.771 in5.2 Number of teeth5.2.1 Pinion number of teeth n = 115.2.2 Gear number of teeth N = 455.3 Hypoid offset E = 1.500 in below center5.4 Face width FG = 1.600 in5.5 Diametral pitch Pd = 4.1785.6 Pinion spiral angle ψp = 48°5.7 Pressure angle Ôave = 20°5.8 Hand of spiral Left Right5.9 Shaft angle Σ = 90°6 Cutting methods6.1 Tooth taper Duplex depth taper

Face milling process ρ= rc6.8 Cutter radius ρ = rc = 4.500 in7 Gear tooth design

7.14 Hypoid dimensionsPitch diameter D = 10.771 inGear ratio mG = 4.09091Desired pinion spiralangle

ψoP = 48°

(continued)



Table B.1 (continued)



7.1.4(cont.)

Shaft angle departurefrom 90°

∆Σ = 0°( )

Approximate gear pitchangle

Γi = 73.6518°

Gear mean pitch radius R = 4.6177 inApproximate pinion offsetangle in pitch plane

ε′2i = 18.1619°

Approximate hypoid di-mension factor

K1 = 1.2964

Approximate pinion meanradius

R2P = 1.46330 in

Gear offset angle in axialplane

η = 4.9825° 1st trial

Intermediate pinion offsetangle in axial plane

ε2 = 17.2964°

Intermediate pinion pitchangle

γ2 = 15.5844°

Intermediate pinion offsetangle in pitch plane

ε′2 = 17.9787°

Intermediate pinion meanspiral angle

ψ2P = 48.1975°

Increment in hypoid di-mension factor

∆K = --0.00238

Ratio of pinion mean ra-dius increment to gearmean pitch radius

∆RP/R = --0.00058

Pinion offset angle in axialplane

ε1 = 17.2994°

Pinion pitch angle γ = 15.5817°Pinion offset angle inpitch plane at inside

ε′1 = 17.9816°

Spiral angle ψP = 47.9968° ψG = 30.0153°Pitch angle Γ = 73.6599°Mean cone distance AmG = 4.8121 inPinion mean radius incre-ment

∆RP = --0.00269 in

Mean cone distance AmP = 5.43765 inMean pinion radius RP = 1.46062 inLimit pressure angle Ôo = --5.2059°Limit curvature radius rc1 = 5.10681 inTest (ρ/rc1 -- 1) = --0.11882

(ρ/rc1 -- 1)>0.001--test failedend of 1st trial


η = 5.2655° 2nd trial


ε2 = 17.2029°


γ2 = 16.5106°


ε′2= 17.9674°


ψ2P = 48.2098°


∆K = -- 0.00253

(continued)




Standardl

Item Selection or calculationclause Pinion Both pinion and gear Gear

7.1.4(cont.)

Ratio of pinion mean ra-dius increment to gearmean pitch radius

∆RP/R = --0.000619


ε1 = 17.2063°

Pinion pitch angle γ = 16.5073°Pinion offset angle inpitch plane

ε′1 = 17.9706°

Spiral angle ψP = 47.9965° ψG = 30.0259°Gear pitch angle Γ = 72.6955°Mean cone distance AmG = 4.8366 inPinion mean radius incre-ment

∆RP = --0.00286 in

Mean cone distance AmP = 5.1399 inMean pinion radius RP = 1.4604 inLimit pressure angle Ôo = --4.6924°Limit curvature radius rc1 = 4.653 inTest (ρ/rc1) -- 1 = --0.0329

(ρ/rc1) -- 1>0.001--test failedend of 2nd trial


η = 5.3705° 3rd trial


ε2 = 17.1682°


γ2 = 16.8545°


ε′2 = 17.9644°


ψ2P = 48.213°


∆K = --0.00257

Ratio of pinion mean pitchradius to gear mean pitchradius

∆RP/R = --0.00063


ε1= 17.1717°

Pinion pitch angle γ = 16.8511°Pinion offset angle inpitch plane

ε′1 = 17.9678°

Spiral angle ψP = 47.9964° ψG = 30.0286°Pitch angle Γ = 72.3375°Mean cone distance AmG = 4.8461 inPinion mean pitch radiusincrement

∆RP = --0.00290 in

Pinion mean cone dis-tance

AmP = 5.0378 in

Pinion mean radius RP = 1.4604 inLimit pressure angle Ôo = --4.502°Limit curvature radius rc1 = 4.5042 inTest (ρ/rc1) -- 1 = 0.00093 < 0.001

Test passedPressure angle on con-cave side of pinion

Ô1 = 15.498° Ô2 = 24.502°

Pressure angle on convexside of pinion

Ô2 = 24.502° Ô1= 15.498°

(continued)




Standardl

Item Selection or calculationclause Pinion Both pinion and gear Gear

7.1.4(cont.)

Crossing point to meanpoint along gear axis

ZG = 1.454 in( )

Gear pitch apex beyondcrossing point

Z = 0.0164 in

Outer cone distance AoG = 5.6518 inGear face width from cal-culation point to outside

∆Fo = 0.8056 in

Equivalent 90° ratio m90 = 3.1405Depth factor k1 = 2.0000Mean addendum factor c1 = 0.2384 inMean working depth h = 0.3554 inMean addendum aP = 0.2707 in aG = 0.0847 inClearance factor k2 = 0.125Mean dedendum bP = 0.1291 in bG = 0.3151 inClearance c = 0.0444 inMean whole depth hm = 0.3998 inSum of dedendum angles ΣδD = 5.5769° duplexDedendum angle δG = 4.2474°Addendum angle αG = 1.3295°Outer addendum aoG = 0.1034 inOuter dedendum boG = 0.3747 inGear whole depth htG = 0.4781 inOuter working depth hk = 0.4337 inRoot angle ΓR = 68.0901°Face angle Γo = 73.6669°Gear outside diameter Do = 10.8335 inGear pitch cone apex tocrown

Xo = 1.5999 in

Root apex beyond cross-ing point

ZR = 0.0636 in

Face apex beyond cross-ing point

Zo = --0.0125 in

Auxiliary angle for calcu-lating pinion offset anglein root plane

ζR = 0°

Auxiliary angle for calcu-lating pinion offset anglein face plane

ζo = 0°

Pinion offset angle in rootplane

εR = 16.7576°

Pinion offset angle in faceplane

εo = 16.7576°

Face angle γo = 20.9346°Root angle γR = 15.5748°Face apex beyond cross-ing point

Go = 0.1621 in


GR = 0.3465 in

Addendum angle αP = 4.0835°Dedendum angle δP = 1.2763°

(continued)




Standardl

Item Selection or calculationclause Pinion Both pinion and gear Gear7.1.4(cont.)

Angle between projectionof pinion axis into pitchplane and pitch element

λ′ = 1.2754°

Gear face width from cal-culating point to inside

∆Fi = 0.7944 in

Pinion face width incre-ment

∆FoP = 0.0774 in

Pinion face width fromcalculating point to out-side

FoP = 0.8409 in

Pinion face width fromcalculating point to inside

FiP = 0.8291 in

Increment along pinionaxis from calculating pointto outside

∆Bo = 0.7863 in

Increment along pinionaxis from calculating pointto inside

∆Bi = 0.9322 in

Crown to crossing point xo = 5.1982 inFront crown to crossingpoint

xi = 3.4796 in

Whole depth htP = 0.4866 inOutside diameter do = 4.1012 inFace width FP = 1.8400 inMean circular pitch pm = 0.6448 inMean diametral pitch Pdm = 4.8726 in--1

Thickness factor k3 = 0.1275Mean pitch diameter dm = 2.92078 in Dm = 9.2354 inPitch diameter d = 3.4542 inMean normal circulartooth thickness

tn = 0.3694 in Tn = 0.1888 in

Outer normal backlash al-lowance

B = 0.006 in

Outer gear spiral angle ψoG = 36.5388°Mean normal chordaltooth thickness

tnc = 0.3659 in Tnc = 0.1862 in

Mean chordal addendum acP = 0.2818 in acG = 0.0850 in7.15 Undercut check

Inner gear cone distance AiG= 4.0461 inInner gear spiral angle ψiG = 23.8300°Gear inside pitch radius RiG = 3.8554 inCrossing point to insidepoint along pinion axis

ZiP = 1.21127 in

Pinion inner offset anglein axial plane

εi = 20.71288°

Pinion inside pitch angle γi = 16.48704°Pinion offset angle inpitch plane

ε′i = 21.644759°

Inner pinion spiral angle ψiP = 45.474822°Gear offset angle at in-side

ηi = 6.425593°

Inner pinion radius RiP = 1.218927 inInner pinion transversepressure angle

ÔTi = 21.57550°

(continued)




Standardl

Item Selection or calculationclause Pinion Both pinion and gear Gear7.15(cont )

Limit inner dedendum bilP = 0.170815 in(cont.) Pinion inner dedendum biP = 0.11063 in, no

undercut problem10 Tolerance requirements10.1 Gear blank tolerances

Face angle distance toler-ance

+0.0000 to --0.0040 in

Back angle distance toler-ance

--0.0040 to +0.0040 in

Pinion shank tolerance +0.0000 to --0.0005 inGear bore tolerance +0.0010 to --0.0000 inOutside diameter toler-ance

+0.0000 to --0.0050 in

Crown to back tolerance +0.0000 to --0.0030 inFace angle tolerance +8’ to --0’Back angle tolerance +15’ to --15’

10.2 Accuracies of tooth compo-nentsMaximum accumulatedpitch variation

0.0017 in

Allowable pitch variation +0.0004 in10.3 Tooth contact pattern

Position Central toeProfile Slight relief top and flankLength 1/2 of tooth length at light

load10.4 Backlash in gear set

Normal backlash in as-sembly

0.006 to 0.008 in

10.5 Surface finishCut 70 m inLapped 40 m in

13 Material and heat treatment(see ANSI/AGMA 2003--B97and 2004--B89)

14 Lubrication (see ANSI/AGMA 9005--E02)

15 Analysis of forces15.1.1 Tangential force WTP = 3424 lb WTG = 4430 lb15.1.2 Axial force

Convex WxP = --2962 lb WxG = 575 lbConcave WxP = 4050 lb WxG = 2999 lb

15.1.3 Radial separating forceConvex WRP = 3334 lb WRG = 2871 lbConcave WRP = 255 lb WRG = --1732 lb

Hypoid dimension sheetNumber of teeth n = 11 N = 45Hand of spiral Left RightDiametral pitch Pd = 4.178Face width FP = 1.840 in FG = 1.600 inPinion offset E = 1.500 in

(continued)



Table B.1 (concluded)

Standardl

Item Selection or calculationclause Pinion Both pinion and gear Gear15.1.3(cont )

Pressure angle;(cont.) Pinion concave Ô1 = 15°30’

Pinion convex Ô2 = 24°30’Shaft angle Σ = 90°Cutter radius rc = 4.500 inOuter cone distance AoG = 5.6518 inMean cone distance AmP = 5.038 in AmG = 4.846 inPitch diameter d = 3.454 in D = 10.771 inOuter addendum aoG = 0.103 inOuter dedendum boG = 0.375 inWorking depth hk = 0.434 inWhole depth htP = 0.487 in htG = 0.478 inOutside diameter do = 4.101 in Do = 10.834 inPitch apex beyond cross-ing point

Z = 0.016 in

Face apex beyond cross-ing point

Go = 0.162 in Zo = --0.011 in


GR = 0.347 in ZR = 0.065 in

Crown to crossing point xo = 5.198 inPitch angle γ = 16°51’ Γ = 72°20’Face angle of blank γo = 20°56’ Γo = 73°40’Root angle of blank γR = 15°34’ ΓR = 68°05’Mean spiral angle ψP = 48°00’ ψG = 30°02’Backlash allowance B = 0.006 inMean normal chordalthickness

tnc = 0.366 in Tnc = 0.186 in

Mean chordal addendum acP = 0.282 in acG = 0.085 in



Annex C(Informative)

Machine tool vendor data


C.1 Purpose

This annex provides vendor data which influencehypoid gear design.

C.2 Cutter table

Since bevel gear design and manufacture arefunctions of the cutter radius and, for face hobbed

gears, also the number of blade groups, table C.1provides a list of standard cutters.

C.3 Design method

Gears designed using Gleason and Klingelnbergcalculations are usually designed by Method 1.Gears designed using Oerlikon calculations areusually designed by Method 2. Methods 1 and 2 aredescribed in 6.5 of ANSI/AGMA 2005--D03.

Table C.1 -- Nominal cutter radii, rc, and blade groups, NSFace hobbing

Klingelnberg Oerlikon Gleason

Face millingGleason

in

Cutterradius, rc,

mm

Number ofblade

groups, NS

Cutterradius, rc,

mm

Number ofblade

groups, NS

Cutterradius, rc,

mm

Number ofblade

groups, NS0.250 25 1 39 5 51 70.500 30 2 49 7 64 110.750 40 3 62 5 76 131.000 55 5 74 11 76 71.375 75 5 88 13 88 171.750 100 5 110 9 88 112.250 135 5 140 11 105 192.500 170 5 150 12 105 133.000 210 5 160 13 125 133.125 260 5 180 13 150 173.750 270 3 175 194.500 350 35.250 450 36.0007.0008.0009.000

Gleasonmm250320400500600



Annex D(Informative)

Hypoid geometry

[This annex is provided for informational purposes only, and should not be construed as a part of ANSI/AGMA 2005--D03,Design Manual for Bevel Gears.]

D.1 Most general type gearing

Hypoid gears are the most general type of gearing.The gear and pinion axes are skew and non--inter-secting. The teeth are curved in the lengthwisedirection. All other types of gears can be consideredsubsets of the hypoid. Spiral bevel gears are hypoidgears with zero offset between the axes. Straightbevel gears are hypoid gears with zero offset andzero tooth curvature. Helical gears are hypoid gearswith zero shaft angle and zero tooth curvature.

D.2 Hypoid geometry

Whenever a most general case is defined, thedefinition becomes complex. Hypoid gear geometryis no exception. Figure D.1 shows the major angles

and quantities involved. Figure D.1(A) is a side viewlooking along the pinion axis. Figure D.1(B) is a frontview looking along the gear axis. Figure D.1(C) is atop view showing the shaft angle between the gearand pinion axes. Figure D.1(D) is a view of the gearsection along the plane making the offset angle, ε, inthe pinion axial plane. Figure D.1(E) is a view of thepitch plane, T. Figure D.1(F) is a view of the pinionsection along the plane making the offset angle, η, inthe gear axial plane. Figure D.1(G) is a view of thepitch plane, T.

The scope of this text does not permit an adequateexplanation or derivation of the formulas involved.The readerwhohas a desire to better understand thegeometry is referred to the articles in annex G.

ZP

B

ZO2

OPPB

OG

XGnG η

(A)

A

OG

OPO1

e

np

A

XpE

(B)

nG

P

XP

ZG

O1′ O2

G

OP

OG

XGΣ

np

(C)

P

Qt

OP

OG

tVS T

P

εi

ψPAP

ψG

View B--B

DT

OP

O1

npD

nG

ZG

P γ

OG

(F)

View A--A

nG

np

OG

O2

Γ

CT

ZP

(D)View D--D(G)

Qt

OF

View C--C

VS

P

t

ε'

OP

OG

Tt A

ψPP

C

(E)

ψG

Figure D.1 -- Hypoid geometry



Annex E(Informative)

Tabulation of bevel and hypoid gear tolerances

[This annex is provided for informational purposes only and should not be construed as a part of ANSI/AGMA 2005--C96,Design Manual for Bevel Gears.]

E.1 AGMA quality number tolerances

This annex has tabulations for (1) maximum pitchvariation, table E.1 (table E.1M for metric), and (2)cumulative pitch variation, table E.2 (table E.2M formetric) tolerances for eachAGMAQuality Number ofcoarse and fine pitch gearing.

E.1.1 Use of tables

Straight line interpolation may be used in table E.1and E.1M for intermediate values of diametral pitchas well as for values of pitch diameter. Five decimalplace accuracy is shown in table E.1, six place fortable E.1M, for aid in interpolation. It is suggestedthat design values be rounded to four places, fiveplaces for metric, for use on drawings orspecifications.

E.1.2 Special considerations

Conditions may require that one or more of theindividual element tolerances be of a lower or higherQuality Number than the other element tolerances.In such cases it is possible to modify the AGMAClass Number to include the Quality Number foreach special element tolerance.

E.2 Spacing measurement example

Figure E.1 is an example of pitch spacing andcumulative pitch relationships. The sketch in thefigure shows the actual position of the teeth on aseven tooth gear as manufactured. They are com-pared to the true, or theoretically correct, indexposition.

When the single probe method is used, cumulativepitch variation and maximum pitch variation areobtained by scanning the measured data in ColumnA. The largest algebraic difference between adja-cent tooth measurements is the maximum pitchvariation. The largest algebraic difference betweenall the measurements is the cumulative pitch vari-ation. Spacing variation as shown in Column C iscalculated by taking the algebraic differencebetween adjacent pitch variations.

When the two probemethod is used, interpretation ofthe readings is somewhat more difficult. The probesare set to read zero for the pitch between tooth A andtooth B. Readings between adjacent pairs of teethare then recorded as shown in Column D. Spacingvariation is calculated directly from these readingsas shown in Column E. However, to calculate thepitch variation, any difference in the pitch measure-ment between the measured pitch A to B and theaverage measured pitch must be considered. To dothis, the average reading variation is calculated.Subtracting this average value from the readinggives the actual pitch variation which is shown inColumn F. Maximum pitch variation is the largestalgebraic difference in Column F. Index variation inColumn G is calculated by accumulating the valuesin Column F. The first value in Column G is set tozero. Successive values in Column G are obtainedby adding the value from Column F to the precedingvalue in Column G. The largest algebraic differencebetween the values in Column G is the cumulativepitch variation.



Table E.1 -- Bevel and hypoid gear tolerances

AGMAAllowable pitch variation¦ (ten--thousandths of an inch)

AGMAQuality Diametral Pitch diameter (inches)Qualitynumber

Diametralpitch 0.75 1.5 3 6 12 25 50 100 200

3

0.5124

No values indicated

4

0.5124

No values indicated

5

0.51248

No values indicated

6

0.51248

16--20 161816

221816

26221917

3127242118

503329262319

553833282521

624237322823

70504237

7

0.51248

16--20 1113.511.5

161412

191614.512.5

23201715.513

372522191714

402824211915.5

453227242117.5

50373128

8

0.51248

16--20 898

11108

1411103

161412119

2618151312

28191715

312219

9

0.51248

16--20 676

876

1087.56.5

1110987

1912119.58.5

20141210

221614

10

1248

16--20 4.554.5

654.5

765.54.5

8.57.56.565

9876.5

11

1248

16--20 33.53

43.53

5443.5

654.543.5

6654.5

12

248

16--20 2.52.52.5

32.52.5

3.5332.5

43.532.5

43.53.5

13

248

16--20 222

222

2.5222

32.522

32.52.5



Table E.1M -- Bevel and hypoid gear metric tolerances

AGMA DiametralAllowable pitch variation¦ (mm)AGMA

Qualityb

Diametralpitch Pitch diameter (mm)y

number pitch20 40 80 150 300 600 1200 2500 5000

3

502512.56

No values indicated

4

502512.56

No values indicated

5

502512.56

No values indicated

6

502512.563

1.5--1.25 414641

564641

66564843

7969615346

1278474665848

1409784716453

15710794817158

17812710794

7

502512.563

1.5--1.25 283429

413630

48413732

5851433933

946456484336

1027161534839

1148169615344

127947971

8

502512.563

1.5--1.25 202320

282520

36282523

4136302823

6646383330

71484338

795648

9

502512.563

1.5--1.25 151815

201815

25201917

2625222018

4830282422

51363028

564136

10

2512.563

1.5--1.25 111311

151311

18171411

2219171411

23201817

11

2512.563

1.5--1.25 898

1098

1310109

151311109

15151311

12

12.563

1.5--1.25 666

886

9886

10986

1099

13

12.563

1.5--1.25 555

555

6555

8655

866



Table E.2 -- Bevel and hypoid gear tolerances

AGMAAccumulated pitch variation (ten--thousandths of an inch)

AGMAQuality Diametral Pitch diameter (inches)Qualitynumber

Diametralpitch 0.75 1.5 3 6 12 25 50 100 200

3

0.5124 280

382355

770540498460

1010710660608

1360930860800

12501150

4

0.5124 198

272250

378348320

540496452419

700640590542

940860790720

5

0.51248 91

130112

184160140

270233203177

396350302262228

510450390340290

665582510440380

880775680590

6

0.51248

16--20 466455

927666

1311109380

18816013511498

280235200170143122

350295250210180152

450378322270230193

600508425360

7

0.51248

16--20 263731

554437

84675445

132103826655

2091651301038269

26020516513010386

335261210167132110

445350280225

8

0.51248

16--20 192521

362826

58413230

95684736

160115825642

20014010067

255180125

9

0.51248

16--20 141815

262016

40292218

6848342621

11381584030

1401007048

18012588

10

1248

16--20 101311

181412

30211613

5034241815

58402821

11

1248

16--20 798

13108

2115119

3424171311

41282015

12

248

16--20 5.56.56

977

151188

18129

211411

13

248

16--20 555

75.55

117.565

13975.5

1510.58



Table E.2M -- Bevel and hypoid gear metric tolerances

AGMA DiametralAccumulated pitch variation (mm)AGMA

Qualityb

Diametralpitch

Pitch diameter (mm)Qua ynumber pitch

20 40 80 150 300 600 1200 2500 5000

3

502512.56 710

870900

137012601170

1950180016801340

2560236021802030

345031702920

4

502512.56 500

690635

960880810

1370126011501065

1780162015001380

2390218020101830

5

502512.563 231

330280

470410360

690590520450

1010890768670580

13001140990860740

1690148013001120970

2230197017301500

6

502512.563

1.5--1.25 117163140

234193168

330280236203

480410340290250

710600510430360310

890750640530460390

1140960820690580490

152012901080940

7

502512.563

1.5--1.25 339476

14011294

213170137114

330260208168140

530420330260208175

660520420330260218

850660530420330280

1130890710570

8

502512.563

1.5--1.25 486453

947166

1471048176

24017311991

400290208142107

500340255170

650450320

9

502512.563

1.5--1.25 364638

665141

102745646

173122866653

29020614710276

355255178122

460320224

10

2512.563

1.5--1.25 253328

463630

76534133

12786614638

1471027153

11

2512.563

1.5--1.25 182320

332520

53382823

8661433328

104715138

12

12.563

1.5--1.25 141715

231818

38282020

463023

533628

13

12.563

1.5--1.25 131313

181413

28191513

33231814

382720



A 0 0 Ref.

B +2 B minus A +2 2 A to B 0 2 +2 +2

C +2 C minus B 0 2 B to C --2 2 0 +2

D +4 D minus C +2 8 C to D 0 8 +2 +4

E --2 E minus D --6 8 D to E --8 8 --6 --2

F 0 F minus E +2 4 E to F 0 4 +2 0

G --2 G minus F --2 4 F to G --4 4 --2 --2

A 0 A minus G +2 0 G to A 0 0 +2 0

Index VariationVx

Index VariationVx

AccumulatedPitch Variation

Diff. BetweenReadings inColumn A

Diff. BetweenAdj. Pitches

Diff. BetweenAdj. Pitches

Readings MinusAverage

AccumulatedPitch Variation

Pitch VariationVp

Spacing VariationVs

Teeth Readings Spacing VariationVs

Pitch VariationVp

CA D E F G

Index Variation

Single Probe -- Precision Method Two Probe Method

Position

TrueActual

A B C D E F G A

00 +2 --2 +4 --2 0 --2

Total IndexVariationVap = 6

Max. PitchVariationVp max = 6

Max. PitchVariationVp max = 8

Max. SpacingVariationVsmax = 8

Max. SpacingVariationVs max = 8

Avg. Read-ing Variation

N = 7

--14 Sum--2

Total AccumulatedPitch Variation

Vap = 6

B

}6 }6

Figure E.1 -- Pitch and spacing example



Annex F(Informative)

Loaded tooth contact patterns


F.1 Purpose

This annex provides guidance as to the appearanceof loaded contact tooth patterns.

Typical satisfactorily loaded contact patterns areshown in figure F.1.

Typical unsatisfactorily loaded contact patterns areshown in figure F.2.

Idealized 80--85% coverage of lengthwise tooth surface --relief at top and edges, no concentrations

Contact zone at calculated load

min 85%

min 85%

max 95%

max 95%

Slight cross pattern --still 80--85% coverage

Slightly lame pattern --still 80--85% coverage

Slight heel pattern --still 80--85% coverage

Slight toe pattern --still 80--85% coverage

Figure F.1 -- Typical satisfactorily loaded contact patterns



Full length -- full width, no relief at edges

Lame (high on onelow on the other)

High on the heel

Cross (heel on onetoe on the other)

Heavy toeboth sides

Too much profile relief Too much lengthwise relief

Figure F.2 -- Typical unsatisfactorily loaded contact patterns



Annex G(Informative)Bibliography


1. “Basic Relationship of Hypoid Gears”, by Ernst Wildhaber, published in the American Machinist, 1946.

2. “Design and Manufacture of Hypoid Gears”, by Dr. Boris Shtipelman, published by John Wiley and Sons,1978.

3. ANSI/AGMA 2008--C01, Assembling Bevel Gears.

PUBLISHED BYAMERICAN GEAR MANUFACTURERS ASSOCIATION1500 KING STREET, ALEXANDRIA, VIRGINIA 22314

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