1、AGMA 908-B89(Revision of AGMA 226.01)April 1989(Reaffirmed August 1999)AMERICAN GEAR MANUFACTURERS ASSOCIATIONGeometry Factors for Determining the Pitting Resistanceand Bending Strength of Spur, Helical and HerringboneGear TeethAGMA INFORMATION SHEET(This Information Sheet is not an AGMA Standard)90
2、8-B89iiAGMAINFORMATION SHEETGeometry Factors for Determining the Pitting Resistance and Bending Strength of Spur,Helical and Herringbone Gear TeethAGMA 908-B89(Revision of AGMA 226.01 1984)Tables or other self-supporting sections may be quotedor extractedin theirentirety. Credit lineshouldread: Extr
3、actedfromAGMAStandard908-B89, INFORMATIONSHEET,GeometryFactorsforDeterminingthePittingResistanceandBendingStrengthofSpur,HelicalandHerringboneGearTeeth,withthepermissionofthepublisher, American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, Virginia22314.AGMA standards are
4、subject to constant improvement, revision or withdrawal as dictated by experience.Any person who refers to any AGMA Technical Publication should determine that it is the latest informationavailable from the Association on the subject.Suggestions for the improvement of this Standard will be welcome.
5、They should be sent to the AmericanGear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, Virginia 22314.ABSTRACT:This Information Sheet gives the equations for calculating the pitting resistance geometry factor, I,forexternalandinternalspurandhelicalgears, andthe bending strengthg
6、eometry factor, J, forexternal spurandhelical gears that are generated by rack-type tools (hobs, rack cutters or generating grinding wheels) orpinion-typetools(shapercutters).TheInformationSheetalsoincludeschartswhichprovidegeometryfactors,I and J, for a range of typical gear sets and tooth forms.Co
7、pyrightE, 1989American Gear Manufacturers Assocation1500 King Street, Suite 201Alexandria, Virginia 22314April, 1989ISBN: 1-55589-525-5Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth908-B89iiiAGMAFOREWORDThe foreword, footnotes, andappendic
8、esareprovidedforinformationalpurposesonly andshouldnotbeconstruedaspartofAmericanGearManufacturersAssociationInformationSheet 908-B89,GeometryFactorsfor Determining the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth.This Information Sheet, AGMA 908-B89, was prepa
9、red to assist designers making preliminary designstudies, and to present data that might prove useful for those designers without accessto computerprograms.The tables for geometry factors contained in this Information Sheet do not cover all tooth forms, pressureangles, andpinionandgearmodifications,
10、 andare notapplicable toall geardesigns. However, informationisalso contained for determining geometry factors for other conditions and applications. It is hoped thatsufficient geometry factor data is included to be of help to the majority of gear designers.Geometry factors for strength were first p
11、ublished in Information Sheet AGMA 225.01, March, 1959,StrengthofSpur,Helical,HerringboneandBevelGearTeeth. AdditionalgeometryfactorswerelaterpublishedinStandardsAGMA220.02,AGMA221.02,AGMA222.02,andAGMA223.01. AGMATechnicalPaper229.07,October, 1963, Spur and Helical Gear Geometry Factors, contained
12、many geometry factors not previouslypublished. Due to the number of requests for this paper, it was decided to publish the data in the form of anInformationSheetwhichbecameAGMA226.01,GeometryFactorsforDeterminingtheStrengthofSpur,Helical,Herringbone and Bevel Gear Teeth.AGMA 218.01, AGMA Standard fo
13、r Rating the Pitting Resistance and Bending Strength of Spur and HelicalInvolute Gear Teeth, was published with the methods for determining the geometry factors. When AGMA218.01wasrevisedasANSI/AGMA2001-B88, thecalculationproceduresforGeometryFactors, IandJ,weretransferred to this revision of the Ge
14、ometry Factor Information Sheet. The values of I and J factors obtainedusingthemethodsofthisInformationsheetarethesameasthoseofAGMA218.01.Thecalculationprocedurefor I was simplified, but the end result is mathematically identical. Also, the calculation of J was modified toinclude shaper cutters and
15、an equation was added for the addendum modification coefficient, x,previouslyundefinedandalltoooftenmisunderstood.Appendiceshavebeenaddedtodocumentthehistoricalderivationof both I and J.BecauseananalyticalmethodforcalculatingtheBendingStrengthGeometryFactor,J,isnowavailable,thelayoutprocedureforesta
16、blishingJhasbeeneliminatedfromthisdocument. Allreferencestogeometryfactorsforbevel gearshave beenremoved. This informationis nowavailable inAGMA 2003-A86, Rating thePittingResistance and Bending Strength of Generated Straight Bevel, ZEROL Bevel and Spiral Bevel Gear Teeth.ThefirstdraftofthisInformat
17、ionSheet,AGMA908-B89,waspresentedtotheGearRatingCommitteeinAugust, 1987. It was approved by the AGMA Gear Rating Committee on February 24, 1989, after severalrevisions. It was approved for publication by the AGMA Technical Division Executive Committee on April21,1989.Geometry Factors for Determining
18、 the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth908-B89ivAGMAPERSONNEL of the AGMA Committee for Gear RatingChairman: J. Bentley (Peerless-Winsmith)Vice Chairman: O. LaBath (Cincinnati Gear )ACTIVE MEMBERSM. Antosiewicz (Falk)J. D. Black (General Motors/AGT)E. J. Bodensiec
19、k (Bodensieck Engineering)W. A. Bradley (AGMA)R. Calvert (Morgan Construction)A. S. Cohen (Engranes y Maquinaria)J. DeMarais (Bison Gear)R. Donoho (Clark Equipment)R. J. Drago (Boeing)D. W. Dudley (Honorary Member)R. Errichello (Academic Member)H. Hagan (Nuttall Gear)N. Hulse (General Electric)H. Jo
20、hnson (Browning Co.)R. D. Kemp (Kymmene-Stromberg Santasalo)J. C. Leming (Arrow Gear) (Deceased)L. Lloyd (Lufkin Industries)J. Maddock (Consultant)D. McCarthy (Dorris)D. R. McVittie (Gear Works - Seattle)M. W. Neesley (Westech)J. A. Nelson (General Electric)W. P. Pizzichil (Philadelphia Gear)J. W. P
21、older (Maag/NNI Netherlands)E. E. Shipley (Mechanical Technology)W. L. Shoulders (Reliance Electric) (Deceased)F. A. Thoma (Honorary Member)C. C. Wang (Consultant)R. Wasilewski (Arrow Gear)ASSOCIATE MEMBERSJ. Amendola (MAAG/Artec)K. Beckman (Lufkin)E. R. Braun (Eaton)D. L. Borden (Consultant)A. Brus
22、se (Hamilton)G. Buziuk (Brad-Foote)J. Cianci (General Electric)D. M. Connor (Cummins Engine)J. T. Cook (Dresser)E. Danowski (Sumitomo Heavy Industries)R. DiRusso (Kaman)A. B. Dodd (NAVSEA System Command)L. L. Haas (SPECO Division)F. M. Hager (Cummins Engine)A. C. Hayes (DACA)W. H. Heller (Peerless-W
23、insmith)G. Henriot (Engrenages et Reducteurs)R. W. Hercus (F. W. Hercus)M. Hirt (Renk)W. H. Jogwick (Union Carbide)T. Kameyama (Seiki-Kogyosho)D. L. King (Terrell Gear)P. Losekamp (Xtek)K. Mariager (F. L. Smidth)D. L. Mariet (Falk)T. J. Maluri (Gleason)B. W. McCoy (Marathon Le Tourneau)D. Moser (Nut
24、tall Gear)B. L. Mumford (Alten Foundry)W. Q. Nageli (MAAG)B. C. Newcomb (Chicago Gear - D. O. James)G. E. Olson (Cleveland Gear)J. R. Partridge (Lufkin Industries)A. E. Phillips (Emerson Electric/Browning)B. D. Pyeatt (Amarillo Gear)T. Riley (NWL Control System)G. R. Schwartz (Dresser)A. Seireg (Aca
25、demic Member)E. R. Sewall (Sewall Gear)L. J. Smith (Invincible Gear)M. Tanaka (Nippon Gear)H. J. Trapp (Klingelnberg)T. Urabe (Tsubakimoto Chain)D. A. Wagner (General Motors/AGT)R. E. Weider (Clark Equipment)L. E. Wilcox (Gleason)H. Winter (Academic Member)J. Worek (IMO Delaval)Geometry Factors for
26、Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth908-B89vAGMATable of ContentsSection Title Page1. Scope1.1 Pitting Resistance Geometry Factor, I 11.2 Bending Strength Geometry Factor, J 11.3 Tables 1.1.4 Exceptions 1.1.5 Bending Stress in Internal Gears 12. Defi
27、nitions and Symbols2.1 Definitions 2.2.2 Symbols 2.3. Basic Gear Geometry3.1 Contact Ratios 6.3.2 Minimum Length of the Lines of Contact 6.3.3 Load Sharing Ratio, mN63.4 Operating Helix Angle, r63.5 Operating Normal Pressure Angle, nr6.4. Pitting Resistance Geometry Factor, I4.1 Pitting Resistance G
28、eometry Factor Calculation 7.4.2 Operating Pitch Diameter of Pinion, d 7.4.3 Radii of Curvature of Profiles at Stress Calculation Point 74.4 Helical Overlap Factor, C75. Bending Strength Geometry Factor, J5.1 Virtual Spur Gear 8.5.2 Pressure Angle at the Load Application Point 8.5.3 Generating Rack
29、Shift Coefficient 9.5.4 LoadAngleandLoadRadius 9.5.5 Tool Geometry 105.6 Generating Pressure Angle 125.7 Algorithm for Determining the Critical Point 13.5.8 Iteration Convergence 145.9 Radius of Curvature of Root Fillet 155.10 Helical Factor, Ch15.5.11 Stress Correction Factor, Kf16.5.12 Helix Angle
30、 Factor, K16.5.13 Tooth Form Factor, Y 16.6. Determining Addendum Modification Coefficients6.1 Generating Rack Shift Coefficients 16.6.2 Sum of the Addendum Modification Coefficients for Zero Backlash 16.6.3 Tooth Thinning for Backlash 176.4 Addendum Modification Coefficients 17.Geometry Factors for
31、 Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth908-B89viAGMATable of Contents (cont)Section Title Page7. Geometry Factor Tables7.1 Using the Tables 17.7.2 Whole Depth 187.3 Outside Diameter 187.4 Type of Gearing 18.7.5 Center Distance 18.7.6 Tooth Thickness Ba
32、cklash Allowance 187.7 Undercutting 197.8 Top Land 19.7.9 Cutter Geometry 197.10 Axial Contact Ratio 19Bibliography 53AppendicesAppendix A Original Derivation of AGMA Geometry Factor for Pitting Resistance, I 55.Appendix B ANSI/AGMA 2001-B88 Pitting Resistance Formula Derivation 61Appendix C Explana
33、tion of the AGMA Gear Tooth Strength Rating DerivationFor External Gears 65.Appendix D Selection of Shaper Cutter Geometry 69.Appendix E Derivation of Helical Overlap Factor, C71Appendix F High Transverse Contact Ratio Gears 73.TablesTable 2-1 Symbols Used in Equations 2.Table 5-1 Limiting Variation
34、 in Action for Steel Spur Gears for Load Sharing 8.Tables I and J FACTORS 20FiguresFig3-1 TransversePlaneViewofTheLineofAction 5Fig5-1 LoadAngleandLoadRadius 9.Fig 5-2 Pressure Angle Where Tooth Comes to Point 10.Fig 5-3 Shaper Cutter with Protuberance 11.Fig 5-4 Involute Drawn Through Point “S” 12.
35、Fig 5-5 Pressure Angle Where Cutter Tooth Comes to a Point 12.Fig 5-6 Angle to Center, S, of Tool Tip Radius (Effective Cutter) 12Fig 5-7 Critical Point of Maximum Bending Stress 13.Fig5-8 ShaperCutterGeneration 13.Fig 5-9 Iteration Function 14Fig 5-10 Oblique Contact Line 15.Fig 5 - 11 Helical Fact
36、or, Ch15Fig 7-1 Undercutting Criteria 19.Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth 1. Scope The procedures in this Information Sheet de- scribe the methods for determining Geometry Factors for Pitting Resistance, I, and Bending Streng
37、th, J. These values are then used in con- junction with the rating procedures described in AGMA 2001-B88, Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth, for evaluating various spur and helical gear designs produced using a generat- ing process. 1.1 Pitti
38、ng Resistance Geometry Factor, I. A mathematical procedure is described to determine the Geometry Factor, I, for internal and external gear sets of spur, conventional helical and low ax- ial contact ratio, LACR, helical designs. 1.2 Bending Strength Geometry Factor, J. A mathematical procedure is de
39、scribed to determine the Geometry Factor, J, for external gear sets of spur, conventional helical and low axial contact ratio, LACR, helical design. The procedure is valid for generated root fillets, which are pro- duced by both rack and pinion type tools. 1.3 Tables. Several tables of precalculated
40、 Ge- ometry Factors, I and J, are provided for various combinations of gearsets and tooth forms. 1.4 Exceptions. The formulas of this Informa- tion Sheet are not valid when any of the following conditions exist: (1) Spur gears with transverse contact ratio less than one, mp c 1.0. (2) Spur or helica
41、l gears with transverse con- tact ratio equal to or greater than two, mp 2 2.0. Additional information on high transverse contact ratio gears is provided in Appendix F. (3) Interference exists between the tips of teeth and root fillets. (4) The teeth are pointed. (5) Backlash is zero. (6) Undercut e
42、xists in an area above the theo- retical start of active profile. The effect of this un- dercut is to move the highest point of single tooth contact, negating the assumption of this calcula- tion method. However, the reduction in tooth root Numbers in brackets refer to the bibliography. thickness du
43、e to protuberance below the active profile is handled correctly by this method. (7) The root profiles are stepped or irregular. The J factor calculation uses the stress correction factors developed by Dolan and Broghamerl. These factors may not be valid for root forms which are not smooth curves. Fo
44、r root profiles which are stepped or irregular, other stress correc- tion factors may be more appropriate. (8) Where root fillets of the gear teeth are produced by a process other than generating. (9) The helix angle at the standard (refer- ence) diameter* is greater than 50 degrees. In addition to
45、these exceptions, the following conditions are assumed: (a) The friction effect on the direction of force is neglected. (b) The fillet radius is assumed smooth (it is actually a series of scallops). 1.5 Bending Stress in Internal Gears. The Lewis method 2 is an accepted method for cal- culating the
46、bending stress in external gears, but there has been much research 33 which shows that Lewis method is not appropriate for internal gears. The Lewis method models the gear tooth as a cantilever beam and is most accurate when applied to slender beams (external gear teeth with low pressure angles), an
47、d inaccurate for short, stubby beams (internal gear teeth which are wide at their base). Most industrial internal gears have thin rims, where if bending failure occurs, the fa- tigue crack runs radially through the rim rather than across the root of the tooth. Because of their thin rims, internal ge
48、ars have ring-bending stresses which influence both the magnitude and the location of the maximum bending stress. Since the boundary conditions strongly influence the ring-bending stresses, the method by which the internal gear is constrained must be considered. Also, the time history of the bending
49、 stress at a particular point on the internal gear is important because the stresses alternate from tension to compression. Because the bending stresses in in- ternal gears are influenced by so many variables, no simplified model for calculating the bending stress in internal gears can be offered at this time. * Refer to AGMA 112.05 for further discussion of standard (reference) diameters. AGMA 1 908-B89 Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Hel
