ANSI AGMA 2101-D04-2004 Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth.pdf

1、ANSI/AGMA 2101-D04Metric Edition of ANSI/AGMA 2001-D04Reaffirmed January 2010American National StandardFundamental Rating Factorsand Calculation Methods forInvolute Spur and Helical GearTeethANSI/AGMA2101-D04iiFundamental Rating Factors and Calculation Methods for Involute Spur andHelical Gear Teeth

2、ANSI/AGMA 2101-D04Metric Edition of ANSI/AGMA 2101-D04Approval 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 t

3、he ANSI Board of Standards Review,substantial agreement has been reached by directly and materially affected interests.Substantial agreement means much more than a simple majority, but not necessarily una-nimity. Consensus requires that all views and objections be considered, and that aconcerted eff

4、ort 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 notconformin

5、g 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

6、 the American National 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 wh

7、o 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/AGMA 2101-D04, Fundamental Rating Factors and Calculation Methods

8、 for Invo-lute Spur and Helical Gear Teeth, published by the American Gear Manufacturers Asso-ciation, 500 Montgomery Street, Suite 350, Alexandria, Virginia 22314,http:/www.agma.org.Approved December 28, 2004ABSTRACTThis standard specifies a method for rating the pitting resistance and bending stre

9、ngth of spur and helicalinvolute gear pairs. A detailed discussion of factors influencing gear survival and calculation methods areprovided.Published byAmerican Gear Manufacturers Association500 Montgomery Street, Suite 350, Alexandria, Virginia 22314Copyright 2004 by American Gear Manufacturers Ass

10、ociationAll 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 AmericaISBN: 1-55589-840-8AmericanNationalStandardANSI/AGMA 2101- D04AMERICAN NATION

11、AL STANDARDiii AGMA 2004 - All rights reservedContentsPageForeword v.1 Scope 1.2 Normative references, definitions and symbols 23 Application 2.4 Criteria for tooth capacity 7.5 Fundamental rating formulas 9.6 Geometry factors, ZIand YJ11.7 Transmitted tangential load, Ft12.8 Dynamic factor, Kv12.9

12、Overload factor, Ko15.10 Service factor 15.11 Safety factors, SHand SF1612 Elastic coefficient, ZE16.13 Surface condition factor, ZR1614 Hardness ratio factor, ZW1715 Load distribution factor, KH1716 Allowable stress numbers, sHPand sFP2317 Stress cycle factors, ZNand YN3618 Reliability factor, YZ38

13、.19 Temperature factor, Yq3820 Size factor, Ks38.Bibliography 56.AnnexesA Method for determination of dynamic factor with AGMA 2000-A88 39B Rim thickness factor, KB41C Application analysis 43D Discussion of the analytical face or longitudinal load distribution factor 46.E Gear material fatigue life

14、49F Controlling section size considerations for through hardened gearing 54Figures1 Dynamic factor, Kv14.2 Hardness ratio factor, ZW(through hardened) 183 Hardness ratio factor, ZW(surface hardened pinions) 184 Instantaneous contact lines in the plane of action 19.5 Pinion proportion factor, KHpf216

15、 Evaluation of S and S1217 Mesh alignment factor, KHma228 Allowable contact stress number for through hardened steel gears, HP24.9 Allowable bending stress number for through hardened steel gears, FP25.10 Allowable bending stress numbers for nitrided through hardened steel gears(i.e., AISI 4140, AIS

16、I 4340), FP2611 Allowable bending stress numbers for nitriding steel gears, FP27.12 Variations in hardening pattern obtainable on gear teeth with flame orinduction hardening 3213 Minimum effective case depth for carburized gears, hemin33.14 Core hardness coefficient, Uc3415 - Minimum total case dept

17、h for nitrided gears, hcmin3416 Allowable yield strength number for steel gears, s35.ANSI/AGMA 2101- D04 AMERICAN NATIONAL STANDARDiv AGMA 2004 - All rights reserved17 Pitting resistance stress cycle factor, ZN37.18 Bending strength stress cycle factor, YN37.Tables1 Symbols used in gear rating equat

18、ions 3.2 Empirical constants; A, B, and C 22.3 Allowable contact stress number, HP, for steel gears 23.4 Allowable bending stress number, FP, for steel gears 24.5 Allowable contact stress number, HP, for iron and bronze gears 256 Allowable bending stress number, FP, for iron and bronze gears 26.7 Ma

19、jor metallurgical factors affecting the allowable contact stressnumber, HP, and allowable bending stress number, FP, of throughhardened steel gears 27.8 Major metallurgical factors affecting the allowable contact stress number,HP, and allowable bending stress number, FP, of flame or inductionhardene

20、d steel gears 28.9 Major metallurgical factors affecting the allowable contact stress number,HP, and allowable bending stress number, FP, of carburized and hardenedsteel gears 2910 Major metallurgical factors affecting the allowable contact stress number,HP, and allowable bending stress number, FP,

21、for nitrided steel gears 3111 Reliability factors, YZ38.ANSI/AGMA 2101- D04AMERICAN NATIONAL STANDARDv AGMA 2004 - All rights reservedForewordThe foreword, footnotes and annexes, if any, in this document are provided forinformational purposes only and are not to be construed as a part of ANSI/AGMA21

22、01-D04, Fundamental Rating Factors and Calculation Methods for Involute Spur andHelical Gear Teeth.This standard presents general formulas for rating the pitting resistance and bendingstrength of spur and helical involute gear teeth using ISO symbology and SI units, andsupersedes AGMA 2101-C95.The p

23、urpose of this standard is to establish a common base for rating various types of gearsfor differing applications, and to encourage the maximum practical degree of uniformity andconsistency between rating practices within the gear industry. It provides the basis fromwhich more detailed AGMA applicat

24、ion standards are developed, and provides a basis forcalculation of approximate ratings in the absence of such standards.The formulas presented in this standard contain factors whose values vary significantlydepending on application, system effects, gear accuracy, manufacturing practice, anddefiniti

25、on of gear failure. Proper evaluation of these factors is essential for realistic ratings.This standard is intended for use by the experienced gear designer capable of selectingreasonable values for rating factors and aware of the performance of similar designsthrough test results or operating exper

26、ience.In AGMA 218.01 the values for Life Factor, ZNand YN, Dynamic Factor, Kv, and LoadDistribution Factor, KH, were revised. Values for factors assigned in standards prior to thatwere not applicable to 218.01 nor were the values assigned in 218.01 applicable to previousstandards.The detailed inform

27、ation on the Geometry Factors, ZIand YJ, were removed fromANSI/AGMA 2001-B88, the revision of AGMA 218.01. This material was amplified andmoved to AGMA 908-B89, Geometry Factors for Determining the Pitting Resistance andBending Strength for Spur, Helical and Herringbone Gear Teeth. The values of ZIa

28、nd ZJhave not been changed from previous Standards.In ANSI/AGMA 2001-B88 the Allowable Stress Number section was expanded.Metallurgical quality factors for steel materials were defined, establishing minimum qualitycontrol requirements and allowable stress numbers for various steel quality grades.Add

29、itional higher allowable stress numbers for carburized gears were added when madewith high quality steel. A new rim thickness factor, KB, was introduced to reduce allowablebending loads on gears with thin rims. Material on scuffing (scoring) resistance was addedas an annex. ANSI/AGMA 2001-B88 was fi

30、rst drafted in January, 1986, approved by theAGMA Membership in May 1988, and approved as an American National Standard onSeptember 30, 1988.ANSI/AGMA 2101-C95 was a revision of the rating method described in its supersededpublications. The changes include: the Miners rule annex was removed; the ana

31、lyticalmethod for load distribution factors, KH, was revised and placed in an annex; nitridedallowable stress numbers were expanded to cover three grades; nitrided stress cyclefactors were introduced; through hardened allowable stresses were revised; applicationfactor was replaced by overload factor

32、; safety factors SHand SFwere introduced; life factorwas replaced by stress cycle factor and its use with service factor redefined; and thedynamic factor was redefined as the reciprocal of that used in previous AGMA standardsand was relocated to the denominator of the power equation.This standard, A

33、NSI/AGMA 2101-D04, is a revision of its superseded version. Clause 8was changed to incorporate ANSI/AGMA 2015-1-A01 and the Kvmethod using AGMAANSI/AGMA 2101- D04 AMERICAN NATIONAL STANDARDvi AGMA 2004 - All rights reserved2000-A88 was moved to Annex A. References to old Annex A, “Method for Evaluat

34、ing theRisk of Scuffing and Wear” were changed to AGMA 925-A03. It also reflects a change toclause 10, dealing with the relationship between service factor and stress cycle factor.Editorial corrections were implemented to table 8, figure 14 and table E-1, and style wasupdated to latest standards.Thi

35、s AGMA Standard and related publications are based on typical or average data,conditions, or applications. The Association intends to continue working to update thisStandard and to incorporate in future revisions the latest acceptable technology fromdomestic and international sources.The first draft

36、 of ANSI/AGMA 2101-D04 was completed in February 2002. It was approvedby the AGMA membership in October 23, 2004. It was approved as an American NationalStandard on December 28, 2004.Suggestions for improvement of this standard will be welcome. They should be sent to theAmerican Gear Manufacturers A

37、ssociation, 500 Montgomery Street, Suite 350, Alexandria,Virginia 22314.ANSI/AGMA 2101- D04AMERICAN NATIONAL STANDARDvii AGMA 2004 - All rights reservedPERSONNEL of the AGMA Helical Gear Rating CommitteeChairman: John V. Lisiecki Falk Corporation.Vice Chairman: Michael B. Antosiewicz Falk Corporatio

38、nACTIVE MEMBERSK.E. Acheson Gear Works - Seattle, IncJ.B. Amendola MAAG Gear AGT.A. Beveridge Caterpillar, Inc.M. Broglie Dudley Technical GroupG.A. DeLange Hansen Transmissions.G. Elliott Lufkin Industries, Inc.R.L. Errichello GEARTECH.R.W. Holzman Innovative Gearing Solutions LLCO.A. LaBath Gear C

39、onsulting Services of Cincinnati, LLCG. Lian Amarillo Gear Company.L. Lloyd Lufkin Industries, Inc.D. McCarthy Gear Products, Inc.D.R. McVittie Gear Engineers, Inc.A.G. Milburn Milburn Engineering, Inc.G.W. Nagorny Nagorny ZEis elastic coefficient, N/mm20.5(see clause12);Ftis transmitted tangential

40、load, N (see clause7);Kois overload factor (see clause 9);Kvis dynamic factor (see clause 8);Ksis size factor (see clause 20);KHis load distribution factor (see clause15);ZRis surface condition factor for pitting resis-tance (see clause 13);b is net face width of narrowest member, mm;ZIis geometry f

41、actor for pitting resistance (seeclause 6);dw1is operating pitch diameter of pinion, mm.dw1=2 au + 1for external gears (2)dw1=2 au 1for internal gears (3)wherea is operating center distance, mm;u is gear ratio (never less than 1.0).5.1.2 Allowable contact stress numberThe relation of calculated cont

42、act stress number toallowable contact stress number is:HHPSHZNYZWYZ(4)whereHPis allowable contact stress number, N/mm2(see clause 16);ZNis stress cycle factor for pitting resistance(see clause 17);ANSI/AGMA 2101- D04 AMERICAN NATIONAL STANDARD10 AGMA 2004 - All rights reservedZWis hardness ratio fac

43、tor for pitting resistance(see clause 14);SHis safety factor for pitting (see clause 11);Yis temperature factor (see clause 19);YZis reliability factor (see clause 18).5.1.3 Pitting resistance power ratingThe pitting resistance power rating is:Paz=1b6 107ZIKoKvKsKHZRdw1HPZESHZNZWYYZ2(5)wherePazis al

44、lowable transmitted power for pitting re-sistance, kW;1is pinion speed, rpm.CAUTION: The ratings of both pinion and gear teethmust be calculated to evaluate differences in materialproperties and the number of tooth contact cycles un-der load. The pitting resistance power rating is basedon the lowest

45、 value of the productHPZNZWfor each ofthe mating gears.5.1.4 Contact load factor, KIn some industries, pitting resistance is rated interms of K factor.(6)K =Ftdw1b1CGwhereK is contact load factor for pitting resistance,N/mm2;CGis gear ratio factor.(7)CG=uu + 1orz2z2+ z1for external gearsand(8)CG=uu

46、1orz2z2 z1for internal gearswherez2is number of teeth in gear;z1is number of teeth in pinion.In terms of this standard, the allowable K factor isdefined as:(9)Kaz=ZIKoKvKsKHZRCGHPZESHZNZWYYZ2Kazis allowable contact load factor, N/mm2.The allowable contact load factor, Kaz,isthelowestof the ratings c

47、alculated using the different values ofHP, ZWand ZNfor pinion and gear.5.2 Bending strength5.2.1 Fundamental formulaThe fundamental formula for bending stress numberin a gear tooth is:(10)F= FtKoKvKs1bmtKHKBYJwhereFis bending stress number, N/mm2;KBis rim thickness factor (see 5.2.5);YJis geometry f

48、actor for bending strength (seeclause 6);mtis transverse metric module, mm.*;mtis mnfor spur gears.(11)mt=pxtan =mncosfor helical gearswheremnis normal metric module, mm;pxis axial pitch, mm; is helix angle at standard pitch diameter. = arcsin mnpx(12)5.2.2 Allowable bending stress numberThe relatio

49、n of calculated bending stress number toallowable bending stress number is:(13)FFPYNSFYYZwhereFPis allowable bending stress number, N/mm2(see clause 16);YNis stress cycle factor for bending strength(see clause17);_* This calculation is based on standard gear hobbing practice, with mtand pxgiven. For a detailed text on geometry,see AGMA 933-B03, Information Sheet - Basic Gear GeometryANSI/AGMA 2101- D04AMERICAN NATIONAL STANDARD11 AGMA 2004 - All rig