ANSI AGMA 2001-D04-2004 Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth.pdf

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1、ANSI/AGMA 2001-D04Revision of ANSI/AGMA 2001-C95Reaffirmed January 2010American National StandardFundamental Rating Factorsand Calculation Methods forInvolute Spur and Helical GearTeethANSI/AGMA2001-D04iiFundamentalRatingFactorsandCalculationMethodsforInvoluteSpurandHelical Gear TeethANSI/AGMA 2001-

2、D04Revision of ANSI/AGMA 2001-C95ApprovalofanAmericanNationalStandardrequiresverificationbyANSIthattherequire-ments for due process, consensus, and other criteria for approval have been met by thestandards developer.Consensusisestablishedwhen,inthejudgmentoftheANSIBoardofStandardsReview,substantial

3、agreement has been reached by directly and materially affected interests.Substantialagreementmeansmuchmorethanasimplemajority,butnotnecessarilyuna-nimity. Consensus requires that all views and objections be considered, and that aconcerted effort be made toward their resolution.TheuseofAmericanNation

4、alStandardsiscompletelyvoluntary;theirexistencedoesnotin 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

5、develop standards and will in nocircumstances give an interpretation of any American National Standard. Moreover, noperson shall have the right or authority toissue an interpretation ofan American NationalStandardinthenameoftheAmericanNationalStandardsInstitute. Requestsforinterpre-tation of this st

6、andard 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 th

7、e latest available from theAssociation on the subject matter.Tablesorotherself-supportingsectionsmaybereferenced. Citationsshouldread: SeeANSI/AGMA 2001-D04, Fundamental Rating Factors and Calculation Methods for Invo-lute Spur and Helical Gear Teeth, published by the American Gear Manufacturers Ass

8、o-ciation, 500 Montgomery Street, Suite 350, Alexandria, Virginia 22314,http:/www.agma.org.Approved December 28, 2004ABSTRACTThisstandardspecifiesamethodforratingthepittingresistanceandbendingstrengthofspurandhelicalinvo-lutegearpairs. Adetaileddiscussionoffactorsinfluencinggearsurvivalandcalculatio

9、nmethodsareprovided.Published byAmerican Gear Manufacturers Association500 Montgomery Street, Suite 350, Alexandria, Virginia 22314Copyright 2004 by American Gear Manufacturers AssociationAll rights reserved.No part of this publication may be reproduced in any form, in an electronicretrieval system

10、or otherwise, without prior written permission of the publisher.Printed in the United States of AmericaISBN: 1-55589-839-4AmericanNationalStandardANSI/AGMA 2001-D04AMERICAN NATIONAL STANDARDiii AGMA 2004 - All rights reservedContentsPageForeword v.1 Scope 1.2 Normative references, definitions and sy

11、mbols 23 Application 2.4 Criteria for tooth capacity 75 Fundamental rating formulas 9.6 Geometry factors, I and J 11.7 Transmitted tangential load, Wt128 Dynamic factor, Kv12.9 Overload factor, Ko15.10 Service factor 15.11 Safety factors, SHand SF1612 Elastic coefficient, Cp16.13 Surface condition f

12、actor, Cf1714 Hardness ratio factor, CH1715 Load distribution factor, Km1716 Allowable stress numbers, sacand sat23.17 Stress cycle factors, ZNand YN3618 Reliability factor, KR3819 Temperature factor, KT3820 Size factor, Ks38.Bibliography 56.AnnexesA Method for determination of dynamic factor with A

13、GMA 2000-A88 39B Rim thickness factor, KB41C Application analysis 43D Discussion of the analytical face or longitudinal load distribution factor 46E Gear material fatigue life 49F Controlling section size considerations for through hardened gearing 54.Figures1 Dynamic factor, Kv14.2 Hardness ratio f

14、actor, CH(through hardened) 183 Hardness ratio factor, CH(surface hardened pinions) 18.4 Instantaneous contact lines in the plane of action 195 Pinion proportion factor, Cpf21.6 Evaluation of S and S1217 Mesh alignment factor, Cma22.8 Allowable contact stress number for through hardened steel gears,

15、 sac249 Allowable bending stress number for through hardened steel gears, sat2510 Allowable bending stress numbers for nitrided through hardened steel gears(i.e., AISI 4140, AISI 4340), sat25.11 Allowable bending stress numbers for nitriding steel gears, sat26.12 Variations in hardening pattern obta

16、inable on gear teeth with flame orinduction hardening 3213 Minimum effective case depth for carburized gears, hemin33.14 Core hardness coefficient, Uc3415 Minimum total case depth for nitrided gears, hcmin34.16 Allowable yield strength number for steel gears, say35.ANSI/AGMA 2001-D04 AMERICAN NATION

17、AL 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 equations 3.2 Empirical constants; A, B, and C 22.3 Allowable contact stress number, sac, for steel gears 234 Allowable bendi

18、ng stress number, sat, for steel gears 24.5 Allowable contact stress number, sac, for iron and bronze gears 266 Allowable bending stress number, sat, for iron and bronze gears 277 Major metallurgical factors affecting the allowable contact stress number,sac, and allowable bending stress number, sat,

19、 of through hardened steelgears 278 Major metallurgical factors affecting the allowable contact stress number,sac, and allowable bending stress number, sat, of flame or induction hardenedsteel gears 289 Major metallurgical factors affecting the allowable contact stress number,sac, and allowable bend

20、ing stress number, sat, of carburized and hardenedsteel gears 2910 Major metallurgical factors affecting the allowable contact stress number,sac, and allowable bending stress number, sat, of nitrided steel gears 3111 Reliability factors, KR38.ANSI/AGMA 2001-D04AMERICAN NATIONAL STANDARDv AGMA 2004 -

21、 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/AGMA2001-D04, Fundamental Rating Factors and Calculation Methods for Involute Spur andHelical Gear Teeth.This standard p

22、resents general formulas for rating the pitting resistance and bendingstrength of spur and helical involute gear teeth, and supersedes ANSI/AGMA 2001-C95.Thepurposeofthisstandardistoestablishacommonbaseforratingvarioustypesofgearsfordifferingapplications,andtoencouragethemaximumpracticaldegreeofunif

23、ormityandconsistency between rating practices within the gear industry. It provides the basis fromwhich more detailed AGMA application standards are developed, and provides a basis forcalculation of approximate ratings in the absence of such standards.The formulas presented in this standard contain

24、factors whose values vary significantlydepending on application, system effects, gear accuracy, manufacturing practice, anddefinitionofgearfailure. Properevaluationofthesefactorsisessentialforrealisticratings.This standard is intended for use by the experienced gear designer capable of selectingreas

25、onable values for rating factors and aware of the performance of similar designsthrough test results or operating experience.InAGMA218.01thevaluesforLifeFactor,CLandKL,DynamicFactor,CvandKv,andLoadDistributionFactor,CmandKm,wererevised.Valuesforfactorsassignedinstandardspriorto that were not applica

26、ble to 218.01 nor were the values assigned in 218.01 applicable toprevious standards.ThedetailedinformationontheGeometryFactors,IandJ,wereremovedfromANSI/AGMA2001-B88,therevisionofAGMA218.01. ThismaterialwasamplifiedandmovedtoAGMA908-B89, GeometryFactors forDeterminingthePittingResistanceandBendingS

27、trengthforSpur,HelicalandHerringboneGearTeeth. ThevaluesofIandJhavenotbeenchangedfrom previous Standards.In ANSI/AGMA 2001-B88 the Allowable Stress Number section was expanded.Metallurgical quality factors for steel materials were defined,establishing minimumqualitycontrol requirements and allowable

28、 stress numbers for various steel quality grades.Additional higher allowable stress numbers for carburized gears were added when madewith high quality steel. A new rim thickness factor, KB,was introduced to reduce allowablebendingloadsongearswiththinrims. Materialonscuffing(scoring)resistancewasadde

29、das an annex. ANSI/AGMA 2001-B88 was first drafted in January, 1986, approved by theAGMA Membership in May 1988, and approved as an American National Standard onSeptember 30, 1988.ANSI/AGMA 2001-C95 was a revision of the rating method described in its supersededpublications. The changes included: th

30、e Miners rule annex was removed; the analyticalmethod for load distribution factors, Cmand Km, was revised and placed in an annex;nitrided allowable stress numbers were expanded to cover three grades; nitrided stresscycle factors were introduced; through hardened allowable stresses were revised;appl

31、icationfactorwasreplacedbyoverloadfactor;safetyfactorsSHandSFwereintroduced;lifefactorwasreplacedbystresscyclefactoranditsusewithservicefactorredefined;and,thedynamicfactorwasredefinedasthereciprocalofthatusedinpreviousAGMAstandardsand was relocated to the denominator of the power equation.This stan

32、dard, ANSI/AGMA 2001-D04, is a revision of its superseded version. Clause 8was changed to incorporate ANSI/AGMA 2015-1-A01 and the Kvmethod using AGMA2000-A88wasmovedtoAnnexA. ReferencestooldAnnexA,“MethodforEvaluatingtheANSI/AGMA 2001-D04 AMERICAN NATIONAL STANDARDvi AGMA 2004 - All rights reserved

33、Risk 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.This AGMA

34、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.ThefirstdraftofANSI/AG

35、MA2001-D04wascompletedinFebruary2002. ItwasapprovedbytheAGMAmembershiponOctober23,2004. ItwasapprovedasanAmericanNationalStandard on December 28, 2004.Suggestionsforimprovementofthisstandardwillbewelcome. TheyshouldbesenttotheAmericanGearManufacturersAssociation,500MontgomeryStreet,Suite350,Alexandr

36、ia,Virginia 22314.ANSI/AGMA 2001-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 CorporationACTIVE MEMBERSK.E. Acheson Gear Works - Seattle, IncJ.

37、B. Amendola MAAG Gear AGT.A. Beveridge Caterpillar, Inc.M. Broglie Dudley Technical GroupG.A. DeLange Hansen TransmissionsG. Elliott Lufkin Industries, Inc.R.L. Errichello GEARTECH.R.W. Holzman Innovative Gearing Solutions LLCO.A. LaBath Gear Consulting Services of Cincinnati, LLCG. Lian Amarillo Ge

38、ar Company.L. Lloyd Lufkin Industries, Inc.D. McCarthy Gear Products, Inc.D.R. McVittie Gear Engineers, IncA.G. Milburn Milburn Engineering, Inc.G.W. Nagorny Nagorny Cpis elastic coefficient, lb/in20.5(see clause12);Wtistransmittedtangentialload,lb(seeclause7);Kois overload factor (see clause 9);Kvi

39、s dynamic factor (see clause 8);Ksis size factor (see clause 20);Kmis load distribution factor (see clause15);Cfis surface condition factor for pitting resist-ance (see clause 13);F is net face width of narrowest member, in;I isgeometryfactorforpittingresistance(seeclause 6);d is operating pitch dia

40、meter of pinion, in.d =2CmG+ 1for external gears(2)d =2CmG 1for internal gears (3)whereC is operating center distance, in;mGis gear ratio (never less than 1.0).5.1.2 Allowable contact stress numberThe relation of calculated contact stress number toallowable contact stress number is:scsacSHZNKTCHKR(4

41、)wheresacis allowable contact stress number, lb/in2(see clause 16);ZNis stress cycle factor for pitting resistance(see clause 17);CHishardnessratiofactorforpittingresistance(see clause 14);SHis safety factor for pitting (see clause 11);ANSI/AGMA 2001-D04 AMERICAN NATIONAL STANDARD10 AGMA 2004 - All

42、rights reservedKTis temperature factor (see clause 19);KRis reliability factor (see clause 18).5.1.3 Pitting resistance power ratingThe pitting resistance power rating is:Pac= npF396 000IKoKvKsKmCfdsacCpSHZNCHKTKR2(5)wherePacisallowabletransmitted powerfor pittingre-sistance, hp;npis pinion speed, r

43、pm.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 value of the product sacZNCHfor each ofthe mating gears.5.1.4 Contact lo

44、ad factor, KIn some industries, pitting resistance is rated interms of K factor.(6)K =WtdF1CGwhereK is contact load factor for pitting resistance,lb/in2;CGis gear ratio factor.(7)CG=mGmG+ 1orNGNG+ NPfor external gearsand(8)CG=mGmG 1orNGNG NPfor internal gearswhereNGis number of teeth in gear;NPis nu

45、mber of teeth in pinion.In terms of this standard, the allowable K factor isdefined as:(9)Kac=IKoKvKsKmCfCGsacCpSHZNCHKTKR2whereKacis allowable contact load factor, lb/in2.The allowable contact load factor, Kac,isthelowestoftheratingscalculatedusingthedifferentvaluesofsac, CHand ZNfor pinion and gea

46、r.5.2 Bending strength5.2.1 Fundamental formulaThefundamentalformulaforbendingstressnumberin a gear tooth is:(10)st= WtKoKvKsPdFKmKBJwherestis bending stress number, lb/in2;KBis rim thickness factor (see 5.2.5);J isgeometryfactorforbendingstrength(seeclause 6);Pdis transverse diametral pitch, in- 1*

47、;Pdis Pndfor spur gears.(11)Pd=pxtan s= Pndcossfor helical gearswherePndis normal diametral pitch, in- 1;pxis axial pitch, in;sis helix angle at standard pitch diameter.s= arcsinpxPnd (12)5.2.2 Allowable bending stress numberThe relation of calculated bending stress number toallowable bending stress

48、 number is:(13)stsatYNSFKTKRwheresatis allowable bending stress number, lb/in2(see clause 16);_* This calculation is based on standard gear hobbing practice, with Pndand pxgiven. For a detailed text on geometry,see AGMA 933-B03, Information Sheet - Basic Gear GeometryANSI/AGMA 2001-D04AMERICAN NATIO

49、NAL STANDARD11 AGMA 2004 - All rights reservedYNis stress cycle factor for bending strength(see clause17);SFis safety factor for bending strength (seeclause 11).5.2.3 Bending strength power ratingThe bending strength power rating is:(14)Pat= npd396 000 KoKvFPdJKsKmKBsatYNSFKTKRwherePatis allowable transmitted power for bendingstrength, hp.CAUTION: The ratings of both pinion and gear teethmust be calculated to evaluate differences in geometryfactors,numberofloadcycles,andmaterialp