1、AGMAINFORMATIONSHEET(This Information Sheet is NOT an AGMA Standard)AGMA932-A05AGMA 932-A05AMERICAN GEAR MANUFACTURERS ASSOCIATIONRating the Pitting Resistance and BendingStrength of Hypoid GearsiiRating the Pitting Resistance and Bending Strength of Hypoid GearsAGMA 932-A05CAUTION NOTICE: AGMA tech
2、nical 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.Tablesorotherself-supportingsectionsma
3、ybereferenced. Citationsshouldread: SeeAGMA 932-A05, Rating the Pitting Resistance and Bending Strength of Hypoid Gear,published by the American Gear Manufacturers Association, 500 Montgomery Street,Suite 350, Alexandria, Virginia 22314, http:/www.agma.org.Approved January 19, 2005ABSTRACTThisinform
4、ationsheetprovidesamethodbywhichdifferenthypoidgeardesignscanbecompared. Theformu-las are intended to establish a uniformly acceptable method for calculating the pitting resistance and bendingstrengthcapacityofbothcurvedandskewedtoothhypoidgears. Theyapplyequallytotapereddepthanduni-form depth teeth
5、.Published byAmerican Gear Manufacturers Association500 Montgomery Street, Suite 350, Alexandria, Virginia 22314Copyright 2005 by American Gear Manufacturers AssociationAll rights reserved.No part of this publication may be reproduced in any form, in an electronicretrieval system or otherwise, witho
6、ut prior written permission of the publisher.Printed in the United States of AmericaISBN: 1-55589-869-6AmericanGearManufacturersAssociationAGMA 932-A05AMERICAN GEAR MANUFACTURERS ASSOCIATIONiii AGMA 2005 - All rights reservedContentsPageForeword iv.1 Scope 1.2 Normative references 1.3 Nomenclature 1
7、4 Applicability 35 Fundamental rating formulas 4.6 Geometry factors, I (ZI) and J (YJ)7.AnnexesA Geometry factor graphs 9B Hypoid gear sample calculations 15.Tables1 Symbols 2.AGMA 932-A05 AMERICAN GEAR MANUFACTURERS ASSOCIATIONiv AGMA 2005 - All rights reservedForewordThe foreword, footnotes and an
8、nexes, if any, in this document are provided forinformational purposes only and are not to be construed as a part of AGMA InformationSheet 932-A05, Rating the Pitting Resistance and Bending Strength of Hypoid Gears.Thematerialpresentin AGMA932-A05 wasoriginally includedin anannex ofthe draftforANSI/
9、AGMA 2003-B97. The intent was to have a proposed rating method that wouldcomplement the hypoid geometry presented in ANSI/AGMA 2005-C95. It was removedfromANSI/AGMA2003-B97duringtheballotprocesstoallowforitstimelypublication. Thecommittee felt this material should be expanded and presented in a sepa
10、rate informationsheet prior to standardization.The first draft of AGMA 932-A05 was made in June, 2003. It was approved by the AGMATechnical Division Executive Committee in January, 2005.Suggestions for improvement of this information sheet will be welcome. They should besenttotheAmericanGearManufact
11、urersAssociation,500MontgomeryStreet,Suite350,Alexandria, Virginia 22314.AGMA 932-A05AMERICAN GEAR MANUFACTURERS ASSOCIATIONv AGMA 2005 - All rights reservedPERSONNEL of the AGMA Bevel Gearing CommitteeChairman: R. F. Wasilewski Arrow Gear Company.Vice Chairman: G. Lian Amarillo Gear CompanyACTIVE M
12、EMBERST. Guertin Liebherr Gear Technology Company.J. Kolonko Falk Corporation.T.J. Krenzer Gleason Corporation.P.A. McNamara Caterpillar, Inc.K. Miller Dana Spicer Off Highway Products.W. Tsung Dana CorporationAGMA 932-A05 AMERICAN GEAR MANUFACTURERS ASSOCIATIONvi AGMA 2005 - All rights reserved(Thi
13、s page is intentionally blank)1 2005 AGMA - All rights reservedAGMA 932-A05AMERICAN GEAR MANUFACTURERS ASSOCIATIONAmerican Gear ManufacturersAssociation -Rating the PittingResistance and BendingStrength of HypoidGears1 ScopeThis information sheet provides a method forcalculating the pitting resistan
14、ce and bendingstrength of hypoid gears using the procedures ofANSI/AGMA 2003-B97.1.1 Rating formulasThe knowledge and judgment required to evaluatethe various rating factors come from years ofaccumulated experience in designing, manufactur-ingandoperatinggearunits. Empiricalfactorsgivenin this docum
15、ent are general in nature. AGMAapplication standards may use other empiricalfactors that are more closely suited to the particularfield of application. This document is intended foruse by the experienced gear designer, capable ofselecting reasonable values for the factors. It is notintended for use
16、by the engineering public at large.1.2 ExceptionsThe exceptions in clause 1.2 of ANSI/AGMA2003-B97 apply for hypoid gears. Lengthwisesliding in hypoids reduces their efficiency. Torquelossesbetweendrivingpinionandgearrangefrom2to15percentdependingon theoffset,spiralangles,velocity and lubrication. T
17、he equations neglectefficiency. The user can adjust input or output toaccount for losses.2 Normative referencesThe following documents contain provisions which,throughreferenceinthistext,constituteprovisionsofthisinformationsheet. Atthetimeofpublication,theeditions were valid. All publications are s
18、ubject torevision, and the users of this document areencouraged to investigate thepossibility ofapplyingthe most recent editions of the publications listed.ANSI/AGMA 2003-B97, Rating the Pitting Resist-ance and Bending Strength of Generated StraightBevel, Zerol Bevel and Spiral Bevel Gear TeethANSI/
19、AGMA 2005-D03, Design Manual for BevelGears3 NomenclatureThe symbols used in this information sheet areshown in table 1.NOTE: The symbols and terms contained in thisdocument may vary from those used in other AGMAstandards. Users of this information sheet should as-surethemselvesthattheyareusingthese
20、symbolsandterms in the manner indicated herein.System international (SI) units of measure areshown in parentheses in table 1 and in the text.Equations are shown in two formats: the first isnon-metric, the second is with SI units, constantsandISOsymbols,designatedby“M”intheequationnumber.Example:swc=
21、sacCLCHSHKTCR(2)HP=H limZNTZWSHKZZ(2M)AGMA 932-A05 AMERICAN GEAR MANUFACTURERS ASSOCIATION2 2005 AGMA - All rights reservedTable 1 - SymbolsAGMAsymbolISOsymbolTerms Units Wherefirst usedAmRmMean cone distance in (mm) Eq 5AmGRm2Gear mean cone distance in (mm) Eq 5CHZWHardness ratio factor - - Eq 8CiZ
22、iInertia factor for gears with low contact ratio, pittingresistance- - Eq 18CLZNTStress cycle factor for pitting resistance - - Eq 8CpZEElastic coefficient Ib/in20.5(N/mm20.5)Eq 7CRZZReliability factor for pitting resistance - - Eq 8CsZxSize factor for pitting resistance - - Eq 7CxcZxcCrowning facto
23、r - - Eq 7D de2Gear outer pitch diameter in (mm) Eq 1d de1Pinion outer pitch diameter in (mm) Eq 1E a Hypoid offset in (mm) Annex AF b Net face width in (mm) Eq 2FePb1Effective face width of pinion in (mm) Eq 19FeGb2Effective face width of gear in (mm) Eq 20FGb2Gear face width in (mm) Eq 2FPb1Pinion
24、 face width in (mm) Eq 11I ZIGeometry factor for pitting resistance - - Eq 7JPYJ1Modified pinion bending strength geometry factor - - Eq 13JGYJ2Geometry factor for gear bending strength - - Eq 12JPYJ1Geometry factor for pinion bending strength - - Eq 11KiYiInertia factor for gears with low contact r
25、atio, bendingstrength- - Eq 19KLYNTStress cycle factor for bending strength - - Eq 14KmKHLoad distribution factor - - Eq 7KoKAOverload factor - - Eq 7KRYzReliability factor for bending strength - - Eq 14KsYXSize factor for bending strength - - Eq 11KTKTemperature factor - - Eq 8KvKvDynamic factor -
26、- Eq 7KxYTooth lengthwise curvature factor - - Eq 11mNINILoad sharing ratio for pitting resistance - - Eq 18mNJNJLoad sharing ratio for bending strength - - Eq 19N z2Number of teeth on gear - - Eq 1n z1Number of teeth on pinion - - Eq 1nGn2Gear speed rpm Eq 10PacPazAllowable transmitted power for pi
27、tting resistance hp (kw) Eq 10Pat P, GPay 1, 2Allowable transmitted power, pinion or gear, for bend-ing strengthhp (kw) Eq 16Pd- - Outer transverse diametral pitch in- 1Eq 6PdG- - Outer transverse diametral pitch of gear in- 1Eq 6(continued)AGMA 932-A05AMERICAN GEAR MANUFACTURERS ASSOCIATION3 2005 A
28、GMA - All rights reservedAGMAsymbolISOsymbolTerms Units Wherefirst usedPmGMean transverse diametral pitch of gear in- 1Eq 20PmPMean transverse diametral pitch of pinion in- 1Eq 18R rmpt2Mean transverse pitch radius of gear in (mm) Eq 20Rtrmyo2Mean transverse radius to point of load application forge
29、arin (mm) Eq 20r rmpt1Mean transverse pitch radius of pinion in (mm) Eq 19rtrmyo1Mean transverse radius to point of load application forpinionin (mm) Eq 19SFSFSafety factor for bending strength - - Eq 14SHSHSafety factor for pitting resistance (contact) - - Eq 8s gcLength of line of contact in (mm)
30、Eq 18sacH limAllowable stress number for pitting resistance lb/in2(N/mm2) Eq 8satF limAllowable stress number for bending strength lb/in2(N/mm2) Eq 14scHCalculated stress number for pitting resistance lb/in2(N/mm2) Eq 7stFCalculated stress number for bending strength lb/in2(N/mm2) Eq 15stGF2Calculat
31、ed gear bending stress number at the root ofthe toothlb/in2(N/mm2) Eq 12stPF1Calculated pinion bending stress number at the rootof the toothlb/in2(N/mm2) Eq 11swcHPPermissible stress number for pitting resistance lb/in2(N/mm2) Eq 8swtFPPermissible stress number for bending strength lb/in2(N/mm2) Eq
32、14TGT2Operating gear torque lb in (Nm) Eq 3TPT1Operating pinion torque lb in (Nm) Eq 3YKGYK2Tooth form factor including the stress concentrationfactor, gear- - Eq 20YKPYK1Tooth form factor including the stress concentrationfactor, pinion- - Eq 19- - metOuter transverse module (mm) Eq 6M- - met2Outer
33、 transverse module, gear (mm) Eq 6M- - mmt1Mean transverse module, pinion (mm) Eq 18M- - mmt2Mean transverse module, gear (mm) Eq 20MoyoRelative radius of profile curvature in (mm) Eq 18 nNormal pressure angle degrees Eq 18 mMean spiral angle degrees Eq 4Gm2Mean spiral angle, gear degrees Eq 1Pm1Mea
34、n spiral angle, pinion degrees Eq 14 Applicability4.1 Rating practicesWhere applicable AGMA application standardsexist, they should be used in preference to thisinformationsheet. ConsultAGMAHeadquartersforcurrent list of applicable standards. Where noapplicable AGMA application standard exists, nu-m
35、erical values may be estimated for the factors inthese general formulas, and approximate pittingresistance and strength ratings calculated.AGMA 932-A05 AMERICAN GEAR MANUFACTURERS ASSOCIATION4 2005 AGMA - All rights reservedThe use of this information sheet for specificapplicationsdemandsarealistica
36、ndknowledgeableappraisalofallapplicableconsiderations,particular-ly of the:- allowable stress for the material and the numberof load repetitions;- consequences of any percentage of failure (fail-ure rate);- appropriate safety factor.4.2 Calculation proceduresThis document is intended to be used with
37、 ANSI/AGMA 2003-B97. However, many of the calcula-tionsinANSI/AGMA2003-B97aremadewithpiniondimensions. Since some hypoid pinion dimensionsare not defined or easily calculated, the equationsmust be adjusted to use the gear geometry. Theequations presented in this document have alreadybeen adjusted. U
38、nless otherwise specified, makethe following substitutions for pinion values whenusing the equations in ANSI/AGMA 2003-B97.Pinion pitch diameter, dd = DnNcosGcosP(1)de1= de2z1z2cosm2cosm1(1M)whered (de1) is pinion outer pitch diameter, in (mm);D (de2) is gear outer pitch diameter, in (mm);n (z1) is
39、number of teeth, pinion;N (z2) is number of teeth, gear;G(m2) is gear mean spiral angle, degrees;P(m1) is pinion mean spiral angle, degrees.Net face width, FF = FG(2)b = b2(2M)whereF (b) is net face width, in (mm);FG(b2) is gear face width, in (mm).Gear torque, TGTG=NnTP(3)T2=z2z1T1(3M)whereTG(T2) i
40、s operating gear torque, lb in (Nm);TP(T1) is operating pinion torque, lb in (Nm),see ANSI/AGMA 2003-B97, clause 6.Mean spiral angle = G(4)m= m2(4M)where (m) is mean spiral angle at pitch surface,degrees.Mean cone distanceAm= AmG(5)Rm= Rm2(5M)whereAm(Rm) is mean cone distance, in (mm);AmG(Rm2) is ge
41、ar mean cone distance, in (mm).Outer transverse diametral pitchPd= PdG(6)wherePdisoutertransversediametralpitch,in- 1;PdGisgearoutertransversediametralpitch,in- 1.Outer transverse modulemet= met2(6M)wheremetis outer transverse module, mm;met2is gear outer transverse module, mm.5 Fundamental rating f
42、ormulasThe rating of both pinion and gear teeth must becalculatedtoevaluatedifferencesinmaterialproper-ties and the number of tooth contact cycles underload.5.1 Pitting resistance5.1.1 Fundamental contact stress formulaThe fundamental contact stress formula for pittingresistance of hypoid gear teeth
43、 is:sc= Cp2 TGFGD2INnKoKvKmCsCxc(7)H= ZE2000 T2b2d2e2ZIz2z1KAKvKHZxZxc(7M)AGMA 932-A05AMERICAN GEAR MANUFACTURERS ASSOCIATION5 2005 AGMA - All rights reservedwheresc(H) is calculated stress number for pittingresistance, lb/in2(N/mm2);Cp(ZE) is elastic coefficient, Ib/in20.5(N/mm20.5), see ANSI/AGMA2
44、003-B97 clause 20;I (ZI) is pitting resistance geometry factor,see ANSI/AGMA 2003-B97 clause 15and annex A;Ko(KA) is overload factor, see ANSI/AGMA2003-B97 clause 7;Kv(Kv) is dynamic factor, see ANSI/AGMA2003-B97 clause 10, used = DnNcosGcosPde1= de2z1z2cosm2cosm1, see clause4.2;Km(KH) is load distr
45、ibution factor, see ANSI/AGMA2003-B97clause12,useF = FG(b = b2),seeclause4.2;Cs(Zx) is size factor, see ANSI/AGMA2003-B97 clause 11, use F = FGb = b2, see clause 4.2;Cxc(Zxc) is crowning factor, see ANSI/AGMA2003-B97 clause 13.5.1.2 Permissible stress number for pittingresistanceThe values of sac(H
46、lim), CL(ZNT) and CH(ZW)maybe different for the pinion and gear. Therefore, theratingshouldbebasedonthememberwhichhasthelowestvalueoftheproductsacCLCH(HlimZNTZW).The formula for pittingresistance permissiblestressnumber is:swc=sacCLCHSHKTCR(8)HP=H limZNTZWSHKZZ(8M)whereswc(HP) ispermissiblestressnum
47、berforpittingresistance, lb/in2(N/mm2);sac(H lim) is allowable stress number for pittingresistance, lb/in2(N/mm2), see ANSI/AGMA 2003-B97 clause 21;CL(ZNT) isstresscyclefactor,seeANSI/AGMA2003-B97 clause 16;CH(ZW) is hardness ratio factor, seeANSI/AGMA 2003-B97 clause 17;SH(SH) is safety factor for
48、pitting resistance,see ANSI/AGMA 2003-B97 clause 8;KT(K) is temperature factor, seeANSI/AGMA 2003-B97 clause 18;CR(ZZ) is reliability factor, see ANSI/AGMA2003-B97 clause 19.The calculated stress number for pitting resistancemust be equal to or less than the permissible stressnumber:sc swc(9)H HP(9M
49、)5.1.3 Pitting resistance power formulaThe values of sac(H lim), CL(ZNT) and CH(ZW)maybe different for the pinion and gear. Therefore, theratingshouldbebasedonthememberwhichhasthelowestvalueoftheproductsacCLCH(HlimZNTZW).Theformulafortheratedpowerataspecifiedspeedto resist pitting of the gear teeth is: sacDCLCHSHCpKTCR2(10)Pac=nGFG126 000nNIKvKmKoCsC
