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1、ReturntoMenuAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONMethodforSpecifyingtheGeometryofSpurandHelicalGearsAGMAINFORMATIONSHEET(ThisInformationSheetisNOTanAGMAStandard)AmericanGearMethodforSpecifyingtheGeometryofSpurandHelicalGearsAGMA913-A98ManufacturersCAUTIONNOTICE:AGMAtechnicalpublicationsare

2、subjecttoconstantimprovement,Associationrevision,orwithdrawalasdictatedbyexperienee.AnypersonwhoreferstoanyAGMATechnicalPublicationshouldbesurethatthepublicationisthelatestavailablefromtheAssociationonthesubjectmatter.Tablesorotherself-supportingsectionsmaybequotedorextractedCreditlinesshouldread:Ex

3、tractedfromAGMA913*A98,MethodforSpecifyingtheGeometryofSpurandHelicalGears,withthepermissionofthepublisher,theAmericanGearManufacturersAssociation,1500KingStreet,Suite201,Alexandria,Virginia22314.)ApprovedMarch13,1998ABSTRACTThisinformationsheetprovidesinformationtotranslatetooththicknessspecificati

4、onswhichareexpressedintermsoftooththickness,centerdistanceordiameterintoprofileshiftcoefficients,asthattermisusedininternationalstandards.PublishedbyAmericanGearManufacturersAssociation1500KingStreet,Suite201,Alexandria,Virginia22314Copyright1998byAmericanGearManufacturersAssociationAllrightsreserve

5、dNopartofthispublicationmaybereproducedinanyform,inanelectronicretrievalsystemorotherwise,withoutpriorwrittenpermissionofthepublisher.PrintedintheUnitedStatesofAmericaISBN:1-55589-714-2AMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98IIIIIIReturntoMenuCon

6、ten恰PageTOC o 1-5 h zForewordiv HYPERLINK l bookmark14Scope1 HYPERLINK l bookmark16Termsandsymbols1 HYPERLINK l bookmark22Definitions3 HYPERLINK l bookmark48Profileshift6 HYPERLINK l bookmark88Internalgearpaircalculations11TablesSymbolsusedinequations1 HYPERLINK l bookmark26Obsoleteterms3Figures HYP

7、ERLINK l bookmark28Thebasicrack3 HYPERLINK l bookmark34Hypotheticaltool4Profileshiftofahelicalgear5Effectofprofileshiftoninvolutetoothprofiles7Distancesalongthelineofaction9Rootradiicutwithracktool10Distancesalongthelineofactionforaninternalgearpair12Annexes HYPERLINK l bookmark122AToolproportions15

8、 HYPERLINK l bookmark158BCalculationofprofileshift19 HYPERLINK l bookmark172Bibliography25AGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATION iv #ReturntoMenuForewordTheforeword,footnotesandannexes,ifany,inthisdocumentareprovidedforinformationalpurposesonly

9、andarenottobeconstruedasapartofAGMAInformationSheet913-A98,MethodforSpecifyingtheGeometryofSpurandHelicalGears.Thisinformationsheetisintendedtoprovidesufficientinformationtoallowitsuserstobeabletotranslatetooththicknessspecificationswhichareexpressedintermsoftooththickness,centerdistanceordiameterin

10、toprofileshiftcoefficients,asthattermisusedininternationalstandardsThisAGMAinformationsheetandrelatedpublicationsarebasedontypicaloraveragedata,conditionsorapplication.AGMA913-A98was即provedbytheAGMAmembershiponMarch13,1998.Suggest!onsforimprovementofthisstandardwillbewelcomeTheyshouldbesenttotheAmer

11、icanGearManufacturersAssociation,1500KingStreet,Suite201,Alexandria,Virginia22314AMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98ReturntoMenuPERSONNELoftheAGMANomenclatureCommitteeChairman:JohnR.ColbourneUniversityofAlbertaViceChairman:D.McCarrollGleason

12、WorksACTIVEMEMBERSW.A.BradleyIIIConsultantR.L.ErrichelloGEARTECHD.GonnellaTexacoLubricantsCompanyD.R.McVittieGearEngineers,Inc.OALaBathCincinnatiGearCompanyI.LaskinIrvingLaskin,PEGW.NagornyNagorny&AssociatesJW.PolderDelftUniversityofTechnologyL.J.SmithInvincibleGearCompanyR.E.SmithR.E.Smith&Co.,Inc.

13、ASSOCIATEMEMBERSK.AchesonTheGearWorksSeattle,Inc.M.AllardUNITRAMMRChaplinContourHardening,Inc.ASCohenEngranesyMaquinariaFaureCMDR.GreenEatonCorporationT.OkamotoNipponGearAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATION vi #ReturntoMenu(Thispageisintentio

14、nallyleftblank.)AGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 ReturntoMenuAmericanGearManufacturersAssociation-AnnexesAandBprovidepracticalexamplesonthecalculationoftoolproportionsandprofileshiftMethodforSpecifyingtheGeometryofSpurandHelicalGears1Scop

15、eThisinformationsheetprovidesageneralmethodforspecifyingprofileshiftandrackshift,withgearnomenclatureanddefinitionsThisdocumentdescribestheeffectthatprofileshifthasonthegeometryandperformaneeofgears,butdoesnotmakespecificdesignrecommendations.Theequationsinthefirstpartofthisdocument(clauses3and4)app

16、lytoexternalgearpairsonly.Thecorrespondingequationsforinternalgearpairsarecontainedinclause5.2TermsandsymbolsTermsThetermsused,whereverapplicableconformtothefollowingstandardsISO701:1998,Internationalgearnotation-SymbolsforgeometricaldataANSI/AGMA1012-F90,GearNomenclature,Def-initionsofTermswithSymb

17、olsSymbolsThisinformationsheetusestheISOsymbolsintable1IncaseswheretherearenoISOsymbols,orthedefinitionsaredifferent,othersymbolsareused.NOTE:Thesymbols,definitionsandterminologyusedinthisinformationsheetmaydifferfromotherAGMApublicationsTheusershouldnotassumethatfamiliarsymbolscanbeusedwithoutacare

18、fulstudyofthesedefinitionsTable1SymbolsusedinequationsISOSymbolsOtherSymbolsTermsUnitsWherefirstusedDistancetoSAPmmq23C3,C4DistancesalonglineofactionmmEq27DistancetoEAPmmEq23DistaneebetweeninterfereneepointsmmEq23Yji,Yj2Bendingstrengthgeometryfactor,pinionandgearEq30QrefReferencecenterdistaneemmEq5a

19、wOperatingcenterdistaneemmEq16CRootclearaneemmEq42Ci2RequiredclearaneeatthetoothrootoftheinternalgearmmEq70dDiametermmEq4九0AddendumofthetoolmmEq22ab九2Addendum,pinionandgearmmEq34haP0Distaneeonthecuttingtoolfromtherefereneelinetothepointnearthetoothtipwherethestraightpartoftheprofileendsandthecircula

20、rtipbeginsmmEq21(continued)Table1(concluded)ISOSymbolsOtherSymbolsTermsUnitsWherefirstusedJnNormaloperatingcircularbacklashmmq31kTip-shorteningcoefficientEq32mModulemmEq3PCircularpitchmmEq1H,rzRefereneeradius,pinionandgearmmEq5ra.ra2Outsideradius,pinionandgearmmEq25ZrblBasecircleradius,pinionandgear

21、mmEq1371,72Rootradius,pinionandgearmmEq42r/PlRadiusofthepinionfilletcirclemmEq60sTooththicknessmmEq2snlisn2Refereneenormalcirculartooththickness,pinionandgearmmEq7UGearration1.0Eq10XEUXE2Generatingrackshiftcoefficient,p泊ionandgearEq46Profileshiftcoefficient,pinionandgearEq6xlminMinimumpinionprofiles

22、hiftcoefficienttoavoidundercutEq20yProfileshiftmmEq6yERackshiftEq8yiminMinimumpinionprofileshifttoavoidundercutmmEq20Z1，Z2Numberofteeth,pinionandgearEq4%RefereneenormalpressureangleEq7CQRefereneetransversepressureangleEq9OperatingtransversepressureangleEq9PRefereneehelixangleEq1SefCenterdistaneemodi

23、ficationmmEq32gAmountoftooththinningmmEq8Tooththinningforbacklash,pinionandgearmmEq31PnORadiusofthecirculartipofthetoolmmEq22PfPFilletradiusofthebasicrackmmFigi&SumofprofileshiftcoefficientsEq53ErgSumofgeneratingrackshiftcoefficientsEq52OfbOF2Allowablebendingstress,pinionandgearMPaEq30Subscriptconve

24、rsion(none)AtreferencediameteraAtaddendum(tip)diameterbfAtbasecylinderdiameterAtrootdiameternNormalplanetTransverseplanewOperating,runningorworkingyAtany(undefined)diameter0looldimensions1Pinion2GearorrackAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98

25、# ReturntoMenuAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 # #ReturntoMenu3DefinitionsTable2ObsoletetermsAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 # #ReturntoMenuThisinformationsheetprovidesdefinit

26、ionsofprofileshiftandrackshiftandshowstherelationsbetweenthemandothergearquantitiesThetermsprofileshiftandrackshiftareusedinthisinformationsheetforstandardization.Theintentionistoreplacethesimilarorrelatedtermslistedintable2.BasicrackThestandardbasicracktoothprofileisthetoothprofilenormalsectionthro

27、ughtheteethofabasicrackwhichcorrespondstoanexternalgearwithnumberofteethz=xanddiameterd=8,seefigure1Agearwithnormalmodule,m加andnormalpressureangle,a”，hasabasicrackwhosenormalcircularpitch,pntisnmnandwhosenormalpressureangleisa”.Therefereneeplaneofthebasicrackisparalleltoitstoothtipplaneandistheplane

28、onwhichthenormalcirculartooththickness,sn,isequaltoonehalfthenormalcircularpitchFromthisdefinitionitfollowsthatthenormalcirculartooththicknessonthereferenceplaneisequaltothenormalcircularspacewidthAddendumcorrect!onAddendumelongationAddendumincrementAddendummodificationAddendumratioBasicrackoffsetCu

29、tteroffsetDeltaaddendumDeltateethDrop-toothdesignEnlargement/reductionEnlarged/reducedcenterdistaneeEnlarged/reducednumberofteethHalfpitchhobpullHigh/lowaddendumHoboffsetHobpullIncrease/decreaseInvoluteshiftLong/shortaddendumNonstandardaddendaOver/undersizeProfiledisplacementProfilewithdrawalRackwit

30、hdrawalToolshiftToolwithdrawalUnequaladdendaXfactorAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 # #ReturntoMenuAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 # #ReturntoMenu2NormalpressureangleNormalbas

31、epitch,pbnNormalcircularthickness,snRefereneelineAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 #ReturntoMenuNormalcircularpitch,處=兀mnFigure1ThebasicrackAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 # Re

32、turntoMenuIfthebasicrackisorientedsothatitsteethmakeananglepwiththegearaxis,seefigure3,thesectionthroughthebasicrackperpendiculartothegearaxisiscalledthetransversesection.Onthissection,thetransversecircularpitch,phandthetransversetooththickness,sharegivenby:andthetransversemodule,mbisdefinedby:Theba

33、sicrackrepresentsthetheoreticalgeartoothform,nottheformofthecuttingtool.Noallowaneeismadeforbacklash,finishingstockormanufactur-泊gmethodThestandard20normalpressureanglebasicrackofISO53iscommonlyusedThisdocumentisvalidforthatbasicrackandforanyotherbasicrackwhichmeetsthecriteriaoffigure1.Referencecyli

34、nderofthegear(standardpitchcylinder)ThereferencecylinderofagearisdefinedasthepitchcylinderwherecircularpitchofthegearisequaltocircularpitchofthebasicrackIfthegearhaszteethandtherackisorientedwithitsteethmakingananglepwiththegearaxis,thenthediameter,d、ofthereferencecylinderisgivenbyd=半cospThepitchpla

35、neofthebasicrackisparalleltotherefereneeplaneandistheplanethatistangenttotherefereneecylinderofthegear.ThehelixangleofthegearatitsrefereneecylinderisequaltoBReferencecenterdistanceTherefereneecenterdistaneeofanexternalgearpairisdefinedashalfthesumoftherefereneediameters.Pl+況2)丄aref=2=rl+r2(5)where口a

36、ndrzaretheradiioftherefereneecylindersTherefereneecenterdistaneeisnotnecessarilyequaltotheoperat泊gcenterdistanee.Itisoneoftheadvantagesofinvolutegears,thattheoperatingcenterdistaneecanvaryfromtherefereneecenterdistaneewithoutchangeinoperation.HypotheticaltoolThehypotheticaltoolisthecomplementoftheba

37、sicrackasshowninfigure2.Therefereneelineofthehypotheticaltoolisthelineatwhichitsnormalcirculartooththicknessisequalto兀笄Theuseofthephrasehypotheticaltoolinthisdocumentreferstoarack-typecutter.Foradditionalinformationandanexamplecalculation,seeannexesAandBAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIO

38、NAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 # #ReturntoMenuAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 #ReturntoMenuEnpuepeQEnpuppvFigure2HypotheticaltoolAAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA91

39、3-A98 # ReturntoMenuZerobacklashgearpairAzerobacklashgearpairisonewhichoperatesintightmesh(hasnobacklash)ontheoperatingcenterdistanee.ProfileshiftTheprofileshift,ytofthegearisdefinedastheamountbywhichtherefereneeplaneofthehypotheticaltool(conjugatetothebasicrack)isdisplacedfromtherefereneecylinderof

40、thegear.Inotherwords,thegearhasprofileshiftyifthereferenceplaneofthehypotheticaltoolliesadistanee(r+y)fromthegearaxis,whererishalfthediameter,d.Profileshift,y,canbeeitherplusorminusdependingonwhethertheprofileshiftistotheoutsideortotheinsideoftherefereneediameter.Seefigure3ProfileshiftcoefficientThe

41、profileshiftcoefficient,xyofthegearisdefinedastheprofileshiftdividedbythenormalmoduleTooththicknessThenormalcirculartooththickness,sntofthezerobacklashgearatitsrefereneecylinderisequaltothenormalcircularspacewidthofthehypotheticaltoolatitspitchplanewhenintightmeshwiththezerobacklashgear.=寺?！?tananNO

42、TE:Equations7,8and9areforexternalgearsonly.Thecorrespondingequationsforinternalgearsaregivenin5.1RackshiftItiscustomarytofirstchoosethetooththicknessesinagearpair,assumingthereisnobacklash,andtothenreducethetooththicknessestoallowforbacklashThephraseprofileshift”willbeusedforthevalueofycorresponding

43、tothetooththicknessbeforethinning,andthephrase“rackshiftforthevalueofyafterthinning.Sincetherackshiftdeterminestheactualtooththicknessatthetimeofcuttingorgenerating,thesymbolyEisusedfortherackshiftandxE1ortherackshiftcoefficient.Iftheamountofthinningisg,therelationshipbetweenrackshiftandprofileshift

44、is:AGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 # #ReturntoMenuAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 #ReturntoMenuHypotheticaltoolNormalplaneProfileshiftuynBasecircleFigure3Profileshiftofahelic

45、algearBasicrackintightmeshwithzerobacklashgearHypotheticaltoolreferencelineGearrefereneepitchcylinderZerobacklashgearwithouttooththinningHelixangleTransverseplaneAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 ReturntoMenu+2=tanat(9)歹-2；但)Iftwoexternalg

46、earsaretomeshwithnobacklash,theirprofileshiftvaluesmustsatisfy:wherearefistherefereneecenterdistance;5%istheoperatingtransversepressureangle;atistherefereneetransversepressureangle.AddendumvaluesThegearaddendum,measuredfromthereferencecylinder,isusuallychosenas(haP+y).Thisvaluedependsontheprofileshi

47、ftratherthantherackshiftandisthereforeindependentofthevaluechosenforbacklash.Incertaindesigns,particularlywhenthecenterdistaneeissignificantlylargerthanthereferencestandardcenterdistanee,thegearad-dendummayneedtobereducedtoallowadequateclearaneeattherootsofthemeshinggear,see4.10.Forinternalgearpaire

48、quationswhichreplaceequations7through9,see514ProfileshiftProfileshiftcalculationProfileshiftisselectedconsideringthefollowingcriteria:avoidingundercut;avoidingnarrowtopIands;balaneedspecificsliding;balaneedflashtemperature;balancedbendingfatiguelife.Theprofileshiftshouldbelargeenoughtoavoidundercuta

49、ndsmallenoughtoavoidnarrowtoplands.Theprofileshiftsrequiredforbalaneedspecificsliding,balaneedflashtemperatureandbalaneedbendingfatiguelifeareusuallydifferent.Therefore,thevalueusedshouldbebasedonthecriterionthatisjudgedtobethemostimportantfortheparticularapplication.Figure4illustrateshowtheshapeofa

50、geartoothisinflueneedbythenumberofteethonthegearandthevalueoftheprofileshiftcoefficient.Theinflueneethatthenumberofteethhasontoothformcanbeseenbyviewingtheteethwithinanygivencolumnoffigure4Withsmallnumbersofteeth,thetoothhaslargercurvatureandtherelativethicknessoftheteethatthetoplandandattheformdiam

51、eterissmaller.Asthenumberofteethincreases,thetoplandandtooththicknessesincreaseandthecurvatureoftheprofilesdecrease.Tooththicknessesaremaximumforarackwithstraight-sidedprofilesandtheoreticallyinfinitenumberofteethViewingfigure4horizontallywithinanygivenrowshowshowprofileshiftchangestoothform.Rowsnea

52、rthetopoffigure4showthatgearswithfewteethhaveatoothformthatdependsstronglyonthevalueoftheprofileshiftcoefficientForgearswithfewteeth,thesensitivitytoprofileshiftnarrowsthechoiceforprofileshiftcoefficientbecausetoolittleprofileshiftresultsinundercutteeth,whereastoomuchprofileshiftgivesteethwithtoplan

53、dsthataretoonarrow.Forexample,theacceptablevaluesofprofileshiftcoefficientfora12toothgearrangefromx=0.4nearundercut,tox=0.44foratoplandthicknessequalto30%ofthemoduleIncontrast,rowsnearthebottomoffigure4showthatgearswithlargenumbersofteetharerelativelyinsensitivetoprofileshiftThismeansthatthegeardesi

54、gnerhaswiderlatitudewhenchoosingprofileshiftforgearswithalargenumberofteeth.Asalimitingcase,theshapeoftheteethofarackareindependentofprofileshiftGenerally,theperformaneeofagearisenhancedwithincreasingnumbersofteethandtheoptimumvalueofprofileshiftForafixedgeardiameter,withtheexceptionofbendingstrengt

55、h,loadcapacityisincreasedwhenthenumberofteethincreasesandtheprofileshiftisdesignedproperly.Resistaneetomacropitting,adhesivewearandscuffingisimprovedandthegearsusuallyoperatemorequietly.ThemaximumnumberofteethislimitedbybendingstrengthbecausealargenumberofrelativelysmallteethhavehighbendingstressesT

56、herefore,thegeardesignermustlimitthenumberofteethinthepinionbasedonmaintainingadequatebendingstrength.Loadcapacitycanbemaximizedbybalancingthepittingresistaneeandthebendingstrengthofthegearset(seeAGMA901-A92).Abalaneeddesignhasarelativelylargenumberofteethinthepinion.Thismakesthegearsetrelativelyins

57、ensitivetoprofileshift,andallowsthedesignertoselecttheprofileshifttominimizespecificsliding,minimizeflashtemperatureorbalaneethebendingfatiguelifeofthepinionandgear.AGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 # #ReturntoMenuAGMA913-A98AMERICANGEARMA

58、NUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 # #ReturntoMenu122030joaqumN50AGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 # #ReturntoMenuAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913

59、-A98 # ReturntoMenu0.41000.80.00.4ProfileshiftcoefficientFigure4EffectofprofileshiftoninvolutetoothprofilesAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAGMA913-A98 #ReturntoMenuAGMA913-A98AMERICANGEARMANUFACTURERSASSOCIATIONAMERICANGEARMANUFACTURERSASSOCIATIONAG

60、MA913-A98 # ReturntoMenu4.2BasicgeargeometryTheminimumprofileshiftcoefficient(toavoidundercut)forthepinionisgivenby:u=wherez23ziZmnZ2mnfn=rU22cosP1rbl=rlcosar=arctantana”cosBarccos%cosqinvar=tanataginva脫=tanawl一awl.(10)(12).(13)-.(14).(15)(16)-.(17).(18)=min1minmnymin=haP0一r山“atwhere(20)(21)hapoisth