外文文献原文及译文-动力传动圆锥渐开线齿轮的设计、制造和应用

外文原文APPLICATION,DESIGN,ANDMANUFACTURINGOFCONICALINVOLUTEGEARSFORPOWERTRANSMISSIONSDRJBRNER,KHUMM,DRFJOACHIM,DRHYAKARIA,ZFFRIEDRICHSHAFENAG,88038FRIEDRICHSHAFEN,GERMANY；ABSTRACTCONICALINVOLUTEGEARSBEVELOIDSAREUSEDINTRANSMISSIONSWITHINTERSECTINGORSKEWAXESANDFORBACKLASHFREETRANSMISSIONSWITHPARALLELAXESCONICALGEARSARESPURORHELICALGEARSWITHVARIABLEADDENDUMMODIFICATIONTOOTHTHICKNESSACROSSTHEFACEWIDTHTHEGEOMETRYOFSUCHGEARSISGENERALLYKNOWN,BUTAPPLICATIONSINPOWERTRANSMISSIONSAREMOREORLESSEXCEPTIONALZFHASIMPLEMENTEDBEVELOIDGEARSETSINVARIOUSAPPLICATIONS4WDGEARUNITSFORPASSENGERCARS,MARINETRANSMISSIONSMOSTLYUSEDINYACHTS,GEARBOXESFORROBOTICS,ANDINDUSTRIALDRIVESTHEMODULEOFTHESEBEVELOIDSVARIESBETWEEN07MMAND8MMINSIZE,ANDTHECROSSEDAXESANGLEVARIESBETWEEN0AND25THESEBOUNDARYCONDITIONSREQUIREADEEPUNDERSTANDINGOFTHEDESIGN,MANUFACTURING,ANDQUALITYASSURANCEOFBEVELOIDGEARSFLANKMODIFICATIONS,WHICHARENECESSARYFORACHIEVINGAHIGHLOADCAPACITYANDALOWNOISEEMISSIONINTHECONICALGEARS,CANBEPRODUCEDWITHTHECONTINUOUSGENERATIONGRINDINGPROCESSINORDERTOREDUCETHEMANUFACTURINGCOSTS,THEMACHINESETTINGSASWELLASTHEFLANKDEVIATIONSCAUSEDBYTHEGRINDINGPROCESSCANBECALCULATEDINTHEDESIGNPHASEUSINGAMANUFACTURINGSIMULATIONTHISPRESENTATIONGIVESANOVERVIEWOFTHEDEVELOPMENTOFCONICALGEARSFORPOWERTRANSMISSIONSBASICGEOMETRY,DESIGNOFMACROANDMICROGEOMETRY,SIMULATION,MANUFACTURING,GEARMEASUREMENT,ANDTESTING1INTRODUCTIONINTRANSMISSIONSWITHSHAFTSTHATARENOTARRANGEDPARALLELTOTHEAXIS,TORQUETRANSMISSIONISPOSSIBLEBYMEANSOFVARIOUSDESIGNSSUCHASBEVELORCROWNGEARS,UNIVERSALSHAFTS,ORCONICALINVOLUTEGEARSBEVELOIDSTHEUSEOFCONICALINVOLUTEGEARSISPARTICULARLYIDEALFORSMALLSHAFTANGLESLESSTHAN15,ASTHEYOFFERBENEFITSWITHREGARDTOEASEOFPRODUCTION,DESIGNFEATURES,ANDOVERALLINPUTCONICALINVOLUTEGEARSCANBEUSEDINTRANSMISSIONSWITHINTERSECTINGORSKEWAXESORINTRANSMISSIONSWITHPARALLELAXESFORBACKLASHFREEOPERATIONDUETOTHEFACTTHATSELECTIONOFTHECONEANGLEDOESNOTDEPENDONTHECROSSEDAXESANGLE,PAIRINGISALSOPOSSIBLEWITHCYLINDRICALGEARSASBEVELOIDSCANBEPRODUCEDASEXTERNALANDINTERNALGEARS,AWHOLEMATRIXOFPAIRINGOPTIONSRESULTSANDTHEDESIGNERISPROVIDEDWITHAHIGHDEGREEOFFLEXIBILITYTABLE1CONICALGEARSARESPURORHELICALGEARSWITHVARIABLEADDENDUMCORRECTIONTOOTHTHICKNESSACROSSTHEFACEWIDTHTHEYCANMESHWITHALLGEARSMADEWITHATOOLWITHTHESAMEBASICRACKTHEGEOMETRYOFBEVELOIDSISGENERALLYKNOWN,BUTTHEYHAVESOFARRARELYBEENUSEDINPOWERTRANSMISSIONSNEITHERTHELOADCAPACITYNORTHENOISEBEHAVIOROFBEVELOIDSHASBEENEXAMINEDTOANYGREATEXTENTINTHEPASTSTANDARDSSUCHASISO6336FORCYLINDRICALGEARS,CALCULATIONMETHODS,ANDSTRENGTHVALUESARENOTAVAILABLETHEREFORE,ITWASNECESSARYTODEVELOPTHECALCULATIONMETHOD,OBTAINTHELOADCAPACITYVALUES,ANDCALCULATESPECIFICATIONSFORPRODUCTIONANDQUALITYASSURANCEINTHELAST15YEARS,ZFHASDEVELOPEDVARIOUSAPPLICATIONSWITHCONICALGEARSMARINETRANSMISSIONSWITHDOWNANGLEOUTPUTSHAFTS/1,3/,FIG1STEERINGTRANSMISSIONS/1/LOWBACKLASHPLANETARYGEARSCROSSEDAXESANGLE13FORROBOTS/2/TRANSFERGEARSFORCOMMERCIALVEHICLESDUMPERAUTOMATICCARTRANSMISSIONSFORAWD/4/,FIG22GEARGEOMETRY21MACROGEOMETRYTOPUTITSIMPLY,ABEVELOIDISASPURGEARWITHCONTINUOUSLYCHANGINGADDENDUMMODIFICATIONACROSSTHEFACEWIDTH,ASSHOWNINFIG3TOACCOMPLISHTHIS,THETOOLISTILTEDTOWARDSTHEGEARAXISBYTHEROOTCONEANGLE/1/THISRESULTSINTHEBASICGEARDIMENSIONSHELIXANGLE,RIGHT/LEFTTANTANCOSLR,1COSINTATRANSVERSEPRESSUREANGLERIGHT/LEFTTANCOSTANT,LTR2BASECIRCLEDIAMETERRIGHT/LEFT3LRTNLDRZIM,COSTHEDIFFERINGBASECIRCLESFORTHELEFTANDRIGHTFLANKSLEADTOASYMMETRICALTOOTHPROFILESATHELICALGEARS,FIG3MANUFACTURINGWITHARACKTYPECUTTERRESULTSINATOOTHROOTCONEWITHROOTCONEANGLETHEADDENDUMANGLEISDESIGNEDSOTHATTIPEDGEINTERFERENCESWITHTHEMATINGGEARAREAVOIDEDANDAMAXIMALLYLARGECONTACTRATIOISOBTAINEDTHUS,ADIFFERINGTOOTHHEIGHTRESULTSACROSSTHEFACEWIDTHDUETOTHEGEOMETRICDESIGNLIMITSFORUNDERCUTANDTIPFORMATION,THEPOSSIBLEFACEWIDTHDECREASESASTHECONEANGLEINCREASESSUFFICIENTLYWELLPROPORTIONEDGEARINGISPOSSIBLEUPTOACONEANGLEOFAPPROX1522MICROGEOMETRYTHEPAIRINGOFTWOCONICALGEARSGENERALLYLEADSTOAPOINTSHAPEDTOOTHCONTACTOUTSIDETHISCONTACT,THEREISGAPINGBETWEENTHETOOTHFLANKS,FIG7THEGOALOFTHEGEARINGCORRECTIONDESIGNISTOREDUCETHISGAPINGINORDERTOCREATEAFLATANDUNIFORMCONTACTANEXACTCALCULATIONOFTHETOOTHFLANKISPOSSIBLEWITHTHESTEPBYSTEPAPPLICATIONOFTHEGEARINGLAW/5/,FIG4TOTHATEND,APOINTP1WITHTHERADIUSRP1ANDNORMALVECTORN1ISGENERATEDONTHEORIGINALFLANKTHISGENERATESTHESPEEDVECTORVWITH1P40COSIN11PPRVFORTHEPOINTCREATEDONTHEMATINGFLANK,THERADIALVECTORRP2512PPRAANDTHESPEEDVECTORAPPLY2V60COSIN212PPRVTHEANGULARVELOCITIESAREGENERATEDFROMTHEGEARRATIO712ZTHEANGLEISITERATEDUNTILTHEGEARINGLAWINTHEFORM80121PVNISFULFILLEDTHEMESHINGPOINTPAFOUNDISTHENROTATEDTHROUGHTHEANGLE29212ZAROUNDTHEGEARAXIS,ANDTHISRESULTSINTHECONJUGATEFLANKPOINTP23GEARINGDESIGN31UNDERCUTANDTIPFORMATIONTHEUSABLEFACEWIDTHONTHEBEVELOIDGEARINGISLIMITEDBYTIPFORMATIONONTHEHEELANDUNDERCUTONTHETOEASSHOWNINFIG3THEGREATERTHESELECTEDTOOTHHEIGHTINORDERTOOBTAINALARGERADDENDUMMODIFICATION,THESMALLERTHETHEORETICALLYUSEABLEFACEWIDTHISUNDERCUTONTHETOEANDTIPFORMATIONONTHEHEELRESULTFROMCHANGINGTHEADDENDUMMODIFICATIONALONGTHEFACEWIDTHTHEMAXIMUMUSABLEFACEWIDTHISACHIEVEDWHENTHECONEANGLEONBOTHGEARSOFTHEPAIRINGISSELECTEDTOBEAPPROXIMATELYTHESAMESIZEWITHPAIRSHAVINGASIGNIFICANTLYSMALLERPINION,ASMALLERCONEANGLEMUSTBEUSEDONTHISPINIONTIPFORMATIONONTHEHEELISLESSCRITICALIFTHETIPCONEANGLEISSMALLERTHANTHEROOTCONEANGLE,WHICHOFTENPROVIDESGOODUSEOFTHEAVAILABLEINVOLUTEONTHETOEANDFORSUFFICIENTTIPCLEARANCEINTHEHEEL32FIELDOFACTIONANDSLIDINGVELOCITYTHEFIELDOFACTIONFORTHEBEVELOIDGEARINGISDISTORTEDBYTHERADIALCONICITYWITHATENDENCYTOWARDSTHESHAPEOFAPARALLELOGRAMINADDITION,THEFIELDOFACTIONISTWISTEDDUETOTHEWORKINGPRESSUREANGLECHANGEACROSSTHEFACEWIDTHFIG5SHOWSANEXAMPLEOFTHISTHEREISAROLLAXISONTHEBEVELOIDGEARINGWITHCROSSEDAXESTHEREISNOSLIDINGONTHISAXISASTHEREISONTHEROLLPOINTOFCYLINDRICALGEARPAIRSWITHASKEWEDAXISARRANGEMENT,THEREISALWAYSYETANOTHERAXIALSLIDEINTHETOOTHENGAGEMENTDUETOTHEWORKINGPRESSUREANGLETHATCHANGESACROSSTHEFACEWIDTH,THEREISVARYINGDISTRIBUTIONOFTHECONTACTPATHTOTHETIPANDROOTCONTACTTHUS,SIGNIFICANTLYDIFFERINGSLIDINGVELOCITIESCANRESULTONTHETOOTHTIPANDTHETOOTHROOTALONGTHEFACEWIDTHINTHECENTERSECTION,THESELECTIONOFTHEADDENDUMMODIFICATIONSHOULDBEBASEDONTHESPECIFICATIONSFORTHECYLINDRICALGEARPAIRSTHEROOTCONTACTPATHATTHEDRIVERSHOULDBESMALLERTHANTHETIPCONTACTPATHFIG6SHOWSTHEDISTRIBUTIONOFTHESLIDINGVELOCITYONTHEDRIVEROFABEVELOIDGEARPAIR4CONTACTANALYSISANDMODIFYCATIONS41POINTCONTACTANDEASEOFFATTHEUNCORRECTEDGEARING,THEREISONLYONEPOINTINCONTACTDUETOTHETILTINGOFTHEAXESTHEGAPINGTHATRESULTSALONGTHEPOTENTIALCONTACTLINECANBEAPPROXIMATELYDESCRIBEDBYHELIXCROWNINGANDFLANKLINEANGLEDEVIATIONCROSSEDAXESRESULTINNODIFFERENCEBETWEENTHEGAPSONTHELEFTANDRIGHTFLANKSONSPURGEARSWITHHELICALGEARING,THERESULTINGGAPINGISALMOSTEQUIVALENTWHENBOTHBEVELOIDGEARSSHOWAPPROXIMATELYTHESAMECONEANGLETHEDIFFERENCEBETWEENTHEGAPVALUESONTHELEFTANDRIGHTFLANKSINCREASESASTHEDIFFERENCEBETWEENTHECONEANGLESINCREASESANDASTHEHELIXANGLEINCREASESTHISPROCESSRESULTSINLARGERGAPVALUESONTHEFLANKWITHTHESMALLERWORKINGPRESSUREANGLEFIG7SHOWSTHERESULTINGGAPINGEASEOFFFORABEVELOIDGEARPAIRWITHCROSSEDAXESANDBEVELOIDGEARSWITHANIDENTICALCONEANGLEFIG8SHOWSTHEDIFFERENCESINTHEGAPINGTHATRESULTSFORTHELEFTANDRIGHTFLANKSFORTHESAMECROSSEDAXESANGLEOF10ANDAHELICALANGLEOFAPPROX30THEMEANGAPINGOBTAINEDFROMBOTHFLANKSIS,TOALARGEEXTENT,INDEPENDENTOFTHEHELIXANGLEANDTHEDISTRIBUTIONOFTHECONEANGLETOBOTHGEARSTHESELECTIONOFTHEHELICALANDCONEANGLESONLYDETERMINESTHEDISTRIBUTIONOFTHEMEANGAPINGTOTHELEFTANDRIGHTFLANKSASKEWEDAXISARRANGEMENTRESULTSINADDITIONALINFLUENCEONTHECONTACTGAPINGTHEREISASIGNIFICANTREDUCTIONINTHEEFFECTIVEHELIXCROWNINGONONEFLANKIFTHEAXISPERPENDICULARISIDENTICALTOTHETOTALOFTHEBASERADIIANDTHEDIFFERENCEINTHEBASEHELIXANGLEISEQUIVALENTTOTHEPROJECTEDCROSSEDAXESANGLE,THENTHEGAPINGDECREASESTOZEROANDLINECONTACTAPPEARSHOWEVER,SIGNIFICANTGAPINGREMAINSONTHEOPPOSITEFLANKIFTHEAXISPERPENDICULARISFURTHERENLARGEDUPTOTHEPOINTATWHICHACYLINDRICALCROSSEDHELICALGEARPAIRISOBTAINED,THISRESULTSINEQUIVALENTMINORHELIXCROWNINGINTHEEASEOFFONBOTHFLANKSINADDITIONTOHELIXCROWNING,ANOTABLEPROFILETWISTSEEFIG8ISALSOCHARACTERISTICOFTHEEASEOFFOFHELICALBEVELOIDSTHISPROFILETWISTGROWSSIGNIFICANTLYASTHEHELIXANGLEINCREASESFIG9SHOWSHOWTHEPROFILETWISTONTHEEXAMPLEGEARSETFROMFIG7ISCHANGEDDEPENDINGONTHEHELIXANGLEINORDERTOCOMPENSATEFORTHEEXISTINGGAPINGINTHETOOTHENGAGEMENT,TOPOLOGICALFLANKCORRECTIONSARENECESSARYTHESECORRECTIONSGREATLYCOMPENSATEFORTHEEFFECTIVEHELIXCROWNINGASWELLASTHEPROFILETWISTWITHOUTTHECOMPENSATIONOFTHEPROFILETWIST,ONLYADIAGONALLYPATTERNEDCONTACTSTRIPISOBTAINEDINTHEFIELDOFACTION,ASSHOWNINFIG1042FLANKMODIFICATIONSFORAGIVENDEGREEOFCOMPENSATION,THENECESSARYTOPOGRAPHYCANBEDETERMINEDFROMTHEEXISTINGEASEOFFFIG11SHOWSTHESETYPESOFTYPOGRAPHIES,WHICHWEREPRODUCEDONPROTOTYPESTHECONTACTRATIOSHAVEIMPROVEDGREATLYWITHTHESECORRECTIONSASCANBESEENINFIG12FORUSEINSERIESPRODUCTION,THETARGETISALWAYSTOMANUFACTURESUCHTOPOGRAPHIESONCOMMONLYUSEDGRINDINGMACHINESTHEOPTIONSFORTHISAREDESCRIBEDINSECTION6INADDITIONTOTHEGAPINGCOMPENSATION,TIPRELIEFISALSOBENEFICIALTHISRELIEFREDUCESTHELOADATTHESTARTANDATTHEENDOFMESHINGANDCANALSOPROVIDELOWERNOISEEXCITATIONHOWEVER,TIPRELIEFMANUFACTUREDATBEVELOIDGEARSISNOTCONSTANTINAMOUNTANDLENGTHACROSSTHEFACEWIDTHTHEPROBLEMPRIMARILYOCCURSONGEARINGWITHALARGEROOTCONEANGLEANDATIPCONEANGLEDEVIATINGFROMTHISANGLETHETIPRELIEFATTHETOEISSIGNIFICANTLYLARGERTHANTHATATTHEHEELTHISUNEVENTIPRELIEFMUSTBEACCEPTEDIFRELIEFOFTHESTARTANDENDOFMESHINGISREQUIREDTHEPRODUCTIONOFTIPRELIEFUSINGANOTHERCONEANGLEASTHEROOTCONEANGLEISPOSSIBLEHOWEVER,THISREQUIRESANADDITIONALGRINDINGSTEPONLYFORTHETIPRELIEFINDEPENDENTLYOFTHEGENERATINGGRINDINGPROCESS,TARGETEDFLANKTOPOGRAPHYCANBEMANUFACTUREDBYCORONINGORHONINGTHEAPPLICATIONOFTHISMETHODONBEVELOIDS,HOWEVER,ISSTILLINTHEEARLYSTAGESOFDEVELOPMENT5LOADCAPACITYANDNOISEEXCITATION51APPLICATIONOFTHECALCULATIONSTANDARDSTHEFLANKANDROOTLOADCAPACITYOFBEVELOIDGEARINGCANONLYAPPROXIMATELYBEDETERMINEDUSINGTHECALCULATIONSTANDARDSISO6336,DIN3990,AGMAC95FORCYLINDRICALGEARINGASUBSTITUTECYLINDRICALGEARPAIRHASTOBEUSED,WHICHISDEFINEDBYTHEGEARPARAMETERSATTHECENTEROFTHEFACEWIDTHTHEPROFILEOFTHEBEVELOIDTOOTHISASYMMETRICALTHATCAN,HOWEVER,BEIGNOREDONTHESUBSTITUTEGEARSTHESUBSTITUTECENTERDISTANCEISOBTAINEDBYADDINGUPTHEOPERATINGPITCHRADIIATTHECENTEROFTHEFACEWIDTHWHENVIEWEDACROSSTHEFACEWIDTH,INDIVIDUALPARAMETERSWILLCHANGE,WHICHSIGNIFICANTLYINFLUENCETHELOADCAPACITYTABLE2SHOWSTHEMAININFLUENCESONTHEROOTANDFLANKLOADCAPACITIESTHELARGERNOTCHEFFECTDUETOTHEDECREASEINTHETOOTHROOTFILLETRADIUSTOWARDSTHEHEELISINOPPOSITIONTOTHEINCREASEINTHEROOTTHICKNESSINADDITION,THEREISASMALLERTANGENTIALFORCEONTHELARGEROPERATINGPITCHCIRCLEATTHEHEELATTHESAMETIME,HOWEVER,THEADDENDUMMODIFICATIONONTHEHEELISSMALLERTHEPRIMARYINFLUENCESARENEARLYWELLBALANCEDSOTHATTHELOADCAPACITYCANBECALCULATEDSUFFICIENTLYAPPROXIMATEWITHTHESUBSTITUTEGEARPAIRTHELOADDISTRIBUTIONACROSSTHEFACEWIDTHCANBECONSIDEREDWITHTHEWIDTHFACTORSEGKANDKINDIN/ISOANDSHOULDBEDETERMINEDFROMADDITIONALHFLOADPATTERNANALYSES52USEOFTHETOOTHCONTACTANALYSISAMOREPRECISECALCULATIONOFTHELOADCAPACITYISPOSSIBLEWITHATHREEDIMENSIONALTOOTHCONTACTANALYSIS,ASUSEDATCYLINDRICALGEARPAIRSTHESUBSTITUTECYLINDRICALGEARPAIRCANBEUSEDINTHISANALYSISANDTHECONTACTCONDITIONSARECONSIDEREDVERYWELLWITHFLANKTOPOGRAPHYTHISTOPOGRAPHYISOBTAINEDFROMTHESUPERIMPOSITIONOFTHELOADFREECONTACTEASEOFFWITHTHEFLANKCORRECTIONSUSEDONTHEGEARINTHISPROCESS,THECONTACTLINESAREDETERMINEDONTHESUBSTITUTECYLINDRICALGEARANDTHEYDIFFERSLIGHTLYFROMTHECONTACTATTHEBEVELOIDGEARFIG13SHOWSTHELOADDISTRIBUTIONSCALCULATEDINTHISMANNERASCOMPAREDTOTHELOADPATTERNSRECORDED,ANDAVERYGOODCORRELATIONCANBESEENTHISTOOTHCONTACTANALYSISALSOGENERATESTHETRANSMISSIONERRORRESULTINGFROMTHETOOTHMESHASVIBRATIONALEXCITATIONITCAN,HOWEVER,ONLYBEUSEDASAROUGHGUIDETHEIMPRECISENESSINTHECONTACTBEHAVIORCALCULATEDHASASTRONGEREFFECTONTHETRANSMISSIONERRORTHANITDOESONTHELOADDISTRIBUTION53EXACTMODELINGUSINGTHEFINITEELEMENTMETHODTHESTRESSATTHEBEVELOIDGEARSCANALSOBECALCULATEDUSINGTHEFINITEELEMENTMETHODFIG14SHOWSEXAMPLESOFTHEMODELINGOFTHETRANSVERSESECTIONONTHEGEARSFIG15SHOWSTHECOMPUTERGENERATEDMODELINTHETOOTHMESHSECTIONANDTHESTRESSDISTRIBUTIONCALCULATEDWITHPERMAS/7/ONTHEDRIVENGEARINAMESHPOSITIONTHECALCULATIONWASCARRIEDOUTFORMULTIPLEMESHPOSITIONSANDTHETRANSMISSIONERRORCANBEDETERMINEDFROMTHEROTATIONOFTHEGEARS54TESTSREGARDINGLOADCAPACITYANDNOISEABACKTOBACKTESTBENCHWITHCROSSEDAXES,UPONWHICHGEARPAIRSFROMAWDTRANSMISSIONSWERETESTED,WASUSEDTODETERMINETHELOADCAPACITY,FIG16DIFFERENTCORRECTIONSWEREPRODUCEDONTHETESTGEARSINORDERTOASCERTAINTHEIRINFLUENCEONTHELOADCAPACITYTHEREWASGOODCORRELATIONBETWEENTHELOADCAPACITYINTHETESTANDTHEFEFINITEELEMENTRESULTSPARTICULARLYNOTEWORTHYISANADDITIONALSHIFTOFTHELOADPATTERNTOWARDSTHEHEELDUETOTHEINCREASEDSTIFFNESSINTHISAREATHISSHIFTISNOTDISCERNABLEINTHECALCULATIONWITHTHESUBSTITUTECYLINDRICALGEARPAIRSIMULTANEOUSTOTHELOADCAPACITYTESTS,MEASUREMENTSOFTHETRANSMISSIONERRORANDROTATIONALACCELERATIONWERECONDUCTEDINAUNIVERSALNOISETESTBOX,FIG17INADDITIONTOTHELOADINFLUENCE,THEINFLUENCEOFADDITIONALAXISTILTONTHENOISEEXCITATIONWASALSOEXAMINEDINTHESETESTSWITHREGARDTOTHISAXISTILT,NOLARGEAMOUNTOFSENSITIVITYINTHETESTEDGEARSETSWASFOUND6MANUFACTURINGSIMULATIONWITHTHEASSISTANCEOFTHEMANUFACTURINGSIMULATION,MACHINESETTINGSANDMOVEMENTSWITHCONTINUOUSGENERATIONGRINDINGASWELLASTHEPRODUCEDPROFILETWISTCANBEOBTAINEDPRODUCTIONCONSTRAINEDPROFILETWISTCANBECONSIDEREDASEARLYASTHEDESIGNPHASEOFATRANSMISSIONANDCANBEINCORPORATEDINTOTHELOADCAPACITYANDNOISEANALYSESSIMULATIONSOFTWAREFORTHEMANUFACTURINGOFBEVELOIDSWASSPECIALLYDEVELOPEDATZF,WHICHISCOMPARABLETO/9/61PRODUCTIONMETHODSTHATCANBEUSEDFORBEVELOIDSONLYGENERATINGMETHODSCANBEUSEDTOPRODUCETHEBEVELOIDGEARING,BECAUSETHESHAPEOFTHETOOTHPROFILECHANGESSIGNIFICANTLYALONGTHEFACEWIDTHONLYVERYSLIGHTLYCONICALBEVELOIDSCANBEMANUFACTUREDWITHTHEACKNOWLEDGMENTTHATTHEREISPROFILEANGLEDEVIATIONEVENWITHTHESHAPINGPROCESSHOBSARETHEEASIESTTOUSEFORPRECUTTINGGEARPLANNINGWOULDTHEORETICALLYBEUSEABLEASWELLHOWEVER,THEKINEMATICSREQUIREDMAKESTHISNOTREALLYFEASIBLEONEXISTINGMACHINESINTERNALCONICALGEARSCANTHENONLYBEPRECISELYMANUFACTUREDWITHPINIONTYPECUTTERSIFTHECUTTERAXISISPARALLELTOTHETOOLAXISANDTHECONEISCREATEDBYCHANGINGTHECENTERDISTANCEIFTHEINTERNALGEARISMANUFACTUREDWITHATILTEDPINIONCUTTERAXISSUCHASUSEDFORCROWNGEARS,THISRESULTSINAHOLLOWCROWNINGANDAPROFILETWISTWITHOUTCORRECTIVEMOVEMENTSTHESEDEVIATIONSARESMALLENOUGHTOBEIGNOREDFORMINORCONEANGLESFORFINALPROCESSING,CONTINUOUSGENERATIONGRINDINGWITHAGRINDINGWORMAPPEARSTOBETHEBESTOPTIONIFTHEWORKPIECEORTOOLFIXTURECANBEADDITIONALLYTILTED，THENPARTIALGENERATIONMETHODSAREALSOAPPLICABLEPROCESSINGINATOPOLOGICALGRINDINGPROCESSISALSOPOSSIBLEEG5AXISMACHINES,BUTWITHGREATEFFORT,WHENTHECONEANGLEOFTHEGEARINGCANBECONSIDEREDINTHEMACHINECONTROLINPRINCIPLE,HONINGANDCORONINGCANALSOBEUSEDFORTHEPROCESSINGHOWEVER,THEAPPLICATIONOFTHESEMETHODSINBEVELOIDSSTILLNEEDSEXTENSIVEDEVELOPMENTTHETARGETEDHOLLOWCROWNINGCANBECREATEDINTHEGENERATIONGRINDINGPROCESSINTHEDUALFLANKGRINDINGPROCESSVIAABOWSHAPEDREDUCTIONINTHECENTERDISTANCETHISMETHODRESULTSINAPROFILETWIST,THATISTHEREVERSEOFTHEPROFILETWISTFROMTHECONTACTGAPINGTHUS,THISMETHODPROVIDESEXTENSIVECOMPENSATIONFORTHEPROFILETWISTANDASIGNIFICANTLYMOREVOLUMINOUSLOADPATTERNASISTYPICALONCYLINDRICALGEARS62WORKPIECEGEOMETRYTHEFOLLOWINGWORKPIECEDESCRIPTIONSAREUSEDINTHESIMULATIONINITIALGEARWITHSTOCKALLOWANCEFORTHEGRINDPROCESSINGIDEALGEARFROMTHEGEARDATA,WITHOUTFLANKCORRECTIONSFINISHEDGEARWITHPRODUCTIONCONSTRAINEDDEVIATIONSANDFLANKCORRECTIONS动力传动圆锥渐开线齿轮的设计、制造和应用DRJBRNER,KHUMM,DRFJOACHIM,DRHAKARIA,ZFFRIEDRICHSHAFENAG,88038FRIEDRICHSHAFEN,GERMANY；摘要圆锥渐开线齿轮斜面体齿轮被用于交叉或倾斜轴变速器和平行轴自由侧隙变速器中。圆锥齿轮是在齿宽横断面上具有不同齿顶高修正齿厚的直齿或斜齿圆柱齿轮。这类齿轮的几何形状是已知的，但应用在动力传动上则多少是个例外。ZF公司已将该斜面体齿轮装置应用于各种场合4WD轿车传动装置、船用变速器主要用于快艇机器人齿轮箱和工业传动等领域。斜面体齿轮的模数在07MM8MM之间，交叉传动角在025。之间。这些边界条件需要对斜面体齿轮的设计、制造和质量有一个深入的理解。在锥齿轮传动中为获得高承载能力和低噪声所必须进行的齿侧修形可采用范成法磨削工艺制造。为降低制造成本，机床设定和由于磨削加工造成的齿侧偏差可在设计阶段利用仿真制造进行计算。本文从总体上介绍了动力传动变速器斜面体齿轮的研发，包括基本几何形状、宏观及微观几何形状的设计、仿真、制造、齿轮测量和试验。1前言在变速器中如果各轴轴线不平行的话，转矩传递可采用多种设计，例如伞齿轮或冠齿轮、万向节轴或圆锥渐开线齿轮斜面体齿轮。圆锥渐开线齿轮特别适用于小轴线角度小于15，该齿轮的优点是在制造、结构特点和输入多样性等方而的简易。圆锥渐开线齿轮被用于直角或交叉轴传动的变速器或被用于平行轴自由侧隙工况的变速器。由于锥角的选择并不取决于轴线交角，配对的齿轮也可能采用圆柱齿轮。斜面体齿轮可制成外啮合和内齿轮，整个可选齿轮副矩阵见表1，它为设计者提供了高度的灵活性。圆锥齿轮是在齿宽横截面上具有不同齿顶高修正齿厚量的直齿轮或斜齿轮。它们能与各种用同一把基准齿条刀具切制成的齿轮相啮合。斜面体齿轮的几何形状是已知的，但它们很少应用在动力传动上。过去，未曾对斜面体齿轮的承载能力和噪声进行过任何大范围的试验研究。标准诸如适用于圆柱齿轮的IS06336、计算方法和强度值都是未知的。因此，必须开发计算方法、获得承载能力数值和算出用于生产和质量保证的规范。在过去的15年中，ZF公司已为锥齿轮开发了多种应用1、输出轴具有下倾角的船用变速1、3图12、转向器13、机器人用小齿隙行星齿轮装置交叉轴角度1一324、商用车辆的输送齿轮箱垃圾倾倒车5、AWD用自动变速器4，图22齿轮几何形状21宏观几何形状简而言之，斜面体齿轮可看成是一个在齿宽横截面上连续改变齿顶高修正的圆柱齿轮，如图3。为此，根据齿根锥角刀具向齿轮轴线倾斜1。结果形成了齿轮基圆尺寸。螺旋角，左/右TANTANCOSLLR,COSINTA横向压力角左/右TANCOSTANT,LTR（2）基圆直径左/右3LRTNLDRZIM,COS左右侧不同的基圆导致斜齿轮齿廓形状的不均匀，图3。采用齿条类刀具加工将使得齿根锥具有相应的根锥角。齿顶角设计成这样以使得顶端避免与被啮合齿轮发生干涉，并获得最大接触区域。由此导致在齿宽横截面上具有不同的齿高。由于几何设计限制了根切和齿顶形状，实际齿宽随锥角增加而减小。锥齿轮传动合适的锥角最大约为15。22微观几何形状一对伞齿轮通常形成点状接触。除接触外，在齿侧还存在间隙，如图7。齿轮修形设计的目的是减小这些间隙以形成平坦而均匀的接触。通过逐步应用啮合定律有可能对齿侧进行精确的计算5,图4。最后，在原始侧生成半径为RP和法1向矢量为N的P1点。这生成速度矢量V及对于在啮合一侧所生成的点，有半径11P矢量RP240COSIN11PPRV512PPAR和速度矢量2V0COSIN212PPR（6）角速度根据齿轮速比确定12Z（7）角度被反复迭代直至满足下代。80121PVN啮合点PA偏转角度2212Z（9）绕齿轮轴转动，形成共轭点P。23传动装置设计31根切和齿顶形状斜面体齿轮的可用齿宽受到大端齿顶形状和小端根切的限制，见图3。齿高愈高为获得较大的齿高变位量，理论可用齿宽愈窄。小端根切和大端齿顶形状导致齿高变位量沿齿宽方向发生变化。当一对齿轮的锥角大致相同时可获得最大的可用齿宽。若齿轮副中小齿轮愈小，则该小齿轮必须采用更小的锥角。齿顶锥角小于齿根锥角时，通常能在小端获得有用的渐开线，而在大端处有足够齿顶间隙，这时大端的齿顶形状并不太严重。32工作区域和滑动速度斜面体齿轮工作区域产生扭歪的原因是圆锥半径有形成平行四边形趋势。另外，工作压力角在齿宽横截面方向的改变也造成工作区域的扭曲。图5是一个例子。在交叉轴传动的斜面体齿轮上存在一滚动轴如同圆柱齿轮副的滚动点一样，在该轴上不存在滑动。对于倾斜轴布置而言，在轮齿啮合处总存在另外的轴向滑动。由于工作压力角在齿宽横截面上变化，从小端到大端的接触区内的接触轨迹有很大的变化。因此，沿齿宽方向在齿顶和齿根处具有明显不同的滑动速度。在齿轮中部，齿顶高修正的选择是基于圆柱齿轮副的规范在主动齿轮根部的接触轨迹将小于齿顶的接触轨迹。图6给出了斜面体齿轮副主动齿轮滑动速度的分布。4接触分析和修形41点接触和间隙在未修正齿轮传动中，由于轴线倾斜，通常仅有一点接触。沿可能接触线出现的间隙可大致解释为螺旋凸起和齿侧廓线角度的偏差所致。圆柱齿轮左右侧间隙与轴线交叉无关。对于螺旋齿轮而言，当两斜面体齿轮锥角大致相同时，其产生的间隙也几乎相等。随两齿轮锥角和螺旋角不一致的增加，左右侧间隙的不同程度也增加。在工作压力角较小时将导致更大的间隙。图7给出了具有相同锥角交叉轴传动的斜面体齿轮副所出现的间隙。图8显示了具有相同10交叉轴线和30螺旋角齿轮在左右侧间隙方而的差异。两侧平均间隙的数值在很大程度上与螺旋角无关，但与两齿轮的锥角相关。螺旋角和锥角的选择决定了齿轮左右侧平均间隙的分布。倾斜轴线布置对接触间隙产生额外影响。这将有效减少齿轮一侧的螺旋凸形。如果垂直轴线与总基圆半径相同，并且基圆柱螺旋角之差等于交叉轴角的话,间隙减小到零并出现线接触。然而,在另一侧将出现明显的间隙。如果正交的轴线进一步扩大直至变成圆柱交叉轴螺旋齿轮副的话,其两侧间隙等同于较小的螺旋凸形。除螺旋凸形外,明显的齿廓扭曲见图8也是斜面体齿轮的间隙特征。随螺旋角增加齿廓扭曲也随之增加。图9表明图7所示齿轮装置的齿廓是如何