外文翻译--用矢量方程计算共轭凸轮轮廓 英文版.pdf

/EngineeringScienceEngineers,PartC:JournalofMechanicalProceedingsoftheInstitutionofMechanical/content/217/10/1117Theonlineversionofthisarticlecanbefoundat:DOI:10.1243/09544060332251713511172003217:ProceedingsoftheInstitutionofMechanicalEngineers,PartC:JournalofMechanicalEngineeringScienceL-IWuCalculatingconjugatecamprofilesbyvectorequationsPublishedby:Onbehalfof:InstitutionofMechanicalEngineerscanbefoundat:EngineeringScienceProceedingsoftheInstitutionofMechanicalEngineers,PartC:JournalofMechanicalAdditionalservicesandinformationfor/cgi/alertsEmailAlerts:/subscriptionsSubscriptions:/journalsReprints.navReprints:/journalsPermissions.navPermissions:/content/217/10/1117.refs.htmlCitations:WhatisThis?-Oct1,2003VersionofRecordatShanghaiJiaotongUniversityonJanuary13,2013DownloadedfromCalculatingconjugatecamprobullet5lesbyvectorequationsL-IWuDepartmentofPowerMechanicalEngineering,NationalTsingHuaUniversity,Hsinchu30013,TaiwanAbstract:Thispaperpresentsananalyticalapproachfordeterminingtheprobullet5lesofconjugatedisccams.Foraconjugatecammechanism,itstwonormallinesthroughthepointsofcontactandthelineofcentresmustalwaysintersectatacommonpoint,whichisaninstantcentre.Onthisbasis,thecontactpointsbetweentheconjugatecamandthefollowercanbedeterminedaccordingtothelocationsofinstantcentresandfollowerposition.Thecamprobullet5les,thepathsofthecutterandthepressureanglescanthenbeexpressedintheformofparametricvectorequations.Forvarioustypesofconjugatecams,theequationsforsuchexpressionsareformulated,andexamplesareprovidedtoillustratetheapproach.Theprocedureisespeciallysimpletoprogram.Keywords:conjugatecamprobullet5le,instantcentre,vectorNOTATIONAcontactpointBcontactpointCrollercentreddistancebetweentherollercentres,breadthofthebullet6at-facedfollowerDrollercentreefolloweroffsetEpointfdistancefromthecamcentretothefollowerpivotpointGcuttercentreHcuttercentreI12,I13,I23instantcentresiunitvectorjunitvectorlarmlengthofthefollowerLdistanceofthefollowercentrefromthecamcentremeasuredparalleltotherollertranslationLyO2bullet5xedpivotofthecamO3bullet5xedpivotoftheoscillatingfollowerqdistancefromthecamcentretotheinstantcentreI23QlocationoftheinstantcentreI23rbbasecircleradiusrccutterradiusrfradiusoftherollerfollowerSfollowermotionprogramSyttimeVQspeedofpointQ(X,Y)Cartesiancoordinatesystembullet5xedonthecamaA,aBanglesZsubtendingangleofthefollowerarmsycamrotationanglexAangulardisplacementfunctionofthefollowerxAyfA,fBpressureangleso2angularvelocityofthecam1INTRODUCTIONInacammechanism,thefollowermustalwaysbeheldincontactwiththecamthroughoutthemotioncycle,andthisisusuallyaccomplishedbyapositivedriveorareturnspring.Anormalconjugatecammechanismcaneliminatethereturn-springforceandthusresultinlowercontactstresses,whencomparedwiththespring-loadedtype.Thisimportantadvantagemakesitespeciallysuitableforhigh-speedapplications.Toperformsafelyandreliablyitsintendedfunction,however,thecon-jugatecamsmustbeproperlydesignedandaccuratelymanufactured.Therefore,thecamprobullet5lesandthepathsofthecuttercentreshouldbedeterminedanalytically.HansonandChurchill1,employingthetheoryofenvelopes,presentedananalyticalmethodforcomput-ingdisccamprobullet5lecoordinates.Althoughthetheoryofenvelopesisnotalwaystaughtinthecollegecourseofcalculus,thismethodhasbeenwidelyadopted.Ontheotherhand,Davidson2suggestedanothermethodTheMSwasreceivedon9September2002andwasacceptedafterrevisionforpublicationon4August2003.1117C11702#IMechE2003Proc.InstnMech.EngrsVol.217PartC:J.MechanicalEngineeringScienceatShanghaiJiaotongUniversityonJanuary13,2013Downloadedfromusinginstantcentres,buthiscontributionseemstohaveattractedlittleattentionfromkinematicians.Asamatteroffact,theanalyticalmethodusingtheinstantcentreapproachcanprovideaconvenientmeansfordeterminingthedisccamprobullet5leandcuttercoordi-nates.Inaddition,itisapplicabletonotonlythecommonspring-loadedtypebutalsotheconjugatecammechanism.2CONJUGATECAMSWITHANOFFSETTRANSLATINGROLLERFOLLOWERFigure1showsaconjugatecammechanismwithanoffsettranslatingrollerfollower.TherearetwocamsAandB,bullet5xedonacommonshaft.TwofollowerrollersCandD,mountedtoacommonfollower,areeachpushedinoppositedirectionsbytheconjugatecams.SettingupaCartesiancoordinatesystem(X,Y)bullet5xedonthecamandwithitsoriginatthebullet5xedpivotO2,thecamprobullet5lecoordinatesmaybeexpressedintermsofthecamrotationangley,whichismeasuredagainstthedirectionofcamrotationfromthereferenceradialtocamcentre-lineparalleltorollertranslation.Aconjugatecammechanismmaybeconsideredasapermanentcriticalformandmustalwayshavethreevelocityinstantcentres3.AsshowninFig.1,thismeansthatthetwonormallinesthroughthepointsofcontactandthelineofcentresmustalwaysintersectatacommonpoint,theinstantcentreI23,whereIdenotestheinstantcentreandsubscriptsindicatetherelatedlinks.Forsimplicity,inthefollowing,thegroundlinkwillbeconsistentlynumberedas1,thecamas2andthefolloweras3.Forthesakeofclarity,twootherinstantcentresI12andI13arealsolocatedandlabelledinthebullet5gure.BylabellinginstantcentreI23asQandO2Qq,thespeedofpointQonthecamcanbeexpressedasVQqo21whereo2istheangularvelocityofthecam.Inordertoletyhaveacounterclockwiseangle,inthispaper,thecamistorotateclockwise.Ontheotherhand,foratranslatingfollower,allpointsonthefollowerhavethesamevelocity.Therefore,thespeedofpointQonthefollowercanbeexpressedasVQdLydtdLydydydtdLydyo22whereLyisthedisplacementfunctionofthefollower:Lybullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3rbrf2e2qSy3whererbisthebasecircleradiusofcamA,rfistheradiusoftherollerfollower,eistheoffsetandSyisthefollowermotionprogram.(Sincethecamistorotateclockwise,thequantityeisnegativeiftheoffsetistotheright；inthepositionshownitispositive.)Bydebullet5nitionoftheinstantcentre,instantcentreI23(pointQ)isapointcommontolinks2(conjugatecam)and3(follower)havingthesamevelocity.Therefore,fromequations(1)and(2),qdLydydSydy4Asaresult,afterrb,rf,eandSyhavebeenselected,foreachspecibullet5edvalueofy,therollercentreCmaybelocatedbyapplicationofequation(3)andpointQbyapplicationofequation(4).Thepressureangleistheanglebetweenthecommonnormalatthecontactpointandthedirectionofmotionofthefollower4.ForcamA,itistheanglebetweenlinesCQandCE.From4CQE,thepressureanglefAofcamAcanbeexpressedasfAtan1qeLytan11LydSydyec1875Therefore,theparametricequationsfortheprobullet5leFig.1ConjugatedisccamswithanoffsettranslatingrollerfollowerL-IWU1118Proc.InstnMech.EngrsVol.217PartC:J.MechanicalEngineeringScienceC11702#IMechE2003atShanghaiJiaotongUniversityonJanuary13,2013DownloadedfromcoordinatesofcamAareO2AO2EECCA6whereO2Eecosy90iesiny90j7ECLycosyiLysinyj8CArfcosy180fAirfsiny180fAj9Inthesamemanner,afterthedistancebetweenrollercentresdhasbeenselected,theotherrollercentreDmaybelocated.From4DQE,thepressureanglefBofcamBcanbeexpressedasfBtan1qedLytan11dLydSydyec18710Similarly,theparametricequationsfortheprobullet5lecoordinatesofcamBareO2BO2EEDDB11whereEDdLycosy180idLysiny180j12DBrfcosyfBirfsinyfBj13Inpractice,thecutterorgrindingwheelisfrequentlychosenlargerthanthefollowerrollerforreasonablegrindingwearlife5.ThelocationsofthecuttercentresforcuttingcamsAandBarealsoshowninFig.1.Becausethecutterandrollercentresmustlieonacommonnormaltothecamprobullet5le5,normallyoutwardextendingthecamprobullet5lebyalengthofcutterradiusrcobtainsthelocationofthecuttercentre.Inotherwords,forcamA,thecuttercentreGandpointsQ,AandCmustalwayslieonaline.Therefore,theparametricequationsforthecoordinatesofthecuttercentreGareO2GO2EECCG14whereCGrcrfcosyfAircrfsinyfAj15ThelocationofthecuttercentreHforcuttingcamBcanalsobelocatedinthesameway:O2HO2EEDDH16whereDHrcrfcosy180fBircrfsiny180fBj17In