外文翻译--用矢量方程计算共轭凸轮轮廓 英文版.pdf
http:/pic.sagepub.com/EngineeringScienceEngineers,PartC:JournalofMechanicalProceedingsoftheInstitutionofMechanicalhttp:/pic.sagepub.com/content/217/10/1117Theonlineversionofthisarticlecanbefoundat:DOI:10.1243/09544060332251713511172003217:ProceedingsoftheInstitutionofMechanicalEngineers,PartC:JournalofMechanicalEngineeringScienceL-IWuCalculatingconjugatecamprofilesbyvectorequationsPublishedby:http:/www.sagepublications.comOnbehalfof:InstitutionofMechanicalEngineerscanbefoundat:EngineeringScienceProceedingsoftheInstitutionofMechanicalEngineers,PartC:JournalofMechanicalAdditionalservicesandinformationforhttp:/pic.sagepub.com/cgi/alertsEmailAlerts:http:/pic.sagepub.com/subscriptionsSubscriptions:http:/www.sagepub.com/journalsReprints.navReprints:http:/www.sagepub.com/journalsPermissions.navPermissions:http:/pic.sagepub.com/content/217/10/1117.refs.htmlCitations:WhatisThis?-Oct1,2003VersionofRecord>>atShanghaiJiaotongUniversityonJanuary13,2013pic.sagepub.comDownloadedfromCalculatingconjugatecamprobullet5lesbyvectorequationsL-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.MechanicalEngineeringScienceatShanghaiJiaotongUniversityonJanuary13,2013pic.sagepub.comDownloadedfromusinginstantcentres,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:Lybullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3bullet3rbrf2¡e2qSy3whererbisthebasecircleradiusofcamA,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,thepressureanglefAofcamAcanbeexpressedasfAtan¡1q¡eLytan¡11LydSydy¡eµ¶c187¼5Therefore,theparametricequationsfortheprobullet5leFig.1ConjugatedisccamswithanoffsettranslatingrollerfollowerL-IWU1118Proc.InstnMech.EngrsVol.217PartC:J.MechanicalEngineeringScienceC11702#IMechE2003atShanghaiJiaotongUniversityonJanuary13,2013pic.sagepub.comDownloadedfromcoordinatesofcamAareO2AO2EECCA6whereO2Eecosy90¯iesiny90¯j7ECLycosyiLysinyj8CArfcosy180¯¡fAirfsiny180¯¡fAj9Inthesamemanner,afterthedistancebetweenrollercentresdhasbeenselected,theotherrollercentreDmaybelocated.From4DQE,thepressureanglefBofcamBcanbeexpressedasfBtan¡1q¡ed¡Lytan¡11d¡LydSydy¡eµ¶c187¼10Similarly,theparametricequationsfortheprobullet5lecoordinatesofcamBareO2BO2EEDDB11whereEDd¡Lycosy180¯id¡Lysiny180¯j12DBrfcosyfBirfsinyfBj13Inpractice,thecutterorgrindingwheelisfrequentlychosenlargerthanthefollowerrollerforreasonablegrindingwearlife5.ThelocationsofthecuttercentresforcuttingcamsAandBarealsoshowninFig.1.Becausethecutterandrollercentresmustlieonacommonnormaltothecamprobullet5le5,normallyoutwardextendingthecamprobullet5lebyalengthofcutterradiusrcobtainsthelocationofthecuttercentre.Inotherwords,forcamA,thecuttercentreGandpointsQ,AandCmustalwayslieonaline.Therefore,theparametricequationsforthecoordinatesofthecuttercentreGareO2GO2EECCG14whereCGrc¡rfcosy¡fAirc¡rfsiny¡fAj15ThelocationofthecuttercentreHforcuttingcamBcanalsobelocatedinthesameway:O2HO2EEDDH16whereDHrc¡rfcosy180¯fBirc¡rfsiny180¯fBj17Infact,theconjugatecamprobullet5lesofFig.1havebeendrawn,byapplyingtheseequations,tomeetthefollowingrequirements.Thefolloweristorise20mmwithcycloidalmotionwhilethecamrotatesclockwisefrom08to1008,dwellforthenext508,returnwithcycloidalmotionfor1008camrotationanddwellfortheremaining1108.Bothfollowerrollershavethesameradiusof10mm.Theoffseteis12mmandthedistancebetweentherollercentres,d,is113mm.ThebasecircleradiusofcamAis40mm.3CONJUGATECAMSWITHATRANSLATINGFLAT-FACEDFOLLOWERFigure2showsaconjugatecammechanismwithatranslatingbullet6at-facedfollower.SettingupaCartesiancoordinatesystem(X,Y)bullet5xedonthecamandwithitsFig.2Conjugatedisccamswithatranslatingbullet6at-facedfollowerCALCULATINGCONJUGATECAMPROFILESBYVECTOREQUATIONS1119C11702#IMechE2003Proc.InstnMech.EngrsVol.217PartC:J.MechanicalEngineeringScienceatShanghaiJiaotongUniversityonJanuary13,2013pic.sagepub.comDownloadedfrom