外文翻译--三段式圆弧凸轮分析设计 英文版.pdf
Ananalyticaldesignforthreecircular-arccamsChiaraLanni,MarcoCeccarelli*,GiorgioFiglioliniDipartimentodiMeccanica,Strutture,AmbienteeTerritorio,UniversitC18adiCassino,ViaDiBiasio43,03043Cassino(Fr),ItalyReceived10July2000;accepted22January2002AbstractInthispaperwehavepresentedananalyticaldescriptionforthreecircular-arccamproles.Anana-lyticalformulationforcamproleshasbeenproposedanddiscussedasafunctionofsizeparametersfordesignpurposes.Numericalexampleshavebeenreportedtoprovethesoundnessoftheanalyticaldesignprocedureandshowtheengineeringfeasibilityofsuitablethreecircular-arccams.C2112002ElsevierScienceLtd.Allrightsreserved.1.IntroductionAcamisamechanicalelement,whichisusedtotransmitadesiredmotiontoanotherme-chanicalelementbydirectsurfacecontact.Generally,acamisamechanism,whichiscomposedofthreedierentfundamentalpartsfromakinematicviewpoint1,2:acam,whichisadrivingelement;afollower,whichisadrivenel-ementandaxedframe.Cammechanismsareusuallyimplementedinmostmodernapplicationsandinparticularinautomaticmachinesandinstruments,internalcombustionenginesandcontrolsystems3.Camandfollowermechanismscanbeverycheap,andsimple.Theyhavefewmovingpartsandcanbebuiltwithverysmallsize.Thedesignofcamprolehasbeenbasedonsimplygeometriccurves,4,suchas:parabolic,harmonic,cycloidalandtrapezoidalcurves2,5andtheircombinations1,2,6,7.Inthispaperwehaveaddressedattentiontocamproles,whicharedesignedasacollectionofcirculararcs.Thereforetheyarecalledcircular-arccams5,8.*Correspondingauthor.E-mailaddress:ceccarelliing.unicas.it(M.Ceccarelli).0094-114X/02/$-seefrontmatterC2112002ElsevierScienceLtd.Allrightsreserved.PII:S0094-114X(02)00032-0MechanismandMachineTheory37(2002)915924www.elsevier.com/locate/mechmtCircular-arccamscanbeeasilymachinedandcanbeusedinlow-speedapplications9.Inaddition,circular-arccamscouldbeusedformicro-mechanismsandnano-mechanismssinceverysmallmanufacturingcanbeproperlyobtainedbyusingelementarygeometry.Anundesirablecharacteristicofthistypeofcamisthesuddenchangeintheaccelerationattheprolepointswherearcsofdierentradiiarejoined5.Alimitednumberofcircular-arcsisusuallyadvisablesothatthedesign,constructionandoperationofcamtransmissioncanbenotverycomplicatedandtheycanbecomeacompromiseforsimplicityandeconomiccharacteristicsthatarethebasicadvantagesofcircular-arccams8.Recentlynewattentionhasbeenaddressedtocircular-arccamsbyusingdescriptiveviewpoint10,andfordesignpurposes11,12.Inthispaperwehavedescribedthreecircular-arccamsbytakingintoconsiderationthegeo-metricaldesignparameters.Ananalyticalformulationhasbeenproposedforthreecircular-arccamsasanextensionofaformulationfortwocircular-arccamsthathasbeenpresentedinapreviouspaper12.2.Ananalyticalmodelforthreecircular-arccamsAnanalyticalformulationcanbeproposedforthreecircular-arccamsinagreementwithdesignparametersofthemodelshowninFigs.1and2.Signicantparametersforamechanicaldesignofathreecircular-arccamare:Fig.18;theriseangleas,thedwellanglear,thereturnanglead,theactionangleaa¼asþarþad,themaximumlifth1.Fig.1.Designparametersforgeneralthreecircular-arccams.916C.Lannietal./MechanismandMachineTheory37(2002)915924Thecharacteristiclociofathreecircular-arccamsareshowninFig.2as:therstcircleC1ofthecamprolewithq1radiusandcentreC1;thesecondcircleC2ofthecamprolewithq2radiusandcentreC2;thethirdcircleC3ofthecamprolewithq3radiusandcentreC3;thebasecircleC4withradiusrandthecentreisO;theliftcircleC5ofthecamprolewith(rþh1)radiusandcentreO;therollercirclewithradiusqcentredonthefolloweraxis.Inadditionsignicantpointsare:DC17ðxD;yDÞwhichisthepointjoiningC1withC5;FC17ðxF;yFÞwhichisthepointjoiningC1withC3;GC17ðxG;yGÞwhichisthepointjoiningC3withC2;AC17ðxA;yA)whichisthepointjoiningC2withC4.xandyareCartesianco-ordinatesofpointswithrespecttothexedframeOXY,whoseoriginOisapointofthecamrotationaxis.Additionalsignicantlociare:t13whichistheco-incidenttangentialvectorbetweenC1andC3;t15whichisthecoincidenttangentialvectorbetweenC1andC5;t23whichisthecoincidenttangentialvectorbetweenC2andC3;t24whichistheco-incidenttangentialvectorbetweenC2andC4.ThemodelshowninFigs.1and2canbeusedtodeduceaformulation,whichcanbeusefulbothforcharacterizinganddesigningthreecircular-arccams.Analyticaldescriptioncanbeproposedwhenthecirclesareformulatedinthesuitableform:circleC1withradiusq21¼ðx1C0xFÞ2þðy1C0yFÞ2passingthroughpointFasx2þy2C02xx1C02yy1C0x2FC0y2Fþ2x1xFþ2y1yF¼0ð1ÞcircleC2withradiusq22¼ðx2C0xAÞ2þðy2C0yAÞ2passingthroughpointAasx2þy2C02xx2C02yy2C0x2AC0y2Aþ2x2xAþ2y2yA¼0ð2ÞcircleC2withradiusq22¼ðx2C0xGÞ2þðy2C0yGÞ2passingthroughpointGasx2þy2C02xx2C02yy2C0x2GC0y2Gþ2x2xGþ2y2yG¼0ð3ÞFig.2.Characteristiclociforthreecircular-arccams.C.Lannietal./MechanismandMachineTheory37(2002)915924917circleC3withradiusq23¼ðx3C0xFÞ2þðy3C0yFÞ2passingthroughpointFasx2þy2C02xx3C02yy3C0x2FC0y2Fþ2x3xFþ2y3yF¼0ð4ÞcircleC3withradiusq23¼ðx3C0xGÞ2þðy3C0yGÞ2passingthroughpointGasx2þy2C02xx3C02yy3C0x2GC0y2Gþ2x3xGþ2y3yG¼0ð5ÞcircleC4withradiusrasx2þy2¼r2ð6ÞcircleC5withradius(rþh1)asx2þy2¼ðrþh1Þ2ð7ÞAdditionalcharacteristicconditionscanbeexpressedintheformastherstcircleC1andliftcircleC5musthavethesametangentialvectort15atpointDexpressedasxx1þyy1C0x1xDC0y1yD¼0ð8ÞthebasecircleC4andsecondcircleC2musthavethesametangentialvectort24atpointAex-pressedasxx2þyy2C0x2xAC0y2yA¼0ð9ÞthesecondcircleC2andthirdcircleC3musthavethesametangentialvectort23atpointGex-pressedasxðx3C0x2Þþyðy3C0y2Þþx3xGþy3yGC0x1xGC0y1yG¼0ð10ÞtherstcircleC1andthesecondcircleC2musthavethesametangentialvectort12atpointFexpressedasxðx1C0x3Þþyðy1C0y3Þþx3xFþy3yFC0x1xFC0y1yF¼0ð11ÞEqs.(1)(11)maydescribeageneralmodelforthreecircular-arccamsandcanbeusedtodrawthemechanicaldesignasshowninFig.2.3.AnanalyticaldesignprocedureEqs.(1)(11)canbeusedtodeduceasuitablesystemofequations,whichallowssolvingtheco-ordinatesofthepointsC1,C2,C3,FandGwhensuitabledataareassumed.Itispossibletodistinguishfourdierentdesigncasesbyusingtheproposedanalyticalde-scription.Inarstcasewecanconsiderthatthenumericvalueoftheparametersh1,r,as,ar,ad,q1,q2,andco-ordinatesofthepointsA,C1,C2,DandGaregiven,andtheco-ordinatesofpointsC3,Faretheunknowns.Whentheactionangleaaisequalto180C176,theco-ordinatexAofpointAisequaltozero.SinceAisthepointjoiningC2andC4thenthecentreC2ofthesecondcircleC2liesontheYaxisandthereforetheco-ordinatex2ofthecentreC2isequaltozero.ByusingEqs.(1)(11)itis918C.Lannietal./MechanismandMachineTheory37(2002)915924