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外文翻译--三段式圆弧凸轮分析设计 英文版.pdf

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外文翻译--三段式圆弧凸轮分析设计 英文版.pdf

AnanalyticaldesignforthreecirculararccamsChiaraLanni,MarcoCeccarelli,GiorgioFiglioliniDipartimentodiMeccanica,Strutture,AmbienteeTerritorio,UniversitC18adiCassino,ViaDiBiasio43,03043CassinoFr,ItalyReceived10July2000accepted22January2002AbstractInthispaperwehavepresentedananalyticaldescriptionforthreecirculararccamprofiles.Ananalyticalformulationforcamprofileshasbeenproposedanddiscussedasafunctionofsizeparametersfordesignpurposes.Numericalexampleshavebeenreportedtoprovethesoundnessoftheanalyticaldesignprocedureandshowtheengineeringfeasibilityofsuitablethreecirculararccams.C2112002ElsevierScienceLtd.Allrightsreserved.1.IntroductionAcamisamechanicalelement,whichisusedtotransmitadesiredmotiontoanothermechanicalelementbydirectsurfacecontact.Generally,acamisamechanism,whichiscomposedofthreedifferentfundamentalpartsfromakinematicviewpoint1,2acam,whichisadrivingelementafollower,whichisadrivenelementandafixedframe.Cammechanismsareusuallyimplementedinmostmodernapplicationsandinparticularinautomaticmachinesandinstruments,internalcombustionenginesandcontrolsystems3.Camandfollowermechanismscanbeverycheap,andsimple.Theyhavefewmovingpartsandcanbebuiltwithverysmallsize.Thedesignofcamprofilehasbeenbasedonsimplygeometriccurves,4,suchasparabolic,harmonic,cycloidalandtrapezoidalcurves2,5andtheircombinations1,2,6,7.Inthispaperwehaveaddressedattentiontocamprofiles,whicharedesignedasacollectionofcirculararcs.Thereforetheyarecalledcirculararccams5,8.Correspondingauthor.Emailaddressceccarelliing.unicas.itM.Ceccarelli.0094114X/02/seefrontmatterC2112002ElsevierScienceLtd.Allrightsreserved.PIIS0094114X02000320MechanismandMachineTheory372002915–924www.elsevier.com/locate/mechmtCirculararccamscanbeeasilymachinedandcanbeusedinlowspeedapplications9.Inaddition,circulararccamscouldbeusedformicromechanismsandnanomechanismssinceverysmallmanufacturingcanbeproperlyobtainedbyusingelementarygeometry.Anundesirablecharacteristicofthistypeofcamisthesuddenchangeintheaccelerationattheprofilepointswherearcsofdifferentradiiarejoined5.Alimitednumberofcirculararcsisusuallyadvisablesothatthedesign,constructionandoperationofcamtransmissioncanbenotverycomplicatedandtheycanbecomeacompromiseforsimplicityandeconomiccharacteristicsthatarethebasicadvantagesofcirculararccams8.Recentlynewattentionhasbeenaddressedtocirculararccamsbyusingdescriptiveviewpoint10,andfordesignpurposes11,12.Inthispaperwehavedescribedthreecirculararccamsbytakingintoconsiderationthegeometricaldesignparameters.Ananalyticalformulationhasbeenproposedforthreecirculararccamsasanextensionofaformulationfortwocirculararccamsthathasbeenpresentedinapreviouspaper12.2.AnanalyticalmodelforthreecirculararccamsAnanalyticalformulationcanbeproposedforthreecirculararccamsinagreementwithdesignparametersofthemodelshowninFigs.1and2.SignificantparametersforamechanicaldesignofathreecirculararccamareFig.18theriseangleas,thedwellanglear,thereturnanglead,theactionangleaa¼asþarþad,themaximumlifth1.Fig.1.Designparametersforgeneralthreecirculararccams.916C.Lannietal./MechanismandMachineTheory372002915–924ThecharacteristiclociofathreecirculararccamsareshowninFig.2asthefirstcircleC1ofthecamprofilewithq1radiusandcentreC1thesecondcircleC2ofthecamprofilewithq2radiusandcentreC2thethirdcircleC3ofthecamprofilewithq3radiusandcentreC3thebasecircleC4withradiusrandthecentreisOtheliftcircleC5ofthecamprofilewithrþh1radiusandcentreOtherollercirclewithradiusqcentredonthefolloweraxis.InadditionsignificantpointsareDC17ðxDyDÞwhichisthepointjoiningC1withC5FC17ðxFyFÞwhichisthepointjoiningC1withC3GC17ðxGyGÞwhichisthepointjoiningC3withC2AC17ðxAyAwhichisthepointjoiningC2withC4.xandyareCartesiancoordinatesofpointswithrespecttothefixedframeOXY,whoseoriginOisapointofthecamrotationaxis.Additionalsignificantlociaret13whichisthecoincidenttangentialvectorbetweenC1andC3t15whichisthecoincidenttangentialvectorbetweenC1andC5t23whichisthecoincidenttangentialvectorbetweenC2andC3t24whichisthecoincidenttangentialvectorbetweenC2andC4.ThemodelshowninFigs.1and2canbeusedtodeduceaformulation,whichcanbeusefulbothforcharacterizinganddesigningthreecirculararccams.AnalyticaldescriptioncanbeproposedwhenthecirclesareformulatedinthesuitableformcircleC1withradiusq21¼ðx1C0xFÞ2þðy1C0yFÞ2passingthroughpointFasx2þy2C02xx1C02yy1C0x2FC0y2Fþ2x1xFþ2y1yF¼0ð1ÞcircleC2withradiusq22¼ðx2C0xAÞ2þðy2C0yAÞ2passingthroughpointAasx2þy2C02xx2C02yy2C0x2AC0y2Aþ2x2xAþ2y2yA¼0ð2ÞcircleC2withradiusq22¼ðx2C0xGÞ2þðy2C0yGÞ2passingthroughpointGasx2þy2C02xx2C02yy2C0x2GC0y2Gþ2x2xGþ2y2yG¼0ð3ÞFig.2.Characteristiclociforthreecirculararccams.C.Lannietal./MechanismandMachineTheory372002915–924917circleC3withradiusq23¼ðx3C0xFÞ2þðy3C0yFÞ2passingthroughpointFasx2þy2C02xx3C02yy3C0x2FC0y2Fþ2x3xFþ2y3yF¼0ð4ÞcircleC3withradiusq23¼ðx3C0xGÞ2þðy3C0yGÞ2passingthroughpointGasx2þy2C02xx3C02yy3C0x2GC0y2Gþ2x3xGþ2y3yG¼0ð5ÞcircleC4withradiusrasx2þy2¼r2ð6ÞcircleC5withradiusrþh1asx2þy2¼ðrþh1Þ2ð7ÞAdditionalcharacteristicconditionscanbeexpressedintheformasthefirstcircleC1andliftcircleC5musthavethesametangentialvectort15atpointDexpressedasxx1þyy1C0x1xDC0y1yD¼0ð8ÞthebasecircleC4andsecondcircleC2musthavethesametangentialvectort24atpointAexpressedasxx2þyy2C0x2xAC0y2yA¼0ð9ÞthesecondcircleC2andthirdcircleC3musthavethesametangentialvectort23atpointGexpressedasxðx3C0x2Þþyðy3C0y2Þþx3xGþy3yGC0x1xGC0y1yG¼0ð10ÞthefirstcircleC1andthesecondcircleC2musthavethesametangentialvectort12atpointFexpressedasxðx1C0x3Þþyðy1C0y3Þþx3xFþy3yFC0x1xFC0y1yF¼0ð11ÞEqs.1–11maydescribeageneralmodelforthreecirculararccamsandcanbeusedtodrawthemechanicaldesignasshowninFig.2.3.AnanalyticaldesignprocedureEqs.1–11canbeusedtodeduceasuitablesystemofequations,whichallowssolvingthecoordinatesofthepointsC1,C2,C3,FandGwhensuitabledataareassumed.Itispossibletodistinguishfourdifferentdesigncasesbyusingtheproposedanalyticaldescription.Inafirstcasewecanconsiderthatthenumericvalueoftheparametersh1,r,as,ar,ad,q1,q2,andcoordinatesofthepointsA,C1,C2,DandGaregiven,andthecoordinatesofpointsC3,Faretheunknowns.Whentheactionangleaaisequalto180C176,thecoordinatexAofpointAisequaltozero.SinceAisthepointjoiningC2andC4thenthecentreC2ofthesecondcircleC2liesontheYaxisandthereforethecoordinatex2ofthecentreC2isequaltozero.ByusingEqs.1–11itis918C.Lannietal./MechanismandMachineTheory372002915–924

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