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65ClaudiaMariPopa,DinelPopaOptimisationMethodsforCamMechanismsAbstract.Inthispaperwepresentthecriteriawhichrepresentthebaseofoptimizingthecammechanismsandalsoweperformthecalculationsforseveraltypesofmechanisms.Westudytheinfluenceoftheconstructiveparametersincaseofthesimplemachineswithrotationcamandfollower(flatorcurve)oftranslationonthecurvatureradiusandthatofthetransmissionangle.Asitfollows,wepresenttheoptimizationcalculationsofthecamandflatrotationfollowermechanisms,aswellasthecalculationsforoptimizingthecammechanismsbycirculargroovefollowershelp.Foraneasierinterpretationoftheresults,wehavevisualizedtheobtainedcaminAutoCADaccordingtothescriptfilesgeneratedbyacalculationprogram.Keywords:cam,curvatureradius,constructiveparameters,pressureangle,circulargrove.1.OptimisationcriteriaThetermofoptimizationcomesfromtheLatinwordoptimus,whichisthesu-perlativeofgood,whichmeansthebest,verygood,properlyindicated,suitedetc.AccordingtoExplainingDictionaryofRomanianLanguage,byoptimizationisunder-stoodtechnicallytheensembleofscientificresearch(papers)thatislookingforthebestoptioninfindingasolutionforaproblemor,accordingtoanotherdefinition,theprocessofconstantimprovinguntilthebestsolutionitisreached.Mathematically,byoptimizationisunderstoodthereasoning,thecalculuspermitsinfindingvaluesofoneormoreparameterswhichcorrespondtothemaximumofafunction.Inthecaseofacammechanism,oneoftheoptimizationcriteriaisthecriteriaofthecurvatureradius,accordingtothat,thecurvatureradiusofthecaminthecaseofafollowerwhichisflatorhasapositivecurvatureradiusmustbepositiveandevenhigherthenanimposedvalue.ANALELEUNIVERSITII“EFTIMIEMURGU”REIAANULXVII,NR.1,2010,ISSN1453-739766Anothercriteriathatmustbetakenintoaccountisthatofthepressureangle(notedwith)whichmustfulfilltheconditioncr,where030=cratin-creasingand060atdecreasing.Onthebasisofthistwocriteriawillbeobtainedbetterconditionforthecom-plexcammechanismstofunction.Nextwewilldefineasatechnicallyfunctionalcamthecamthatisobtainedbyclassicproceduresofprocessingofatoolmachine,havingthecurvatureradiuspositiveandthatrespectstheconditionofthecriticalpressureangle(cr).2.Theoptimisationofsimplecammechanismswithtransla-tionfollowerThereisconsideredthecaseofaflatfollower(fig.1),casewherethepara-metricalcoordinatesofthecamare:,sincos)(;cossin)(00ssRyssRx+=+=(1)and.2sAO=(2)xOA2OYysRX0Figure1.Mechanismwithrotationcamandflattranslationfollower.From(1)arededucted:;sin)(;cos)(00ssRyssRx+=+=(3),cos)(sin)(;sin)(cos)(00ssRssyssRssx+=+=(4)anditsalsodeductedtheexpressionofthecurvatureradius:67|)()(2/322yxyxyxRc+=;0ssRRc+=.(5)If,forexample,thedisplacementlawis:)2cos1(0=hs.(6)Thenthecurvatureradiusis2cos3000hhRRc+=(7)andbecomesminimumfor2pi=whenisgivenby:00min2hRRc=.(8)Inthiscase,forhR20=theminimumcurvatureradiusbecomesnullandthecamhastheshapefromfigure2,a,andif002hRthecurvatureradiusiscanceledinthepointswhere2pi;pipi2(fig.2,b)andhavenegativevaluefor2piandthecambecomesnonfunctional.Ifweuseflatfollowerintheseconditionswecanobtaincamstechnicallyfunctional.yxyxFigure2.Nonfunctionalcamswithnullornegativecurvatureradius.Letusconsiderthegeneralcasewherethecurvatureradiusatthetopinthecaseofaflatfollowerbecomesnegative0)(max0+ssRandtodeterminetheradiusrofthecircularfollowersothatthecamwillbefunctionally.Theequationsofthefollowersgroove(fig.3)are,cos;sin22ryrx=(8)andfromtheequalities:68,coscossin;sinsincos0rsrRyxyryxxAA+=(9)aredeductedtheequationsofthecurvaturefamily),()cos(cos)();,()sin(sin)(210frsrRyfrsrRx=+=+=;(10)thatdependsontheparameters,.OxAr220vA2R+r+syXyxYFigure3.Mechanismwithrotationcamandflatrotationfollower.Theequationoftheen
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