PergamonMechanicsResearchCommumcations,Vol.27,No.5,pp.529-538,2000Copyright2000ElsevierScienceLtdPrintedintheUSA.Allrightsreserved0093-6413/00IS-seefrontmatterPlhS0093-6413(00)00126-9DESIGNOFASPRING-ACTUATEDHIGH-SPEEDCAMMECHANISMWITHNON-CONSTANTANGULARVELOCITYK.Y.Ahn,J.H.KimandS.H.KimDepartmentofMechanicalEngineering,KAIST,373-I,Kusong-dong,Yusong-gu,Taejon305-701,Korea(Received11January2000；acceptedforprint24July2000)IntroductionAspring-actuatedcammechanismisasimpleandreliabledeviceformovementofheavyloadsatahighaccelerationandforthecontrolofdynamiccharacteristicsoffollowers.Suchamechanismisusedtoavacuumcircuitbreaker(VCB)whichcompletesswitchingactionwithinseveraltensmilliseconds1.Inthismechanism,theangularvelocityofacamisnotconstantbecausepre-loadedspringsrotatethecam.Forthisreason,conventionaldesigntechniquesassumingthatthecamoperatesataconstantvelocityarenotapplicable.Thedesignofaspring-actuatedoravariablespeedcamhasseldombeenstudiedintheliterature.RothbartdesignedavariablespeedcamactuatedbyaWhitworthquick-returnmechanismusingagraphicalcamprofilesynthesis2.Barkanproposedacamdesignmethodusingtheenergyequationsofasimplifiedspring-actuatedcamsystemforonlysimplelonghandcalculation3.Thelatterauthorsimplyconsideredenergylossasempiricallosscoefficientsintheenergyequations.Thispaperpresentsthedesignmethodforacamwithnon-constantangularvelocitybasedonthedynamicmodelofacompletespring-actuatedcamsystem.Inthederiveddynamicmodel,theexternalforcesandfrictionareincorporated.Thefollowermotion,whichisdependentontherequirementsduringtheclosingperiodofaVCB,isdesignedusingapolynomialfunction.Thecammotionandthecamshapeareobtainedaccordingtotheproposeddesignmethod.Analyzingtheeffectsofthecamshapewithdifferentcaminertia,theinitialcamismodifiedtosatisfythespecificrequirementsofthecamrotationangle.Thesimulationresultsofthedesignedcamarecomparedwiththoseoftheoriginalcam.Spring-actuatedcammechanismFigure1showsaVCBwithaspring-actuatedhigh-speedcammechanism.Theratedvoltageandtheinterruptingcurrentofthebreakerare12kVand40kArespectively.Theessentialpartsofthemechanismconsistofclosing529530K.Y.AHN,J.H.KIMandS.H.KIMspringsthatdrivethecam,afollowerwithopeningsprings,wipespringsthatpushelectriccontacts,andmechanicalpartsincludinglinkagesandlatches.TheclosingprocedureofVCBisasfollows:thecam(0inFig.I)isinitiallyconstrainedbytheclosinglatch(inFig.1).Afterreleasingtheclosinglatch,pre-loadedclosingsprings(inFig.1)rotatethecamandthecampushesthefollower(inFig.1)toaclosedpositionoftheelectriccontacts(inFig.1).Duringtheclosingoperation,theopeningspringsareextendedandthewipespringscompressedaftertheclosingoftheelectriccontacts.Figure2showsthecamvelocityduringtherapidclosingoperationwithin30msec.Itisobtainedbydifferentiatingthecammotionobtainedaccordingtotheproposeddesignmethod.Itcanbeseenthatthecamvelocitybeginsat0rad/sandreachesover-200rad/s.mcamO-supporterelectriccontacts:fixedandmovablecontactI/-,.cmsmgclosinglatch:-.,)(camwfixedopeningspr,ngcontact,.!vh,4)I,Xooenlngot.ivacuumlatchL-.-rollermovableJIcontactff-._/followerwipespring(a)structure(b)representationFig.1Vacuumcircuitbreaker/-tI-2ool-.3oo1o；o12o23o354oTimemsecFig.2CamvelocityduringrapidclosingoperationPerformancecriteriaofclosingoperationPerformancecriteriamaybeimposedondesigningacam.Inthispaper,thesecriteriaareestablishedbyconsideringtherequirementsduringtheclosingoperationofaVCBandacam-followersystem.TheHIGH-SPEEDCAMMECHANISMDESIGN531performancecriteriaduringtheclosingoperationareasfollows:1.Theaverageclosingvelocityofthelast20%ofthefullstroke10mmbetweenthefixedandmovablecontactsmustbe1m/s.Thisvelocityisthemostimportantcriterionbecauseitsviolationreducesthelifetimeofelectriccontacts.2.Thecamrotationfroma0toa,mustcompletethefollowerrotationfrom00to0.Thecamrotationangle,ao-as,mustbelessthan150.Subscriptsoandsdenotetheinitialandthefinalpositionrespectively.Thecamradiusoutsidethisrangeisthesameasthecamradiusofas.3.Whenwipespringsarefullycompressedaftertheclosingofelectriccontacts,thevelocityandaccelerationofthefollowershouldbezero.4.TheoveralloperatingtimeofaVCBmustnotexceed35msec.5.Thecamandthefollowershouldbeincontinuouscontactduringtherapidclosingoperationexceptainitialimpact,whichiscausedbytheinitialclearancebetweencamandfollower.Inthesecondcondition,thecamrotationanglecanbecontrolledbycaminertia.Theinitialcaminertiaisassumedastheoriginalcaminertia.Thecaminertiaofthefinaldesignisdeterminedbysatisfyingthespecificrequirementsofthecamrotationangle.Thelastconditionischeckedfromthesimulationofthefinaldesign.Thefollowermotionbasedonthesecriteriaislaterdesigned.Dynamicsofspring-actuatedcammechanismInthispaper,becausethecamprofileisnotknown,thecamandthefollowerareconsideredasrigidbodiesthatareindependentofeachother.Thecontactforcesbetweencamandfollowerareregardedasexternalforces.Therefore,thecammechanismhastwodegreesoffreedom.TheequationsofmotionofthecamandthefollowerarederivedusingLagrangianequationsrespectively.Consideringthatthecontactforcesareactionandreactionforces,thenonlineardifferentialequationbetweentherotationofcamandfollowerisderived.Forthepurposeofillustration,letusconsiderthesystemmodelshowninFig.3.Here,theconstituentmainlinkssuchascam,followerandmovablecontactsareassumedasrigidbodies.ThecamsupporterisfixedtothegroundframethroughapointO.Theequationsofmotionarederivedasfollows.Generalizedcoordinate:q=a:camangleq2=0:followerangledLoZLagrangesEq.:cltoq,-7(77-)-=Q.r=l,2whereL=T-V:LagrangianQroc:non-conservativegeneralizedforceInFig.3,thekineticandpotentialenergiesare(1)532K.Y.AHN,J.H.KIMandS.H.KIMwhere+7Kw,Xw,+F,LBe(8-8)+Mcghc+M/ghe-M,gLsr(8-8,)I,1z=momentofinertiaofcamandfollowerMc,My,M,=massofcam,follower,andmovablecontactinthevacuuminterruptLBr=distancebetweenapivotpointoffollowerBandapointFFv,=externalforceactingonmovablecontactbythepressuredifferencebetweenatmosphereandvacuum,25kgfh=ACcsin(ct-ct,),06,=/CAChI=BCisin(8+,.),0,=ZCIBEK,Ko,Kw=springstiffnessofclosingspring,openingspring,andwipespringXcs,xos,x,s=displacementalongaxialdirectionofclosingspring,openingspring,andwipespringOc=followeranglewhentheelectriccontactsareclosedfixedcamsupportercontactvacuum0InterrupterclosingCc*movableclosing