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PERGAMONMECHANICSRESEARCHCOMMUMCATIONS,VOL27,NO5,PP529538,2000COPYRIGHT2000ELSEVIERSCIENCELTDPRINTEDINTHEUSAALLRIGHTSRESERVED00936413/00ISSEEFRONTMATTERPLHS0093641300001269DESIGNOFASPRINGACTUATEDHIGHSPEEDCAMMECHANISMWITHNONCONSTANTANGULARVELOCITYKYAHN,JHKIMANDSHKIMDEPARTMENTOFMECHANICALENGINEERING,KAIST,373I,KUSONGDONG,YUSONGGU,TAEJON305701,KOREARECEIVED11JANUARY2000;ACCEPTEDFORPRINT24JULY2000INTRODUCTIONASPRINGACTUATEDCAMMECHANISMISASIMPLEANDRELIABLEDEVICEFORMOVEMENTOFHEAVYLOADSATAHIGHACCELERATIONANDFORTHECONTROLOFDYNAMICCHARACTERISTICSOFFOLLOWERSSUCHAMECHANISMISUSEDTOAVACUUMCIRCUITBREAKERVCBWHICHCOMPLETESSWITCHINGACTIONWITHINSEVERALTENSMILLISECONDS\1\INTHISMECHANISM,THEANGULARVELOCITYOFACAMISNOTCONSTANTBECAUSEPRELOADEDSPRINGSROTATETHECAMFORTHISREASON,CONVENTIONALDESIGNTECHNIQUESASSUMINGTHATTHECAMOPERATESATACONSTANTVELOCITYARENOTAPPLICABLETHEDESIGNOFASPRINGACTUATEDORAVARIABLESPEEDCAMHASSELDOMBEENSTUDIEDINTHELITERATUREROTHBARTDESIGNEDAVARIABLESPEEDCAMACTUATEDBYAWHITWORTHQUICKRETURNMECHANISMUSINGAGRAPHICALCAMPROFILESYNTHESIS\2\BARKANPROPOSEDACAMDESIGNMETHODUSINGTHEENERGYEQUATIONSOFASIMPLIFIEDSPRINGACTUATEDCAMSYSTEMFORONLYSIMPLELONGHANDCALCULATION\3\THELATTERAUTHORSIMPLYCONSIDEREDENERGYLOSSASEMPIRICALLOSSCOEFFICIENTSINTHEENERGYEQUATIONSTHISPAPERPRESENTSTHEDESIGNMETHODFORACAMWITHNONCONSTANTANGULARVELOCITYBASEDONTHEDYNAMICMODELOFACOMPLETESPRINGACTUATEDCAMSYSTEMINTHEDERIVEDDYNAMICMODEL,THEEXTERNALFORCESANDFRICTIONAREINCORPORATEDTHEFOLLOWERMOTION,WHICHISDEPENDENTONTHEREQUIREMENTSDURINGTHECLOSINGPERIODOFAVCB,ISDESIGNEDUSINGAPOLYNOMIALFUNCTIONTHECAMMOTIONANDTHECAMSHAPEAREOBTAINEDACCORDINGTOTHEPROPOSEDDESIGNMETHODANALYZINGTHEEFFECTSOFTHECAMSHAPEWITHDIFFERENTCAMINERTIA,THEINITIALCAMISMODIFIEDTOSATISFYTHESPECIFICREQUIREMENTSOFTHECAMROTATIONANGLETHESIMULATIONRESULTSOFTHEDESIGNEDCAMARECOMPAREDWITHTHOSEOFTHEORIGINALCAMSPRINGACTUATEDCAMMECHANISMFIGURE1SHOWSAVCBWITHASPRINGACTUATEDHIGHSPEEDCAMMECHANISMTHERATEDVOLTAGEANDTHEINTERRUPTINGCURRENTOFTHEBREAKERARE12KVAND40KARESPECTIVELYTHEESSENTIALPARTSOFTHEMECHANISMCONSISTOFCLOSING529530KYAHN,JHKIMANDSHKIMSPRINGSTHATDRIVETHECAM,AFOLLOWERWITHOPENINGSPRINGS,WIPESPRINGSTHATPUSHELECTRICCONTACTS,ANDMECHANICALPARTSINCLUDINGLINKAGESANDLATCHESTHECLOSINGPROCEDUREOFVCBISASFOLLOWSTHECAM0INFIGIISINITIALLYCONSTRAINEDBYTHECLOSINGLATCHINFIG1AFTERRELEASINGTHECLOSINGLATCH,PRELOADEDCLOSINGSPRINGSINFIG1ROTATETHECAMANDTHECAMPUSHESTHEFOLLOWERINFIG1TOACLOSEDPOSITIONOFTHEELECTRICCONTACTSINFIG1DURINGTHECLOSINGOPERATION,THEOPENINGSPRINGSAREEXTENDEDANDTHEWIPESPRINGSCOMPRESSEDAFTERTHECLOSINGOFTHEELECTRICCONTACTSFIGURE2SHOWSTHECAMVELOCITYDURINGTHERAPIDCLOSINGOPERATIONWITHIN30MSECITISOBTAINEDBYDIFFERENTIATINGTHECAMMOTIONOBTAINEDACCORDINGTOTHEPROPOSEDDESIGNMETHODITCANBESEENTHATTHECAMVELOCITYBEGINSAT0RAD/SANDREACHESOVER200RAD/SMCAMOSUPPORTERELECTRICCONTACTS\\FIXEDANDMOVABLECONTACTI/,\\CMSMGCLOSINGLATCH\,CAMWFIXEDOPENINGSPR,NG\CONTACT,VH,4I,XOOENLNGOTIVACUUMLATCHLROLLERMOVABLEJICONTACTFF_/FOLLOWERWIPESPRINGASTRUCTUREBREPRESENTATIONFIG1VACUUMCIRCUITBREAKER/TI2OOL3OO1O;O12O23O354OTIME\MSEC\FIG2CAMVELOCITYDURINGRAPIDCLOSINGOPERATIONPERFORMANCECRITERIAOFCLOSINGOPERATIONPERFORMANCECRITERIAMAYBEIMPOSEDONDESIGNINGACAMINTHISPAPER,THESECRITERIAAREESTABLISHEDBYCONSIDERINGTHEREQUIREMENTSDURINGTHECLOSINGOPERATIONOFAVCBANDACAMFOLLOWERSYSTEMTHEHIGHSPEEDCAMMECHANISMDESIGN531PERFORMANCECRITERIADURINGTHECLOSINGOPERATIONAREASFOLLOWS1THEAVERAGECLOSINGVELOCITYOFTHELAST20OFTHEFULLSTROKE10MMBETWEENTHEFIXEDANDMOVABLECONTACTSMUSTBE1M/STHISVELOCITYISTHEMOSTIMPORTANTCRITERIONBECAUSEITSVIOLATIONREDUCESTHELIFETIMEOFELECTRICCONTACTS2THECAMROTATIONFROMA0TOA,MUSTCOMPLETETHEFOLLOWERROTATIONFROM00TO0THECAMROTATIONANGLE,AOAS,MUSTBELESSTHAN150SUBSCRIPTSOANDSDENOTETHEINITIALANDTHEFINALPOSITIONRESPECTIVELYTHECAMRADIUSOUTSIDETHISRANGEISTHESAMEASTHECAMRADIUSOFAS3WHENWIPESPRINGSAREFULLYCOMPRESSEDAFTERTHECLOSINGOFELECTRICCONTACTS,THEVELOCITYANDACCELERATIONOFTHEFOLLOWERSHOULDBEZERO4THEOVERALLOPERATINGTIMEOFAVCBMUSTNOTEXCEED35MSEC5THECAMANDTHEFOLLOWERSHOULDBEINCONTINUOUSCONTACTDURINGTHERAPIDCLOSINGOPERATIONEXCEPTAINITIALIMPACT,WHICHISCAUSEDBYTHEINITIALCLEARANCEBETWEENCAMANDFOLLOWERINTHESECONDCONDITION,THECAMROTATIONANGLECANBECONTROLLEDBYCAMINERTIATHEINITIALCAMINERTIAISASSUMEDASTHEORIGINALCAMINERTIATHECAMINERTIAOFTHEFINALDESIGNISDETERMINEDBYSATISFYINGTHESPECIFICREQUIREMENTSOFTHECAMROTATIONANGLETHELASTCONDITIONISCHECKEDFROMTHESIMULATIONOFTHEFINALDESIGNTHEFOLLOWERMOTIONBASEDONTHESECRITERIAISLATERDESIGNEDDYNAMICSOFSPRINGACTUATEDCAMMECHANISMINTHISPAPER,BECAUSETHECAMPROFILEISNOTKNOWN,THECAMANDTHEFOLLOWERARECONSIDEREDASRIGIDBODIESTHATAREINDEPENDENTOFEACHOTHERTHECONTACTFORCESBETWEENCAMANDFOLLOWERAREREGARDEDASEXTERNALFORCESTHEREFORE,THECAMMECHANISMHASTWODEGREESOFFREEDOMTHEEQUATIONSOFMOTIONOFTHECAMANDTHEFOLLOWERAREDERIVEDUSINGLAGRANGIANEQUATIONSRESPECTIVELYCONSIDERINGTHATTHECONTACTFORCESAREACTIONANDREACTIONFORCES,THENONLINEARDIFFERENTIALEQUATIONBETWEENTHEROTATIONOFCAMANDFOLLOWERISDERIVEDFORTHEPURPOSEOFILLUSTRATION,LETUSCONSIDERTHESYSTEMMODELSHOWNINFIG3HERE,THECONS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