ORIGINALARTICLEDEFORMATIONCONTROLTHROUGHFIXTURELAYOUTDESIGNANDCLAMPINGFORCEOPTIMIZATIONWEIFANGCHEN2JJJC12C12C12C12NJJC0C1SJ12N1SUBJECTTOMFNIJJC21F2TIF2HIQ2FNIC2103POSI2VII12P4WHEREJREFERSTOTHEMAXIMUMELASTICDEFORMATIONATAMACHININGREGIONINTHEJTHSTEPOFTHEMACHININGOPERATION,XNJ1JC0C0C16C172C30NVUUTISTHEAVERAGEOFJFNIISTHENORMALFORCEATTHEITHCONTACTPOINTISTHESTATICCOEFFICIENTOFFRICTIONFTIFHIARETHETANGENTIALFORCESATTHEITHCONTACTPOINTPOSIISTHEITHCONTACTPOINTVIISTHECANDIDATEREGIONOFTHEITHCONTACTPOINTTHEOVERALLPROCESSISILLUSTRATEDINFIG1TODESIGNAFEASIBLEFIXTURELAYOUTANDTOOPTIMIZETHECLAMPINGFORCETHEMAXIMALCUTTINGFORCEISCALCULATEDINCUTTINGMODELANDTHEFORCEISSENTTOFINITEELEMENTANALYSISFEAMODELOPTIMIZATIONPROCEDURECREATESSOMEFIXTURELAYOUTANDCLAMPINGFORCEWHICHARESENTTOTHEFEAMODELTOOINFEABLOCK,MACHININGDEFORMATIONUNDERTHECUTTINGFORCEANDTHECLAMPINGFORCEISCALCULATEDUSINGFINITEELEMENTMETHODUNDERACERTAINFIXTURELAYOUT,ANDTHEDEFORMATIONISTHENSENTTOOPTIMIZATIONPROCEDURETOSEARCHFORANOPTIMALFIXTURESCHEME4FIXTURELAYOUTDESIGNANDCLAMPINGFORCEOPTIMIZATION41AGENETICALGORITHMGENETICALGORITHMSGAAREROBUST,STOCHASTICANDHEURISTICOPTIMIZATIONMETHODSBASEDONBIOLOGICALREPRODUCTIONPROCESSESTHEBASICIDEABEHINDGAISTOSIMULATE“SURVIVALOFTHEFITTEST”PHENOMENAEACHINDIVIDUALCANDIDATEINTHEPOPULATIONISASSIGNEDAFITNESSVALUETHROUGHAFITNESSFUNCTIONTAILOREDTOTHESPECIFICPROBLEMTHEGATHENCONDUCTSREPRODUCTION,CROSSOVERANDMUTATIONPROCESSESTOELIMINATEUNFITINDIVIDUALSANDTHEPOPULATIONEVOLVESTOTHENEXTGENERATIONSUFFICIENTNUMBEROFEVOLUTIONSOFTHEPOPULATIONBASEDONTHESEOPERATORSLEADTOANINCREASEINTHEGLOBALFITNESSOFTHEPOPULATIONANDTHEFITTESTINDIVIDUALREPRESENTSTHEBESTSOLUTIONTHEGAPROCEDURETOOPTIMIZEFIXTUREDESIGNTAKESFIXTURELAYOUTANDCLAMPINGFORCEASDESIGNVARIABLESTOGENERATESTRINGSWHICHREPRESENTDIFFERENTLAYOUTSTHESTRINGSARECOMPAREDTOTHECHROMOSOMESOFNATURALEVOLUTION,ANDTHESTRING,WHICHGAFINDOPTIMAL,ISMAPPEDTOTHEOPTIMALFIXTUREDESIGNSCHEMEINTHISSTUDY,THEGENETICALGORITHMANDDIRECTSEARCHTOOLBOXOFMATLABAREEMPLOYEDTHECONVERGENCEOFGAISCONTROLLEDBYTHEPOPULATIONSIZEPS,THEPROBABILITYOFCROSSOVERPCANDTHEPROBABILITYOFMUTATIONSPMONLYWHENNOCHANGEINTHEBESTVALUEOFFITNESSFUNCTIONINAPOPULATION,NCHG,REACHESAPREDEFINEDVALUENCMAX,ORTHENUMBEROFGENERATIONS,N,REACHESTHESPECIFIEDMAXIMUMNUMBEROFEVOLUTIONS,NMAX,DIDTHEGASTOPTHEREAREFIVEMAINFACTORSINGA,ENCODING,FITNESSFUNCTION,GENETICOPERATORS,CONTROLPARAMETERSANDCONSTRAINTSINTHISPAPER,THESEFACTORSARESELECTEDASWHATISLISTEDINTABLE1SINCEGAISLIKELYTOGENERATEFIXTUREDESIGNSTRINGSTHATDONOTCOMPLETELYRESTRAINTHEFIXTUREWHENSUBJECTEDTOMACHININGLOADSTHESESOLUTIONSARECONSIDEREDINFEASIBLEANDTHEPENALTYMETHODISUSEDTODRIVETHEGATOAFEASIBLESOLUTIONAFIXTUREDESIGNSCHEMEISCONSIDEREDINFEASIBLEORUNCONSTRAINEDIFTHEREACTIONSATTHELOCATORSARENEGATIVE,INOTHERWORDS,ITDOESNOTSATISFYTHECONSTRAINTSINEQUATIONS2AND3THEPENALTYMETHODESSENTIALLYINVOLVESMACHININGPROCESSMODELFEAOPTIMIZATIONPROCEDURECUTTINGFORCESFITNESSOPTIMIZATIONRESULTFIXTURELAYOUTANDCLAMPINGFORCEFIG1FIXTURELAYOUTANDCLAMPINGFORCEOPTIMIZATIONPROCESSTABLE1SELECTIONOFGASPARAMETERSFACTORSDESCRIPTIONENCODINGREALSCALINGRANKSELECTIONREMAINDERCROSSOVERINTERMEDIATEMUTATIONUNIFORMCONTROLPARAMETERSELFADAPTINGINTJADVMANUFTECHNOLASSIGNINGAHIGHOBJECTIVEFUNCTIONVALUETOTHESCHEMETHATISINFEASIBLE,THUSDRIVINGITTOTHEFEASIBLEREGIONINSUCCESSIVEITERATIONSOFGAFORCONSTRAINT4,WHENNEWINDIVIDUALSAREGENERATEDBYGENETICOPERATORSORTHEINITIALGENERATIONISGENERATED,ITISNECESSARYTOCHECKUPWHETHERTHEYSATISFYTHECONDITIONSTHEGENUINECANDIDATEREGIONSARETHOSEEXCLUDINGINVALIDREGIONSINORDERTOSIMPLIFYTHECHECKING,POLYGONSAREUSEDTOREPRESENTTHECANDIDATEREGIONSANDINVALIDREGIONSTHEVERTEXOFTHEPOLYGONSAREUSEDFORTHECHECKINGTHE“INPOLYGON”FUNCTIONINMATLABCOULDBEUSEDTOHELPTHECHECKING42FINITEELEMENTANALYSISTHESOFTWAREPACKAGEOFANSYSISUSEDFORFEACALCULATIONSINTHISSTUDYTHEFINITEELEMENTMODELISASEMIELASTICCONTACTMODELCONSIDERINGFRICTIONEFFECT,WHERETHEMATERIALSAREASSUMEDLINEARLYELASTICASSHOWNINFIG2,EACHLOCATORORSUPPORTISREPRESENTEDBYTHREEORTHOGONALSPRINGSTHATPROVIDERESTRAINSINTHEX,YANDZDIRECTIONSANDEACHCLAMPISSIMILARTOLOCATORBUTCLAMPINGFORCEINNORMALDIRECTIONTHESPRINGINNORMALDIRECTIONISCALLEDNORMALSPRINGANDTHEOTHERTWOSPRINGSARECALLEDTANGENTIALSPRINGSTHECONTACTSPRINGSTIFFNESSCANBECALCULATEDACCORDINGTOTHEHERZCONTACTTHEORY8ASFOLLOWSKIZ16RC3IEC32I9C16C1713FIZ13KIZKIY6EC3I2C0VFIGFI2C0VWIGWIC16C17C01C1KIZ85WHEREKIZ,KIX,KIYARETHETANGENTIALANDNORMALCONTACTSTIFFNESS,1RC3I1RWI1RFIISTHENOMINALCONTACTRADIUS,1EC3I1C0V2WIEWI1C0V2FIEFIISTHENOMINALCONTACTELASTICMODULUS,RWI,RFIARERADIUSOFTHEITHWORKPIECEANDFIXTUREELEMENT,EWI,EFIAREYOUNGSMODULIFORTHEITHWORKPIECEANDFIXTUREMATERIALS,WI,FIAREPOISSONRATIOSFORTHEITHWORKPIECEANDFIXTUREMATERIALS,GWI,GFIARESHEARMODULIFORTHEITHWORKPIECEANDFIXTUREMATERIALSANDFIZISTHEREACTIONFORCEATTHEITHCONTACTPOINTINTHEZDIRECTIONCONTACTSTIFFNESSVARIESWITHTHECHANGEOFCLAMPINGFORCEANDFIXTURELAYOUTAREASONABLELINEARAPPROXIMATIONOFTHECONTACTSTIFFNESSCANBEOBTAINEDFROMALEASTSQUARESFITTOTHEABOVEEQUATIONTHECONTINUOUSINTERPOLATION,WHICHISUSEDTOAPPLYBOUNDARYCONDITIONSTOTHEWORKPIECEFEAMODEL,ISFIG2SEMIELASTI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