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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,ISFIG2SEMIELASTICCONTACTMODELTAKINGFRICTIONINTOACCOUNTSPRINGPOSITIONFIXTUREELEMENTPOSITION12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849FIG3CONTINUOUSINTERPOLATIONFIG4AHOLLOWWORKPIECETABLE2MACHININGPARAMETERSANDCONDITIONSPARAMETERDESCRIPTIONTYPEOFOPERATIONENDMILLINGCUTTERDIAMETER254MMNUMBEROFFLUTES4CUTTERRPM500FEED01016MM/TOOTHRADIALDEPTHOFCUT254MMAXIALDEPTHOFCUT254MMRADIALRAKEANGLE10HELIXANGLE30PROJECTIONLENGTH9207MMINTJADVMANUFTECHNOLILLUSTRATEDINFIG3THREEFIXTUREELEMENTLOCATIONSARESHOWNASBLACKCIRCLESEACHELEMENTLOCATIONISSURROUNDEDBYITSFOURORSIXNEARESTNEIGHBORINGNODESTHESESETSOFNODES,WHICHAREILLUSTRATEDBYBLACKSQUARES,ARE37,38,31AND30,9,10,11,18,17AND16AND26,27,34,41,40AND33ASETOFSPRINGELEMENTSAREATTACHEDTOEACHOFTHESENODESFORANYSETOFNODES,THESPRINGCONSTANTISKIJDIJPK2HIDIKKI6WHEREKIJISTHESPRINGSTIFFNESSATTHEJTHNODESURROUNDINGTHEITHFIXTUREELEMENT,DIJISTHEDISTANCEBETWEENTHEITHFIXTUREELEMENTANDTHEJTHNODESURROUNDINGIT,KIISTHESPRINGSTIFFNESSATTHEITHFIXTUREELEMENTLOCATIONIISTHENUMBEROFNODESSURROUNDINGTHEITHFIXTUREELEMENTLOCATIONFOREACHMACHININGLOADSTEP,APPROPRIATEBOUNDARYCONDITIONSHAVETOBEAPPLIEDTOTHEFINITEELEMENTMODELOFTHEWORKPIECEINTHISWORK,THENORMALSPRINGSARECONSTRAINEDINTHETHREEDIRECTIONSX,Y,ZANDTHETANGENTIALSPRINGSARECONSTRAINEDINTHETANGENTIALDIRECTIONSX,YCLAMPINGFORCESAREAPPLIEDINTHENORMALDIRECTIONZATTHECLAMPNODESTHEENTIRETOOLPATHISSIMULATEDFOREACHFIXTUREDESIGNSCHEMEGENERATEDBYTHEGABYAPPLYINGTHEPEAKX,Y,ZCUTTINGFORCESSEQUENTIALLYTOTHEELEMENTSURFACESOVERWHICHTHECUTTERPASSES23INTHISWORK,CHIPREMOVALFROMTHETOOLPATHISTAKENINTOACCOUNTTHEREMOVALOFTHEMATERIALDURINGMACHININGALTERSTHEGEOMETRY,SODOESTHESTRUCTURALSTIFFNESSOFTHEWORKPIECETHUS,ITISNECESSARYTOCONSIDERCHIPREMOVALAFFECTSTHEFEAMODELISANALYZEDWITHRESPECTTOTOOLMOVEMENTANDCHIPREMOVALUSINGTHEELEMENTDEATHTECHNIQUEINORDERTOCALCULATETHEFITNESSVALUEFORAGIVENFIXTUREDESIGNSCHEME,DISPLACEMENTSARESTOREDFOREACHLOADSTEPTHENTHEMAXIMUMDISPLACEMENTISSELECTEDASFITNESSVALUEFORTHISFIXTUREDESIGNSCHEMETHEINTERACTIONBETWEENGAPROCEDUREANDANSYSISIMPLEMENTEDASFOLLOWSBOTHTHEPOSITIONSOFLOCATORSANDCLAMPS,ANDTHECLAMPINGFORCEAREEXTRACTEDFROMREALSTRINGSTHESEPARAMETERSAREWRITTENTOATEXTFILETHEINPUTBATCHFILEOFANSYSCOULDREADTHESEPARAMETERSANDCALCULATETHEDEFORMATIONOFMACHINEDSURFACESTHUSTHEFITNESSVALUESINGAPROCEDURECANALSOBEWRITTENTOATEXTFILEFORCURRENTFIXTUREDESIGNSCHEMEITISCOSTLYTOCOMPUTETHEFITNESSVALUEWHENTHEREAREALARGENUMBEROFNODESINANFEMMODELTHUSITISNECESSARYTOSPEEDUPTHECOMPUTATIONFORGAPROCEDUREASTHEGENERATIONGOESBY,CHROMOSOMESINTHEPOPULATIONAREGETTINGSIMILARINTHISWORK,CALCULATEDFITNESSVALUESARESTOREDINASQLSERVERDATABASEWITHTHECHROMOSOMESANDFITNESSVALUESGAPROCEDUREFIRSTCHECKSIFCURRENTCHROMOSOMESFITNESSVALUEHASBEENCALCULATEDBEFORE,IFNOT,FIXTUREDESIGNSCHEMEARESENTTOANSYS,OTHERWISEFITNESSVALUESAREDIRECTLYTAKENFROMTHEDATABASETHEMESHINGOFWORKPIECEFEAMODELKEEPSSAMEINEVERYCALCULATINGTIMETHEDIFFERENCEAMONGEVERYCALCULATINGMODELISTHEBOUNDARYCONDITIONSTHUS,THEMESHEDWORKPIECEFEAMODELCOULDBEUSEDREPEATEDLYBYTHE“RESUME”COMMANDINANSYS5CASESTUDYANEXAMPLEOFMILLINGFIXTUREDESIGNOPTIMIZATIONPROBLEMFORALOWRIGIDITYWORKPIECEDISPLAYEDINPREVIOUSRESEARCHPAPERS16,18,22ISPRESENTEDINTHEFOLLOWINGSECTIONSFIG5CANDIDATEREGIONSFORTHELOCATORSANDCLAMPSTABLE3BOUNDOFDESIGNVARIABLESMINIMUMMAXIMUMX/MMZ/MMX/MMZ/MML100762381L276201524381L30381762762L47623811524762C100762762C276201524762F1/N066732F2/N066732INTJADVMANUFTECHNOL51WORKPIECEGEOMETRYANDPROPERTIESTHEGEOMETRYANDFEATURESOFTHEWORKPIECEARESHOWNINFIG4THEMATERIALOFTHEHOLLOWWORKPIECEISALUMINUM390WITHAPOISSONRATIONOF03ANDYOUNGSMODULUSOF71GPATHEOUTLINEDIMENSIONSARE1524MM127MM762MMTHEONETHIRDTOPINNERWALLOFTHEWORKPIECEISUNDERGOINGANENDMILLINGPROCESSANDITSCUTTERPATHISALSOSHOWNINFIG4THEMATERIALOFTHEEMPLOYEDFIXTUREELEMENTSISALLOYSTEELWITHAPOISSONRATIONOF03ANDYOUNGSMODULUSOF220GPA52SIMULATINGANDMACHININGOPERATIONAPERIPHERALENDMILLINGOPERATIONISCARRIEDOUTONTHEEXAMPLEWORKPIECETHEMACHININGPARAMETERSOFTHEOPERATIONAREGIVENINTABLE2BASEDONTHESEPARAMETERS,THEMAXIMUMVALUESOFCUTTINGFORCESTHATARECALCULATEDANDAPPLIEDASELEMENTSURFACELOADSONTHEINNERWALLOFTHEWORKPIECEATTHECUTTERPOSITIONARE33094NTANGENTIAL,39811NRADIALAND2284NAXIALTHEENTIRETOOLPATHISDISCRETIZEDINTO26LOADSTEPSANDCUTTINGFORCEDIRECTIONSAREDETERMINEDBYTHECUTTERPOSITION53FIXTUREDESIGNPLANTHEFIXTUREPLANFORHOLDINGTHEWORKPIECEINTHEMACHININGOPERATIONISSHOWNINFIG5GENERALLY,THE321LOCATORPRINCIPLEISUSEDINFIXTUREDESIGNTHEBASECONTROLS3DEGREESONESIDECONTROLSTWODEGREES,ANDANOTHERORTHOGONALSIDECONTROLSONEDEGREEHERE,ITUSESFOURLOCATORSL1,L2,L3ANDL4ONTHEY0MMFACETOLOCATETHEWORKPIECECONTROLLINGTWODEGREES,ANDTWOCLAMPSC1,C2ONTHEOPPOSITEFACEWHEREY127MM,TOHOLDITONTHEORTHOGONALSIDE,ONELOCATORISNEEDEDTOCONTROLTHEREMAININGDEGREE,WHICHISNEGLECTEDINTHEOPTIMALMODELTHECOORDINATEBOUNDSFORTHELOCATING/CLAMPINGREGIONSAREGIVENINTABLE3SINCETHEREISNOSIMPLERULEOFTHUMBPROCEDUREFORDETERMININGTHECLAMPINGFORCE,ALARGEVALUEOFTHECLAMPINGFORCEOF66732NWASINITIALLYASSUMEDTOACTATEACHCLAMP,ANDTHENORMALANDTANGENTIALCONTACTSTIFFNESSOBTAINEDFROMALEASTSQUARESFITTOEQ5ARE443107N/MAND547107N/MSEPARATELY54GENETICCONTROLPARAMETERSANDPENALTYFUNCTIONTHECONTROLPARAMETERSOFTHEGAAREDETERMINEDEMPIRICALLYFORTHISEXAMPLE,THEFOLLOWINGPARAMETERVALUESAREFIG6CONVERGENCEOFGAFORFIXTURELAYOUTANDCLAMPINGFORCEOPTIMIZATIONPROCEDUREFIG7CONVERGENCEOFTHEFIRSTFUNCTIONVALUESFIG8CONVERGENCEOFTHESECONDFUNCTIONVALUESTABLE4RESULTOFTHEMULTIOBJECTIVEOPTIMIZATIONMODELMULTIOBJECTIVEOPTIMIZATIONX/MMZ/MML11710230641L210816925855L32131556948L412784660202C12298962659C211761525360F1/N167614F2/N382435F1/MM0006568/MM0002683INTJADVMANUFTECHNOLUSEDPS30,PC085,PM001,NMAX100ANDNCMAX20THEPENALTYFUNCTIONFORF1ANDISFVFV50HEREFVCANBEREPRESENTEDBYF1ORWHENNCHGREACHES6THEPROBABILITYOFCROSSOVERANDMUTATIONWILLBECHANGEINTO06AND01SEPARATELY55OPTIMIZATIONRESULTTHECONVERGENCEBEHAVIORFORTHESUCCESSIVEOPTIMIZATIONSTEPSISSHOWNINFIG6,ANDTHECONVERGENCEBEHAVIORSOFCORRESPONDINGFUNCTIONS1AND2ARESHOWNINFIG7ANDFIG8THEOPTIMALDESIGNSCHEMEISGIVENINTABLE456COMPARISONOFTHERESULTSTHEDESIGNVARIABLESANDOBJECTIVEFUNCTIONVALUESOFFIXTUREPLANSOBTAINEDFROMSINGLEOBJECTIVEOPTIMIZATIONANDFROMTHATDESIGNEDBYEXPERIENCEARESHOWNINTABLE5THESINGLEOBJECTIVEOPTIMIZATIONRESULTINTHEPAPER22ISQUOTEDFORCOMPARISONTHESINGLEOBJECTIVEOPTIMIZATIONMETHODHASITSPREPONDERANCECOMPARINGWITHTHATDESIGNEDBYEXPERIENCEINTHISEXAMPLECASETHEMAXIMUMDEFORMATIONHASREDUCEDBY575,THEUNIFORMITYOFTHEDEFORMATIONHASENHANCEDBY604ANDTHEMAXIMUMCLAMPINGFORCEVALUEHASDEGRADEDBY494WHATCOULDBEDRAWNFROMTHECOMPARISONBETWEENTHEMULTIOBJECTIVEOPTIMIZATIONMETHODANDTHESINGLEOBJECTIVEOPTIMIZATIONMETHODISTHATTHEMAXIMUMDEFORMATIONHASREDUCEDBY502,THEUNIFORMITYOFTHEDEFORMATIONHASENHANCEDBY529ANDTHEMAXIMUMCLAMPINGFORCEVALUEHASDEGRADEDBY696THEDEFORMATIONDISTRIBUTIONOFTHEMACHINEDSURFACESALONGCUTTERPATHISSHOWNINFIG9OBVIOUSLY,THEDEFORMATIONFROMTHATOFMULTIOBJECTIVEOPTIMIZATIONMETHODDISTRIBUTESMOSTUNIFORMLYINTHEDEFORMATIONSAMONGTHREEMETHODSWITHTHERESULTOFCOMPARISON,WEARESURETOAPPLYTHEOPTIMALLOCATORSDISTRIBUTIONANDTHEOPTIMALCLAMPINGFORCETOREDUCETHEDEFORMATIONOFWORKPIECEFIGURE10SHOWSTHECONFIGURATIONOFAREALCASEFIXTURE6CONCLUSIONSTHISPAPERPRESENTEDAFIXTURELAYOUTDESIGNANDCLAMPINGFORCEOPTIMIZATIONPROCEDUREBASEDONTHEGAANDFEMTHEOPTIMIZATIONPROCEDUREISMULTIOBJECTIVEMINIMIZINGTHEMAXIMUMDEFORMATIONOFTHEMACHINEDSURFACESANDMAXIMIZINGTHEUNIFORMITYOFTHEDEFORMATIONTHEANSYSSOFTWAREPACKAGEHASBEENUSEDFORFEMCALCULATIONOFFITNESSVALUESTHECOMBINATIONOFGAANDFEMISPROVENTOBEAPOWERFULAPPROACHFORFIXTUREDESIGNOPTIMIZATIONPROBLEMSINTHISSTUDY,BOTHFRICTIONEFFECTSANDCHIPREMOVALEFFECTSARECONSIDEREDINORDERTOREDUCETHECOMPUTATIONTIME,ADATABASEISESTABLISHEDFORTHECHROMOSOMESANDFITNESSVALUES,ANDTHEMESHEDWORKPIECEFEAMODELISREPEATEDLYUSEDINTHEOPTIMIZATIONPROCESSTABLE5COMPARISONOFTHERESULTSOFVARIOUSFIXTUREDESIGNSCHEMESEXPERIMENTALOPTIMIZATIONSINGLEOBJECTIVEOPTIMIZATIONX/MMZ/MMX/MMZ/MML112700127001672034070L213971270014536017070L312700635001840057120L41397006350014626058590C11270038100583056010C21397003810010440022740F1/N248244488F2/N2482125613F1/MM00310120013178/MM00143770005696FIG9DISTRIBUTIONOFTHEDEFORMATIONALONGCUTTERPATHFIG10AREALCASEFIXTURECONFIGURATIONINTJADVMANUFTECHNOLTHETRADITIONALFIXTUREDESIGNMETHODSARESINGLEOBJECTIVEOPTIMIZATIONMETHODORBYEXPERIENCETHERESULTSOFTHISSTUDYSHOWTHATTHEMULTIOBJECTIVEOPTIMIZATIONMETHODISMOREEFFECTIVEINMINIMIZINGTHEDEFORMATIONANDUNIFORMINGTHEDEFORMATIONTHANOTHERTWOMETHODSITISMEANINGFULFORMACHININGDEFORMATIONCONTROLINNCMACHININGREFERENCES1KINGLS,HUTTERI1993THEORETICALAPPROACHFORGENERATINGOPTIMALFIXTURINGLOCATIONSFORPRISMATICWORKPARTSINAUTOMATEDASSEMBLYJMANUFSYST1254094162DEMETEREC1995MINMAXLOADMODELFOROPTIMIZINGMACHINEFIXTUREPERFORMANCEASMEJENGIND11721831863DEMETEREC1998FASTSUPPORTLAYOUTOPTIMIZATIONINTJMACHTOOLSMANUF381011122112394LIB,MELKOTESN1999IMPROVEDWORKPIECELOCATIONACCURACYTHROUGHFIXTURELAYOUTOPTIMIZATIONINTJMACHTOOLSMANUF3968718835LIB,MELKOTESN2001FIXTURECLAMPINGFORCEOPTIMIZATIONANDITSIMPACTONWORKPIECELOCATIONACCURACYINTJADVMANUFTECHNOL1721041136LIB,MELKOTESN2001OPTIMALFIXTUREDESIGNACCOUNTINGFORTHEEFFECTOFWORKPIECEDYNAMICSINTJADVMANUFTECHNOEEJD,HAYNESLS1987FINITEELEMENTANALYSISOFFLEXIBLEFIXTURINGSYSTEMASMEJENGIND10921341398MENASSARJ,DEVRIESWR1991OPTIMIZATIONMETHODSAPPLIEDTOSELECTINGSUPPORTPOSITIONSINFIXTUREDESIGNASMEJENGIND1134124189CAIW,HUSJ,YUANJX1996DEFORMABLESHEETMETALFIXTURINGPRINCIPLES,ALGORITHMSANDSIMULATIONSASMEJMANUFSCIENG118331832410QINGH,ZHANGWH,ZHOUXL2005MODELINGANDOPTIMALDESIGNOFFIXTURECLAMPINGSCHEMEMECHSCITECHNOL244438442,446,INCHINESE11DENGHY,MELKOTESN2006DETERMINATIONOFMINIMUMCLAMPINGFORCESFORDYNAMICALLYSTABLEFIXTURINGINTJMACHTOOLSMANUF467884785712WUNH,CHANKC1996AGENETICALGORITHMBASEDAPPROACHTOOPTIMALFIXTURECONFIGURATIONCOMPUTEENG313/491992413ISHIKAWAY,AOYAMAT1996OPTIMIZATIONOFFIXTURINGCONDITIONBYMEANSOFTHEGENETICALGORITHMTRANSJSCIMANUFENG,PARTC652409241614VALLAPUZHAS,DEMETEREC,CHOUDHURIS,ETAL2002ANINVESTIGATIONINTOTHEUSEOFSPATIALC