夹具设计外文翻译采用遗传算法优化加工夹具定位和加紧位置.docx

夹具设计外文翻译采用遗传算法优化加工夹具定位和加紧位置.docx

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夹具设计外文翻译采用遗传算法优化加工夹具定位和加紧位置

附

录

Machiningfixturelocatingandclampingpositionoptimizationusing

geneticalgorithms

NecmettinKaya*

DepartmentofMechanicalEngineering,UludagUniversity,Go¨ru¨kle,Bursa16059,

TurkeyReceived8July2004;accepted26May2005

Availableonline6September2005

Abstract

Deformationoftheworkpiecemaycausedimensionalproblemsinmachining.Supportsandlocatorsareusedinordertoreducetheerrorcausedbyelasticdeformationoftheworkpiece.Theoptimizationofsupport,locatorandclamplocationsisacriticalproblemtominimizethegeometricerrorinworkpiecemachining.Inthispaper,theapplicationofgeneticalgorithms（GAs）tothefixturelayoutoptimizationispresentedtohandlefixturelayoutoptimizationproblem.Ageneticalgorithmbasedapproachisdevelopedtooptimisefixturelayoutthroughintegratingafiniteelementcoderunninginbatchmodetocomputetheobjectivefunctionvaluesforeachgeneration.Casestudiesaregiventoillustratetheapplicationofproposedapproach.Chromosomelibraryapproachisusedtodecreasethetotalsolutiontime.DevelopedGAkeepstrackofpreviouslyanalyzeddesigns;thereforethenumbersoffunctionevaluationsaredecreasedabout93%.Theresultsofthisapproachshowthatthefixturelayoutoptimizationproblemsaremulti-modalproblems.Optimizeddesignsdonothaveanyapparentsimilaritiesalthoughtheyprovideverysimilarperformances.

Keywords:

Fixturedesign;Geneticalgorithms;Optimization

1.Introduction

Fixturesareusedtolocateandconstrainaworkpieceduringamachiningoperation,minimizingworkpieceandfixturetoolingdeflectionsduetoclampingandcuttingforcesarecriticaltoensuringaccuracyofthemachiningoperation.Traditionally,machiningfixturesaredesignedandmanufacturedthroughtrial-and-error,whichprovetobebothexpensiveandtime-consumingtothemanufacturingprocess.Toensureaworkpieceismanufacturedaccordingtospecifieddimensionsandtolerances,itmustbeappropriatelylocatedandclamped,makingitimperativetodeveloptoolsthatwilleliminatecostlyandtime-consumingtrial-and-errordesigns.Proper

[1]

[2]

[3]

workpiecelocationandfixturedesignarecrucialtoproductqualityintermsofprecision,accuracyandfinishofthemachinedpart.

Theoretically,the3-2-1locatingprinciplecansatisfactorilylocateallprismaticshapedworkpieces.Thismethodprovidesthemaximumrigiditywiththeminimumnumberoffixtureelements.Topositionapartfromakinematicpointofviewmeansconstrainingthesixdegreesoffreedomofafreemovingbody（threetranslationsandthreerotations）.Threesupportsarepositionedbelowtheparttoestablishthelocationoftheworkpieceonitsverticalaxis.Locatorsareplacedontwoperipheraledgesandintendedtoestablishthelocationoftheworkpieceonthexandyhorizontalaxes.Properlylocatingtheworkpieceinthefixtureisvitaltotheoverallaccuracyandrepeatabilityofthemanufacturingprocess.Locatorsshouldbepositionedasfarapartaspossibleandshouldbeplacedonmachinedsurfaceswhereverpossible.Supportsareusuallyplacedtoencompassthecenterofgravityofaworkpieceandpositionedasfarapartaspossibletomaintainitsstability.Theprimaryresponsibilityofaclampinfixtureistosecurethepartagainstthelocatorsandsupports.Clampsshouldnotbeexpectedtoresistthecuttingforcesgeneratedinthemachiningoperation.

Foragivennumberoffixtureelements,themachiningfixturesynthesisproblemisthefindingoptimallayoutorpositionsofthefixtureelementsaroundtheworkpiece.Inthispaper,amethodforfixturelayoutoptimizationusinggeneticalgorithmsispresented.Theoptimizationobjectiveistosearchfora2Dfixturelayoutthatminimizesthemaximumelasticdeformationatdifferentlocationsoftheworkpiece.ANSYSprogramhasbeenusedforcalculatingthedeflectionofthepartunderclampingandcuttingforces.Twocasestudiesaregiventoillustratetheproposedapproach.

2.Reviewofrelatedworks

Fixturedesignhasreceivedconsiderableattentioninrecentyears.However,littleattentionhasbeenfocusedontheoptimumfixturelayoutdesign.MenassaandDeVriesusedFEAforcalculatingdeflectionsusingtheminimizationoftheworkpiecedeflectionatselectedpointsasthedesigncriterion.Thedesignproblemwastodeterminethepositionofsupports.MeyerandLioupresentedanapproachthatuseslinearprogrammingtechniquetosynthesizefixturesfordynamicmachiningconditions.Solutionfortheminimumclampingforcesandlocatorforcesisgiven.LiandMelkoteusedanonlinearprogrammingmethodtosolvethelayoutoptimizationproblem.Themethodminimizesworkpiecelocationerrorsduetolocalizedelastic

[4]

[5]

[6]

[7]

[13]

[16]

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deformationoftheworkpiece.RoyandLiaodevelopedaheuristicmethodtoplanforthebestsupportingandclampingpositions.Taoetal.presentedageometricalreasoningmethodologyfordeterminingtheoptimalclampingpointsandclampingsequenceforarbitrarilyshapedworkpieces.LiaoandHupresentedasystemforfixtureconfigurationanalysisbasedonadynamicmodelwhichanalysesthefixture–workpiecesystemsubjecttotime-varyingmachiningloads.Theinfluenceofclampingplacementisalsoinvestigated.LiandMelkotepresentedafixturelayoutandclampingforceoptimalsynthesisapproachthataccountsforworkpiecedynamicsduringmachining.Acombinedfixturelayoutandclampingforceoptimizationprocedurepresented.Theyusedthecontactelasticitymodelingmethodthataccounts

fortheinfluenceofworkpiecerigidbodydynamicsduringmachining.Amaraletal.

[8]

usedANSYStoverifyfixturedesignintegrity.Theyemployed3-2-1method.The

optimizationanalysisisperformedinANSYS.Tanetal.

[9]

describedthemodeling,

analysisandverificationofoptimalfixturingconfigurationsbythemethodsofforceclosure,optimizationandfiniteelementmodeling.

Mostoftheabovestudiesuselinearornonlinearprogrammingmethodswhichoftendonotgiveglobaloptimumsolution.Allofthefixturelayoutoptimizationproceduresstartwithaninitialfeasiblelayout.Solutionsfromthesemethodsaredependingontheinitialfixturelayout.Theydonotconsiderthefixturelayoutoptimizationonoverallworkpiecedeformation.

TheGAshasbeenproventobeusefultechniqueinsolvingoptimizationproblems

inengineering

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.Fixturedesignhasalargesolutionspaceandrequiresasearch

tooltofindthebestdesign.FewresearchershaveusedtheGAsforfixturedesignandfixturelayoutproblems.Kumaretal.haveappliedbothGAsandneuralnetworks

fordesigningafixture.Marcelin

[14]

hasusedGAstotheoptimizationofsupport

positions.Vallapuzhaetal.

[15]

presentedGAbasedoptimizationmethodthatuses

spatialcoordinatestorepresentthelocationsoffixtureelements.FixturelayoutoptimizationprocedurewasimplementedusingMATLABandthegeneticalgorithmtoolbox.HYPERMESHandMSC/NASTRANwereusedforFEmodel.Vallapuzhaetal.presentedresultsofanextensiveinvestigationintotherelativeeffectivenessofvariousoptimizationmethods.TheyshowedthatcontinuousGAyieldedthebestqualitysolutions.LiandShiudeterminedtheoptimalfixtureconfigurationdesignforsheetmetalassemblyusingGA.MSC/NASTRANhasbeenusedforfitnessevaluation.Liaopresentedamethodtoautomaticallyselecttheoptimalnumbersof

[19]

[10]

locatorsandclampsaswellastheiroptimalpositionsinsheetmetalassemblyfixtures.KrishnakumarandMelkotedevelopedafixturelayoutoptimizationtechniquethatusestheGAtofindthefixturelayoutthatminimizesthedeformationofthemachinedsurfaceduetoclampingandmachiningforcesovertheentiretoolpath.Locatorandclamppositionsarespecifiedbynodenumbers.Abuilt-infiniteelementsolverwasdeveloped.

Someofthestudiesdonotconsidertheoptimizationofthelayoutforentiretoolpathandchipremovalisnottakenintoaccount.Someofthestudiesusednodenumbersasdesignparameters.

Inthisstudy,aGAtoolhasbeendevelopedtofindtheoptimallocatorandclamppositionsin2Dworkpiece.DistancesfromthereferenceedgesasdesignparametersareusedratherthanFEAnodenumbers.FitnessvaluesofrealencodedGAchromosomesareobtainedfromtheresultsofFEA.ANSYShasbeenusedforFEAcalculations.Achromosomelibraryapproachisusedinordertodecreasethesolutiontime.DevelopedGAtoolistestedontwotestproblems.Twocasestudiesaregiventoillustratethedevelopedapproach.Maincontributionsofthispapercanbesummarizedasfollows:

（1）developedaGAcodeintegratedwithacommercialfiniteelementsolver;

（2）GAuseschromosomelibraryinordertodecreasethecomputationtime;

（3）realdesignparametersareusedratherthanFEAnodenumbers;

（4）chipremovalistakenintoaccountwhiletoolforcesmovingontheworkpiece.

3.Geneticalgorithmconcepts

GeneticalgorithmswerefirstdevelopedbyJohnHolland.Goldbergpublishedabookexplainingthetheoryandapplicationexamplesofgeneticalgorithmindetails.Ageneticalgorithmisarandomsearchtechniquethatmimicssomemechanismsofnaturalevolution.Thealgorithmworksonapopulationofdesigns.Thepopulationevolvesfromgenerationtogeneration,graduallyimprovingitsadaptationtotheenvironmentthroughnaturalselection;fitterindividualshavebetterchancesoftransmittingtheircharacteristicstolatergenerations.

Inthealgorithm,theselectionofthenaturalenvironmentisreplacedbyartificialselectionbasedonacomputedfitnessforeachdesign.Thetermfitnessisusedtodesignatethechromosome’schancesofsurvivalanditisessentially