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MachiningfixturelocatingandclampingpositionoptimizationusinggeneticalgorithmsNecmettinKaya*DepartmentofMechanicalEngineering,UludagUniversity,Go¨ru¨kle,Bursa16059,TurkeyReceived8July2004;accepted26May2005Availableonline6September2005AbstractDeformationoftheworkpiecemaycausedimensionalproblemsinmachining.Supportsandlocatorsareusedinordertoreducetheerrorcausedbyelasticdeformationoftheworkpiece.Theoptimizationofsupport,locatorandclamplocationsisacriticalproblemtominimizethegeometricerrorinworkpiecemachining.Inthispaper,theapplicationofgeneticalgorithms(GAs)tothefixturelayoutoptimizationispresentedtohandlefixturelayoutoptimizationproblem.Ageneticalgorithmbasedapproachisdevelopedtooptimisefixturelayoutthroughintegratingafiniteelementcoderunninginbatchmodetocomputetheobjectivefunctionvaluesforeachgeneration.Casestudiesaregiventoillustratetheapplicationofproposedapproach.Chromosomelibraryapproachisusedtodecreasethetotalsolutiontime.DevelopedGAkeepstrackofpreviouslyanalyzeddesigns;thereforethenumbersoffunctionevaluationsaredecreasedabout93%.Theresultsofthisapproachshowthatthefixturelayoutoptimizationproblemsaremulti-modalproblems.Optimizeddesignsdonothaveanyapparentsimilaritiesalthoughtheyprovideverysimilarperformances.Keywords:Fixturedesign;Geneticalgorithms;Optimization1.IntroductionFixturesareusedtolocateandconstrainaworkpieceduringamachiningoperation,minimizingworkpieceandfixturetoolingdeflectionsduetoclampingandcuttingforcesarecriticaltoensuringaccuracyofthemachiningoperation.Traditionally,machiningfixturesaredesignedandmanufacturedthroughtrial-and-error,whichprovetobebothexpensiveandtime-consumingtothemanufacturingprocess.Toensureaworkpieceismanufacturedaccordingtospecifieddimensionsandtolerances,itmustbeappropriatelylocatedandclamped,makingitimperativetodeveloptoolsthatwilleliminatecostlyandtime-consumingtrial-and-errordesigns.Properworkpiecelocationandfixturedesignarecrucialtoproductqualityintermsofprecision,accuracyandfinishofthemachinedpart.Theoretically,the3-2-1locatingprinciplecansatisfactorilylocateallprismaticshapedworkpieces.Thismethodprovidesthemaximumrigiditywiththeminimumnumberoffixtureelements.Topositionapartfromakinematicpointofviewmeansconstrainingthesixdegreesoffreedomofafreemovingbody(threetranslationsandthreerotations).Threesupportsarepositionedbelowtheparttoestablishthelocationoftheworkpieceonitsverticalaxis.Locatorsareplacedontwoperipheraledgesandintendedtoestablishthelocationoftheworkpieceonthexandyhorizontalaxes.Properlylocatingtheworkpieceinthefixtureisvitaltotheoverallaccuracyandrepeatabilityofthemanufacturingprocess.Locatorsshouldbepositionedasfarapartaspossibleandshouldbeplacedonmachinedsurfaceswhereverpossible.Supportsareusuallyplacedtoencompassthecenterofgravityofaworkpieceandpositionedasfarapartaspossibletomaintainitsstability.Theprimaryresponsibilityofaclampinfixtureistosecurethepartagainstthelocatorsandsupports.Clampsshouldnotbeexpectedtoresistthecuttingforcesgeneratedinthemachiningoperation.Foragivennumberoffixtureelements,themachiningfixturesynthesisproblemisthefindingoptimallayoutorpositionsofthefixtureelementsaroundtheworkpiece.Inthispaper,amethodforfixturelayoutoptimizationusinggeneticalgorithmsispresented.Theoptimizationobjectiveistosearchfora2Dfixturelayoutthatminimizesthemaximumelasticdeformationatdifferentlocationsoftheworkpiece.ANSYSprogramhasbeenusedforcalculatingthedeflectionofthepartunderclampingandcuttingforces.Twocasestudiesaregiventoillustratetheproposedapproach.2.ReviewofrelatedworksFixturedesignhasreceivedconsiderableattentioninrecentyears.However,littleattentionhasbeenfocusedontheoptimumfixturelayoutdesign.MenassaandDeVries[1]usedFEAforcalculatingdeflectionsusingtheminimizationoftheworkpiecedeflectionatselectedpointsasthedesigncriterion.Thedesignproblemwastodeterminethepositionofsupports.MeyerandLiou[2]presentedanapproachthatuseslinearprogrammingtechniquetosynthesizefixturesfordynamicmachiningconditions.Solutionfortheminimumclampingforcesandlocatorforcesisgiven.LiandMelkote[3]usedanonlinearprogrammingmethodtosolvethelayoutoptimizationproblem.Themethodminimizesworkpiecelocationerrorsduetolocalizedelasticdeformationoftheworkpiece.RoyandLiao[4]developedaheuristicmethodtoplanforthebestsupportingandclampingpositions.Taoetal.[5]presentedageometricalreasoningmethodologyfordeterminingtheoptimalclampingpointsandclampingsequenceforarbitrarilyshapedworkpieces.LiaoandHu[6]presentedasystemforfixtureconfigurationanalysisbasedonadynamicmodelwhichanalysesthefixture–workpiecesystemsubjecttotime-varyingmachiningloads.Theinfluenceofclampingplacementisalsoinvestigated.LiandMelkote[7]presentedafixturelayoutandclampingforceoptimalsynthesisapproachthataccountsforworkpiecedynamicsduringmachining.Acombinedfixturelayoutandclampingforceoptimizationprocedurepresented.Theyusedthecontactelasticitymodelingmethodthataccountsfortheinfluenceofworkpiecerigidbodydynamicsduringmachining.Amaraletal.[8]usedANSYStoverifyfixturedesignintegrity.Theyemployed3-2-1method.TheoptimizationanalysisisperformedinANSYS.Tanetal.[9]describedthemodeling,analysisandverificationofoptimalfixturingconfigurationsbythemethodsofforceclosure,optimizationandfiniteelementmodeling.Mostoftheabovestudiesuselinearornonlinearprogrammingmethodswhichoftendonotgiveglobaloptimumsolution.Allofthefixturelayoutoptimizationproceduresstartwithaninitialfeasiblelayout.Solutionsfromthesemethodsaredependingontheinitialfixturelayout.Theydonotconsiderthefixturelayoutoptimizationonoverallworkpiecedeformation.TheGAshasbeenproventobeusefultechniqueinsolvingoptimizationproblemsinengineering[10–12].Fixturedesignhasalargesolutionspaceandrequiresasearchtooltofindthebestdesign.FewresearchershaveusedtheGAsforfixturedesignandfixturelayoutproblems.Kumaretal.[13]haveappliedbothGAsandneuralnetworksfordesigningafixture.Marcelin[14]hasusedGAstotheoptimizationofsupportpositions.Vallapuzhaetal.[15]presentedGAbasedoptimizationmethodthatusesspatialcoordinatestorepresentthelocationsoffixtureelements.FixturelayoutoptimizationprocedurewasimplementedusingMATLABandthegeneticalgorithmtoolbox.HYPERMESHandMSC/NASTRANwereusedforFEmodel.Vallapuzhaetal.[16]presentedresultsofanextensiveinvestigationintotherelativeeffectivenessofvariousoptimizationmethods.TheyshowedthatcontinuousGAyieldedthebestqualitysolutions.LiandShiu[17]determinedtheoptimalfixtureconfigurationdesignforsheetmetalassemblyusingGA.MSC/NASTRANhasbeenusedforfitnessevaluation.Liao[18]presentedamethodtoautomaticallyselecttheoptimalnumbersoflocatorsandclampsaswellastheiroptimalpositionsinsheetmetalassemblyfixtures.KrishnakumarandMelkote[19]developedafixturelayoutoptimizationtechniquethatusestheGAtofindthefixturelayoutthatminimizesthedeformationofthemachinedsurfaceduetoclampingandmachiningforcesovertheentiretoolpath.Locatorandclamppositionsarespecifiedbynodenumbers.Abuilt-infiniteelementsolverwasdeveloped.Someofthestudiesdonotconsidertheoptimizationofthelayoutforentiretoolpathandchipremovalisnottakenintoaccount.Someofthestudiesusednodenumbersasdesignparameters.Inthisstudy,aGAtoolhasbeendevelopedtofindtheoptimallocatorandclamppositionsin2Dworkpiece.DistancesfromthereferenceedgesasdesignparametersareusedratherthanFEAnodenumbers.FitnessvaluesofrealencodedGAchromosomesareobtainedfromtheresultsofFEA.ANSYShasbeenusedforFEAcalculations.Achromosomelibraryapproachisusedinordertodecreasethesolutiontime.DevelopedGAtoolistestedontwotestproblems.Twocasestudiesaregiventoillustratethedevelopedapproach.Maincontributionsofthispapercanbesummarizedasfollows:(1)developedaGAcodeintegratedwithacommercialfiniteelementsolver;(2)GAuseschromosomelibraryinordertodecreasethecomputationtime;(3)realdesignparametersareusedratherthanFEAnodenumbers;(4)chipremovalistakenintoaccountwhiletoolforcesmovingontheworkpiece.3.GeneticalgorithmconceptsGeneticalgorithmswerefirstdevelopedbyJohnHolland.Goldberg[10]publishedabookexplainingthetheoryandapplicationexamplesofgeneticalgorithmindetails.Ageneticalgorithmisarandomsearchtechniquethatmimicssomemechanismsofnaturalevolution.Thealgorithmworksonapopulationofdesigns.Thepopulationevolvesfromgenerationtogeneration,graduallyimprovingitsadaptationtotheenvironmentthroughnaturalselection;fitterindividualshavebetterchancesoftransmittingtheircharacteristicstolatergenerations.Inthealgorithm,theselectionofthenaturalenvironmentisreplacedbyartificialselectionbasedonacomputedfitnessforeachdesign.Thetermfitnessisusedtodesignatethechromosome’schancesofsurvivalanditisessentiallytheobjectivefunctionoftheoptimizationproblem.Thechromosomesthatdefinecharacteristicsofbiologicalbeingsarereplacedbystringsofnumericalvaluesrepresentingthedesignvariables.GAisrecognizedtobedifferentthantraditionalgradientbasedoptimizationtechniquesinthefollowingfourmajorways[10]:1.GAsworkwithacodingofthedesignvariablesandparametersintheproblem,ratherthanwiththeactualparametersthemselves.2.GAsmakesuseofpopulation-typesearch.Manydifferentdesignpointsareevaluatedduringeachiterationinsteadofsequentiallymovingfromonepointtothenext.3.GAsneedsonlyafitnessorobjectivefunctionvalue.Noderivativesorgradientsarenecessary.4.GAsuseprobabilistictransitionrulestofindnewdesignpointsforexplorationratherthanusingdeterministicrulesbasedongradientinformationtofindthesenewpoints.4.Approach4.1.FixturepositioningprinciplesInmachiningprocess,fixturesareusedtokeepworkpiecesinadesirablepositionforoperations.Themostimportantcriteriaforfixturingareworkpiecepositionaccuracyandworkpiecedeformation.Agoodfixturedesignminimizesworkpiecegeometricandmachiningaccuracyerrors.Anotherfixturingrequirementisthatthefixturemustlimitdeformationoftheworkpiece.Itisimportanttoconsiderthecuttingforcesaswellastheclampingforces.Withoutadequatefixturesupport,machiningoperationsdonotconformtodesignedtolerances.Finiteelementanalysisisapowerfultoolintheresolutionofsomeoftheseproblems[22].Commonlocatingmethodforprismaticpartsis3-2-1method.Thismethodprovidesthemaximumrigiditywiththeminimumnumberoffixtureelements.Aworkpiecein3Dmaybepositivelylocatedbymeansofsixpointspositionedsothattheyrestrictninedegreesoffreedomoftheworkpiece.Theotherthreedegreesoffreedomareremovedbyclampelements.Anexamplelayoutfor2Dworkpiecebased3-2-1locatingprincipleisshowninFig.4.Fig.4.3-2-1locatinglayoutfor2DprismaticworkpieceThenumberoflocatingfacesmustnotexceedtwosoastoavoidaredundantlocation.Basedonthe3-2-1fixturingprincipletherearetwolocatingplanesforaccuratelocationcontainingtwoandonelocators.Therefore,therearemaximumoftwosideclampingsagainsteachlocatingplane.Clampingforcesarealwaysdirectedtowardsthelocatorsinordertoforcetheworkpiecetocontactalllocators.Theclampingpointshouldbepositionedoppositethepositioningpointstopreventtheworkpiecefrombeingdistortedbytheclampingforce.Sincethemachiningforcestravelalongthemachiningarea,itisnecessarytoensurethatthereactionforcesatlocatorsarepositiveforallthetime.Anynegativereactionforceindicatesthattheworkpieceisfreefromfixtureelements.Inotherwords,lossofcontactortheseparationbetweentheworkpieceandfixtureelementmighthappenwhenthereactionforceisnegative.Positivereactionforcesatthelocatorsensurethattheworkpiecemaintainscontactwithallthelocatorsfromthebeginningofthecuttotheend.Theclampingforcesshouldbejustsufficienttoconstrainandlocatetheworkpiecewithoutcausingdistortionordamagetotheworkpiece.Clampingforceoptimizationisnotconsideredinthispaper.4.2.GeneticalgorithmbasedfixturelayoutoptimizationapproachInrealdesignproblems,thenumberofdesignparameterscanbeverylargeandtheirinfluenceontheobjectivefunctioncanbeverycomplicated.Theobjectivefunctionmustbesmoothandaprocedureisneededtocomputegradients.Geneticalgorithmsstronglydifferinconceptionfromothersearchmethods,includingtraditionaloptimizationmethodsandotherstochasticmethods[23].ByapplyingGAstofixturelayoutoptimization,anoptimalorgroupofsub-optimalsolutionscanbeobtained.Inthisstudy,optimumlocatorandclamppositionsaredeterminedusinggeneticalgorithms.Theyareideallysuitedforthefixturelayoutoptimizationproblemsincenodirectanalyticalrelationshipexistsbetweenthemachiningerrorandthefixturelayout.SincetheGAdealswithonlythedesignvariablesandobjectivefunctionvalueforaparticularfixturelayout,nogradientorauxiliaryinformationisneeded[19].TheflowchartoftheproposedapproachisgiveninFig.5.FixturelayoutoptimizationisimplementedusingdevelopedsoftwarewritteninDelphilanguagenamedGenFix.DisplacementvaluesarecalculatedinANSYSsoftware[24].TheexecutionofANSYSinGenFixissimplydonebyWinExecfunctioninDelphi.TheinteractionbetweenGenFixandANSYSisimplementedinfoursteps:(1)Locatorandclamppositionsareextractedfrombinarystringasrealparameters.(2)TheseparametersandANSYSinputbatchfile(modeling,solutionandpostprocessingcommands)aresenttoANSYSusingWinExecfunction.(3)Displacementvaluesarewrittentoatextfileaftersolution.(4)GenFixreadsthisfileandcomputesfitnessvalueforcurrentlocatorandclamppositions.Inordertoreducethecomputationtime,chromosomesandfitnessvaluesarestoredinalibraryforfurtherevaluation.GenFixfirstchecksifcurrentchromosome’sfitnessvaluehasbeencalculatedbefore.Ifnot,locatorpositionsaresenttoANSYS,otherwisefitnessvaluesaretakenfromthelibrary.Duringgeneratingoftheinitialpopulation,everychromosomeischeckedwhetheritisfeasibleornot.Iftheconstraintisviolated,itiseliminatedandnewchromosomeiscreated.Thisprocesscreatesentirelyfeasibleinitialpopulation.Thisensuresthatworkpieceisstableundertheactionofclampingandcuttingforcesforeverychromosomeintheinitialpopulation.ThewrittenGAprogramwasvalidatedusingtwotestcases.ThefirsttestcaseusesHimmelblaufunction[21].Inthesecondtestcase,theGAprogramwasusedtooptimisethesupportpositionsofabeamunderuniformloading.5.FixturelayoutoptimizationcasestudiesThefixturelayoutoptimizationproblemisdefinedas:findingthepositionsofthelocatorsandclamps,sothatworkpiecedeformationatspecificregionisminimized.Notethatnumberoflocatorsandclampsarenotdesignparameter,sincetheyareknownandfixedforthe3-2-1locatingscheme.Hence,thedesignparametersareselectedaslocatorandclamppositions.Frictionisnotconsideredinthispaper.Twocasestudiesaregiventoillustratetheproposedapproach.6.ConclusionInthispaper,anevolutionaryoptimizationtechniqueoffixturelayoutoptimizationispresented.ANSYShasbeenusedforFEcalculationoffitnessvalues.ItisseenthatthecombinedgeneticalgorithmandFEmethodapproachseemstobeapowerfulapproachforpresenttypeproblems.GAapproachisparticularlysuitedforproblemswheretheredoesnotexistawell-definedmathematicalrelationshipbetweentheobjectivefunctionandthedesignvariables.TheresultsprovethesuccessoftheapplicationofGAsforthefixturelayoutoptimizationproblems.Inthisstudy,themajorobstacleforGAapplicationinfixturelayoutoptimizationisthehighcomputationcost.Re-meshingoftheworkpieceisrequiredforeverychromosomeinthepopulation.But,usagesofchromosomelibrary,thenumberofFEevaluationsaredecreasedfrom6000to415.Thisresultsinatremendousgainincomputationalefficiency.Theotherwaytodecreasethesolutiontimeistousedistributedcomputationinalocalareanetwork.Theresultsofthisapproachshowthatthefixturelayoutoptimizationproblemsaremulti-modalproblems.Optimizeddesignsdonothaveanyapparentsimilaritiesalthoughtheyprovideverysimilarperformances.Itisshownthatfixturelayoutproblemsaremulti-modalthereforeheuristicrulesforfixturedesignshouldbeusedinGAtoselectbestdesignamongothers.Fig.5.TheflowchartoftheproposedmethodologyandANSYSinterface.采用遗传算法优化加工夹具定位和加紧位置摘要：工件变形的问题可能导致机械加工中的空间问题。支撑和定位器是用于减少工件弹性变形引起的误差。支撑、定位器的优化和夹具定位是最大限度的减少几何在工件加工中的误差的一个关键问题。本文应用夹具布局优化遗传算法〔GAs〕来处理夹具布局优化问题。遗传算法的方法是基于一种通过整合有限的运行于批处理模式的每一代的目标函数值的元素代码的方法，用于来优化夹具布局。给出的个案研究说明已开发的方法的应用。采用染色体文库方法减少整体解决问题的时间。已开发的遗传算法保持跟踪先前的分析设计，因此先前的分析功能评价的数量降低大约93%。结果说明，该方法的夹具布局优化问题是多模式的问题。优化设计之间没有任何明显的相似之处，虽然它们提供非常相似的表现。关键词：夹具设计；遗传算法；优化1.引言夹具用来定位和束缚机械操作中的工件，减少由于对确保机械操作准确性的夹紧方案和切削力造成的工件和夹具的变形。传统上，加工夹具是通过反复试验法来设计和制造的，这是一个既造价高又耗时的制造过程。为确保工件按规定尺寸和公差来制造，工件必须给予适当的定位和夹紧以确保有必要开发工具来消除高造价和耗时的反复试验设计方法。适当的工件定位和夹具设计对于产品质量的精密度、准确度和机制件的完饰是至关重要的。从理论上说，3-2-1定位原那么对于定位所有的棱柱形零件是很令人满意的。该方法具有最大的刚性与最少量的夹具元件。从动力学观点来看定位零件意味着限制了自由移动物体的六自由度〔三个平动自由度和三个旋转自由度〕。在零件下部设置三个支撑来建立工件在垂直轴方向的定位。在两个外围边缘放置定位器旨在建立工件在水平x轴和y轴的定位。正确定位夹具的工件对于制造过程的全面准确性和重复性是至关重要的。定位器应该尽可能的远距离的分开放置并且应该放在任何可能的加工面上。放置的支撑器通常用来包围工件的重力中心并且尽可能的将其分开放置以维持其稳定性。夹具夹子的首要任务是固定夹具以抵抗定位器和支撑器。不应该要求夹子对抗加工操作中的切削力。对于给定数量的夹具元件，加工夹具合成的问题是寻找夹具优化布局或工件周围夹具元件的位置。本篇文章提出一种优化夹具布局遗传算法。优化目标是研究一个二维夹具布局使工件不同位置上最大的弹性变形最小化。ANSYS程序以用于计算工件变形情况下夹紧力和切削力。本文给出两个实例来说明给出的方法。2.回忆相关工程结构最近几年夹具设计问题受到越来越多的重视。然而，很少有注意力集中于优化夹具布局设计。Menassa和Devries用FEA计算变形量使设计准那么要求的位点的工件变形最小化。设计问题是确定支撑器位置。Meyer和Liou提出一个方法就是使用线性编程技术合成动态编程条件中的夹具。给出了使夹紧力和定位力最小化的解决方案。Li和Melkote用非线性规划方法解决布局优化问题。这个方法使工件位置误差最小化归于工件的局部弹性变形。Roy和Liao开发出一种启发式方法来方案最好的支撑和夹紧位置。Tao等人提出一个几何推理的方法来确定最优夹紧点和任意形状工件的夹紧顺序。Liao和Hu提出一种夹具结构分析系统这个系统基于动态模型分析受限于时变加工负载的夹具—工件系统。本文也调查了夹紧位置的影响。Li和Melkote提出夹具布局和夹紧力最优合成方法帮我们解释加工过程中的工件动力学。本文提出一个夹具布局和夹紧力优化结合的程序。他们用接触弹性建模方法解释工件刚体动力学在加工期间的影响。Amaral等人用ANSYS验证夹具设计的完整性。他们用3-2-1方法。ANSYS提出优化分析。Tan等人通过力锁合、优化与有限建模方法描述了建模、优化夹具的分析与验证。以上大局部的研究使用线性和非线性编程方式这通常不会给出全局最优解决方案。所有的夹具布局优化程序开始于一个初始可行布局。这些方法给出的解决方案在很大程度上取决于初始夹具布局。他们没有考虑到工件夹具布局优化对整体的变形。GAs已被证明在解决工程中优化问题是有用的。夹具设计具有巨大的解决空间并需要搜索工具找到最好的设计。一些研究人员曾使用GAs解决夹具设计及夹具布局问题。Kumar等人用GAs和神经网络设计夹具。Marcelin已经将GAs用于支撑位置的优化。Vallapuzha等人提出基于优化方法的GA，它采用空间坐标来表示夹具元件的位置。夹具布局优化程序设计的实现是使用MATLAB和遗传算法工具箱。HYPERMESH和MSC/NASTRAN用于FE模型。Vallapuzha等人提出一些结果关于一个广泛调查不同优化方法的相对有效性。他们的研究说明连续遗传算法提出了最优质的解决方案。Li和Shiu使用遗传算法确定了夹具设计最优配置的金属片。MSC/NASTRAN已经用于适应度值评价。Liao提出自动选择最正确夹子和夹钳的数目以及它们在金属片整合的夹具中的最优位置。Krishnakumar和Melkote开发了一种夹具布局优化技术，它是利用遗传算法找到了夹具布局，由于整个刀具路径中的夹紧力和加工力使加工外表变形量最小化。通过节点编号使定位器和夹具位置特殊化。一个内置的有限元求解器研制成功。一些研究没考虑到整个刀具路径的优化布局以及磨屑去除。一些研究采用节点编号作为设计参数。在本研究中，开发GA工具用于寻找在二维工件中的最优定位器和夹紧位置。使用参考边缘的距离作为设计参数而不是用FEA节点编号。真正编码遗传算法的染色体的健康指数是从FEA结果中获得的。ANSSYS用于FEA计算。用染色体文库的方法是为了减少解决问题的时间。用两个问题测试已开发的遗传算法工具。给出的两个实例说明了这个开发的方法。本论文的主要奉献可以概括为以下几个方面：开发了遗传算法编码结合商业有限元素求解；遗传算法采用染色体文库以降低计算时间；使用真正的设计参数，而不是有限元节点数字；当工具在工件中移动时考虑磨屑去除工具。3.遗传算法概念遗传算法最初由JohnHolland开发。Goldberg出版了一本书，解释了这个理论和遗传算法应用实例的详细说明。遗传算法是一种随机搜索方法，它模拟一些自然演化的机制。该算法用于种群设计。种群从一代到另一代演化，通过自然选择逐渐提高了适应