夾具設計外文翻譯-采用遺傳算法優(yōu)化加工夾具定位和加緊位置

附錄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.采用遺傳算法優(yōu)化加工夾具定位和加緊位置摘要：工件變形的問題可能導致機械加工中的空間問題。支撐和定位器是用于減少工件彈性變形引起的誤差。支撐、定位器的優(yōu)化和夾具定位是最大限度的減少幾何在工件加工中的誤差的一個關鍵問題。本文應用夾具布局優(yōu)化遺傳算法〔GAs〕來處理夾具布局優(yōu)化問題。遺傳算法的方法是基于一種通過整合有限的運行于批處理模式的每一代的目標函數值的元素代碼的方法，用于來優(yōu)化夾具布局。給出的個案研究說明已開發(fā)的方法的應用。采用染色體文庫方法減少整體解決問題的時間。已開發(fā)的遺傳算法保持跟蹤先前的分析設計，因此先前的分析功能評價的數量降低大約93%。結果說明，該方法的夾具布局優(yōu)化問題是多模式的問題。優(yōu)化設計之間沒有任何明顯的相似之處，雖然它們提供非常相似的表現。關鍵詞：夾具設計；遺傳算法；優(yōu)化1.引言夾具用來定位和束縛機械操作中的工件，減少由于對確保機械操作準確性的夾緊方案和切削力造成的工件和夾具的變形。傳統(tǒng)上，加工夾具是通過反復試驗法來設計和制造的，這是一個既造價高又耗時的制造過程。為確保工件按規(guī)定尺寸和公差來制造，工件必須給予適當的定位和夾緊以確保有必要開發(fā)工具來消除高造價和耗時的反復試驗設計方法。適當的工件定位和夾具設計對于產品質量的精密度、準確度和機制件的完飾是至關重要的。從理論上說，3-2-1定位原那么對于定位所有的棱柱形零件是很令人滿意的。該方法具有最大的剛性與最少量的夾具元件。從動力學觀點來看定位零件意味著限制了自由移動物體的六自由度〔三個平動自由度和三個旋轉自由度〕。在零件下部設置三個支撐來建立工件在垂直軸方向的定位。在兩個外圍邊緣放置定位器旨在建立工件在水平x軸和y軸的定位。正確定位夾具的工件對于制造過程的全面準確性和重復性是至關重要的。定位器應該盡可能的遠距離的分開放置并且應該放在任何可能的加工面上。放置的支撐器通常用來包圍工件的重力中心并且盡可能的將其分開放置以維持其穩(wěn)定性。夾具夾子的首要任務是固定夾具以抵抗定位器和支撐器。不應該要求夾子對抗加工操作中的切削力。對于給定數量的夾具元件，加工夾具合成的問題是尋找夾具優(yōu)化布局或工件周圍夾具元件的位置。本篇文章提出一種優(yōu)化夾具布局遺傳算法。優(yōu)化目標是研究一個二維夾具布局使工件不同位置上最大的彈性變形最小化。ANSYS程序以用于計算工件變形情況下夾緊力和切削力。本文給出兩個實例來說明給出的方法。2.回憶相關工程結構最近幾年夾具設計問題受到越來越多的重視。然而，很少有注意力集中于優(yōu)化夾具布局設計。Menassa和Devries用FEA計算變形量使設計準那么要求的位點的工件變形最小化。設計問題是確定支撐器位置。Meyer和Liou提出一個方法就是使用線性編程技術合成動態(tài)編程條件中的夾具。給出了使夾緊力和定位力最小化的解決方案。Li和Melkote用非線性規(guī)劃方法解決布局優(yōu)化問題。這個方法使工件位置誤差最小化歸于工件的局部彈性變形。Roy和Liao開發(fā)出一種啟發(fā)式方法來方案最好的支撐和夾緊位置。Tao等人提出一個幾何推理的方法來確定最優(yōu)夾緊點和任意形狀工件的夾緊順序。Liao和Hu提出一種夾具結構分析系統(tǒng)這個系統(tǒng)基于動態(tài)模型分析受限于時變加工負載的夾具—工件系統(tǒng)。本文也調查了夾緊位置的影響。Li和Melkote提出夾具布局和夾緊力最優(yōu)合成方法幫我們解釋加工過程中的工件動力學。本文提出一個夾具布局和夾緊力優(yōu)化結合的程序。他們用接觸彈性建模方法解釋工件剛體動力學在加工期間的影響。Amaral等人用ANSYS驗證夾具設計的完整性。他們用3-2-1方法。ANSYS提出優(yōu)化分析。Tan等人通過力鎖合、優(yōu)化與有限建模方法描述了建模、優(yōu)化夾具的分析與驗證。以上大局部的研究使用線性和非線性編程方式這通常不會給出全局最優(yōu)解決方案。所有的夾具布局優(yōu)化程序開始于一個初始可行布局。這些方法給出的解決方案在很大程度上取決于初始夾具布局。他們沒有考慮到工件夾具布局優(yōu)化對整體的變形。GAs已被證明在解決工程中優(yōu)化問題是有用的。夾具設計具有巨大的解決空間并需要搜索工具找到最好的設計。一些研究人員曾使用GAs解決夾具設計及夾具布局問題。Kumar等人用GAs和神經網絡設計夾具。Marcelin已經將GAs用于支撐位置的優(yōu)化。Vallapuzha等人提出基于優(yōu)化方法的GA，它采用空間坐標來表示夾具元件的位置。夾具布局優(yōu)化程序設計的實現是使用MATLAB和遺傳算法工具箱。HYPERMESH和MSC/NASTRAN用于FE模型。Vallapuzha等人提出一些結果關于一個廣泛調查不同優(yōu)化方法的相對有效性。他們的研究說明連續(xù)遺傳算法提出了最優(yōu)質的解決方案。Li和Shiu使用遺傳算法確定了夾具設計最優(yōu)配置的金屬片。MSC/NASTRAN已經用于適應度值評價。Liao提出自動選擇最正確夾子和夾鉗的數目以及它們在金屬片整合的夾具中的最優(yōu)位置。Krishnakumar和Melkote開發(fā)了一種夾具布局優(yōu)化技術，它是利用遺傳算法找到了夾具布局，由于整個刀具路徑中的夾緊力和加工力使加工外表變形量最小化。通過節(jié)點編號使定位器和夾具位置特殊化。一個內置的有限元求解器研制成功。一些研究沒考慮到整個刀具路徑的優(yōu)化布局以及磨屑去除。一些研究采用節(jié)點編號作為設計參數。在本研究中，開發(fā)GA工具用于尋找在二維工件中的最優(yōu)定位器和夾緊位置。使用參考邊緣的距離作為設計參數而不是用FEA節(jié)點編號。真正編碼遺傳算法的染色體的健康指數是從FEA結果中獲得的。ANSSYS用于FEA計算。用染色體文庫的方法是為了減少解決問題的時間。用兩個問題測試已開發(fā)的遺傳算法工具。給出的兩個實例說明了這個開發(fā)的方法。本論文的主要奉獻可以概括為以下幾個方面：開發(fā)了遺傳算法編碼結合商業(yè)有限元素求解；遺傳算法采用染色體文庫以降低計算時間；使用真正的設計參數，而不是有限元節(jié)點數字；當工具在工件中移動時考慮磨屑去除工具。3.遺傳算法概念遺傳算法最初由JohnHolland開發(fā)。Goldberg出版了一本書，解釋了這個理論和遺傳算法應用實例的詳細說明。遺傳算法是一種隨機搜索方法，它模擬一些自然演化的機制。該算法用于種群設計。種群從一代到另一代演化，通過自然選擇逐漸提高了適應