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外文翻译--单门的塑料注塑模具的优化 英文版【优秀】.pdf

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外文翻译--单门的塑料注塑模具的优化 英文版【优秀】.pdf

Lietal./JZhejiangUnivSciA200787107710831077SinglegateoptimizationforplasticinjectionmoldLIJiquan†,LIDequn,GUOZhiying,LVHaiyuanDepartmentofPlasticityTechnology,ShanghaiJiaoTongUniversity,Shanghai200030,China†Emailhutli163.comReceivedNov.22,2006revisionacceptedMar.19,2007AbstractThispaperdealswithamethodologyforsinglegatelocationoptimizationforplasticinjectionmold.Theobjectiveofthegateoptimizationistominimizethewarpageofinjectionmoldedparts,becausewarpageisacrucialqualityissueformostinjectionmoldedpartswhileitisinfluencedgreatlybythegatelocation.Featurewarpageisdefinedastheratioofmaximumdisplacementonthefeaturesurfacetotheprojectedlengthofthefeaturesurfacetodescribepartwarpage.Theoptimizationiscombinedwiththenumericalsimulationtechnologytofindtheoptimalgatelocation,inwhichthesimulatedannealingalgorithmisusedtosearchfortheoptimum.Finally,anexampleisdiscussedinthepaperanditcanbeconcludedthattheproposedmethodiseffective.KeywordsInjectionmold,Gatelocation,Optimization,Featurewarpagedoi10.1631/jzus.2007.A1077DocumentcodeACLCnumberTQ320.66INTRODUCTIONPlasticinjectionmoldingisawidelyused,complexbuthighlyefficienttechniqueforproducingalargevarietyofplasticproducts,particularlythosewithhighproductionrequirement,tighttolerance,andcomplexshapes.Thequalityofinjectionmoldedpartsisafunctionofplasticmaterial,partgeometry,moldstructureandprocessconditions.Themostimportantpartofaninjectionmoldbasicallyisthefollowingthreesetsofcomponentscavities,gatesandrunners,andcoolingsystem.LamandSeow2000andJinandLam2002achievedcavitybalancingbyvaryingthewallthicknessofthepart.Abalancefillingprocesswithinthecavitygivesanevenlydistributedpressureandtemperaturewhichcandrasticallyreducethewarpageofthepart.Butthecavitybalancingisonlyoneoftheimportantinfluencingfactorsofpartqualities.Especially,theparthasitsfunctionalrequirements,anditsthicknessesshouldnotbevariedusually.Fromthepointviewoftheinjectionmolddesign,agateischaracterizedbyitssizeandlocation,andtherunnersystembythesizeandlayout.Thegatesizeandrunnerlayoutareusuallydeterminedasconstants.Relatively,gatelocationsandrunnersizesaremoreflexible,whichcanbevariedtoinfluencethequalityofthepart.Asaresult,theyareoftenthedesignparametersforoptimization.LeeandKim1996aoptimizedthesizesofrunnersandgatestobalancerunnersystemformultipleinjectioncavities.Therunnerbalancingwasdescribedasthedifferencesofentrancepressuresforamulticavitymoldwithidenticalcavities,andasdifferencesofpressuresattheendofthemeltflowpathineachcavityforafamilymoldwithdifferentcavityvolumesandgeometries.Themethodologyhasshownuniformpressuredistributionsamongthecavitiesduringtheentiremoldingcycleofmultiplecavitiesmold.Zhaietal.2005apresentedthetwogatelocationoptimizationofonemoldingcavitybyanefficientsearchmethodbasedonpressuregradientPGSS,andsubsequentlypositionedweldlinestothedesiredlocationsbyvaryingrunnersizesforJournalofZhejiangUniversitySCIENCEAISSN1673565XPrintISSN18621775Onlinewww.zju.edu.cn/jzuswww.springerlink.comEmailjzuszju.edu.cnProjectNo.50675080supportedbytheNationalNaturalScienceFoundationofChinaLietal./JZhejiangUnivSciA200787107710831078multigatepartsZhaietal.,2006.Aslargevolumepart,multiplegatesareneededtoshortenthemaximumflowpath,withacorrespondingdecreaseininjectionpressure.Themethodispromisingfordesignofgatesandrunnersforasinglecavitywithmultiplegates.Manyofinjectionmoldedpartsareproducedwithonegate,whetherinsinglecavitymoldorinmultiplecavitiesmold.Therefore,thegatelocationofasinglegateisthemostcommondesignparameterforoptimization.AshapeanalysisapproachwaspresentedbyCourbebaisseandGarcia2002,bywhichthebestgatelocationofinjectionmoldingwasestimated.Subsequently,theydevelopedthismethodologyfurtherandappliedittosinglegatelocationoptimizationofanLshapeexampleCourbebaisse,2005.Itiseasytouseandnottimeconsuming,whileitonlyservestheturningofsimpleflatpartswithuniformthickness.PandelidisandZou1990presentedtheoptimizationofgatelocation,byindirectqualitymeasuresrelevanttowarpageandmaterialdegradation,whichisrepresentedasweightedsumofatemperaturedifferentialterm,anoverpackterm,andafrictionaloverheatingterm.Warpageisinfluencedbytheabovefactors,buttherelationshipbetweenthemisnotclear.Therefore,theoptimizationeffectisrestrictedbythedeterminationoftheweightingfactors.LeeandKim1996bdevelopedanautomatedselectionmethodofgatelocation,inwhichasetofinitialgatelocationswereproposedbyadesignerandthentheoptimalgatewaslocatedbytheadjacentnodeevaluationmethod.Theconclusiontoagreatextentdependsmuchonthehumandesignersintuition,becausethefirststepofthemethodisbasedonthedesignersproposition.Sotheresultistoalargeextentlimitedtothedesignersexperience.LamandJin2001developedagatelocationoptimizationmethodbasedontheminimizationoftheStandardDeviationofFlowPathLengthSDLandStandardDeviationofFillingTimeSDTduringthemoldingfillingprocess.Subsequently,Shenetal.2004a2004boptimizedthegatelocationdesignbyminimizingtheweightedsumoffillingpressure,fillingtimedifferencebetweendifferentflowpaths,temperaturedifference,andoverpackpercentage.Zhaietal.2005binvestigatedoptimalgatelocationwithevaluationcriteriaofinjectionpressureattheendoffilling.Theseresearcherspresentedtheobjectivefunctionsasperformancesofinjectionmoldingfillingoperation,whicharecorrelatedwithproductqualities.Butthecorrelationbetweentheperformancesandqualitiesisverycomplicatedandnoclearrelationshiphasbeenobservedbetweenthemyet.Itisalsodifficulttoselectappropriateweightingfactorsforeachterm.Anewobjectivefunctionispresentedheretoevaluatethewarpageofinjectionmoldedpartstooptimizegatelocation.Tomeasurepartqualitydirectly,thisinvestigationdefinesfeaturewarpagetoevaluatepartwarpage,whichisevaluatedfromtheflowpluswarpagesimulationoutputsofMoldflowPlasticsInsightMPIsoftware.Theobjectivefunctionisminimizedtoachieveminimumdeformationingatelocationoptimization.Simulatedannealingalgorithmisemployedtosearchfortheoptimalgatelocation.Anexampleisgiventoillustratetheeffectivityoftheproposedoptimizationprocedure.QUALITYMEASURESFEATUREWARPGEDefinitionoffeaturewarpageToapplyoptimizationtheorytothegatedesign,qualitymeasuresofthepartmustbespecifiedinthefirstinstance.Thetermqualitymaybereferredtomanyproductproperties,suchasmechanical,thermal,electrical,optical,ergonomicalorgeometricalproperties.Therearetwotypesofpartqualitymeasuresdirectandindirect.Amodelthatpredictsthepropertiesfromnumericalsimulationresultswouldbecharacterizedasadirectqualitymeasure.Incontrast,anindirectmeasureofpartqualityiscorrelatedwithtargetquality,butitcannotprovideadirectestimateofthatquality.Forwarpage,theindirectqualitymeasuresinrelatedworksareoneofperformancesofinjectionmoldingflowingbehaviororweightedsumofthose.Theperformancesarepresentedasfillingtimedifferentialalongdifferentflowpaths,temperaturedifferential,overpackpercentage,andsoon.Itisobviousthatwarpageisinfluencedbytheseperformances,buttherelationshipbetweenwarpageandtheseperformancesisnotclearandthedeterminationoftheseweightingfactorsisratherdifficult.Therefore,theoptimizationwiththeaboveobjectivefunctionLietal./JZhejiangUnivSciA200787107710831079probablywillnotminimizepartwarpageevenwithperfectoptimizationtechnique.Sometimes,improperweightingfactorswillresultinabsolutelywrongresults.Somestatisticalquantitiescalculatedfromthenodaldisplacementswerecharacterizedasdirectqualitymeasurestoachieveminimumdeformationinrelatedoptimizationstudies.Thestatisticalquantitiesareusuallyamaximumnodaldisplacement,anaverageoftop10percentilenodaldisplacements,andanoverallaveragenodaldisplacementLeeandKim,19951996b.Thesenodaldisplacementsareeasytoobtainfromthesimulationresults,thestatisticalvalues,tosomeextents,representingthedeformation.Butthestatisticaldisplacementcannoteffectivelydescribethedeformationoftheinjectionmoldedparts.Inindustry,designersandmanufacturersusuallypaymoreattentiontothedegreeofpartwarpageonsomespecificfeaturesthanthewholedeformationoftheinjectionmoldedparts.Inthisstudy,featurewarpageisdefinedtodescribethedeformationoftheinjectionparts.ThefeaturewarpageistheratioofthemaximumdisplacementofthefeaturesurfacetotheprojectedlengthofthefeaturesurfaceFig.1100,hLγ1whereγisthefeaturewarpage,histhemaximumdisplacementonthefeaturesurfacedeviatingfromthereferenceplatform,andListheprojectedlengthofthefeaturesurfaceonareferencedirectionparallelingthereferenceplatform.Forcomplicatedfeaturesonlyplanefeaturediscussedhere,thefeaturewarpageisusuallyseparatedintotwoconstituentsonthereferenceplane,whicharerepresentedona2Dcoordinatesystem100,100,xyhhLLγγ2whereγx,γyaretheconstituentfeaturewarpagesintheX,Ydirection,andLx,LyaretheprojectedlengthsofthefeaturesurfaceonX,Ycomponent.EvaluationoffeaturewarpageAfterthedeterminationoftargetfeaturecombinedwithcorrespondingreferenceplaneandprojectiondirection,thevalueofLcanbecalculatedimmediatelyfromthepartwiththecalculatingmethodofanalyticgeometryFig.2.Lisaconstantforanypartonthespecifiedfeaturesurfaceandprojecteddirection.ButtheevaluationofhismorecomplicatedthanthatofL.Simulationofinjectionmoldingprocessisacommontechniquetoforecastthequalityofpartdesign,molddesignandprocesssettings.TheresultsofwarpagesimulationareexpressedasthenodaldeflectionsonX,Y,ZcomponentWx,Wy,Wz,andthenodaldisplacementW.WisthevectorlengthofvectorsumofWxi,Wyj,andWzk,wherei,j,karetheunitvectorsonX,Y,Zcomponent.Thehisthemaximumdisplacementofthenodesonthefeaturesurface,whichiscorrelatedwiththenormalorientationofthereferenceplane,andcanbederivedfromtheresultsofwarpagesimulation.Tocalculateh,thedeflectionofithnodeisevaluatedfirstlyasfollowscoscoscos,iixiyiziAAiBBWWWWWWαβγωω−3whereWiisthedeflectioninthenormaldirectionofthereferenceplaneofithnodeWix,Wiy,WizarethedeflectionsonX,Y,Zcomponentofithnodeα,β,γaretheanglesofnormalvectorofthereferenceAandBaretheterminalnodesofthefeaturetoprojectingdirectionFig.2WAandWBarethedeflectionsofnodesAandBFig.1ThedefinitionoffeaturewarpagehReferenceplaneSurfaceLFig.2TheprojectedlengthevaluationFeatureYXLxBALyLietal./JZhejiangUnivSciA200787107710831080coscoscos,coscoscos,AAxAyAzBBxByBzWWWWWWWWαβγαβγ4whereWAx,WAy,WAzarethedeflectionsonX,Y,ZcomponentofnodeAWBx,WByandWBzarethedeflectionsonX,Y,ZcomponentofnodeBωiAandωiBaretheweightingfactorsoftheterminalnodedeflectionscalculatedasfollows1/,1,iAiAiBiALLωωω−−5whereLiAistheprojectordistancebetweenithnodeandnodeA.Ultimately,histhemaximumoftheabsolutevalueofWi12max{||,||,,||}.khWWW6Inindustry,theinspectionofthewarpageiscarriedoutwiththehelpofafeelergauge,whilethemeasuredpartshouldbeplacedonareferenceplatform.Thevalueofhisthemaximumnumericalreadingofthespacebetweenthemeasuredpartsurfaceandthereferenceplatform.GATELOCATIONOPTIMIZATIONPROBLEMFORMATIONThequalitytermwarpagemeansthepermanentdeformationofthepart,whichisnotcausedbyanappliedload.Itiscausedbydifferentialshrinkagethroughoutthepart,duetotheimbalanceofpolymerflow,packing,cooling,andcrystallization.Theplacementofagateinaninjectionmoldisoneofthemostimportantvariablesofthetotalmolddesign.Thequalityofthemoldedpartisgreatlyaffectedbythegatelocation,becauseitinfluencesthemannerthattheplasticflowsintothemoldcavity.Therefore,differentgatelocationsintroduceinhomogeneityinorientation,density,pressure,andtemperaturedistribution,accordinglyintroducingdifferentvalueanddistributionofwarpage.Therefore,gatelocationisavaluabledesignvariabletominimizetheinjectionmoldedpartwarpage.Becausethecorrelationbetweengatelocationandwarpagedistributionistoalargeextentindependentofthemeltandmoldtemperature,itisassumedthatthemoldingconditionsarekeptconstantinthisinvestigation.Theinjectionmoldedpartwarpageisquantifiedbythefeaturewarpagewhichwasdiscussedintheprevioussection.ThesinglegatelocationoptimizationcanthusbeformulatedasfollowsMinimizeminfXγSubjectto0/10,gpp−≤X,1,2,...,,iXiN∈Xwhereγisthefeaturewarpagepistheinjectionpressureatthegatepositionp0istheallowableinjectionpressureofinjectionmoldingmachineortheallowableinjectionpressurespecifiedbythedesignerormanufacturerXisthecoordinatevectorofthecandidategatelocationsXiisthenodeonthefiniteelementmeshmodelofthepartforinjectionmoldingprocesssimulationNisthetotalnumberofnodes.Inthefiniteelementmeshmodelofthepart,everynodeisapossiblecandidateforagate.Therefore,thetotalnumberofthepossiblegatelocationNpisafunctionofthetotalnumberofnodesNandthetotalnumberofgatelocationstobeoptimizednp11.NNNnNn−⋅⋅⋅−−Inthisstudy,onlythesinglegatelocationproblemisinvestigated.SIMULATEDANNEALINGALGORITHMThesimulatedannealingalgorithmisoneofthemostpowerfulandpopularmetaheuristicstosolveoptimizationproblemsbecauseoftheprovisionofgoodglobalsolutionstorealworldproblems.ThealgorithmisbaseduponthatofMetropolisetal.1953,whichwasoriginallyproposedasameanstofindanequilibriumconfigurationofacollectionofatomsatagiventemperature.TheconnectionbetweenthisalgorithmandmathematicalminimizationwasfirstnotedbyPincus1970,butitwasKirkpatricketal.1983whoproposedthatitformedthebasisofanoptimizationtechniqueforcombinationalandotherproblems.Toapplythesimulatedannealingmethodtoop

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