已阅读5页,还剩5页未读, 继续免费阅读
版权说明:本文档由用户提供并上传,收益归属内容提供方,若内容存在侵权,请进行举报或认领
文档简介
GJournalofMechanicalScienceandTechnology21(2007)789798JournalofMechanicalScienceandTechnologyMicroGeneticAlgorithmBasedOptimalGatePositioninginInjectionMoldingDesignJongsooLee*,JonghunKimSchoolofMechanicalEngineeringYonseiUniversity,Seoul120-749Korea(ManuscriptReceivedDecember12,2006;RevisedMarch26,2007;AcceptedMarch26,2007)-AbstractThepaperdealswiththeoptimizationofrunnersystemininjectionmoldingdesign.Thedesignobjectiveistolocategatepositionsbyminimizingbothmaximuminjectionpressureattheinjectionportandmaximumpressuredifferenceamongallthegatesonaproductwithconstraintsonshearstressand/orweld-line.Theanalysisoffillingprocessisconductedbyafiniteelementbasedprogramforpolymerflow.Microgeneticalgorithm(mGA)isusedasaglobaloptimizationtoolduetothenatureofinherentnonlinearlityinflowanalysis.Fourdifferentdesignapplicationsininjectionmoldsareexploredtoexaminetheproposeddesignstrategies.ThepapershowstheeffectivenessofmGAinthecontextofoptimizationofrunnersystemininjectionmoldingdesign.GKeywords:Microgeneticalgorithm;Designoptimization;Fillinginjectionmold-1.IntroductionInjectionmoldingprocesshasbeenrecognizedasoneofthemostefficientmanufacturingtechnologiessincehighperformancepolymermaterialscanbeutilizedtoaccuratelymanufactureaproductwithcomplicatedshape(Chiang,etal.,1991;ChangandYang,2001;Himasekhar,etal.,1992;KwonandPark,2004).Also,thedemandoninjectionmoldedproductssuchasfromconventionalplasticgoodstomicroopticaldevicesisbeingdramaticallyincreasedovertherecentyears(Piotter,etal.,2001;Kang,etal.,2000).Ingeneral,theinjectionmoldprocessisinitiatedbythefillingstagewherethepolymermaterialsfillintoacavityundertheinjectiontemperature.Afterthecavityiscompletelyfilled,thepost-fillingstage,thatis,thepackingstageisconductedtobeadditionallyfilledwiththehighpressurepolymer,therebyresultingintheavoidanceofmaterialshrinkage.Subsequently,thecoolingstageisrequiredforamoldedproducttobeejectedwithoutanydeformation.Itisimportanttoaccommodatethemoldingconditionsinthefillingstagesinceitisthefirststageintheoverallinjectionmoldingdesign(ZhouandD.Li,2001).Afterthat,onecansuccess-fullyexpectmoreimprovedmoldingconditionsduringpost-fillingstagessuchaspacking,coolingstages.Thepaperdealswithoptimalconditionsofthefillinginjectionmoldingdesigninwhichtheflowpatternandpressureforthepolymermaterialstobefilledthroughgatesofarunnerareofsignificant.Thatis,oneofdesignrequirementsaresuchthatwhenthepolymercomesintoacavitythroughanumberofgateslocatedatdifferentpositions,pressurelevelsonthesurfaceofaproductshouldbeasuniformaspossible.Suchdesigncanbeperformedthroughtheintelligentgatepositioningtogeneratethemore*Correspondingauthor.Tel.:+82221234474;Fax.:+8223622736E-mailaddress:jleejyonsei.ac.kr790JongsooLeeandJonghunKim/JournalofMechanicalScienceandTechnology21(2007)740749uniformdistributionofinjectionpressureovertheproductsurface.TherehavebeenanumberofstudiesofoptimalgatelocationinthecontextofCAEfillinginjectionmoldingdesignproblemswherevariouskindsofoptimizerhavebeenemployedtoconductdesignoptimization(Kimetal.,1996;Young,1994;Pan-delidisandZou,2004;Lin,2001;LiandShen,1995).Thepaperexploresthedesignofinjectionmoldsystemusingmicrogeneticalgorithm(mGA).Ge-neticalgorithm(conventionalGA)isbasedontheDarwinstheoryofthesurvivalofthefittest,andadoptstheconceptofnaturalevolution;thecompetitivedesignswithmorefitaresurvivedbyselection,andthenewdesignsarecreatedbycrossoverandmutation(Lee,1996;LeeandHajela,1996).AconventionalGAworkswithamultiplenumberofdesignsinapopulation.Handlingwithsuchdesignsresultsinincreasingahigherprobabilityoflocatingaglobaloptimumaswellasmultiplelocaloptima.GAisalsoadvantageouswhenthedesignproblemisrepresentedbyamixtureofinteger/dis-creteandcontinuousdesignvariables.Nevertheless,itrequiresexpensivecomputationalcostsespeciallywhencombiningwithfiniteelementbasedCAEanalysistools.AconventionalGAdeterminesthepopulationsizedependinguponthestringlengthofachromosomethatisacodedvalueofasetofdesignvariables.Themaindifferencebetweenaconven-tionalGAandmGAresidesonthepopulationsize.ThepopulationsizeinmGAisbasedonGoldbergsconceptsuchthatEvolutionprocessispossiblewithsmallpopulationstoreducethecostoffitnessfunctionevaluation(Goldberg,1988).ThisimpliesthatmGAemploysafewnumberofpopulationsforGAevolutionregardlessofthenumberofdesignvariablesandthecomplexityofdesignparameters(Krishnakumar,1989;DennisandDulikravich,2001).Thepaperdiscussesthedesignrequirementsoffillinginjectionmoldoptimizationtoconstructtheproperobjectivefunctionsanddesignconstraints.Fourdifferentdesignapplicationsininjectionmoldsareexploredtoexaminetheproposeddesignstrategies.ThepapershowstheeffectivenessofmGAinthecontextofoptimizationofrunnersystemininjectionmoldingdesign.2.MoldflowanalysisTheflowofapolymerininjectionmoldingprocessobeysthefollowinggoverningequations:22()()0ppSSxxyywwwwwwww(1)222()pxyTTTTCktxyzUQQKJwwwwwwww(2)where,220hzSdzK.Intheaboveequations,pisaflowpressure,Tisatemperatureofpolymer,andtisdenotedastime.ParametersK,J,andkareviscosity,shearrateandthermalconductivity,respectively(Lee,2003).Itisassumedthatpolymerisanon-compactionsubstanceinthefillinganalysis.TheflowanalysisinthepresentstudyisconductedbyComputerAidedPlasticsApplication(CAPA)(Koo,2003),afiniteelementbasedcommercialcodeforpolymerflowofinjectionmolding.Therunnersystemininjectionmoldcoversthepassageofmoltenpolymerfrominjectionporttogates.Thepresentstudydevelopstwodifferentrunnersystemswhereacoldsystemrequiresthechangeinpolymertemperature,andahotsystemkeepitunchangedwhiletheflowpassesthroughtherunner.ForthehotrunnersystemhasageometricallyconsistentthicknessduetotheconstanttemperatureasshowninFig.1a.However,theCAEresultofacoldrunnersystemdependsonthethicknessandshapeTable1.Ten-bartrussdesignresults.microGAconventionalGACase1Case2Case3Case1Case2Case3Reference20X17.868.157.858.157.307.817.90X20.400.830.450.10X38.387.978.378.10X45.053.833.893.973.274.163.90X50.120.950.550.10X60.400.820.300.10X76.415.675.875.846.746.305.80X85.236.295.525.685.065.265.51X93.833.855.055.072.893.863.68OptimalareaX100.5001.160.420.14Optimalweight1599158715881593159015851499#offunctionevaluations575405423025335788946949773533JongsooLeeandJonghunKim/JournalofMechanicalScienceandTechnology21(2007)789798791(a)Hotrunnersystem(b)ColdrunnersystemFig.1.Modelingofrunnersystem.shapeofarunner.ThetypicalillustrationofthegeometricmodelinacoldrunnersystemisshowninFig.1bwheretherunnerthicknessischangedaccordingtothetemperaturegradient.3.Moldingdesignrequirements3.1ObjectivefunctionsOneofthemostsignificantfactorsconsideredintheinjectionmoldingdesignisaflowpattern,whichimpliesthatabalancedflowshouldbemaintainedwhileapolymerarrivesateachpartofadesignproduct.Oncetheimprovementonflowbalanceisobtained,theflowofmoltenpolymersmoothesandthemaximuminjectionpressureisdecreasedwiththesameoratleastevenlydistributedinjectionpressurelevelateachgate.Inacasewherethecertainpartofaproductwithinthemoldisfilledupearlierthanotherparts,eachpartwouldfallintoover-packingandunder-packingsituationsduringthefillingprocessofapolymerintomold.Suchproblemfurtherevokesamalformationliketwistingandbending,resultingfromthedifferenceincontractionrateduringthecourseofcooling-off.Thedifferenceinpressuretriggerstheflowofpolymerduringthefillingprocess,inwhichthemaximuminjectionpressureisdetectedattheinjectionportofpolymer.Thepolymeralwaysflowsfromhigh-pressureregiontolow-pressureone.Whenaflowpatternimproves,theflowofpolymergetssmootherwiththemaximuminjectionpressuredecreased.However,theflowinstabilitysometimeshappens,therebyrequiringahigherpressuretofillup.Thatis,themaximuminjectionpressureneedstobereducedinordertoimprovetheflowinstability.Thepressuregap(i.e.,thehighestandlowestpressurevalues)amongallofgatesisalsotakenasanotherobjectivefunctiontodeterminewhetherthewholemoldisbeingfilledatonce.Mostcommonlyaccepteddesignstrategytoimprovetheflowpatternistheadjustmentofgatelocation.Thepresentstudycontrolstheflowpatternbydevelopingtheoptimalgatepositioningproblemswithproperobjectivefunction(s)anddesigncons-traints.Objectivefunctionsforinjectionmoldingdesignareconsideredasbothmaximuminjectionpressure(MIP)andmaximumpressuredifference(MPD).Itshouldbenotedthatthemaximuminjectionpressureiscalculatedattheinjectionportandthemaximumpressuredifferenceisanumericaldifferencebetweenthehighestandlowestvaluesofpressureamongallofgates.Theaforementionedstatementscouldbeinterpretedasamultiobjectivedesignproblem,hencethepresentstudysimplyemploysaweightingmethodasfollows:*()()()MIPxMPDxFxMIPMPDDE(3)where,DandEareweightingfactorsasD+E=1,andxisasetofdesignvariableswhichareCartesiancoordinatesofgatesonaproduct.Eachcomponentintheaboveequationisnormalizedbyoptimalsingle-objectivefunctionvalue,(i.e.,MIP*,MPD*).Itismentionedthatthenumberofgatesisconsideredasaproblemparameterinthestudy.3.1ConstraintsWeld-linesareeasilydetectedwhenmorethantwoflowfrontshavingdifferenttemperaturevaluesmeetduringthefillingprocess.Theweld-lineisoneoftheweakestpointsinmoldedproduct;itisvery792JongsooLeeandJonghunKim/JournalofMechanicalScienceandTechnology21(2007)740749vulnerabletoashockandsubsequentlycausesexternaldefectsofaveryglossypolymer.Theweld-lineshouldbemovedintoalessweakregionbyadjustingthewidthofaproduct,thesizeand/orshapeofgatesandrunners,andthepositionofgates,etc.Thepresentstudyconsidersthepositionofaweld-lineasaconstraintinoptimalgatepositioningofmolddesign.Onceadesignerspecifiesareaswhereweld-linesshouldnotbegenerated,allofthefiniteelementnodesinsuchareasareconstrainednottoformtheweld-lines.Shearstressisdefinedasashearforceimposedonthewallofamoldbytheshearflowofapolymer.Themagnitudeofshearstressisproportionaltothepressuregradientofeachposition.Ingeneral,theshearstressiszeroatthecenterofamoldedproduct,andreachesamaximumvalueonthewall.Highshearstresstriggersthemoleculecultivationonthesurfaceofamoldedproduct.Flowinstabilitysuchasmeltfracturehasacloserelationshipwiththeshearstress.Theclearsurfaceofamoldedproductcanbeobtainedbyreducingthemagnitudeofshearstress.Thatis,shearstressshouldbeminimizedduringthemoldfillingprocessinordertoimprovethequalityofamoldedproduct,particularlyonitssurface.Maximumallowableshearstressdependsonthekindsofpolymer,andisgenerallytakenas1%oftensilestrengthofapolymer.Shearstressaffectingthequalityofendproductisconsideredasanotherconstraint.3.3FormulationofoptimizationproblemThestatementofamolddesignoptimizationproblemcanbewrittenasfollows:Find12(,)(,),(,),.,(,)Nxijkxijkxijkxijk(4)tominimize*()()()MIPxMPDxFxMIPMPDDE(5)subjecttoshearstress(i,j,k)shearstressallowable(6)weld-line(i,j,k)=designatedarea(s)only(7)where,lowerupperxxxddAsetofdesignvariables,xareCartesiancoordi-nates(i,j,k)ofgatesonthesurfaceofamoldedproduct,whereNisthenumberofgates.Atraditionalweighted-summethodinthecontextofmultiob-jectiveoptimizationisemployedbyusingtwowei-Fig.2.MicroGAprocess.ghtingfactorsofDandE,whereD+E=1.Multi-objectivefunctionsconsideredinthepresentstudyaremaximuminjectionpressure(MIP)measuredattheinjectionportandmaximumpressuredifferen
温馨提示
- 1. 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
- 2. 本站的文档不包含任何第三方提供的附件图纸等,如果需要附件,请联系上传者。文件的所有权益归上传用户所有。
- 3. 本站RAR压缩包中若带图纸,网页内容里面会有图纸预览,若没有图纸预览就没有图纸。
- 4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
- 5. 人人文库网仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对用户上传分享的文档内容本身不做任何修改或编辑,并不能对任何下载内容负责。
- 6. 下载文件中如有侵权或不适当内容,请与我们联系,我们立即纠正。
- 7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
最新文档
- 高三班级期末总结(30篇)
- 音乐课题开题报告(30篇)
- 采购部的工作总结与计划(5篇)
- 酒店人员年度工作总结(4篇)
- 部门季度工作总结模板(5篇)
- 购买办公桌请示格式范文(6篇)
- 2024春季中国铁塔福建分公司校园招聘24人高频考题难、易错点模拟试题(共500题)附带答案详解
- 2024广西靖西市扶贫办政府招聘编外人员282人高频考题难、易错点模拟试题(共500题)附带答案详解
- 电机与拖动基础课件
- 疫情防控紧急预案处置方案5篇
- 中国移动智能终端行业市场现状供需分析及市场深度研究发展前景及规划可行性分析研究报告(2024-2030)
- 人教版九年级下册世界历史全册复习课件市公开课一等奖省赛课获奖课件
- 2023年烟草四川公司考试真题及答案
- 《后现代主义》课件
- (2024年)幼儿园教职工安全教育培训
- 安全技术交底书(一级)
- 七年级上册信息技术第三单元第十一课即时通信
- 同伴关系对学生心理健康的影响
- 2024年江苏省生态环境监测专业技术人员大比武竞赛备考试题库(含答案)
- 八年级下册语文作文教案
- 生物骨干教师述职报告.doc
评论
0/150
提交评论