




已阅读5页,还剩24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
附录2INTEGRATEDSIMULATIONOFTHEINJECTIONMOLDINGPROCESSWITHSTEREOLITHOGRAPHYMOLDSABSTRACTFUNCTIONALPARTSARENEEDEDFORDESIGNVERICATIONTESTING,ELDTRIALS,CUSTOMEREVALUATION,ANDPRODUCTIONPLANNINGBYELIMINATINGMULTIPLESTEPS,THECREATIONOFTHEINJECTIONMOLDDIRECTLYBYARAPIDPROTOTYPINGRPPROCESSHOLDSTHEBESTPROMISEOFREDUCINGTHETIMEANDCOSTNEEDEDTOMOLDLOWVOLUMEQUANTITIESOFPARTSTHEPOTENTIALOFTHISINTEGRATIONOFINJECTIONMOLDINGWITHRPHASBEENDEMONSTRATEDMANYTIMESWHATISMISSINGISTHEFUNDAMENTALUNDERSTANDINGOFHOWTHEMODICATIONSTOTHEMOLDMATERIALANDRPMANUFACTURINGPROCESSIMPACTBOTHTHEMOLDDESIGNANDTHEINJECTIONMOLDINGPROCESSINADDITION,NUMERICALSIMULATIONTECHNIQUESHAVENOWBECOMEHELPFULTOOLSOFMOLDDESIGNERSANDPROCESSENGINEERSFORTRADITIONALINJECTIONMOLDINGBUTALLCURRENTSIMULATIONPACKAGESFORCONVENTIONALINJECTIONMOLDINGARENOLONGERAPPLICABLETOTHISNEWTYPEOFINJECTIONMOLDS,MAINLYBECAUSETHEPROPERTYOFTHEMOLDMATERIALCHANGESGREATLYINTHISPAPER,ANINTEGRATEDAPPROACHTOACCOMPLISHANUMERICALSIMULATIONOFINJECTIONMOLDINGINTORAPIDPROTOTYPEDMOLDSISESTABLISHEDANDACORRESPONDINGSIMULATIONSYSTEMISDEVELOPEDCOMPARISONSWITHEXPERIMENTALRESULTSAREEMPLOYEDFORVERICATION,WHICHSHOWTHATTHEPRESENTSCHEMEISWELLSUITEDTOHANDLERPFABRICATEDSTEREOLITHOGRAPHYSLMOLDSKEYWORDSINJECTIONMOLDINGNUMERICALSIMULATIONRAPIDPROTOTYPING1INTRODUCTIONININJECTIONMOLDING,THEPOLYMERMELTATHIGHTEMPERATUREISINJECTEDINTOTHEMOLDUNDERHIGHPRESSURE1THUS,THEMOLDMATERIALNEEDSTOHAVETHERMALANDMECHANICALPROPERTIESCAPABLEOFWITHSTANDINGTHETEMPERATURESANDPRESSURESOFTHEMOLDINGCYCLETHEFOCUSOFMANYSTUDIESHASBEENTOCREATETHEINJECTIONMOLDDIRECTLYBYARAPIDPROTOTYPINGRPPROCESSBYELIMINATINGMULTIPLESTEPS,THISMETHODOFTOOLINGHOLDSTHEBESTPROMISEOFREDUCINGTHETIMEANDCOSTNEEDEDTOCREATELOWVOLUMEQUANTITIESOFPARTSINAPRODUCTIONMATERIALTHEPOTENTIALOFINTEGRATINGINJECTIONMOLDINGWITHRPTECHNOLOGIESHASBEENDEMONSTRATEDMANYTIMESTHEPROPERTIESOFRPMOLDSAREVERYDIFFERENTFROMTHOSEOFTRADITIONALMETALMOLDSTHEKEYDIFFERENCESARETHEPROPERTIESOFTHERMALCONDUCTIVITYANDELASTICMODULUSRIGIDITYFOREXAMPLE,THEPOLYMERSUSEDINRPFABRICATEDSTEREOLITHOGRAPHYSLMOLDSHAVEATHERMALCONDUCTIVITYTHATISLESSTHANONETHOUSANDTHTHATOFANALUMINUMTOOLINUSINGRPTECHNOLOGIESTOCREATEMOLDS,THEENTIREMOLDDESIGNANDINJECTIONMOLDINGPROCESSPARAMETERSNEEDTOBEMODIEDANDOPTIMIZEDFROMTRADITIONALMETHODOLOGIESDUETOTHECOMPLETELYDIFFERENTTOOLMATERIALHOWEVER,THEREISSTILLNOTAFUNDAMENTALUNDERSTANDINGOFHOWTHEMODICATIONSTOTHEMOLDTOOLINGMETHODANDMATERIALIMPACTBOTHTHEMOLDDESIGNANDTHEINJECTIONMOLDINGPROCESSPARAMETERSONECANNOTOBTAINREASONABLERESULTSBYSIMPLYCHANGINGAFEWMATERIALPROPERTIESINCURRENTMODELSALSO,USINGTRADITIONALAPPROACHESWHENMAKINGACTUALPARTSMAYBEGENERATINGSUBOPTIMALRESULTSSOTHEREISADIRENEEDTOSTUDYTHEINTERACTIONBETWEENTHERAPIDTOOLINGRTPROCESSANDMATERIALANDINJECTIONMOLDING,SOASTOESTABLISHTHEMOLDDESIGNCRITERIAANDTECHNIQUESFORANRTORIENTEDINJECTIONMOLDINGPROCESSINADDITION,COMPUTERSIMULATIONISANEFFECTIVEAPPROACHFORPREDICTINGTHEQUALITYOFMOLDEDPARTSCOMMERCIALLYAVAILABLESIMULATIONPACKAGESOFTHETRADITIONALINJECTIONMOLDINGPROCESSHAVENOWBECOMEROUTINETOOLSOFTHEMOLDDESIGNERANDPROCESSENGINEER2UNFORTUNATELY,CURRENTSIMULATIONPROGRAMSFORCONVENTIONALINJECTIONMOLDINGARENOLONGERAPPLICABLETORPMOLDS,BECAUSEOFTHEDRAMATICALLYDISSIMILARTOOLMATERIALFORINSTANCE,INUSINGTHEEXISTINGSIMULATIONSOFTWAREWITHALUMINUMANDSLMOLDSANDCOMPARINGWITHEXPERIMENTALRESULTS,THOUGHTHESIMULATIONVALUESOFPARTDISTORTIONAREREASONABLEFORTHEALUMINUMMOLD,RESULTSAREUNACCEPTABLE,WITHTHEERROREXCEEDING50THEDISTORTIONDURINGINJECTIONMOLDINGISDUETOSHRINKAGEANDWARPAGEOFTHEPLASTICPART,ASWELLASTHEMOLDFORORDINARILYMOLDS,THEMAINFACTORISTHESHRINKAGEANDWARPAGEOFTHEPLASTICPART,WHICHISMODELEDACCURATELYINCURRENTSIMULATIONSBUTFORRPMOLDS,THEDISTORTIONOFTHEMOLDHASPOTENTIALLYMOREINUENCE,WHICHHAVEBEENNEGLECTEDINCURRENTMODELSFORINSTANCE,3USEDASIMPLETHREESTEPSIMULATIONPROCESSTOCONSIDERTHEMOLDDISTORTION,WHICHHADTOOMUCHDEVIATIONINTHISPAPER,BASEDONTHEABOVEANALYSIS,ANEWSIMULATIONSYSTEMFORRPMOLDSISDEVELOPEDTHEPROPOSEDSYSTEMFOCUSESONPREDICTINGPARTDISTORTION,WHICHISDOMINATINGDEFECTINRPMOLDEDPARTSTHEDEVELOPEDSIMULATIONCANBEAPPLIEDASANEVALUATIONTOOLFORRPMOLDDESIGNANDPROCESSOPTIMIZATIONOURSIMULATIONSYSTEMISVERIEDBYANEXPERIMENTALEXAMPLEALTHOUGHMANYMATERIALSAREAVAILABLEFORUSEINRPTECHNOLOGIES,WECONCENTRATEONUSINGSTEREOLITHOGRAPHYSL,THEORIGINALRPTECHNOLOGY,TOCREATEPOLYMERMOLDSTHESLPROCESSUSESPHOTOPOLYMERANDLASERENERGYTOBUILDAPARTLAYERBYLAYERUSINGSLTAKESADVANTAGEOFBOTHTHECOMMERCIALDOMINANCEOFSLINTHERPINDUSTRYANDTHESUBSEQUENTEXPERTISEBASETHATHASBEENDEVELOPEDFORCREATINGACCURATE,HIGHQUALITYPARTSUNTILRECENTLY,SLWASPRIMARILYUSEDTOCREATEPHYSICALMODELSFORVISUALINSPECTIONANDFORMTSTUDIESWITHVERYLIMITEDFUNCTIONALAPPLICATIONSHOWEVER,THENEWERGENERATIONSTEREOLITHOGRAPHICPHOTOPOLYMERSHAVEIMPROVEDDIMENSIONAL,MECHANICALANDTHERMALPROPERTIESMAKINGITPOSSIBLETOUSETHEMFORACTUALFUNCTIONALMOLDS2INTEGRATEDSIMULATIONOFTHEMOLDINGPROCESS21METHODOLOGYINORDERTOSIMULATETHEUSEOFANSLMOLDINTHEINJECTIONMOLDINGPROCESS,ANITERATIVEMETHODISPROPOSEDDIFFERENTSOFTWAREMODULESHAVEBEENDEVELOPEDANDUSEDTOACCOMPLISHTHISTASKTHEMAINASSUMPTIONISTHATTEMPERATUREANDLOADBOUNDARYCONDITIONSCAUSESIGNICANTDISTORTIONSINTHESLMOLDTHESIMULATIONSTEPSAREASFOLLOWS1THEPARTGEOMETRYISMODELEDASASOLIDMODEL,WHICHISTRANSLATEDTOALEREADABLEBYTHEOWANALYSISPACKAGE2SIMULATETHEMOLDLLINGPROCESSOFTHEMELTINTOAPHOTOPOLYMERMOLD,WHICHWILLOUTPUTTHERESULTINGTEMPERATUREANDPRESSUREPROLES3STRUCTURALANALYSISISTHENPERFORMEDONTHEPHOTOPOLYMERMOLDMODELUSINGTHETHERMALANDLOADBOUNDARYCONDITIONSOBTAINEDFROMTHEPREVIOUSSTEP,WHICHCALCULATESTHEDISTORTIONTHATTHEMOLDUNDERGODURINGTHEINJECTIONPROCESS4IFTHEDISTORTIONOFTHEMOLDCONVERGES,MOVETOTHENEXTSTEPOTHERWISE,THEDISTORTEDMOLDCAVITYISTHENMODELEDCHANGESINTHEDIMENSIONSOFTHECAVITYAFTERDISTORTION,ANDRETURNSTOTHESECONDSTEPTOSIMULATETHEMELTINJECTIONINTOTHEDISTORTEDMOLD5THESHRINKAGEANDWARPAGESIMULATIONOFTHEINJECTIONMOLDEDPARTISTHENAPPLIED,WHICHCALCULATESTHENALDISTORTIONSOFTHEMOLDEDPARTINABOVESIMULATIONOW,THEREARETHREEBASICSIMULATIONMODULES22FILLINGSIMULATIONOFTHEMELT221MATHEMATICALMODELINGINORDERTOSIMULATETHEUSEOFANSLMOLDINTHEINJECTIONMOLDINGPROCESS,ANITERATIVEMETHODISPROPOSEDDIFFERENTSOFTWAREMODULESHAVEBEENDEVELOPEDANDUSEDTOACCOMPLISHTHISTASKTHEMAINASSUMPTIONISTHATTEMPERATUREANDLOADBOUNDARYCONDITIONSCAUSESIGNIFICANTDISTORTIONSINTHESLMOLDTHESIMULATIONSTEPSAREASFOLLOWS1THEPARTGEOMETRYISMODELEDASASOLIDMODEL,WHICHISTRANSLATEDTOAFILEREADABLEBYTHEFLOWANALYSISPACKAGE2SIMULATETHEMOLDFILLINGPROCESSOFTHEMELTINTOAPHOTOPOLYMERMOLD,WHICHWILLOUTPUTTHERESULTINGTEMPERATUREANDPRESSUREPROFILES3STRUCTURALANALYSISISTHENPERFORMEDONTHEPHOTOPOLYMERMOLDMODELUSINGTHETHERMALANDLOADBOUNDARYCONDITIONSOBTAINEDFROMTHEPREVIOUSSTEP,WHICHCALCULATESTHEDISTORTIONTHATTHEMOLDUNDERGODURINGTHEINJECTIONPROCESS4IFTHEDISTORTIONOFTHEMOLDCONVERGES,MOVETOTHENEXTSTEPOTHERWISE,THEDISTORTEDMOLDCAVITYISTHENMODELEDCHANGESINTHEDIMENSIONSOFTHECAVITYAFTERDISTORTION,ANDRETURNSTOTHESECONDSTEPTOSIMULATETHEMELTINJECTIONINTOTHEDISTORTEDMOLD5THESHRINKAGEANDWARPAGESIMULATIONOFTHEINJECTIONMOLDEDPARTISTHENAPPLIED,WHICHCALCULATESTHEFINALDISTORTIONSOFTHEMOLDEDPARTINABOVESIMULATIONFLOW,THEREARETHREEBASICSIMULATIONMODULES22FILLINGSIMULATIONOFTHEMELT221MATHEMATICALMODELINGCOMPUTERSIMULATIONTECHNIQUESHAVEHADSUCCESSINPREDICTINGFILLINGBEHAVIORINEXTREMELYCOMPLICATEDGEOMETRIESHOWEVER,MOSTOFTHECURRENTNUMERICALIMPLEMENTATIONISBASEDONAHYBRIDFINITEELEMENT/FINITEDIFFERENCESOLUTIONWITHTHEMIDDLEPLANEMODELTHEAPPLICATIONPROCESSOFSIMULATIONPACKAGESBASEDONTHISMODELISILLUSTRATEDINFIG21HOWEVER,UNLIKETHESURFACE/SOLIDMODELINMOLDDESIGNCADSYSTEMS,THESOCALLEDMIDDLEPLANEASSHOWNINFIG21BISANIMAGINARYARBITRARYPLANARGEOMETRYATTHEMIDDLEOFTHECAVITYINTHEGAPWISEDIRECTION,WHICHSHOULDBRINGABOUTGREATINCONVENIENCEINAPPLICATIONSFOREXAMPLE,SURFACEMODELSARECOMMONLYUSEDINCURRENTRPSYSTEMSGENERALLYSTLFILEFORMAT,SOSECONDARYMODELINGISUNAVOIDABLEWHENUSINGSIMULATIONPACKAGESBECAUSETHEMODELSINTHERPANDSIMULATIONSYSTEMSAREDIFFERENTCONSIDERINGTHESEDEFECTS,THESURFACEMODELOFTHECAVITYISINTRODUCEDASDATUMPLANESINTHESIMULATION,INSTEADOFTHEMIDDLEPLANEACCORDINGTOTHEPREVIOUSINVESTIGATIONS46,FILLINGGOVERNINGEQUATIONSFORTHEFLOWANDTEMPERATUREFIELDCANBEWRITTENASWHEREX,YARETHEPLANARCOORDINATESINTHEMIDDLEPLANE,ANDZISTHEGAPWISECOORDINATEU,V,WARETHEVELOCITYCOMPONENTSINTHEX,Y,ZDIRECTIONSU,VARETHEAVERAGEWHOLEGAPTHICKNESSESAND,CPT,KTREPRESENTVISCOSITY,DENSITY,SPECIFICHEATANDTHERMALCONDUCTIVITYOFPOLYMERMELT,RESPECTIVELYFIG21ADSCHEMATICPROCEDUREOFTHESIMULATIONWITHMIDDLEPLANEMODELATHE3DSURFACEMODELBTHEMIDDLEPLANEMODELCTHEMESHEDMIDDLEPLANEMODELDTHEDISPLAYOFTHESIMULATIONRESULTINADDITION,BOUNDARYCONDITIONSINTHEGAPWISEDIRECTIONCANBEDEFINEDASWHERETWISTHECONSTANTWALLTEMPERATURESHOWNINFIG2ACOMBININGEQS14WITHEQS56,ITFOLLOWSTHATTHEDISTRIBUTIONSOFTHEU,V,T,PATZCOORDINATESSHOULDBESYMMETRICAL,WITHTHEMIRRORAXISBEINGZ0,ANDCONSEQUENTLYTHEU,VAVERAGEDINHALFGAPTHICKNESSISEQUALTOTHATAVERAGEDINWHOLEGAPTHICKNESSBASEDONTHISCHARACTERISTIC,WECANDIVIDETHEWHOLECAVITYINTOTWOEQUALPARTSINTHEGAPWISEDIRECTION,ASDESCRIBEDBYPARTIANDPARTIIINFIG2BATTHESAMETIME,TRIANGULARFINITEELEMENTSAREGENERATEDINTHESURFACESOFTHECAVITYATZ0INFIG2B,INSTEADOFTHEMIDDLEPLANEATZ0INFIG2AACCORDINGLY,FINITEDIFFERENCEINCREMENTSINTHEGAPWISEDIRECTIONAREEMPLOYEDONLYINTHEINSIDEOFTHESURFACESWALLTOMIDDLE/CENTERLINE,WHICH,INFIG2B,MEANSFROMZ0TOZBTHISISSINGLESIDEDINSTEADOFTWOSIDEDWITHRESPECTTOTHEMIDDLEPLANEIEFROMTHEMIDDLELINETOTWOWALLSINADDITION,THECOORDINATESYSTEMISCHANGEDFROMFIG2ATOFIG2BTOALTERTHEFINITEELEMENT/FINITEDIFFERENCESCHEME,ASSHOWNINFIG2BWITHTHEABOVEADJUSTMENT,GOVERNINGEQUATIONSARESTILLEQS14HOWEVER,THEORIGINALBOUNDARYCONDITIONSINTHEGAPWISEDIRECTIONAREREWRITTENASMEANWHILE,ADDITIONALBOUNDARYCONDITIONSMUSTBEEMPLOYEDATZBINORDERTOKEEPTHEFLOWSATTHEJUNCTUREOFTHETWOPARTSATTHESAMESECTIONCOORDINATE7WHERESUBSCRIPTSI,IIREPRESENTTHEPARAMETERSOFPARTIANDPARTII,RESPECTIVELY,ANDCMIANDCMIIINDICATETHEMOVINGFREEMELTFRONTSOFTHESURFACESOFTHEDIVIDEDTWOPARTSINTHEFILLINGSTAGEITSHOULDBENOTEDTHAT,UNLIKECONDITIONSEQS7AND8,ENSURINGCONDITIONSEQS9AND10AREUPHELDINNUMERICALIMPLEMENTATIONSBECOMESMOREDIFFICULTDUETOTHEFOLLOWINGREASONS1THESURFACESATTHESAMESECTIONHAVEBEENMESHEDRESPECTIVELY,WHICHLEADSTOADISTINCTIVEPATTERNOFFINITEELEMENTSATTHESAMESECTIONTHUS,ANINTERPOLATIONOPERATIONSHOULDBEEMPLOYEDFORU,V,T,PDURINGTHECOMPARISONBETWEENTHETWOPARTSATTHEJUNCTURE2BECAUSETHETWOPARTSHAVERESPECTIVEFLOWFIELDSWITHRESPECTTOTHENODESATPOINTAANDPOINTCASSHOWNINFIG2BATTHESAMESECTION,ITISPOSSIBLETOHAVEEITHERBOTHFILLEDORONEFILLEDANDONEEMPTYTHESETWOCASESSHOULDBEHANDLEDSEPARATELY,AVERAGINGTHEOPERATIONFORTHEFORMER,WHEREASASSIGNINGOPERATIONFORTHELATTER3ITFOLLOWSTHATASMALLDIFFERENCEBETWEENTHEMELTFRONTSISPERMISSIBLETHATALLOWANCECANBEIMPLEMENTEDBYTIMEALLOWANCECONTROLORPREFERABLELOCATIONALLOWANCECONTROLOFTHEMELTFRONTNODES4THEBOUNDARIESOFTHEFLOWFIELDEXPANDBYEACHMELTFRONTADVANCEMENT,SOITISNECESSARYTOCHECKTHECONDITIONEQ10AFTEREACHCHANGEINTHEMELTFRONT5INVIEWOFABOVEMENTIONEDANALYSIS,THEPHYSICALPARAMETERSATTHENODESOFTHESAMESECTIONSHOULDBECOMPAREDANDADJUSTED,SOTHEINFORMATIONDESCRIBINGFINITEELEMENTSOFTHESAMESECTIONSHOULDBEPREPAREDBEFORESIMULATION,THATIS,THEMATCHINGOPERATIONAMONGTHEELEMENTSSHOULDBEPREFORMEDFIG2A,BILLUSTRATIVEOFBOUNDARYCONDITIONSINTHEGAPWISEDIRECTIONAOFTHEMIDDLEPLANEMODELBOFTHESURFACEMODEL222NUMERICALIMPLEMENTATIONPRESSUREFIELDINMODELINGVISCOSITY,WHICHISAFUNCTIONOFSHEARRATE,TEMPERATUREANDPRESSUREOFMELT,THESHEARTHINNINGBEHAVIORCANBEWELLREPRESENTEDBYACROSSTYPEMODELSUCHASWHERENCORRESPONDSTOTHEPOWERLAWINDEX,ANDCHARACTERIZESTHESHEARSTRESSLEVELOFTHETRANSITIONREGIONBETWEENTHENEWTONIANANDPOWERLAWASYMPTOTICLIMITSINTERMSOFANARRHENIUSTYPETEMPERATURESENSITIVITYANDEXPONENTIALPRESSUREDEPENDENCE,0T,PCANBEREPRESENTEDWITHREASONABLEACCURACYASFOLLOWSEQUATIONS11AND12CONSTITUTEAFIVECONSTANTN,B,TB,REPRESENTATIONFORVISCOSITYTHESHEARRATEFORVISCOSITYCALCULATIONISOBTAINEDBYBASEDONTHEABOVE,WECANINFERTHEFOLLOWINGFILLINGPRESSUREEQUATIONFROMTHEGOVERNINGEQS14WHERESISCALCULATEDBYSB0/BZ2DZAPPLYINGTHEGALERKINMETHOD,THEPRESSUREFINITEELEMENTEQUATIONISDEDUCEDASWHEREL_TRAVERSESALLELEMENTS,INCLUDINGNODEN,ANDWHEREIANDJREPRESENTTHELOCALNODENUMBERINELEMENTL_CORRESPONDINGTOTHENODENUMBERNANDN_INTHEWHOLE,RESPECTIVELYTHEDL_IJISCALCULATEDASFOLLOWSWHEREAL_REPRESENTSTRIANGULARFINITEELEMENTS,ANDLL_IISTHEPRESSURETRIALFUNCTIONINFINITEELEMENTSTEMPERATUREFIELDTODETERMINETHETEMPERATUREPROFILEACROSSTHEGAP,EACHTRIANGULARFINITEELEMENTATTHESURFACEISFURTHERDIVIDEDINTONZLAYERSFORTHEFINITEDIFFERENCEGRIDTHELEFTITEMOFTHEENERGYEQUATIONEQ4CANBEEXPRESSEDASWHERETN,J,TREPRESENTSTHETEMPERATUREOFTHEJLAYEROFNODENATTIMETTHEHEATCONDUCTIONITEMISCALCULATEDBYWHERELTRAVERSESALLELEMENTS,INCLUDINGNODEN,ANDIANDJREPRESENTTHELOCALNODENUMBERINELEMENTLCORRESPONDINGTOTHENODENUMBERNANDN_INTHEWHOLE,RESPECTIVELYTHEHEATCONVECTIONITEMISCALCULATEDBYFORVISCOUSHEAT,ITFOLLOWSTHATSUBSTITUTINGEQS1720INTOTHEENERGYEQUATIONEQ4,THETEMPERATUREEQUATIONBECOMES23STRUCTURALANALYSISOFTHEMOLDTHEPURPOSEOFSTRUCTURALANALYSISISTOPREDICTTHEDEFORMATIONOCCURRINGINTHEPHOTOPOLYMERMOLDDUETOTHETHERMALANDMECHANICALLOADSOFTHEFILLINGPROCESSTHISMODELISBASEDONATHREEDIMENSIONALTHERMOELASTICBOUNDARYELEMENTMETHODBEMTHEBEMISIDEALLYSUITEDFORTHISAPPLICATIONBECAUSEONLYTHEDEFORMATIONOFTHEMOLDSURFACESISOFINTERESTMOREOVER,THEBEMHASANADVANTAGEOVEROTHERTECHNIQUESINTHATCOMPUTINGEFFORTISNOTWASTEDONCALCULATINGDEFORMATIONWITHINTHEMOLDTHESTRESSESRESULTINGFROMTHEPROCESSLOADSAREWELLWITHINTHEELASTICRANGEOFTHEMOLDMATERIALTHEREFORE,THEMOLDDEFORMATIONMODELISBASEDONATHERMOELASTICFORMULATIONTHETHERMALANDMECHANICALPROPERTIESOFTHEMOLDAREASSUMEDTOBEISOTROPICANDTEMPERATUREINDEPENDENTALTHOUGHTHEPROCESSISCYCLIC,TIMEAVERAGEDVALUESOFTEMPERATUREANDHEATFLUXAREUSEDFORCALCULATINGTHEMOLDDEFORMATIONTYPICALLY,TRANSIENTTEMPERATUREVARIATIONSWITHINAMOLDHAVEBEENRESTRICTEDTOREGIONSLOCALTOTHECAVITYSURFACEANDTHENOZZLETIP8THETRANSIENTSDECAYSHARPLYWITHDISTANCEFROMTHECAVITYSURFACEANDGENERALLYLITTLEVARIATIONISOBSERVEDBEYONDDISTANCESASSMALLAS25MMTHISSUGGESTSTHATTHECONTRIBUTIONFROMTHETRANSIENTSTOTHEDEFORMATIONATTHEMOLDBLOCKINTERFACEISSMALL,ANDTHEREFOREITISREASONABLETONEGLECTTHETRANSIENTEFFECTSTHESTEADYSTATETEMPERATUREFIELDSATISFIESLAPLACESEQUATION2T0ANDTHETIMEAVERAGEDBOUNDARYCONDITIONSTHEBOUNDARYCONDITIONSONTHEMOLDSURFACESAREDESCRIBEDINDETAILBYTANGETAL9ASFORTHEMECHANICALBOUNDARYCONDITIONS,THECAVITYSURFACEISSUBJECTEDTOTHEMELTPRESSURE,THESURFACESOFTHEMOLDCONNECTEDTOTHEWORKTABLEAREFIXEDINSPACE,ANDOTHEREXTERNALSURFACESAREASSUMEDTOBESTRESSFREETHEDERIVATIONOFTHETHERMOELASTICBOUNDARYINTEGRALFORMULATIONISWELLKNOWN10ITISGIVENBYWHEREUK,PKANDTARETHEDISPLACEMENT,TRACTIONANDTEMPERATURE,REPRESENTTHETHERMALEXPANSIONCOEFFICIENTANDPOISSONSRATIOOFTHEMATERIAL,ANDR|YX|CLKXISTHESURFACECOEFFICIENTWHICHDEPENDSONTHELOCALGEOMETRYATX,THEORIENTATIONOFTHECOORDINATEFRAMEANDPOISSONSRATIOFORTHEDOMAIN11THEFUNDAMENTALDISPLACEMENTULKATAPOINTYINTHEXKDIRECTION,INATHREEDIMENSIONALINFINITEISOTROPICELASTICDOMAIN,RESULTSFROMAUNITLOADCONCENTRATEDATAPOINTXACTINGINTHEXLDIRECTIONANDISOFTHEFORMWHERELKISTHEKRONECKERDELTAFUNCTIONANDISTHESHEARMODULUSOFTHEMOLDMATERIALTHEFUNDAMENTALTRACTIONPLK,MEASUREDATTHEPOINTYONASURFACEWITHUNITNORMALN,ISDISCRETIZINGTHESURFACEOFTHEMOLDINTOATOTALOFNELEMENTSTRANSFORMSEQ22TOWHERENREFERSTOTHENTHSURFACEELEMENTONTHEDOMAINSUBSTITUTINGTHEAPPROPRIATELINEARSHAPEFUNCTIONSINTOEQ25,THELINEARBOUNDARYELEMENTFORMULATIONFORTHEMOLDDEFORMATIONMODELISOBTAINEDTHEEQUATIONISAPPLIEDATEACHNODEONTHEDISCRETIZEDMOLDSURFACE,THUSGIVINGASYSTEMOF3NLINEAREQUATIONS,WHERENISTHETOTALNUMBEROFNODESEACHNODEHASEIGHTASSOCIATEDQUANTITIESTHREECOMPONENTSOFDISPLACEMENT,THREECOMPONENTSOFTRACTION,ATEMPERATUREANDAHEATFLUXTHESTEADYSTATETHERMALMODELSUPPLIESTEMPERATUREANDFLUXVALUESASKNOWNQUANTITIESFOREACHNODE,ANDOFTHEREMAININGSIXQUANTITIES,THREEMUSTBESPECIFIEDMOREOVER,THEDISPLACEMENTVALUESSPECIFIEDATACERTAINNUMBEROFNODESMUSTELIMINATETHEPOSSIBILITYOFARIGIDBODYMOTIONORRIGIDBODYROTATIONTOENSUREANONSINGULARSYSTEMOFEQUATIONSTHERESULTINGSYSTEMOFEQUATIONSISASSEMBLEDINTOAINTEGRATEDMATRIX,WHICHISSOLVEDWITHANITERATIVESOLVER24SHRINKAGEANDWARPAGESIMULATIONOFTHEMOLDEDPARTINTERNALSTRESSESININJECTIONMOLDEDCOMPONENTSARETHEPRINCIPALCAUSEOFSHRINKAGEANDWARPAGETHESERESIDUALSTRESSESAREMAINLYFROZENINTHERMALSTRESSESDUETOINHOMOGENEOUSCOOLING,WHENSURFACELAYERSSTIFFENSOONERTHANTHECOREREGION,ASINFREEQUENCHINGBASEDONTHEASSUMPTIONOFTHELINEARTHERMOELASTICANDLINEARTHERMOVISCOELASTICCOMPRESSIBLEBEHAVIOROFTHEPOLYMERICMATERIALS,SHRINKAGEANDWARPAGEAREOBTAINEDIMPLICITLYUSINGDISPLACEMENTFORMULATIONS,ANDTHEGOVERNINGEQUATIONSCANBESOLVEDNUMERICALLYUSINGAFINITEELEMENTMETHODWITHTHEBASICASSUMPTIONSOFINJECTIONMOLDING12,THECOMPONENTSOFSTRESSANDSTRAINAREGIVENBYTHEDEVIATORICCOMPONENTSOFSTRESSANDSTRAIN,RESPECTIVELY,AREGIVENBYUSINGASIMILARAPPROACHDEVELOPEDBYLEEANDROGERS13FORPREDICTINGTHERESIDUALSTRESSESINTHETEMPERINGOFGLASS,ANINTEGRALFORMOFTHEVISCOELASTICCONSTITUTIVERELATIONSHIPSISUSED,ANDTHEINPLANESTRESSESCANBERELATEDTOTHESTRAINSBYTHEFOLLOWINGEQUATIONWHEREG1ISTHERELAXATIONSHEARMODULUSOFTHEMATERIALTHEDILATATIONALSTRESSESCANBERELATEDTOTHESTRAINASFOLLOWSWHEREKISTHERELAXATIONBULKMODULUSOFTHEMATERIAL,ANDTHEDEFINITIONOFANDISIFT0,APPLYINGEQ27TOEQ29RESULTSINSIMILARLY,APPLYINGEQ31TOEQ28ANDELIMINATINGSTRAINXXZ,TRESULTSINEMPLOYINGALAPLACETRANSFORMTOEQ32,THEAUXILIARYMODULUSRISGIVENBYUSINGTHEABOVECONSTITUTIVEEQUATIONEQ33ANDSIMPLIFIEDFORMSOFTHESTRESSESANDSTRAINSINTHEMOLD,THEFORMULATIONOFTHERESIDUALSTRESSOFTHEINJECTIONMOLDEDPARTDURINGTHECOOLINGSTAGEISOBTAINBYEQUATION34CANBESOLVEDTHROUGHTHEAPPLICATIONOFTRAPEZOIDALQUADRATUREDUETOTHERAPIDINITIALCHANGEINTHEMATERIALTIME,AQUASINUMERICALPROCEDUREISEMPLOYEDFOREVALUATINGTHEINTEGRALITEMTHEAUXILIARYMODULUSISEVALUATEDNUMERICALLYBYTHETRAPEZOIDALRULEFORWARPAGEANALYSIS,NODALDISPLACEMENTSANDCURVATURESFORSHELLELEMENTSAREEXPRESSEDASWHEREKISTHEELEMENTSTIFFNESSMATRIX,BEISTHEDERIVATIVEOPERATORMATRIX,DISTHEDISPLACEMENTS,ANDREISTHEELEMENTLOADVECTORWHICHCANBEEVALUATEDBYTHEUSEOFAFULLTHREEDIMENSIONALFEMANALYSISCANACHIEVEACCURATEWARPAGERESULTS,HOWEVER,ITISCUMBERSOMEWHENTHESHAPEOFTHEPARTISVERYCOMPLICATEDINTHISPAPER,ATWODIMENSIONALFEMMETHOD,BASEDONSHELLTHEORY,WASUSEDBECAUSEMOSTINJECTIONMOLDEDPARTSHAVEASHEETLIKEGEOMETRYINWHICHTHETHICKNESSISMUCHSMALLERTHANTHEOTHERDIMENSIONSOFTHEPARTTHEREFORE,THEPART
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
- 2025年及未来5年中国高端物业管理行业市场调查研究及投资战略咨询报告
- 2025福建福州文教职业中专学校招聘1人考前自测高频考点模拟试题及答案详解(网校专用)
- 2025贵州省职工医院第十三届贵州人博会引进高层次人才和急需紧缺人才招聘13人模拟试卷附答案详解(完整版)
- 2025广东省农业科学院设施农业研究所招聘劳动合同制人员1人模拟试卷带答案详解
- 2025湖南省社会科学院(湖南省人民政府发展研究中心)招聘高层次人才14人模拟试卷及答案详解(新)
- 2025年甘肃省兰州新区石化产业投资集团有限公司急需紧缺专业技术岗位招聘14人模拟试卷附答案详解(考试直接用)
- 2025辽宁鞍山立山区教育局招聘2人模拟试卷及完整答案详解一套
- 2025广东清远市英德市招聘教师222人模拟试卷及一套答案详解
- 2025航天六院内蒙古航天红峡化工有限公司招聘30人模拟试卷及1套参考答案详解
- 2025江苏盐城工学院招聘7人模拟试卷及完整答案详解
- 新版中华民族共同体概论课件第十二讲民族危亡与中华民族意识觉醒(1840-1919)-2025年版
- 2025-2026学年人教版(2024)九年级物理全册第十四章 内能的利用(单元同步检测练习)(含答案)
- 第1课时 10的加、减法(教学设计)-2024-2025学年一年级上册数学人教版
- 2025至2030中国聚烯烃行业项目调研及市场前景预测评估报告
- 2025四川达州宣汉县国有资产管理服务中心县属国有企业招聘劳动合同职工26人笔试历年参考题库附带答案详解
- 新教科版小学1-6年级科学需做实验目录
- 传染病学课件:霍乱完整版
- 《电子商务法律法规》课程标准
- 医院关于印发《即时检验临床应用管理办法》的通知
- 三年级下册书法练习指导全册教案(湖南美术出版社)
- GB/T 17880.5-1999平头六角铆螺母
评论
0/150
提交评论