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IntJAdvManufTechnol200016739–7472000SpringerVerlagLondonLimitedAutomatedAssemblyModellingforPlasticInjectionMouldsX.G.Ye,J.Y.H.FuhandK.S.LeeDepartmentofMechanicalandProductionEngineering,NationalUniversityofSingapore,SingaporeAninjectionmouldisamechanicalassemblythatconsistsofproductdependentpartsandproductindependentparts.Thispaperaddressesthetwokeyissuesofassemblymodellingforinjectionmoulds,namely,representinganinjectionmouldassemblyinacomputeranddeterminingthepositionandorientationofaproductindependentpartinanassembly.Afeaturebasedandobjectorientedrepresentationisproposedtorepresentthehierarchicalassemblyofinjectionmoulds.Thisrepresentationrequiresandpermitsadesignertothinkbeyondthemereshapeofapartandstateexplicitlywhatportionsofapartareimportantandwhy.Thus,itprovidesanopportunityfordesignerstodesignforassemblyDFA.Asimplifiedsymbolicgeometricapproachisalsopresentedtoinfertheconfigurationsofassemblyobjectsinanassemblyaccordingtothematingconditions.Basedontheproposedrepresentationandthesimplifiedsymbolicgeometricapproach,automaticassemblymodellingisfurtherdiscussed.KeywordsAssemblymodellingFeaturebasedInjectionmouldsObjectoriented1.IntroductionInjectionmouldingisthemostimportantprocessformanufacturingplasticmouldedproducts.Thenecessaryequipmentconsistsoftwomainelements,theinjectionmouldingmachineandtheinjectionmould.Theinjectionmouldingmachinesusedtodayaresocalleduniversalmachines,ontowhichvariousmouldsforplasticpartswithdifferentgeometriescanbemounted,withincertaindimensionlimits,buttheinjectionmoulddesignhastochangewithplasticproducts.Fordifferentmouldinggeometries,differentmouldconfigurationsareusuallynecessary.Theprimarytaskofaninjectionmouldistoshapethemoltenmaterialintothefinalshapeoftheplasticproduct.Thistaskisfulfilledbythecavitysystemthatconsistsofcore,cavity,inserts,andslider/lifterheads.ThegeometricalshapesCorrespondenceandoffprintrequeststoDrJerryY.H.Fuh,DepartmentofMechanicalandProductionEngineering,NationalUniversityofSingaporeNUS,10KentRidgeCrescent,Singapore119260.EmailmpefuhyhKnus.edu.sgandsizesofacavitysystemaredetermineddirectlybytheplasticmouldedproduct,soallcomponentsofacavitysystemarecalledproductdependentparts.Hereinafter,productreferstoaplasticmouldedproduct,partreferstothecomponentofaninjectionmould.Besidestheprimarytaskofshapingtheproduct,aninjectionmouldhasalsotofulfilanumberoftaskssuchasthedistributionofmelt,coolingthemoltenmaterial,ejectionofthemouldedproduct,transmittingmotion,guiding,andaligningthemouldhalves.Thefunctionalpartstofulfilthesetasksareusuallysimilarinstructureandgeometricalshapefordifferentinjectionmoulds.Theirstructuresandgeometricalshapesareindependentoftheplasticmouldedproducts,buttheirsizescanbechangedaccordingtotheplasticproducts.Therefore,itcanbeconcludedthataninjectionmouldisactuallyamechanicalassemblythatconsistsofproductdependentpartsandproductindependentparts.Figure1showstheassemblystructureofaninjectionmould.Thedesignofaproductdependentpartisbasedonextractingthegeometryfromtheplasticproduct.Inrecentyears,CAD/CAMtechnologyhasbeensuccessfullyusedtohelpmoulddesignerstodesigntheproductdependentparts.TheMouldMouldbaseCoolFillLayoutPlugSocketCav_1Cav_2CAplateGuildbushTCPplateBepplateCbplateEaplateEbplateGuidpinIpplateRetpinSliderbodyguideStopblkHeelblkheadCoreCavityProductindependentpartProductdependentpartMovehalfFixedhalfFig.1.Assemblystructureofaninjectionmould.740X.G.Yeetal.automaticgenerationofthegeometricalshapeforaproductdependentpartfromtheplasticproducthasalsoattractedalotofresearchinterest1,2.However,littleworkhasbeencarriedoutontheassemblymodellingofinjectionmoulds,althoughitisasimportantasthedesignofproductdependentparts.ThemouldindustryisfacingthefollowingtwodifficultieswhenuseaCADsystemtodesignproductindependentpartsandthewholeassemblyofaninjectionmould.First,thereareusuallyaroundonehundredproductindependentpartsinamouldset,andthesepartsareassociatedwitheachotherwithdifferentkindsofconstraints.Itistimeconsumingforthedesignertoorientandpositionthecomponentsinanassembly.Secondly,whilemoulddesigners,mostofthetime,thinkonthelevelofrealworldobjects,suchasscrews,plates,andpins,theCADsystemusesatotallydifferentlevelofgeometricalobjects.Asaresult,highlevelobjectorientedideashavetobetranslatedtolowlevelCADentitiessuchaslines,surfaces,orsolids.Therefore,itisnecessarytodevelopanautomaticassemblymodellingsystemforinjectionmouldstosolvethesetwoproblems.Inthispaper,weaddressthefollowingtwokeyissuesforautomaticassemblymodellingrepresentingaproductindependentpartandamouldassemblyinacomputeranddeterminingthepositionandorientationofacomponentpartinanassembly.Thispapergivesabriefreviewofrelatedresearchinassemblymodelling,andpresentsanintegratedrepresentationfortheinjectionmouldassembly.Asimplifiedgeometricsymbolicmethodisproposedtodeterminethepositionandorientationofapartinthemouldassembly.Anexampleofautomaticassemblymodellingofaninjectionmouldisillustrated.2.RelatedResearchAssemblymodellinghasbeenthesubjectofresearchindiversefields,suchas,kinematics,AI,andgeometricmodelling.Libardietal.3compiledaresearchreviewofassemblymodelling.Theyreportedthatmanyresearchershadusedgraphstructurestomodelassemblytopology.Inthisgraphscheme,thecomponentsarerepresentedbynodes,andtransformationmatricesareattachedtoarcs.However,thetransformationmatricesarenotcoupledtogether,whichseriouslyaffectsthetransformationprocedure,i.e.ifasubassemblyismoved,allitsconstituentpartsdonotmovecorrespondingly.LeeandGossard4developedasystemthatsupportedahierarchicalassemblydatastructurecontainingmorebasicinformationaboutassembliessuchasmatingfeaturebetweenthecomponents.Thetransformationmatricesarederivedautomaticallyfromtheassociationsofvirtuallinks,butthishierarchicaltopologymodelrepresentsonlypartofrelationseffectively.Automaticallyinferringtheconfigurationofcomponentsinanassemblymeansthatdesignerscanavoidspecifyingthetransformationmatricesdirectly.Moreover,thepositionofacomponentwillchangewheneverthesizeandpositionofitsreferencecomponentaremodified.Thereexistthreetechniquestoinferthepositionandorientationofacomponentintheassemblyiterativenumericaltechnique,symbolicalgebraictechnique,andsymbolicgeometrictechnique.LeeandGossard5proposedaniterativenumericaltechniquetocomputethelocationandorientationofeachcomponentfromthespatialrelationships.Theirmethodconsistsofthreestepsgenerationoftheconstraintequations,reducingthenumberofequations,andsolvingtheequations.Thereare16equationsforagainstcondition,18equationsforfitcondition,6propertyequationsforeachmatrix,and2additionalequationsforarotationalpart.Usuallythenumberofequationsexceedsthenumberofvariables,soamethodmustbedevisedtoremovetheredundantequations.TheNewton–Raphsoniterationalgorithmisusedtosolvetheequations.Thistechniquehastwodisadvantagesfirst,thesolutionisheavilydependentontheinitialsolutionsecondly,theiterativenumericaltechniquecannotdistinguishbetweendifferentrootsinthesolutionspace.Therefore,itispossible,inapurelyspatialrelationshipproblem,thatamathematicallyvalid,butphysicallyunfeasible,solutioncanbeobtained.AmblerandPopplestone6suggestedamethodofcomputingtherequiredrotationandtranslationforeachcomponenttosatisfythespatialrelationshipsbetweenthecomponentsinanassembly.Sixvariablesthreetranslationsandthreerotationsforeachcomponentaresolvedtobeconsistentwiththespatialrelationships.Thismethodrequiresavastamountofprogrammingandcomputationtorewriterelatedequationsinasolvableformat.Also,itdoesnotguaranteeasolutioneverytime,especiallywhentheequationcannotberewritteninsolvableforms.Kramer7developedasymbolicgeometricapproachfordeterminingthepositionsandorientationsofrigidbodiesthatsatisfyasetofgeometricconstraints.Reasoningaboutthegeometricbodiesisperformedsymbolicallybygeneratingasequenceofactionstosatisfyeachconstraintincrementally,whichresultsinthereductionoftheobjectsavailabledegreesoffreedomDOF.ThefundamentalreferenceentityusedbyKrameriscalledamarker,thatisapointandtwoorthogonalaxes.Sevenconstraintscoincident,inline,inplane,parallelFz,offsetFz,offsetFxandhelicalbetweenmarkersaredefined.Foraprobleminvolvingasingleobjectandconstraintsbetweenmarkersonthatbody,andmarkerswhichhaveinvariantattributes,actionanalysis7isusedtoobtainasolution.Actionanalysisdecidesthefinalconfigurationofageometricobject,stepbystep.Ateachstepinsolvingtheobjectconfiguration,degreesoffreedomanalysisdecideswhatactionwillsatisfyoneofthebodysasyetunsatisfiedconstraints,giventheavailabledegreesoffreedom.Itthencalculateshowthatactionfurtherreducesthebodysdegreesoffreedom.Attheendofeachstep,oneappropriateactionisaddedtothemetaphoricalassemblyplan.AccordingtoShahandRogers8,Kramersworkrepresentsthemostsignificantdevelopmentforassemblymodelling.Thissymbolicgeometricapproachcanlocateallsolutionstoconstraintconditions,andiscomputationallyattractivecomparedtoaniterativetechnique,buttoimplementthismethod,alargeamountofprogrammingisrequired.Althoughmanyresearchershavebeenactivelyinvolvedinassemblymodelling,littleliteraturehasbeenreportedonfeaturebasedassemblymodellingforinjectionmoulddesign.Kruthetal.9developedadesignsupportsystemforaninjectionmould.Theirsystemsupportedtheassemblydesignforinjectionmouldsthroughhighlevelfunctionalmouldobjectscomponentsandfeatures.BecausetheirsystemwasAutomatedAssemblyModelling741basedonAutoCAD,itcouldonlyaccommodatewireframeandsimplesolidmodels.3.RepresentationofInjectionMouldAssembliesThetwokeyissuesofautomatedassemblymodellingforinjectionmouldsare,representingamouldassemblyincomputers,anddeterminingthepositionandorientationofaproductindependentpartintheassembly.Inthissection,wepresentanobjectorientedandfeaturebasedrepresentationforassembliesofinjectionmoulds.Therepresentationofassembliesinacomputerinvolvesstructuralandspatialrelationshipsbetweenindividualparts.Sucharepresentationmustsupporttheconstructionofanassemblyfromallthegivenparts,changesintherelativepositioningofparts,andmanipulationoftheassemblyasawhole.Moreover,therepresentationsofassembliesmustmeetthefollowingrequirementsfromdesigners1.Itshouldbepossibletohavehighlevelobjectsreadytousewhilemoulddesignersthinkonthelevelofrealworldobjects.2.Therepresentationofassembliesshouldencapsulateoperationalfunctionstoautomateroutineprocessessuchaspocketingandinterferencechecks.Tomeettheserequirements,afeaturebasedandobjectorientedhierarchicalmodelisproposedtorepresentinjectionmoulds.Anassemblymaybedividedintosubassemblies,whichinturnconsistsofsubassembliesand/orindividualcomponents.Thus,ahierarchicalmodelismostappropriateforrepresentingthestructuralrelationsbetweencomponents.Ahierarchyimpliesadefiniteassemblysequence.Inaddition,ahierarchicalmodelcanprovideanexplicitrepresentationofthedependencyofthepositionofonepartonanother.Featurebaseddesign10allowsdesignerstoworkatasomewhathigherlevelofabstractionthanthatpossiblewiththedirectuseofsolidmodellers.Geometricfeaturesareinstanced,sized,andlocatedquicklybytheuserbyspecifyingaminimumsetofparameters,whilethefeaturemodellerworksoutthedetails.Also,itiseasytomakedesignchangesbecauseoftheassociativitiesbetweengeometricentitiesmaintainedinthedatastructureoffeaturemodellers.Withoutfeatures,designershavetobeconcernedwithallthedetailsofgeometricconstructionproceduresrequiredbysolidmodellers,anddesignchangeshavetobestrictlyspecifiedforeveryentityaffectedbythechange.Moreover,thefeaturebasedrepresentationwillprovidehighlevelassemblyobjectsfordesignerstouse.Forexample,whilemoulddesignersthinkonthelevelofarealworldobject,e.g.acounterborehole,afeatureobjectofacounterboreholewillbereadyinthecomputerforuse.Objectorientedmodelling11,12isanewwayofthinkingaboutproblemsusingmodelsorganisedaroundrealworldconcepts.Thefundamentalentityistheobject,whichcombinesbothdatastructuresandbehaviourinasingleentity.Objectorientedmodelsareusefulforunderstandingproblemsanddesigningprogramsanddatabases.Inaddition,theobjectorientedrepresentationofassembliesmakesiteasyforachildobjecttoinheritinformationfromitsparent.Figure2showsthefeaturebasedandobjectorientedhierarchicalrepresentationofaninjectionmould.Therepresentationisahierarchicalstructureatmultiplelevelsofabstraction,fromlowlevelgeometricentitiesformfeaturetohighlevelsubassemblies.TheitemsenclosedintheboxesrepresentassemblyobjectsSUBFAs,PARTsandFFsthesolidlinesrepresentpartofrelationandthedashedlinesrepresentotherrelationships.SubassemblySUBFAconsistsofpartsPARTs.ApartcanbethoughtofasanassemblyofformfeaturesFFs.Therepresentationcombinesthestrengthsofafeaturebasedgeometricmodelwiththoseofobjectorientedmodels.Itnotonlycontainsthepartofrelationsbetweentheparentobjectandthechildobject,butalsoincludesarichersetofstructuralrelationsandagroupofoperationalfunctionsforassemblyobjects.InSection3.1,thereisfurtherdiscussiononthedefinitionofanassemblyobject,anddetailedrelationsbetweenassemblyobjectsarepresentedinSection3.2.3.1DefinitionofAssemblyObjectsInourwork,anassemblyobject,O,isdefinedasaunique,identifiableentityinthefollowingformOOid,A,M,R1WhereOidisauniqueidentifierofanassemblyobjectO.Aisasetofthreetuples,t,a,v.EachaiscalledanattributeofO,associatedwitheachattributeisatype,t,andavalue,v.Misasetoftuples,m,tc1,tc2,,tcn,tc.EachelementofMisafunctionthatuniquelyidentifiesamethod.Thesymbolmrepresentsamethodnameandmethodsdefineoperationsonobjects.ThesymboltciiFig.2.Featurebased,objectorientedhierarchicalrepresentation.742X.G.Yeetal.1,2,,nspecifiestheargumenttypeandtcspecifiesthereturnedvaluetype.RisasetofrelationshipsamongOandotherassemblyobjects.Therearesixtypesofbasicrelationshipsbetweenassemblyobjects,i.e.Partof,SR,SC,DOF,Lts,andFit.Table1showsanassemblyobjectofinjectionmoulds,e.g.ejector.TheejectorinTable1isformallyspecifiedasejectorpinF1,{string,purpose,ejectingmoulding,string,material,nitridesteel,string,catalogFno,THX},{checkFinterference,boolean,pocketFplate,boolean},{partofejectionFsys,SRAlignEBFplate,DOFTx,Ty}.Inthisexample,purpose,materialandcatalogFnoareattributeswithadatatypeofstringcheckFinterferenceandpocketFplatearememberfunctionsandPartof,SRandDOFarerelationships.3.2AssemblyRelationshipsTherearesixtypesofbasicrelationshipsbetweenassemblyobjects,Partof,SR,SC,DOF,Lts,andFit.PartofAnassemblyobjectbelongstoitsancestorobject.SRSpatialrelationsexplicitlyspecifythepositionsandorientationsofassemblyobjectsinanassembly.Foracomponentpart,itsspatialrelationshipisderivedfromspatialconstraintsSC.SCSpatialconstraintsimplicitlylocateacomponentpartwithrespecttotheotherparts.DOFDegreesoffreedomareallowabletranslational/rotationaldirectionsofmotionafterassembly,withorwithoutlimits.LtsMotionlimitsbecauseofobstructions/interferences,theDOFmayhaveunilateralorbilaterallimits.FitSizeconstraintisappliedtodimensions,inordertomaintainagivenclassoffit.Table1.Definitionofanassemblyobjectejector.ObjectOidejectorpinF1InstanceofEjectorFpinDerivedfromejectorclassAPurposeejectingmouldingTypestringMaterialnitridedsteelTypestringCatalogFnoTHXTypestringMCheckFinterferenceCheckinterferencecoolFobjbetweenejectorsandcoolinglinesPocketFplateMakeaholeonplatetoaccommodateejectorpinsRPartofejectorFsysSRalignwithEBplateDOFTx,TyAmongalltheelementsofanassemblyobject,therelationshipsaremostimportantforassemblydesign.Therelationshipsbetweenassemblyobjectswillnotonlydeterminethepositionofobjectsinanassembly,butalsomaintaintheassociativitiesbetweenassemblyobjects.Inthefollowingsubsections,wewillillustratetherelationshipsatthesameassemblylevelwiththehelpofexamples.3.2.1RelationshipsBetweenFormFeaturesMoulddesign,inessence,isamentalprocessmoulddesignersmostofthetimethinkonthelevelofrealworldobjectssuchasplates,screws,grooves,chamfers,andcounterboreholes.Therefore,itisnecessarytobuildthegeometricmodelsofallproductindependentpartsfromformfeatures.Themoulddesignercaneasilychangethesizeandshapeofapart,becauseoftherelationsbetweenformfeaturesmaintainedinthepartrepresentation.Figure3ashowsaplatewithacounterborehole.Thispartisdefinedbytwoformfeatures,i.e.ablockandacounterborehole.ThecounterboreholeFF2isplacedwithreferencetotheblockfeatureFF1,usingtheirlocalcoordinatesF2andF1,respectively.Equations2–5showthespatialrelationshipsbetweenthecounterboreholeFF2andtheblockfeatureFF1.Forformfeatures,thereisnospatialconstraintbetweenthem,sothespatialrelationshipsarespecifieddirectlybythedesigner.ThedetailedassemblyrelationshipsbetweentwoformfeaturesaredefinedasfollowsSRFF2,FF1F2iF1i2F2jF1j3Fig.3.Assemblyrelationships.
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