IntJAdvManufTechnol(2000)16:7397472000Springer-VerlagLondonLimitedAutomatedAssemblyModellingforPlasticInjectionMouldsX.G.Ye,J.Y.H.FuhandK.S.LeeDepartmentofMechanicalandProductionEngineering,NationalUniversityofSingapore,SingaporeAninjectionmouldisamechanicalassemblythatconsistsofproduct-dependentpartsandproduct-independentparts.Thispaperaddressesthetwokeyissuesofassemblymodellingforinjectionmoulds,namely,representinganinjectionmouldassemblyinacomputeranddeterminingthepositionandorientationofaproduct-independentpartinanassembly.Afeature-basedandobject-orientedrepresentationisproposedtorepresentthehierarchicalassemblyofinjectionmoulds.Thisrepresentationrequiresandpermitsadesignertothinkbeyondthemereshapeofapartandstateexplicitlywhatportionsofapartareimportantandwhy.Thus,itprovidesanopportunityfordesignerstodesignforassembly(DFA).Asimplifiedsymbolicgeometricapproachisalsopresentedtoinfertheconfigurationsofassemblyobjectsinanassemblyaccordingtothematingconditions.Basedontheproposedrepresentationandthesimplifiedsymbolicgeometricapproach,automaticassemblymodellingisfurtherdiscussed.Keywords:Assemblymodelling；Feature-based；Injectionmoulds；Object-oriented1.IntroductionInjectionmouldingisthemostimportantprocessformanufac-turingplasticmouldedproducts.Thenecessaryequipmentcon-sistsoftwomainelements,theinjectionmouldingmachineandtheinjectionmould.Theinjectionmouldingmachinesusedtodayareso-calleduniversalmachines,ontowhichvariousmouldsforplasticpartswithdifferentgeometriescanbemounted,withincertaindimensionlimits,buttheinjectionmoulddesignhastochangewithplasticproducts.Fordifferentmouldinggeometries,differentmouldconfigurationsareusuallynecessary.Theprimarytaskofaninjectionmouldistoshapethemoltenmaterialintothefinalshapeoftheplasticproduct.Thistaskisfulfilledbythecavitysystemthatconsistsofcore,cavity,inserts,andslider/lifterheads.ThegeometricalshapesCorrespondenceandoffprintrequeststo:DrJerryY.H.Fuh,Depart-mentofMechanicalandProductionEngineering,NationalUniversityofSingapore(NUS),10KentRidgeCrescent,Singapore119260.E-mail:mpefuhyhK.sgandsizesofacavitysystemaredetermineddirectlybytheplasticmouldedproduct,soallcomponentsofacavitysystemarecalledproduct-dependentparts.(Hereinafter,productreferstoaplasticmouldedproduct,partreferstothecomponentofaninjectionmould.)Besidestheprimarytaskofshapingtheproduct,aninjectionmouldhasalsotofulfilanumberoftaskssuchasthedistributionofmelt,coolingthemoltenmaterial,ejectionofthemouldedproduct,transmittingmotion,guiding,andaligningthemouldhalves.Thefunctionalpartstofulfilthesetasksareusuallysimilarinstructureandgeo-metricalshapefordifferentinjectionmoulds.Theirstructuresandgeometricalshapesareindependentoftheplasticmouldedproducts,buttheirsizescanbechangedaccordingtotheplasticproducts.Therefore,itcanbeconcludedthataninjectionmouldisactuallyamechanicalassemblythatconsistsofproduct-dependentpartsandproduct-independentparts.Figure1showstheassemblystructureofaninjectionmould.Thedesignofaproduct-dependentpartisbasedonextractingthegeometryfromtheplasticproduct.Inrecentyears,CAD/CAMtechnologyhasbeensuccessfullyusedtohelpmoulddesignerstodesigntheproduct-dependentparts.TheMouldMouldbaseCoolFillLayoutPlugSocketCav_1Cav_2CA-plateGuild-bushTCP-plateBep-plateCb-plateEa-plateEb-plateGuid-pinIp-plateRet-pinSliderbodyguideStop-blkHeel-blkheadCoreCavityProduct-independentpartProduct-dependentpartMove-halfFixed-halfFig.1.Assemblystructureofaninjectionmould.740X.G.Yeetal.automaticgenerationofthegeometricalshapeforaproduct-dependentpartfromtheplasticproducthasalsoattractedalotofresearchinterest1,2.However,littleworkhasbeencarriedoutontheassemblymodellingofinjectionmoulds,althoughitisasimportantasthedesignofproduct-dependentparts.Themouldindustryisfacingthefollowingtwodifficult-ieswhenuseaCADsystemtodesignproduct-independentpartsandthewholeassemblyofaninjectionmould.First,thereareusuallyaroundonehundredproduct-independentpartsinamouldset,andthesepartsareassociatedwitheachotherwithdifferentkindsofconstraints.Itistime-consumingforthedesignertoorientandpositionthecomponentsinanassembly.Secondly,whilemoulddesigners,mostofthetime,thinkonthelevelofreal-worldobjects,suchasscrews,plates,andpins,theCADsystemusesatotallydifferentlevelofgeometricalobjects.Asaresult,high-levelobject-orientedideashavetobetranslatedtolow-levelCADentitiessuchaslines,surfaces,orsolids.Therefore,itisnecessarytodevelopanautomaticassemblymodellingsystemforinjectionmouldstosolvethesetwoproblems.Inthispaper,weaddressthefollow-ingtwokeyissuesforautomaticassemblymodelling:rep-resentingaproduct-independentpartandamouldassemblyinacomputer；anddeterminingthepositionandorientationofacomponentpartinanassembly.Thispapergivesabriefreviewofrelatedresearchinassemblymodelling,andpresentsanintegratedrepresentationfortheinjectionmouldassembly.Asimplifiedgeometricsym-bolicmethodisproposedtodeterminethepositionandorien-tationofapartinthemouldassembly.Anexampleofauto-maticassemblymodellingofaninjectionmouldisillustrated.2.RelatedResearchAssemblymodellinghasbeenthesubjectofresearchindiversefields,suchas,kinematics,AI,andgeometricmodelling.Lib-ardietal.3compiledaresearchreviewofassemblymodel-ling.Theyreportedthatmanyresearchershadusedgraphstructurestomodelassemblytopology.Inthisgraphscheme,thecomponentsarerepresentedbynodes,andtransformationmatricesareattachedtoarcs.However,thetransformationmatricesarenotcoupledtogether,whichseriouslyaffectsthetransformationprocedure,i.e.ifasubassemblyismoved,allitsconstituentpartsdonotmovecorrespondingly.LeeandGossard4developedasystemthatsupportedahierarchicalassemblydatastructurecontainingmorebasicinformationaboutassembliessuchas“matingfeature”betweenthecompo-nents.Thetransformationmatricesarederivedautomaticallyfromtheassociationsofvirtuallinks,butthishierarchicaltopologymodelrepresentsonly“part-of”relationseffectively.Automaticallyinferringtheconfigurationofcomponentsinanassemblymeansthatdesignerscanavoidspecifyingthetransformationmatricesdirectly.Moreover,thepositionofacomponentwillchangewheneverthesizeandpositionofitsreferencecomponentaremodified.Thereexistthreetechniquestoinferthepositionandorientationofacomponentintheassembly:iterativenumericaltechnique,symbolicalgebraictechnique,andsymbolicgeometrictechnique.LeeandGossard5proposedaniterativenumericaltechniquetocomputethelocationandorientationofeachcomponentfromthespatialrelationships.Theirmethodconsistsofthreesteps:generationoftheconstraintequations,reducingthenumberofequations,andsolvingtheequations.Thereare16equationsfor“against”condition,18equationsfor“fit”condition,6propertyequationsforeachmatrix,and2additionalequationsforarotationalpart.Usuallythenumberofequationsexceedsthenumberofvariables,soamethodmustbedevisedtoremovetheredundantequations.TheNewtonRaphsoniterationalgorithmisusedtosolvetheequations.Thistechniquehastwodisadvantages:first,thesolutionisheavilydependentontheinitialsolution；secondly,theiterativenumericaltechniquecannotdistinguishbetweendifferentrootsinthesolutionspace.Therefore,itispossible,inapurelyspatialrelationshipproblem,thatamathematicallyvalid,butphysicallyunfeasible,solutioncanbeobtained.AmblerandPopplestone6suggestedamethodofcomput-ingtherequiredrotationandtranslationforeachcomponenttosatisfythespatialrelationshipsbetweenthecomponentsinanassembly.Sixvariables(threetranslationsandthreerotations)foreachcomponentaresolvedtobeconsistentwiththespatialrelationships.Thismethodrequiresavastamountofprogrammingandcomputationtorewriterelatedequationsinasolvableformat.Also,itdoesnotguaranteeasolutioneverytime,especiallywhentheequationcannotberewritteninsolvableforms.Kramer7developedasymbolicgeometricapproachfordeterminingthepositionsandorientationsofrigidbodiesthatsatisfyasetofgeometricconstraints.Reasoningaboutthegeometricbodiesisperformedsymbolicallybygeneratingasequenceofactionstosatisfyeachconstraintincrementally,whichresultsinthereductionoftheobjectsavailabledegreesoffreedom(DOF).ThefundamentalreferenceentityusedbyKrameriscalleda“marker”,thatisapointandtwoorthogonalaxes.Sevenconstraints(coincident,in-line,in-plane,parallelFz,offsetFz,offsetFxandhelical)betweenmarkersaredefined.Foraprobleminvolvingasingleobjectandconstraintsbetweenmarkersonthatbody,andmarkerswhichhaveinvariantattri-butes,actionanalysis7isusedtoobtainasolution.Actionanalysisdecidesthefinalconfigurationofageometricobject,stepbystep.Ateachstepinsolvingtheobjectconfiguration,degreesoffreedomanalysisdecideswhatactionwillsatisfyoneofthebodysasyetunsatisfiedconstraints,giventheavailabledegreesoffreedom.Itthencalculateshowthatactionfurtherreducesthebodysdegreesoffreedom.Attheendofeachstep,oneappropriateactionisaddedtothemetaphoricalassemblyplan.AccordingtoShahandRogers8,Kramersworkrepresentsthemostsignificantdevelopmentforassemblymodelling.Thissymbolicgeometricapproachcanlocateallsolutionstoconstraintconditions,andiscomputationallyattractivecomparedtoaniterativetechnique,buttoimplementthismethod,alargeamountofprogrammingisrequired.Althoughmanyresearchershavebeenactivelyinvolvedinassemblymodelling,littleliteraturehasbeenreportedonfea-turebasedassemblymodellingforinjectionmoulddesign.Kruthetal.9developedadesignsupportsystemforaninjectionmould.Theirsystemsupportedtheassemblydesignforinjectionmouldsthroughhigh-levelfunctionalmouldobjects(componentsandfeatures).BecausetheirsystemwasAutomatedAssemblyModelling741basedonAutoCAD,itcouldonlyaccommodatewire-frameandsimplesolidmodels.3.RepresentationofInjectionMouldAssembliesThetwokeyissuesofautomatedassemblymodellingforinjectionmouldsare,representingamouldassemblyincom-puters,anddeterminingthepositionandorientationofapro-duct-independentpartintheassembly.Inthissection,wepresentanobject-orientedandfeature-basedrepresentationforassembliesofinjectionmoulds.Therepresentationofassembliesinacomputerinvolvesstructuralandspatialrelationshipsbetweenindividualparts.Sucharepresentationmustsupporttheconstructionofanassemblyfromallthegivenparts,changesintherelativepositioningofparts,andmanipulationoftheassemblyasawhole.Moreover,therepresentationsofassembliesmustmeetthefollowingrequirementsfromdesigners:1.Itshouldbepossibletohavehigh-levelobjectsreadytousewhilemoulddesignersthinkonthelevelofreal-worldobjects.2.Therepresentationofassembliesshouldencapsulateoper-ationalfunctionstoautomateroutineprocessessuchaspocketingandinterferencechecks.Tomeettheserequirements,afeature-basedandobject-orientedhierarchicalmodelisproposedtorepresentinjectionmoulds.Anassemblymaybedividedintosubassemblies,whichinturnconsistsofsubassembliesand/orindividualcomponents.Thus,ahierarchicalmodelismostappropriateforrepresentingthestructuralrelationsbetweencomponents.Ahierarchyimpliesadefiniteassemblysequence.Inaddition,ahierarchicalmodelcanprovideanexplicitrepresentationofthedependencyofthepositionofonepartonanother.Feature-baseddesign10allowsdesignerstoworkatasomewhathigherlevelofabstractionthanthatpossiblewiththedirectuseofsolidmodellers.Geometricfeaturesareinstanced,sized,andlocatedquicklybytheuserbyspecifyingaminimumsetofparameters,whilethefeaturemodellerworksoutthedetails.Also,itiseasytomakedesignchangesbecauseoftheassociativitiesbetweengeometricentitiesmaintainedinthedatastructureoffeaturemodellers.Withoutfeatures,designershavetobeconcernedwithallthedetailsofgeometricconstructionproceduresrequiredbysolidmodellers,anddesignchangeshavetobestrictlyspecifiedforeveryentityaffectedbythechange.Moreover,thefeature-basedrepresentationwillprovidehigh-levelassemblyobjectsfordesignerstouse.Forexample,whilemoulddesignersthinkonthelevelofareal-worldobject,e.g.acounterborehole,afeatureobjectofacounterboreholewillbereadyinthecomputerforuse.Object-orientedmodelling11,12isanewwayofthinkingaboutproblemsusingmodelsorganisedaroundreal-worldcon-cepts.Thefundamentalentityistheobject,whichcombinesbothdatastructuresandbehaviourinasingleentity.Object-orientedmodelsareusefulforunderstandingproblemsanddesigningprogramsanddatabases.Inaddition,theobject-orientedrepresentationofassembliesmakesiteasyfora“child”objecttoinheritinformationfromits“parent”.Figure2showsthefeature-basedandobject-orientedhier-archicalrepresentationofaninjectionmould.Therepresen-tationisahierarchicalstructureatmultiplelevelsofabstraction,fromlow-levelgeometricentities(formfeature)tohigh-levelsubassemblies.Theitemsenclosedintheboxesrepresent“assemblyobjects”(SUBFAs,PARTsandFFs)；thesolidlinesrepresent“part-of”relation；andthedashedlinesrepresentotherrelationships.Subassembly(SUBFA)consistsofparts(PARTs).Apartcanbethoughtofasan“assembly”offormfeatures(FFs).Therepresentationcombinesthestrengthsofafeature-basedgeometricmodelwiththoseofobject-orientedmodels.Itnotonlycontainsthe“part-of”relationsbetweentheparentobjectandthechildobject,butalsoincludesarichersetofstructuralrelationsandagroupofoperationalfunctionsforassemblyobjects.InSection3.1,thereisfurtherdiscussiononthedefinitionofanassemblyobject,anddetailedrelationsbetweenassemblyobjectsarepresentedinSectionDefinitionofAssemblyObjectsInourwork,anassemblyobject,O,isdefinedasaunique,identifiableentityinthefollowingform:O=(Oid,A,M,R)(1)Where:Oidisauniqueidentifierofanassemblyobject(O).Aisasetofthree-tuples,(t,a,v).EachaiscalledanattributeofO,associatedwitheachattributeisatype,t,andavalue,v.Misasetoftuples,(m,tc1,tc2,%,tcn,tc).EachelementofMisafunctionthatuniquelyidentifiesamethod.Thesymbolmrepresentsamethodname；andmethodsdefineoperationsonobjects.Thesymboltci(iFig.2.Feature-based,object-orientedhierarchicalrepresentation.742X.G.Yeetal.=1,2,%,n)specifiestheargumenttypeandtcspecifiesthereturnedvaluetype.RisasetofrelationshipsamongOandotherassemblyobjects.Therearesixtypesofbasicrelationshipsbetweenassemblyobjects,i.e.Part-of,SR,SC,DOF,Lts,andFit.Table1showsanassemblyobjectofinjectionmoulds,e.g.ejector.TheejectorinTable1isformallyspecifiedas:(ejector-pinF1,(string,purpose,ejectingmoulding),(string,material,nitridesteel),(string,catalogFno,THX),(checkFinterference(),boolean),(pocketFplate(),boolean),(part-ofejectionFsys),(SRAlignEBFplate),(DOFTx,Ty).Inthisexample,purpose,materialandcatalogFnoareattributeswithadatatypeofstring；checkFinterferenceandpocketFplatearememberfunctions；andPart-of,SRandDOFarerelationships.3.2AssemblyRelationshipsTherearesixtypesofbasicrelationshipsbetweenassemblyobjects,Part-of,SR,SC,DOF,Lts,andFit.Part-ofAnassemblyobjectbelongstoitsancestorobject.SRSpatialrelations:explicitlyspecifythepositionsandorientationsofassemblyobjectsinanassembly.Foracomponentpart,itsspatialrelationshipisderivedfromspatialconstraints(SC).SCSpatialconstraints:implicitlylocateacomponentpartwithrespecttotheotherparts.DOFDegreesoffreedom:areallowabletranslational/rotationaldirectionsofmotionafterassembly,withorwithoutlimits.LtsMotionlimits:becauseofobstructions/interferences,theDOFmayhaveunilateralorbilaterallimits.FitSizeconstraint:isappliedtodimensions,inordertomaintainagivenclassoffit.Table1.Definitionofanassemblyobject-ejector.ObjectOidejec