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0第0页共31页AUTOMATEDASSEMBLYMODELLINGFORPLASTICINJECTIONMOULDSANINJECTIONMOULDISAMECHANICALASSEMBLYTHATCONSISTSOFPRODUCTDEPENDENTPARTSANDPRODUCTINDEPENDENTPARTSTHISPAPERADDRESSESTHETWOKEYISSUESOFASSEMBLYMODELLINGFORINJECTIONMOULDS,NAMELY,REPRESENTINGANINJECTIONMOULDASSEMBLYINACOMPUTERANDDETERMININGTHEPOSITIONANDORIENTATIONOFAPRODUCTINDEPENDENTPARTINANASSEMBLYAFEATUREBASEDANDOBJECTORIENTEDREPRESENTATIONISPROPOSEDTOREPRESENTTHEHIERARCHICALASSEMBLYOFINJECTIONMOULDSTHISREPRESENTATIONREQUIRESANDPERMITSADESIGNERTOTHINKBEYONDTHEMERESHAPEOFAPARTANDSTATEEXPLICITLYWHATPORTIONSOFAPARTAREIMPORTANTANDWHYTHUS,ITPROVIDESANOPPORTUNITYFORDESIGNERSTODESIGNFORASSEMBLYDFAASIMPLIFIEDSYMBOLICGEOMETRICAPPROACHISALSOPRESENTEDTOINFERTHECONFIGURATIONSOFASSEMBLYOBJECTSINANASSEMBLYACCORDINGTOTHEMATINGCONDITIONSBASEDONTHEPROPOSEDREPRESENTATIONANDTHESIMPLIFIEDSYMBOLICGEOMETRICAPPROACH,AUTOMATICASSEMBLYMODELLINGISFURTHERDISCUSSEDKEYWORDSASSEMBLYMODELLINGFEATUREBASEDINJECTIONMOULDSOBJECTORIENTED1INTRODUCTIONINJECTIONMOULDINGISTHEMOSTIMPORTANTPROCESSFORMANUFACTURINGPLASTICMOULDEDPRODUCTSTHENECESSARYEQUIPMENTCONSISTSOFTWOMAINELEMENTS,THEINJECTIONMOULDINGMACHINEANDTHEINJECTIONMOULDTHEINJECTIONMOULDINGMACHINESUSEDTODAYARESOCALLEDUNIVERSALMACHINES,ONTOWHICHVARIOUSMOULDSFORPLASTICPARTSWITHDIFFERENTGEOMETRIESCANBEMOUNTED,WITHINCERTAINDIMENSIONLIMITS,BUTTHEINJECTIONMOULDDESIGNHASTOCHANGEWITHPLASTICPRODUCTSFORDIFFERENTMOULDINGGEOMETRIES,DIFFERENTMOULDCONFIGURATIONSAREUSUALLYNECESSARYTHEPRIMARYTASKOFANINJECTIONMOULDISTOSHAPETHEMOLTENMATERIALINTOTHEFINALSHAPEOFTHEPLASTICPRODUCTTHISTASKISFULFILLEDBYTHECAVITYSYSTEMTHATCONSISTSOFCORE,CAVITY,INSERTS,ANDSLIDER/LIFTERHEADSTHEGEOMETRICALSHAPESANDSIZESOFACAVITYSYSTEMAREDETERMINEDDIRECTLYBYTHEPLASTICMOULDEDPRODUCT,SOALLCOMPONENTSOFACAVITYSYSTEMARECALLEDPRODUCTDEPENDENTPARTSHEREINAFTER,PRODUCTREFERSTOAPLASTICMOULDEDPRODUCT,PARTREFERSTOTHECOMPONENTOFANINJECTIONMOULDBESIDESTHEPRIMARYTASKOFSHAPINGTHEPRODUCT,ANINJECTIONMOULDHASALSOTOFULFILANUMBEROFTASKSSUCHASTHEDISTRIBUTIONOFMELT,COOLINGTHEMOLTEN1第1页共31页MATERIAL,EJECTIONOFTHEMOULDEDPRODUCT,TRANSMITTINGMOTION,GUIDING,ANDALIGNINGTHEMOULDHALVESTHEFUNCTIONALPARTSTOFULFILTHESETASKSAREUSUALLYSIMILARINSTRUCTUREANDGEOMETRICALSHAPEFORDIFFERENTINJECTIONMOULDSTHEIRSTRUCTURESANDGEOMETRICALSHAPESAREINDEPENDENTOFTHEPLASTICMOULDEDPRODUCTS,BUTTHEIRSIZESCANBECHANGEDACCORDINGTOTHEPLASTICPRODUCTSTHEREFORE,ITCANBECONCLUDEDTHATANINJECTIONMOULDISACTUALLYAMECHANICALASSEMBLYTHATCONSISTSOFPRODUCTDEPENDENTPARTSANDPRODUCTINDEPENDENTPARTSFIGURE1SHOWSTHEASSEMBLYSTRUCTUREOFANINJECTIONMOULDTHEDESIGNOFAPRODUCTDEPENDENTPARTISBASEDONEXTRACTINGTHEGEOMETRYFROMTHEPLASTICPRODUCTINRECENTYEARS,CAD/CAMTECHNOLOGYHASBEENSUCCESSFULLYUSEDTOHELPMOULDDESIGNERSTODESIGNTHEPRODUCTDEPENDENTPARTSTHEFIG1ASSEMBLYSTRUCTUREOFANINJECTIONMOULDAUTOMATICGENERATIONOFTHEGEOMETRICALSHAPEFORAPRODUCTDEPENDENTPARTFROMTHEPLASTICPRODUCTHASALSOATTRACTEDALOTOFRESEARCHINTEREST1,2HOWEVER,LITTLEWORKHASBEENCARRIEDOUTONTHEASSEMBLYMODELLINGOFINJECTIONMOULDS,ALTHOUGHITISASIMPORTANTASTHEDESIGNOFPRODUCTDEPENDENTPARTSTHEMOULDINDUSTRYISFACINGTHEFOLLOWINGTWODIFFICULTIESWHENUSEACADSYSTEMTODESIGNPRODUCTINDEPENDENTPARTSANDTHEWHOLEASSEMBLYOFANINJECTIONMOULDFIRST,THEREAREUSUALLYAROUNDONEHUNDREDPRODUCTINDEPENDENTPARTSINAMOULDSET,ANDTHESEPARTSAREASSOCIATEDWITHEACHOTHERWITHDIFFERENTKINDSOFCONSTRAINTSITISTIMECONSUMINGFORTHEDESIGNERTOORIENTANDPOSITIONTHECOMPONENTSINANASSEMBLYSECONDLY,WHILEMOULDDESIGNERS,MOSTOFTHETIME,THINKONTHELEVELOFREALWORLDOBJECTS,SUCHASSCREWS,PLATES,ANDPINS,THECADSYSTEMUSESATOTALLYDIFFERENTLEVELOFGEOMETRICAL2第2页共31页OBJECTSASARESULT,HIGHLEVELOBJECTORIENTEDIDEASHAVETOBETRANSLATEDTOLOWLEVELCADENTITIESSUCHASLINES,SURFACES,ORSOLIDSTHEREFORE,ITISNECESSARYTODEVELOPANAUTOMATICASSEMBLYMODELLINGSYSTEMFORINJECTIONMOULDSTOSOLVETHESETWOPROBLEMSINTHISPAPER,WEADDRESSTHEFOLLOWINGTWOKEYISSUESFORAUTOMATICASSEMBLYMODELLINGREPRESENTINGAPRODUCTINDEPENDENTPARTANDAMOULDASSEMBLYINACOMPUTERANDDETERMININGTHEPOSITIONANDORIENTATIONOFACOMPONENTPARTINANASSEMBLYTHISPAPERGIVESABRIEFREVIEWOFRELATEDRESEARCHINASSEMBLYMODELLING,ANDPRESENTSANINTEGRATEDREPRESENTATIONFORTHEINJECTIONMOULDASSEMBLYASIMPLIFIEDGEOMETRICSYMBOLICMETHODISPROPOSEDTODETERMINETHEPOSITIONANDORIENTATIONOFAPARTINTHEMOULDASSEMBLYANEXAMPLEOFAUTOMATICASSEMBLYMODELLINGOFANINJECTIONMOULDISILLUSTRATED2RELATEDRESEARCHASSEMBLYMODELLINGHASBEENTHESUBJECTOFRESEARCHINDIVERSEFIELDS,SUCHAS,KINEMATICS,AI,ANDGEOMETRICMODELLINGLIBARDIETAL3COMPILEDARESEARCHREVIEWOFASSEMBLYMODELLINGTHEYREPORTEDTHATMANYRESEARCHERSHADUSEDGRAPHSTRUCTURESTOMODELASSEMBLYTOPOLOGYINTHISGRAPHSCHEME,THECOMPONENTSAREREPRESENTEDBYNODES,ANDTRANSFORMATIONMATRICESAREATTACHEDTOARCSHOWEVER,THETRANSFORMATIONMATRICESARENOTCOUPLEDTOGETHER,WHICHSERIOUSLYAFFECTSTHETRANSFORMATIONPROCEDURE,IEIFASUBASSEMBLYISMOVED,ALLITSCONSTITUENTPARTSDONOTMOVECORRESPONDINGLYLEEANDGOSSARD4DEVELOPEDASYSTEMTHATSUPPORTEDAHIERARCHICALASSEMBLYDATASTRUCTURECONTAININGMOREBASICINFORMATIONABOUTASSEMBLIESSUCHAS“MATINGFEATURE”BETWEENTHECOMPONENTSTHETRANSFORMATIONMATRICESAREDERIVEDAUTOMATIC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ATHIGHERLEVELOFABSTRACTIONTHANTHATPOSSIBLEWITHTHEDIRECTUSEOFSOLIDMODELLERSGEOMETRICFEATURESAREINSTANCED,SIZED,ANDLOCATEDQUICKLYBYTHEUSERBYSPECIFYINGA5第5页共31页MINIMUMSETOFPARAMETERS,WHILETHEFEATUREMODELLERWORKSOUTTHEDETAILSALSO,ITISEASYTOMAKEDESIGNCHANGESBECAUSEOFTHEASSOCIATIVITIESBETWEENGEOMETRICENTITIESMAINTAINEDINTHEDATASTRUCTUREOFFEATUREMODELLERSWITHOUTFEATURES,DESIGNERSHAVETOBECONCERNEDWITHALLTHEDETAILSOFGEOMETRICCONSTRUCTIONPROCEDURESREQUIREDBYSOLIDMODELLERS,ANDDESIGNCHANGESHAVETOBESTRICTLYSPECIFIEDFOREVERYENTITYAFFECTEDBYTHECHANGEMOREOVER,THEFEATUREBASEDREPRESENTATIONWILLPROVIDEHIGHLEVELASSEMBLYOBJECTSFORDESIGNERSTOUSEFOREXAMPLE,WHILEMOULDDESIGNERSTHINKONTHELEVELOFAREALWORLDOBJECT,EGACOUNTERBOREHOLE,AFEATUREOBJECTOFACOUNTERBOREHOLEWILLBEREADYINTHECOMPUTERFORUSEOBJECTORIENTEDMODELLING11,12ISANEWWAYOFTHINKINGABOUTPROBLEMSUSINGMODELSORGANISEDAROUNDREALWORLDCONCEPTSTHEFUNDAMENTALENTITYISTHEOBJECT,WHICHCOMBINESBOTHDATASTRUCTURESANDBEHAVIOURINASINGLEENTITYOBJECTORIENTEDMODELSAREUSEFULFORUNDERSTANDINGPROBLEMSANDDESIGNINGPROGRAMSANDDATABASESINADDITION,THEOBJECTORIENTEDREPRESENTATIONOFASSEMBLIESMAKESITEASYFORA“CHILD”OBJECTTOINHERITINFORMATIONFROMITS“PARENT”FIGURE2SHOWSTHEFEATUREBASEDANDOBJECTORIENTEDHIERARCHICALREPRESENTATIONOFANINJECTIONMOULDTHEREPRESENTATIONISAHIERARCHICALSTRUCTUREATMULTIPLELEVELSOFABSTRACTION,FROMLOWLEVELGEOMETRICENTITIESFORMFEATURETOHIGHLEVELSUBASSEMBLIESTHEITEMSENCLOSEDINTHEBOXESREPRESENT“ASSEMBLYOBJECTS”SUBFAS,PARTSANDFFSTHESOLIDLINESREPRESENT“PARTOF”RELATIONANDTHEDASHEDLINESREPRESENTOTHERRELATIONSHIPSSUBASSEMBLYSUBFACONSISTSOFPARTSPARTSAPARTCANBETHOUGHTOFASAN“ASSEMBLY”OFFORMFEATURESFFSTHEREPRESENTATIONCOMBINESTHESTRENGTHSOFAFEATUREBASEDGEOMETRICMODELWITHTHOSEOFOBJECTORIENTEDMODELSITNOTONLYCONTAINSTHE“PARTOF”RELATIONSBETWEENTHEPARENTOBJECTANDTHECHILDOBJECT,BUTALSOINCLUDESARICHERSETOFSTRUCTURALRELATIONSANDAGROUPOFOPERATIONALFUNCTIONSFORASSEMBLYOBJECTSINSECTION31,THEREISFURTHERDISCUSSIONONTHEDEFINITIONOFANASSEMBLYOBJECT,ANDDETAILEDRELATIONSBETWEENASSEMBLYOBJECTSAREPRESENTEDINSECTION326第6页共31页FIG2FEATUREBASED,OBJECTORIENTEDHIERARCHICALREPRESENTATION31DEFINITIONOFASSEMBLYOBJECTSINOURWORK,ANASSEMBLYOBJECT,O,ISDEFINEDASAUNIQUE,IDENTIFIABLEENTITYINTHEFOLLOWINGFORMOOID,A,M,R1WHEREOIDISAUNIQUEIDENTIFIEROFANASSEMBLYOBJECTOAISASETOFTHREETUPLES,T,A,VEACHAISCALLEDANATTRIBUTEOFO,ASSOCIATEDWITHEACHATTRIBUTEISATYPE,T,ANDAVALUE,VMISASETOFTUPLES,M,TC1,TC2,TCN,TCEACHELEMENTOFMISAFUNCTIONTHATUNIQUELYIDENTIFIESAMETHODTHESYMBOLMREPRESENTSAMETHODNAMEANDMETHODSDEFINEOPERATIONSONOBJECTSTHESYMBOLTCII1,2,NSPECIFIESTHEARGUMENTTYPEANDTCSPECIFIESTHERETURNEDVALUETYPERISASETOFRELATIONSHIPSAMONGOANDOTHERASSEMBLYOBJECTSTHEREARESIXTYPESOFBASICRELATIONSHIPSBETWEENASSEMBLYOBJECTS,IEPARTOF,SR,SC,DOF,LTS,ANDFITTABLE1SHOWSANASSEMBLYOBJECTOFINJECTIONMOULDS,EGEJECTORTHEEJECTORINTABLE1ISFORMALLYSPECIFIEDASEJECTORPINF1,STRING,PURPOSE,EJECTINGMOULDING,STRING,MATERIAL,NITRIDESTEEL,STRING,CATALOGFNO,THX,CHECKFINTERFERENCE,BOOLEAN,POCKETFPLATE,BOOLEAN,PARTOF7第7页共31页EJECTIONFSYS,SRALIGNEBFPLATE,DOFTX,TYINTHISEXAMPLE,PURPOSE,MATERIALANDCATALOGFNOAREATTRIBUTESWITHADATATYPEOFSTRINGCHECKFINTERFERENCEANDPOCKETFPLATEAREMEMBERFUNCTIONSANDPARTOF,SRANDDOFARERELATIONSHIPS32ASSEMBLYRELATIONSHIPSTHEREARESIXTYPESOFBASICRELATIONSHIPSBETWEENASSEMBLYOBJECTS,PARTOF,SR,SC,DOF,LTS,ANDFITPARTOFANASSEMBLYOBJECTBELONGSTOITSANCESTOROBJECTSRSPATIALRELATIONSEXPLICITLYSPECIFYTHEPOSITIONSANDORIENTATIONSOFASSEMBLYOBJECTSINANASSEMBLYFORACOMPONENTPART,ITSSPATIALRELATIONSHIPISDERIVEDFROMSPATIALCONSTRAINTSSCSCSPATIALCONSTRAINTSIMPLICITLYLOCATEACOMPONENTPARTWITHRESPECTTOTHEOTHERPARTSDOFDEGREESOFFREEDOMAREALLOWABLETRANSLATIONAL/ROTATIONALDIRECTIONSOFMOTIONAFTERASSEMBLY,WITHORWITHOUTLIMITSLTSMOTIONLIMITSBECAUSEOFOBSTRUCTIONS/INTERFERENCES,THEDOFMAYHAVEUNILATERALORBILATERALLIMITSFITSIZECONSTRAINTISAPPLIEDTODIMENSIONS,INORDERTOMAINTAINAGIVENCLASSOFFITAMONGALLTHEELEMENTSOFANASSEMBLYOBJECT,THERELATIONSHIPSAREMOSTIMPORTANTFORASSEMBLYDESIGNTHERELATIONSHIPSBETWEENASSEMBLYOBJECTSWILLNOTONLYDETERMINETHEPOSITIONOFOBJECTSINANASSEMBLY,BUTALSOMAINTAINTHEASSOCIATIVITIESBETWEENASSEMBLYOBJECTSINTHEFOLLOWINGSUBSECTIONS,WEWILLILLUSTRATETHERELATIONSHIPSATTHESAMEASSEMBLYLEVELWITHTHEHELPOFEXAMPLES321RELATIONSHIPSBETWEENFORMFEATURESMOULDDESIGN,INESSENCE,ISAMENTALPROCESSMOULDDESIGNERSMOSTOFTHETIMETHINKONTHELEVELOFREALWORLDOBJECTSSUCHASPLATES,SCREWS,GROOVES,CHAMFERS,ANDCOUNTERBOREHOLESTHEREFORE,ITISNECESSARYTOBUILDTHEGEOMETRICMODELSOFALLPRODUCTINDEPENDENTPARTSFROMFORMFEATURESTHEMOULDDESIGNERCANEASILYCHANGETHESIZEANDSHAPEOFAPART,BECAUSEOFTHERELATIONSBETWEENFORMFEATURESMAINTAINEDINTHEPARTREPRESENTATIONFIGURE3ASHOWSAPLATEWITHACOUNTERBOREHOLETHISPARTISDEFINEDBYTWOFORMFEATURES,IEABLOCKANDACOUNTERBOREHOLETHECOUNTERBOREHOLEFF2ISPLACEDWITHREFERENCETOTHEBLOCKFEATUREFF1,USINGTHEIRLOCALCOORDINATESF2ANDF1,RESPECTIVELYEQUATIONS25SHOWTHESPATIAL8第8页共31页RELATIONSHIPSBETWEENTHECOUNTERBOREHOLEFF2ANDTHEBLOCKFEATUREFF1FORFORMFEATURES,THEREISNOSPATIALCONSTRAINTBETWEENTHEM,SOTHESPATIALRELATIONSHIPSARESPECIFIEDDIRECT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