1、IntJAdvManufTechnol(2000)16/7397472000Springer-VerlagLondonLimitedAutomatedAssemblyModellingforPlasticInjectionMouldsX/G/Ye/J/Y/H/FuhandK/S/LeeDepartmentofMechanicalandProductionEngineering/NationalUniversityofSingapore/SingaporeAninjectionmouldisamechanicalassemblythatconsistsofproduct-dependentpar
2、tsandproduct-independentparts/Thispaperaddressesthetwokeyissuesofassemblymodellingforinjectionmoulds/namely/representinganinjectionmouldassemblyinacomputeranddeterminingthepositionandorientationofaproduct-independentpartinanassembly/Afeature-basedandobject-orientedrepresentationisproposedtorepresent
3、thehierarchicalassemblyofinjectionmoulds/Thisrepresentationrequiresandpermitsadesignertothinkbeyondthemereshapeofapartandstateexplicitlywhatportionsofapartareimportantandwhy/Thus/itprovidesanopportunityfordesignerstodesignforassembly(DFA)/Asimplifiedsymbolicgeometricapproachisalsopresentedtoinferthe
4、configurationsofassemblyobjectsinanassemblyaccordingtothematingconditions/Basedontheproposedrepresentationandthesimplifiedsymbolicgeometricapproach/automaticassemblymodellingisfurtherdiscussed/Keywords/Assemblymodelling；Feature-based；Injectionmoulds；Object-oriented1/IntroductionInjectionmouldingisth
5、emostimportantprocessformanufac-turingplasticmouldedproducts/Thenecessaryequipmentcon-sistsoftwomainelements/theinjectionmouldingmachineandtheinjectionmould/Theinjectionmouldingmachinesusedtodayareso-calleduniversalmachines/ontowhichvariousmouldsforplasticpartswithdifferentgeometriescanbemounted/wit
6、hincertaindimensionlimits/buttheinjectionmoulddesignhastochangewithplasticproducts/Fordifferentmouldinggeometries/differentmouldconfigurationsareusuallynecessary/Theprimarytaskofaninjectionmouldistoshapethemoltenmaterialintothefinalshapeoftheplasticproduct/Thistaskisfulfilledbythecavitysystemthatcon
7、sistsofcore/cavity/inserts/andslider/lifterheads/ThegeometricalshapesCorrespondenceandoffprintrequeststo/DrJerryY/H/Fuh/Depart-mentofMechanicalandProductionEngineering/NationalUniversityofSingapore(NUS)/10KentRidgeCrescent/Singapore119260/E-mail/mpefuhyhKnus/edu/sgandsizesofacavitysystemaredetermine
8、ddirectlybytheplasticmouldedproduct/soallcomponentsofacavitysystemarecalledproduct-dependentparts/(Hereinafter/productreferstoaplasticmouldedproduct/partreferstothecomponentofaninjectionmould/)Besidestheprimarytaskofshapingtheproduct/aninjectionmouldhasalsotofulfilanumberoftaskssuchasthedistribution
9、ofmelt/coolingthemoltenmaterial/ejectionofthemouldedproduct/transmittingmotion/guiding/andaligningthemouldhalves/Thefunctionalpartstofulfilthesetasksareusuallysimilarinstructureandgeo-metricalshapefordifferentinjectionmoulds/Theirstructuresandgeometricalshapesareindependentoftheplasticmouldedproduct
10、s/buttheirsizescanbechangedaccordingtotheplasticproducts/Therefore/itcanbeconcludedthataninjectionmouldisactuallyamechanicalassemblythatconsistsofproduct-dependentpartsandproduct-independentparts/Figure1showstheassemblystructureofaninjectionmould/Thedesignofaproduct-dependentpartisbasedonextractingt
11、hegeometryfromtheplasticproduct/Inrecentyears/CAD/CAMtechnologyhasbeensuccessfullyusedtohelpmoulddesignerstodesigntheproduct-dependentparts/TheMouldMouldbaseCoolFillLayoutPlugSocketCav_1Cav_2CA-plateGuild-bushTCP-plateBep-plateCb-plateEa-plateEb-plateGuid-pinIp-plateRet-pinSliderbodyguideStop-blkHee
12、l-blkheadCoreCavityProduct-independentpartProduct-dependentpartMove-halfFixed-halfFig/1/Assemblystructureofaninjectionmould/740X/G/Yeetal/automaticgenerationofthegeometricalshapeforaproduct-dependentpartfromtheplasticproducthasalsoattractedalotofresearchinterest1/2/However/littleworkhasbeencarriedou
13、tontheassemblymodellingofinjectionmoulds/althoughitisasimportantasthedesignofproduct-dependentparts/Themouldindustryisfacingthefollowingtwodifficult-ieswhenuseaCADsystemtodesignproduct-independentpartsandthewholeassemblyofaninjectionmould/First/thereareusuallyaroundonehundredproduct-independentparts
14、inamouldset/andthesepartsareassociatedwitheachotherwithdifferentkindsofconstraints/Itistime-consumingforthedesignertoorientandpositionthecomponentsinanassembly/Secondly/whilemoulddesigners/mostofthetime/thinkonthelevelofreal-worldobjects/suchasscrews/plates/andpins/theCADsystemusesatotallydifferentl
15、evelofgeometricalobjects/Asaresult/high-levelobject-orientedideashavetobetranslatedtolow-levelCADentitiessuchaslines/surfaces/orsolids/Therefore/itisnecessarytodevelopanautomaticassemblymodellingsystemforinjectionmouldstosolvethesetwoproblems/Inthispaper/weaddressthefollow-ingtwokeyissuesforautomati
16、cassemblymodelling/rep-resentingaproduct-independentpartandamouldassemblyinacomputer；anddeterminingthepositionandorientationofacomponentpartinanassembly/Thispapergivesabriefreviewofrelatedresearchinassemblymodelling/andpresentsanintegratedrepresentationfortheinjectionmouldassembly/Asimplifiedgeometr
17、icsym-bolicmethodisproposedtodeterminethepositionandorien-tationofapartinthemouldassembly/Anexampleofauto-maticassemblymodellingofaninjectionmouldisillustrated/2/RelatedResearchAssemblymodellinghasbeenthesubjectofresearchindiversefields/suchas/kinematics/AI/andgeometricmodelling/Lib-ardietal/3compil
18、edaresearchreviewofassemblymodel-ling/Theyreportedthatmanyresearchershadusedgraphstructurestomodelassemblytopology/Inthisgraphscheme/thecomponentsarerepresentedbynodes/andtransformationmatricesareattachedtoarcs/However/thetransformationmatricesarenotcoupledtogether/whichseriouslyaffectsthetransforma
19、tionprocedure/i/e/ifasubassemblyismoved/allitsconstituentpartsdonotmovecorrespondingly/LeeandGossard4developedasystemthatsupportedahierarchicalassemblydatastructurecontainingmorebasicinformationaboutassembliessuchas“matingfeature”betweenthecompo-nents/Thetransformationmatricesarederivedautomatically
20、fromtheassociationsofvirtuallinks/butthishierarchicaltopologymodelrepresentsonly“part-of”relationseffectively/Automaticallyinferringtheconfigurationofcomponentsinanassemblymeansthatdesignerscanavoidspecifyingthetransformationmatricesdirectly/Moreover/thepositionofacomponentwillchangewheneverthesizea
21、ndpositionofitsreferencecomponentaremodified/Thereexistthreetechniquestoinferthepositionandorientationofacomponentintheassembly/iterativenumericaltechnique/symbolicalgebraictechnique/andsymbolicgeometrictechnique/LeeandGossard5proposedaniterativenumericaltechniquetocomputethelocationandorientationof
22、eachcomponentfromthespatialrelationships/Theirmethodconsistsofthreesteps/generationoftheconstraintequations/reducingthenumberofequations/andsolvingtheequations/Thereare16equationsfor“against”condition/18equationsfor“fit”condition/6propertyequationsforeachmatrix/and2additionalequationsforarotationalp
23、art/Usuallythenumberofequationsexceedsthenumberofvariables/soamethodmustbedevisedtoremovetheredundantequations/TheNewtonRaphsoniterationalgorithmisusedtosolvetheequations/Thistechniquehastwodisadvantages/first/thesolutionisheavilydependentontheinitialsolution；secondly/theiterativenumericaltechniquec
24、annotdistinguishbetweendifferentrootsinthesolutionspace/Therefore/itispossible/inapurelyspatialrelationshipproblem/thatamathematicallyvalid/butphysicallyunfeasible/solutioncanbeobtained/AmblerandPopplestone6suggestedamethodofcomput-ingtherequiredrotationandtranslationforeachcomponenttosatisfythespat
25、ialrelationshipsbetweenthecomponentsinanassembly/Sixvariables(threetranslationsandthreerotations)foreachcomponentaresolvedtobeconsistentwiththespatialrelationships/Thismethodrequiresavastamountofprogrammingandcomputationtorewriterelatedequationsinasolvableformat/Also/itdoesnotguaranteeasolutionevery
26、time/especiallywhentheequationcannotberewritteninsolvableforms/Kramer7developedasymbolicgeometricapproachfordeterminingthepositionsandorientationsofrigidbodiesthatsatisfyasetofgeometricconstraints/Reasoningaboutthegeometricbodiesisperformedsymbolicallybygeneratingasequenceofactionstosatisfyeachconst
27、raintincrementally/whichresultsinthereductionoftheobjectsavailabledegreesoffreedom(DOF)/ThefundamentalreferenceentityusedbyKrameriscalleda“marker”/thatisapointandtwoorthogonalaxes/Sevenconstraints(coincident/in-line/in-plane/parallelFz/offsetFz/offsetFxandhelical)betweenmarkersaredefined/Foraproblem
28、involvingasingleobjectandconstraintsbetweenmarkersonthatbody/andmarkerswhichhaveinvariantattri-butes/actionanalysis7isusedtoobtainasolution/Actionanalysisdecidesthefinalconfigurationofageometricobject/stepbystep/Ateachstepinsolvingtheobjectconfiguration/degreesoffreedomanalysisdecideswhatactionwills
29、atisfyoneofthebodysasyetunsatisfiedconstraints/giventheavailabledegreesoffreedom/Itthencalculateshowthatactionfurtherreducesthebodysdegreesoffreedom/Attheendofeachstep/oneappropriateactionisaddedtothemetaphoricalassemblyplan/AccordingtoShahandRogers8/Kramersworkrepresentsthemostsignificantdevelopmen
30、tforassemblymodelling/Thissymbolicgeometricapproachcanlocateallsolutionstoconstraintconditions/andiscomputationallyattractivecomparedtoaniterativetechnique/buttoimplementthismethod/alargeamountofprogrammingisrequired/Althoughmanyresearchershavebeenactivelyinvolvedinassemblymodelling/littleliterature
31、hasbeenreportedonfea-turebasedassemblymodellingforinjectionmoulddesign/Kruthetal/9developedadesignsupportsystemforaninjectionmould/Theirsystemsupportedtheassemblydesignforinjectionmouldsthroughhigh-levelfunctionalmouldobjects(componentsandfeatures)/BecausetheirsystemwasAutomatedAssemblyModelling741b
32、asedonAutoCAD/itcouldonlyaccommodatewire-frameandsimplesolidmodels/3/RepresentationofInjectionMouldAssembliesThetwokeyissuesofautomatedassemblymodellingforinjectionmouldsare/representingamouldassemblyincom-puters/anddeterminingthepositionandorientationofapro-duct-independentpartintheassembly/Inthiss
33、ection/wepresentanobject-orientedandfeature-basedrepresentationforassembliesofinjectionmoulds/Therepresentationofassembliesinacomputerinvolvesstructuralandspatialrelationshipsbetweenindividualparts/Sucharepresentationmustsupporttheconstructionofanassemblyfromallthegivenparts/changesintherelativeposi
34、tioningofparts/andmanipulationoftheassemblyasawhole/Moreover/therepresentationsofassembliesmustmeetthefollowingrequirementsfromdesigners/1/Itshouldbepossibletohavehigh-levelobjectsreadytousewhilemoulddesignersthinkonthelevelofreal-worldobjects/2/Therepresentationofassembliesshouldencapsulateoper-ati
35、onalfunctionstoautomateroutineprocessessuchaspocketingandinterferencechecks/Tomeettheserequirements/afeature-basedandobject-orientedhierarchicalmodelisproposedtorepresentinjectionmoulds/Anassemblymaybedividedintosubassemblies/whichinturnconsistsofsubassembliesand/orindividualcomponents/Thus/ahierarc
36、hicalmodelismostappropriateforrepresentingthestructuralrelationsbetweencomponents/Ahierarchyimpliesadefiniteassemblysequence/Inaddition/ahierarchicalmodelcanprovideanexplicitrepresentationofthedependencyofthepositionofonepartonanother/Feature-baseddesign10allowsdesignerstoworkatasomewhathigherlevelo
37、fabstractionthanthatpossiblewiththedirectuseofsolidmodellers/Geometricfeaturesareinstanced/sized/andlocatedquicklybytheuserbyspecifyingaminimumsetofparameters/whilethefeaturemodellerworksoutthedetails/Also/itiseasytomakedesignchangesbecauseoftheassociativitiesbetweengeometricentitiesmaintainedinthed
38、atastructureoffeaturemodellers/Withoutfeatures/designershavetobeconcernedwithallthedetailsofgeometricconstructionproceduresrequiredbysolidmodellers/anddesignchangeshavetobestrictlyspecifiedforeveryentityaffectedbythechange/Moreover/thefeature-basedrepresentationwillprovidehigh-levelassemblyobjectsfo
39、rdesignerstouse/Forexample/whilemoulddesignersthinkonthelevelofareal-worldobject/e/g/acounterborehole/afeatureobjectofacounterboreholewillbereadyinthecomputerforuse/Object-orientedmodelling11/12isanewwayofthinkingaboutproblemsusingmodelsorganisedaroundreal-worldcon-cepts/Thefundamentalentityistheobj
40、ect/whichcombinesbothdatastructuresandbehaviourinasingleentity/Object-orientedmodelsareusefulforunderstandingproblemsanddesigningprogramsanddatabases/Inaddition/theobject-orientedrepresentationofassembliesmakesiteasyfora“child”objecttoinheritinformationfromits“parent”/Figure2showsthefeature-basedand
41、object-orientedhier-archicalrepresentationofaninjectionmould/Therepresen-tationisahierarchicalstructureatmultiplelevelsofabstraction/fromlow-levelgeometricentities(formfeature)tohigh-levelsubassemblies/Theitemsenclosedintheboxesrepresent“assemblyobjects”(SUBFAs/PARTsandFFs)；thesolidlinesrepresent“pa
42、rt-of”relation；andthedashedlinesrepresentotherrelationships/Subassembly(SUBFA)consistsofparts(PARTs)/Apartcanbethoughtofasan“assembly”offormfeatures(FFs)/Therepresentationcombinesthestrengthsofafeature-basedgeometricmodelwiththoseofobject-orientedmodels/Itnotonlycontainsthe“part-of”relationsbetweent
43、heparentobjectandthechildobject/butalsoincludesarichersetofstructuralrelationsandagroupofoperationalfunctionsforassemblyobjects/InSection3/1/thereisfurtherdiscussiononthedefinitionofanassemblyobject/anddetailedrelationsbetweenassemblyobjectsarepresentedinSection3/2/3/1DefinitionofAssemblyObjectsInou
44、rwork/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)/Eacheleme
45、ntofMisafunctionthatuniquelyidentifiesamethod/Thesymbolmrepresentsamethodname；andmethodsdefineoperationsonobjects/Thesymboltci(iFig/2/Feature-based/object-orientedhierarchicalrepresentation/742X/G/Yeetal/=1/2/%/n)specifiestheargumenttypeandtcspecifiesthereturnedvaluetype/RisasetofrelationshipsamongO
46、andotherassemblyobjects/Therearesixtypesofbasicrelationshipsbetweenassemblyobjects/i/e/Part-of/SR/SC/DOF/Lts/andFit/Table1showsanassemblyobjectofinjectionmoulds/e/g/ejector/TheejectorinTable1isformallyspecifiedas/(ejector-pinF1/(string/purpose/ejectingmoulding)/(string/material/nitridesteel)/(string
47、/catalogFno/THX)/(checkFinterference()/boolean)/(pocketFplate()/boolean)/(part-ofejectionFsys)/(SRAlignEBFplate)/(DOFTx/Ty)/Inthisexample/purpose/materialandcatalogFnoareattributeswithadatatypeofstring；checkFinterferenceandpocketFplatearememberfunctions；andPart-of/SRandDOFarerelationships/3/2Assembl
48、yRelationshipsTherearesixtypesofbasicrelationshipsbetweenassemblyobjects/Part-of/SR/SC/DOF/Lts/andFit/Part-ofAnassemblyobjectbelongstoitsancestorobject/SRSpatialrelations/explicitlyspecifythepositionsandorientationsofassemblyobjectsinanassembly/Foracomponentpart/itsspatialrelationshipisderivedfromsp
49、atialconstraints(SC)/SCSpatialconstraints/implicitlylocateacomponentpartwithrespecttotheotherparts/DOFDegreesoffreedom/areallowabletranslational/rotationaldirectionsofmotionafterassembly/withorwithoutlimits/LtsMotionlimits/becauseofobstructions/interferences/theDOFmayhaveunilateralorbilaterallimits/
50、FitSizeconstraint/isappliedtodimensions/inordertomaintainagivenclassoffit/Table1/Definitionofanassemblyobject-ejector/ObjectOidejector-pinF1Instance-ofEjectorFpinDerivedfromejectorclassAPurpose“ejectingmoulding”TypestringMaterial“nitridedsteel”TypestringCatalogFno“THX”TypestringMCheckFinterferenceCh
51、eckinterference(coolFobj)betweenejectorsandcoolinglinesPocketFplate()MakeaholeonplatetoaccommodateejectorpinsRPart-ofejectorFsysSRalignwithEBplateDOFTx/TyAmongalltheelementsofanassemblyobject/therelation-shipsaremostimportantforassemblydesign/Therelationshipsbetweenassemblyobjectswillnotonlydetermin
52、ethepositionofobjectsinanassembly/butalsomaintaintheassociativitiesbetweenassemblyobjects/Inthefollowingsub-sections/wewillillustratetherelationshipsatthesameassemblylevelwiththehelpofexamples/3/2/1RelationshipsBetweenFormFeaturesMoulddesign/inessence/isamentalprocess；moulddesignersmostofthetimethin
53、konthelevelofreal-worldobjectssuchasplates/screws/grooves/chamfers/andcounter-boreholes/Therefore/itisnecessarytobuildthegeometricmodelsofallproduct-independentpartsfromformfeatures/Themoulddesignercaneasilychangethesizeandshapeofapart/becauseoftherelationsbetweenformfeaturesmaintainedinthepartrepre
54、sentation/Figure3(a)showsaplatewithacounter-borehole/Thispartisdefinedbytwoformfeatures/i/e/ablockandacounter-borehole/Thecounter-borehole(FF2)isplacedwithreferencetotheblockfeatureFF1/usingtheirlocalcoordinatesF2andF1/respectively/Equations(2)(5)showthespatialrelationshipsbetweenthecounter-borehole(FF2)andtheblockfeature(FF1)/Forformfeatures/thereisnospatialconstraintbetweenthem/sothespatialrelationshipsarespecifieddirectlybythedesigner/Thedetailedassemblyrelationshipsbetweentwoformfeaturesaredefinedasfollows/SR(FF2/FF1)/F2i=-F1i(2)F2j=-F1j(3)Fig/3/Assemblyrelationships/
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