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Computer-AidedDesign40(2008)334–349figurationspacemethodC.G.Li,C.L.Li∗DepartmentofManufacturingEngineeringandEngineeringManagement,CityUniversityofHongKong,HongKongReceived3May2007;accepted18November2007AbstractThecoolingsystemofaninjectionmouldisveryimportanttotheproductivityoftheinjectionmouldingprocessandthequalityofthemouldedpart.Despitethevariousresearcheffortsthathavebeendirectedtowardstheanalysis,optimization,andfabricationofcoolingsystems,supportforthelayoutdesignofthecoolingsystemhasnotbeenwelldeveloped.Inthelayoutdesignphase,amajorconcernisthefeasibilityofbuildingthecoolingsysteminsidethemouldinsertwithoutinterferingwiththeothermouldcomponents.Thispaperreportsaconfigurationspace(C-space)methodtoaddressthisimportantissue.Whileahigh-dimensionalC-spaceisgenerallyrequiredtodealwithacomplexsystemsuchasacoolingsystem,thespecialcharacteristicsofcoolingsystemdesignareexploitedinthepresentstudy,andspecialtechniquesthatallowC-spacecomputationandstorageinthree-dimensionalorlowerdimensionaredeveloped.Thisnewmethodisanimprovementontheheuristicmethoddevelopedpreviouslybytheauthors,becausetheC-spacerepresentationenablesanautomaticlayoutdesignsystemtoconductamoresystematicsearchamongallofthefeasibledesigns.AsimplegeneticalgorithmisimplementedandintegratedwiththeC-spacerepresentationtoautomaticallygeneratecandidatelayoutdesigns.Designexamplesgeneratedbythegeneticalgorithmaregiventodemonstratethefeasibilityofthemethod.c2007ElsevierLtd.Allrightsreserved.Keywords:Coolingsystemdesign;Plasticinjectionmould;Configurationspacemethod1.IntroductionThecoolingsystemofaninjectionmouldisveryimportanttotheproductivityoftheinjectionmouldingprocessandthequalityofthemouldedpart.Extensiveresearchhasbeenconductedintotheanalysisofcoolingsystems[1,2],andcommercialCAEsystemssuchasMOLDFLOW[3]andMoldex3D[4]arewidelyusedintheindustry.Researchintotechniquestooptimizeagivencoolingsystemhasalsobeenreported[5–8].Recently,methodstobuildbettercoolingsystemsbyusingnewformsoffabricationtechnologyhavebeenreported.Xuetal.[9]reportedthedesignandfabricationofconformalcoolingchannelsthatmaintainaconstantdistancefromthemouldimpression.Sunetal.[10,11]usedCNCmillingtoproduceU-shapedmilledgroovesforcoolingchannelsandYu[12]proposedascaffoldingstructureforthedesignofconformalcooling.∗Correspondingauthor.E-mailaddress:meclli@cityu.edu.hk(C.L.Li).Despitethevariousresearcheffortsthathavefocusedmainlyonthepreliminarydesignphaseofthecoolingsystemdesignprocessinwhichthemajorconcernistheperformanceofthecoolingfunctionofthesystem,supportforthelayoutdesignphaseinwhichthefeasibilityandmanufacturabilityofthecoolingsystemdesignareaddressedhasnotbeenwelldeveloped.Amajorconcerninthelayoutdesignphaseisthefeasibilityofbuildingthecoolingsysteminsidethemouldinsertwithoutinterferingwiththeothermouldcomponents.ConsidertheexampleshowninFig.1.Itcanbeseenthatmanydifferentcomponentsofthevarioussubsystemsoftheinjectionmould,suchasejectorpins,slides,sub-inserts,andsoforth,havetobepackedintothemouldinsert.Findingthebestlocationforeachchannelofthecoolingcircuittooptimizethecoolingperformanceofthecoolingsystemandtoavoidinterferencewiththeothercomponentsisnotasimpletask.Anotherissuethatfurthercomplicatesthelayoutdesignproblemisthattheindividualcoolingchannelsneedtobeconnectedtoformapaththatconnectsbetweentheinletandtheoutlet.Therefore,changingthelocationofachannelmay0010-4485/$-seefrontmatterc2007ElsevierLtd.Allrightsreserved.doi:10.1016/j.cad.2007.11.010C.G.Li,C.L.Li/Computer-AidedDesign40(2008)334–349335Fig.1.Thecoolingsysteminsideamouldinsertpackedwithmanyothermouldcomponents.requirechangingtheotherchannelsaswell.ConsidertheexampleshowninFig.2.TheideallocationofeachchanneltooptimizethecoolingperformanceofthesystemisshowninFig.2(a).Assumethatwhenthecoolingsystemandtheothermouldcomponentsarebuiltintothemouldinsert,amouldcomponentO1isfoundtointerferewithchannelC1.AsC1cannotbemovedtoanearbylocationduetothepossibleinterferencewithothercomponents,itisshortened.Asaresult,C2ismovedandC3iselongatedaccordinglytomaintaintheconnectivity,asshowninFig.2(b).Owingtoitsnewlength,C3isfoundtointerferewithanothermouldcomponent,O2,andfurthermodificationisneeded,whichresultsinthefinaldesignshowninFig.2(c).Giventhatatypicalinjectionmouldmayhavemorethantencoolingchannels,witheachchannelpotentiallyinterferingwithafewothermouldcomponents,findinganoptimallayoutdesignmanuallyisverytedious.Thispaperreportsanewtechniquethatsupportstheautomationofthelayoutdesignprocess.Inthisnewtechnique,aconfigurationspace(C-space)methodisusedtoprovideaconciserepresentationofallofthefeasiblelayoutdesigns.TheC-spacerepresentationisconstructedbyanefficientmethodthatexploitsthespecialcharacteristicsofthelayoutdesignproblem.Insteadofusingheuristicrulestogeneratelayoutdesigns,asintheautomaticlayoutdesignsystemdevelopedpreviouslybytheauthors[13,14],thisnewC-spacemethodenablesanautomaticlayoutdesignsystemtoconductamoresystematicsearchamongallofthefeasiblelayoutdesigns.2.