Analysisandoptimizationofapolyurethanereactioninjectionmolding(RIM)processusingmultivariateprojectionmethodsF.Yacoub,J.F.MacGregor*ChemicalEngineeringDepartment,McMasterUniversity,1280MainStreetWest,JHE-374,Hamilton,ON,CanadaL8S4L7Received13April2002；receivedinrevisedform20August2002；accepted25August2002AbstractPrincipalcomponentanalysis(PCA)andprojectiontolatentstructure(PLS)methodsareusedwithindustrialdatatosuccessfullydiagnoseseveraldifferentproblemsarisinginthemanufacturingofrigidpolyurethanefoaminsulationpanels.ThePCAandPLSmodelsareusedtorevealthespatialvariationofqualityvariablesthroughoutthefoamedproduct,andtheirrelationswiththeprocessvariables.DesignedexperimentsareperformedinthekeyprocessvariablesidentifiedfromthePCAstudiesandtheresultsareusedtooptimizetheprocess.D2002ElsevierScienceB.V.Allrightsreserved.Keywords:Polyurethane；Reactioninjectionmolding；Projectionmethod1.IntroductionInthelasttwodecades,chemicalprocesses,likemanyotherindustries,havebeengoingthrougharevolutionintheirdatacollectionsystems.Machineintelligence,immensedatastoragecapacity,andhighthroughputdataacquisitionsystemshavedriventhecostperdatapointdowntoaverylowlevel.Massesofdataarenowavailablebymeasuringprocessvariablesaswellasqualityvariableseitheronlineorinqualitycontrollabs.Projectionmethodssuchasprincipalcomponentanalysis(PCA)andprojectiontolatentstructure(PLS)provideawaytohandlethehighlycorrelateddatacollectedbythesesystems.Inaddition,theydealeffectivelywithmultipleresponsevariablesandwithmissingdata,andtheyprovideagoodtooltoextractandhighlightthesystematicvariationinthesemulti-variatedatasets.Themostimportantpropertyofprojectionmethodsisthecapabilitytoreducethemultivariatedimensionofaproblemintoalow-dimensionalspace,usuallycon-sistingofthreetofourdimensions.TheSIMCA_P8.0softwareofUmetricswasusedforthePCA/PLSanalysesperformedinthiswork.Thefocusofthisstudyistheapplicationofthemultivariateprojectionmethodsforthediagnosisandanalysisofapolyurethanereactioninjectionprocess.Themainobjectivesofthisresearcharetounderstandthespatialvariationintheprocess,correctthecausesofthisvariation,andoptimizethequalityvariables.0169-7439/02/$-seefrontmatterD2002ElsevierScienceB.V.Allrightsreserved.PII:S0169-7439(02)00088-6*Correspondingauthor.Tel.:+1-905-525-9140；fax:+1-905-521-1350.E-mailaddress:macgregmcmaster.ca(J.F.MacGregor)./locate/chemometricsChemometricsandIntelligentLaboratorySystems65(2003)17332.ThemechanismofpolyurethaneformationTheprocessofinsulatingrefrigeratorsinvolvesreactioninjectionmolding(RIM)toformpolyur-ethanefoam.Eachrefrigeratorcavityservesasachemicalreactorwheretwodifferentsetsofreactionstakeplacesimultaneously.Oneisthepolymerizationreaction,inwhichsuchbondsasurethaneandureamaybeformed.Theotheristhefoamingreaction,whichinvolvestheevolutionofcarbondioxideandthevaporizationofblowingagent.Chemicalsflowfromdaytanksthroughheatexchangerstocontrolthetemperatureandthenintothemix-headunderhighpressuretoinsuregoodmixingandthenthemixtureisinjectedinsidethemold1.Inanyreactingpolyurethanefoam,manyphysicalandchemicalchangesoccur,andthesevarywithtimeandextentofreactionasshowninFig.1.Thetemper-aturewithinthefoamrisesasthereactionproceedsand,becausethefoamisagoodthermalinsulator,temper-aturegradientsariseandcanresultinmanyproblemsasdiscussedlaterinthepaper.Ingeneral,themanufactureofpolyurethanerigidfoamcanbecharacterizedbythefollowingfourstages2.(I)Mixingstep,wheretheMasterbatchwhichcontainthepolyol,acatalyst,asurfactantandablowingagentismixedunderhighpressurewiththeisocyanateinthemix-head.(II)Creamperiod,inwhichthetemperatureincreasecausedbytheexothermicchemicalreaction,issuf-ficienttopromotetheactivityoftheblowingagent.(III)Riseperiod,inwhichtheblowingagentevapo-ratesraisingthefoamuntilasufficientrigidityisreachedbyeitherfreerisingorwhenthemoldisfilled.(IV)Postcuringstep,inwhichthepolymeristreatedbyahightemperatureforacertaintime.Themechanicalsystemconsistsofarotarydrumunitthathasasix-stationrotaryframe.Foamfixturesareplacedineachframestation.Refrigeratordoorsorothercavitiestobefoamedareplacedinsidethefix-tureswheretheyarepreheated,theninjectedwiththereactionmixtureinonepositiononthedrumunit.Oncefoamed,thedrumunitrotatesthefixturethroughfiveotherpositionsforcuring,whiletheotherpositionsarefoamed,andeventuallyreturnsthefixturetothefoamposition.EachdrumunithastwoFig.1.Polyurethanefoamformation.F.Yacoub,J.F.MacGregor/ChemometricsandIntelligentLaboratorySystems65(2003)173318polyurethanefoammix-headcarriages.Eachcarriagefoamsadifferentdoor.2.1.ProblemdescriptionTheinstabilityofthefoamingprocessandthecomplexityofcontrollingthequalityvariablescreatedtheneedandmotivationforthiswork.Twoproblemsonthisprocessarediscussedseparatelyastheyaroseatdifferenttimes.Thefirstprojectwastooptimizethefunctionalityofthepolyurethanefoampanelsexpressedbythespatialvariationofitsthermalconductivityanddensity.Theinsulationfunctionofthefoam,measuredbythermalconductivity(k-factor),isconsideredasavitalvariabletobecontrolled.Ithasadirecteffectontherefrigeratorperformanceandenergyconsumption.Intheory,whenthemasterbatchismixedwiththeisocyanateatacer-taintemperature,theblowingagentboils,andcreatesavaporthatblowsthefoamandreducesthedensity.Inrigidfoam,thecellsformedbytheblowingagentredu-cethetransmissionofheat.Thelowerthek-factoris,thebettertheinsulationandtherefrigeratorperformance.Density,whichisanindicationoffoamstrength,isimportantinkeepingthestructuralrigidityoftherefrigerator.Itisaresultofthepressurethatthevaporfromtheblowingagentsexertsinthecell.Thecellgaspressurecausesthefoamtoresistshrinkage.Inordertoreducethescraprateofthisprocess,unacceptablevoidsandleakshavetobeminimized.TheobjectiveofthesecondprojecttreatedinthispaperistominimizethedistortionphenomenainthefoamedpanelsknownasOuterBow(OB).OuterBowismainlycausedbythemovementrestrictionofthesteelandABSplasticpanels.Thepanelsareunabletoexpandorcontractrelativetoeachothersincethedistanceseparatingthemisrelativelysmall.Ifmove-mentistooccur,itwillresultinthewarpingofthepanelsorsheardeformation.2.2.QualitymeasurementsQualityvariablesaremeasuredoff-lineonaweeklybasisinqualitycontrollabs.Theupperspecificationlimitofthethermalconductivityisbasedonenergycalculations,andthelowerspecificationlimitofden-sityisdefinedastheminimumdensitytomaintainstructuralstrength.Allmeasurementsareperformedateightlocationsaroundthefoamedpanels.Thecriterionistohaveallsampleswithinthespecifiedcontrollimits.ThermaldistortionismeasuredusingaCoor-dinateMeasuringMachine(CMM)bydefiningaplanethatpassesthroughpointslocatedinthecornersofthepanelandmeasuresthedeviationfromthisplaneatseveralpointsacrossthepanelsurfacetodeterminetheshapeandmagnitudeofsurfacebow.Thefollowingqualityvariablesaremeasured:2.3.ProcessvariablesProcessvariableswereselectedandretrievedfromthedatabase.Theanalysiswasperformedonsixdiffer-entfixturesfromproductiontounderstandthevariationbetweenfixturesandtheeffectofchangesintheprocessvariables.Asummaryofprocessvariablesusedintheanalysisandthecorrespondingnomencla-turepresentedinthepaperisgivenasfollows:TimetotestT_TAmbienttemperatureA_TMasterbatchdensityMB_DMasterbatchflowMB_FIsocyanateflowI_FRatiobetweenMasterbatchandisocyanateMB/IIsocyanatepressureI_PMasterbatchpressureMB_PMix-headpressureMH_PShotsizeSSIsocyanatetemperatureI_TMasterbatchtemperatureMB_TIsocyanatetemperatureatmix-headI_T_MHMasterbatchtemperatureatmix-headMB_T_MHSurfactanttypeSBlowingagenttypeBFixturecoretemperatureCore_TFixturesidewalltemperatureSidewall_TFixturepreheattemperaturePreheat_TK*K-factorvaluesatvariousspatiallocations(18)D*Densityvaluesatvariousspatiallocations(18)VoidsIdentifiedbysinkmarksintheoutersteelLeaksIdentifiedvisuallyFacebowMaximumwarpageofthefacefoamedobjectsSidebowMaximumwarpageofthesidefoamedobjectsF.Yacoub,J.F.MacGregor/ChemometricsandIntelligentLaboratorySystems65(2003)1733193.Problem1:eliminatingspatialvariationinthermalconductivityanddensity3.1.Principalcomponentanalysisonqualityvaria-bles(Ys)ThemainobjectivesbehindfittingaPCAmodelontheYsaretounderstandthespatialpatternsandthecorrelationstructureamongthevariables.Meas-urementsmadeonatotalof64setsofpanels.Threeprincipalcomponentsaresignificantbycross-validation3andtheyexplain76%ofthevariation.Someoutliersareevidentinthescoreplotsandresidual(DmodX)plotsshowninFigs.2and3,respectively.Outliersareconsideredveryinterestingobservationsthatholdvaluableinformationthatcanbeunderstoodusingcontributionplots.Furtheranal-ysisandinterpretationsoftheseoutlierswillbedis-cussedinalatersection.Theloadingplot,showninFig.4,revealsthattherearetwomaingroups.Ther-malconductivityispositivelycorrelatedwithleaksandnegativelycorrelatedwithbothdensityandvoi