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Analysis and optimization of a polyurethane reaction injectionmolding (RIM) process using multivariate projection methodsF. Yacoub, J.F. MacGregor*Chemical Engineering Department, McMaster University, 1280 Main Street West, JHE-374, Hamilton, ON, Canada L8S 4L7Received 13 April 2002; received in revised form 20 August 2002; accepted 25 August 2002AbstractPrincipal component analysis (PCA) and projection to latent structure (PLS) methods are used with industrial data tosuccessfully diagnose several different problems arising in the manufacturing of rigid polyurethane foam insulation panels. ThePCA and PLS models are used to reveal the spatial variation of quality variables throughout the foamed product, and theirrelations with the process variables. Designed experiments are performed in the key process variables identified from the PCAstudies and the results are used to optimize the process.D 2002 Elsevier Science B.V. All rights reserved.Keywords: Polyurethane; Reaction injection molding; Projection method1. IntroductionIn the last two decades, chemical processes, likemany other industries, have been going through arevolution in their data collection systems. Machineintelligence, immense data storage capacity, and highthroughput data acquisition systems have driven thecost per data point down to a very low level. Masses ofdata are now available by measuring process variablesas well as quality variables either on line or in qualitycontrol labs.Projection methods such as principal componentanalysis (PCA) and projection to latent structure(PLS) provide a way to handle the highly correlateddata collected by these systems. In addition, they dealeffectively with multiple response variables and withmissing data, and they provide a good tool to extractand highlight the systematic variation in these multi-variate data sets.The most important property of projection methodsisthecapabilitytoreducethemultivariatedimensionofa problem into a low-dimensional space, usually con-sisting of three to four dimensions. The SIMCA_P 8.0software of Umetrics was used for the PCA/PLSanalyses performed in this work.The focus of this study is the application of themultivariate projection methods for the diagnosis andanalysis of a polyurethane reaction injection process.The main objectives of this research are to understandthespatial variation intheprocess,correctthecausesofthis variation, and optimize the quality variables.0169-7439/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.PII: S0169-7439(02)00088-6* Corresponding author. Tel.: +1-905-525-9140; fax: +1-905-521-1350.E-mail address: macgregmcmaster.ca (J.F. MacGregor)./locate/chemometricsChemometrics and Intelligent Laboratory Systems 65 (2003) 17332. The mechanism of polyurethane formationThe process of insulating refrigerators involvesreaction injection molding (RIM) to form polyur-ethane foam. Each refrigerator cavity serves as achemical reactor where two different sets of reactionstake place simultaneously. One is the polymerizationreaction, in which such bonds as urethane and ureamay be formed. The other is the foaming reaction,which involves the evolution of carbon dioxide andthe vaporization of blowing agent. Chemicals flowfrom day tanks through heat exchangers to control thetemperature and then into the mix-head under highpressure to insure good mixing and then the mixture isinjected inside the mold 1.In any reacting polyurethane foam, many physicaland chemical changes occur, and these vary with timeand extent of reaction as shown in Fig. 1. The temper-aturewithinthefoamrisesasthereactionproceedsand,because the foam is a good thermal insulator, temper-aturegradientsariseandcanresultinmanyproblemsasdiscussed laterinthepaper.Ingeneral,themanufactureof polyurethane rigid foam can be characterized by thefollowing four stages 2.(I)Mixing step, where the Master batch whichcontain the polyol, a catalyst, a surfactant and ablowing agent is mixed under high pressure withthe isocyanate in the mix-head.(II) Cream period, in which the temperature increasecausedbytheexothermicchemicalreaction,issuf-ficienttopromotetheactivityoftheblowingagent.(III) Rise period, in which the blowing agent evapo-rates raising the foam until a sufficient rigidity isreached by either free rising or when the mold isfilled.(IV) Post curing step, in which the polymer is treatedby a high temperature for a certain time.The mechanical system consists of a rotary drumunit that has a six-station rotary frame. Foam fixturesare placed in each frame station. Refrigerator doors orother cavities to be foamed are placed inside the fix-tures where they are preheated, then injected with thereaction mixture in one position on the drum unit.Once foamed, the drum unit rotates the fixturethrough five other positions for curing, while the otherpositions are foamed, and eventually returns thefixture to the foam position. Each drum unit has twoFig. 1. Polyurethane foam formation.F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173318polyurethane foam mix-head carriages. Each carriagefoams a different door.2.1. Problem descriptionThe instability of the foaming process and thecomplexity of controlling the quality variables createdthe need and motivation for this work. Two problemson this process are discussed separately as they arose atdifferent times.The first project was to optimize the functionality ofthe polyurethane foam panels expressed by the spatialvariation of its thermal conductivity and density. Theinsulation function of the foam, measured by thermalconductivity (k-factor), is considered as a vital variableto be controlled. It has a direct effect on the refrigeratorperformance and energy consumption. In theory, whenthe master batch is mixed with the isocyanate at a cer-tain temperature, the blowing agent boils, and creates avapor that blows the foam and reduces the density. Inrigid foam, the cells formed by the blowing agent redu-cethetransmissionofheat.Thelowerthek-factoris,thebetter the insulation and the refrigerator performance.Density, which is an indication of foam strength, isimportant in keeping the structural rigidity of therefrigerator. It is a result of the pressure that the vaporfrom the blowing agents exerts in the cell. The cell gaspressure causes the foam to resist shrinkage.In order to reduce the scrap rate of this process,unacceptable voids and leaks have to be minimized.The objective of the second project treated in thispaper is to minimize the distortion phenomena in thefoamed panels known as Outer Bow (OB). Outer Bowis mainly caused by the movement restriction of thesteel and ABS plastic panels. The panels are unable toexpand or contract relative to each other since thedistance separating them is relatively small. If move-ment is to occur, it will result in the warping of thepanels or shear deformation.2.2. Quality measurementsQuality variables are measured off-line on a weeklybasis in quality control labs. The upper specificationlimit of the thermal conductivity is based on energycalculations, and the lower specification limit of den-sity is defined as the minimum density to maintainstructural strength. All measurements are performed ateight locations around the foamed panels.The criterionis to have all samples within the specified controllimits. Thermal distortion is measured using a Coor-dinate Measuring Machine (CMM) by defining a planethat passes through points located in the corners of thepanel and measures the deviation from this plane atseveral points across the panel surface to determine theshape and magnitude of surface bow.The following quality variables are measured:2.3. Process variablesProcess variables were selected and retrieved fromthe database. The analysis was performed on six differ-entfixturesfromproductiontounderstandthevariationbetween fixtures and the effect of changes in theprocess variables. A summary of process variablesused in the analysis and the corresponding nomencla-ture presented in the paper is given as follows:Time to testT_TAmbient temperatureA_TMaster batch densityMB_DMaster batch flowMB_FIsocyanate flowI_FRatio between Master batch and isocyanateMB/IIsocyanate pressureI_PMaster batch pressureMB_PMix-head pressureMH_PShot sizeSSIsocyanate temperatureI_TMaster batch temperatureMB_TIsocyanate temperature at mix-headI_T_MHMaster batch temperature at mix-headMB_T_MHSurfactant typeSBlowing agent typeBFixture core temperatureCore_TFixture sidewall temperatureSidewall_TFixture preheat temperaturePreheat_TK*K-factor values at variousspatial locations (18)D*Density values at variousspatial locations (18)VoidsIdentified by sink marksin the outer steelLeaksIdentified visuallyFace bowMaximum warpage of theface foamed objectsSide bowMaximum warpage of theside foamed objectsF. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 1733193. Problem 1: eliminating spatial variation inthermal conductivity and density3.1. Principal component analysis on quality varia-bles (Ys)The main objectives behind fitting a PCA modelon the Ys are to understand the spatial patterns andthe correlation structure among the variables. Meas-urements made on a total of 64 sets of panels.Three principal components are significant bycross-validation 3 and they explain 76% of thevariation. Some outliers are evident in the score plotsand residual (DmodX) plots shown in Figs. 2 and 3,respectively. Outliers are considered very interestingobservations that hold valuable information that canbe understood using contribution plots. Further anal-ysis and interpretations of these outliers will be dis-cussed in a later section. The loading plot, shown inFig. 4, reveals that there are two main groups. Ther-mal conductivity is positively correlated with leaksand negatively correlated with both density and voids.Furthermore, from the loading plot (Fig. 4), apattern distribution of density and thermal conductiv-ity variation inside the cavity and in relation to theaverage value is evident. It is worth noting that at theinjection side (locations 1 and 8) the density washigher and the k-factor was lower than around theedges of the mold.3.2. Projection to latent structure (PLS) betweenfixtures and quality variablesIn order to understand the effect of the six fixturesused in production, a PLS model is built to relate theevent of using a specific fixture to the qualityvariables. The X-matrix consisted of six indicator(0,1) variables indicating the presence or absence ofany particular fixture during an injection. The Y-matrix consisted of the average K-factor, the averagedensity, voids, and leaks for each of the 64 panels.The PLS model explained 72.5% the variation (Ry2) inthe Ys using only the information on which fixturewas used for the molding process, implying that theFig. 2. t1t2scores from PCA on the quality variables (Ys).F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173320fixture differences were major contributors to thevariation in quality. The PLS loading plot in Fig. 5maps the relation between the six fixtures and thequality variables, and reveals some very interestingresults. It is apparent that the presence of fixture 1 ishighly correlated with high thermal conductivity andthe occurrence of leaks while the presence of fixture2 is negatively correlated with density and voids. Itcan be seen as well that the fixtures that have the bestperformance are fixtures 3 and 4. Both have lowthermal conductivity and sufficiently high density,but not many voids. Fixtures 5 and 6 have low K-factor and high density but more voids. From thisanalysis, it was concluded that fixtures 1 and 2provided unacceptable panel quality. Fixture 1 yieldstoo high values for k-factor and leaks, while fixture 2has low k-factor and leaks, but unacceptably lowvalues of density. To understand the reasons for this,both PCA and PLS studies were performed to relatethe fixtures and the quality variables to the processvariables.3.3. Principal component analysis (PCA) of fixturesand process variablesA PCA model was build to map the structurebetween fixtures and process variables. The rationalebehind building this model is to understand thecorrelation between the bad fixtures and certain proc-ess variables. In this model, six fixtures as well asprocess variables such as the temperatures of thechemicals and the fixtures (sidewall and core), andthe preheat temperature were considered.The model yielded three latent variables thatexplain 68% of the variation (Rx2) with a cross-vali-dated (Qx2) value equal to 64%. The score plot in Fig.6 identifies three main clusters. No outliers areobserved in the score and DmodX plots (Fig. 7).The loading plot in Fig. 8 shows that fixtures 3, 4,5, and 6 have similar characteristics while the badfixtures 1 and 2 have a different pattern. Fixture onehas a higher preheat temperature than the otherfixtures. It can be observed as well that high correla-Fig. 3. DmodX plot for PCA on the quality variables (Ys).F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173321tion exists between high preheat temperature and highratio between the master batch and isocyanate (MB/I).This observation can be explained by fact that as thepreheat temperature rises, isocyanate which has alower molecular weight will tend to evaporate andconsequently the ratio of the master batch to isocya-nate reacting in the cavity will rise. It is worth notingthat different operators had already observed that, ingeneral, a high temperature resulted in a high k-factor.Fixture 2, on the other hand, exhibited a lowerpreheat, core, and sidewall temperature, in general,and higher isocyanate temperatures. Defective andfaulty heaters in both the mix-head and the preheatstation in fixture 2 were found to be the root cause ofthese correlations.3.4. Projection to latent structure (PLS) betweenprocess and quality variablesA PLS model was then built between the processvariables and the spatially averaged quality variables.The results of the PLS indicate a very strong correla-tion and a dimensionality of three based on cross-validation. These three components explain 79% ofthe variation of the quality variables. A plot of t1vs.u1(latent vectors in the X and Y space, respectively,for the first component) in Fig. 9 shows a very strongrelationship. The loading plot shown in Fig. 10 high-lights the important variables in the process and pointsto where the variability in the quality variables iscoming from.Master batch temperature at mix-head (MB_T_MH), preheat temperature (Preheat_T), shot size,and ambient temperature (A_T) all prove to have apositive correlation with k-factor and the occurrence ofleaks while the isocyanate temperatures (I_T andI_T_MH) showed a negative correlation with k-factoras well as density.The above PLS model only reveals the correlationstructure of the data during routine plant operation,and the observed correlation among the process andquality variables cannot be interpreted as causalFig. 4. Loading plot on the quality variables (Ys).F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173322relationships. However, the PLS loading plot in Fig.10 reveals some very interesting relationships thatneeded to be explored further. Therefore, at this stage,it was decided to proceed with a designed experimentin order to establish causal relationships among thequality variables and some of the more interestingprocess variables arising from the PLS analysis. Theprocess variables chosen were the ones that had a highcorrelation with the quality variables as discoveredfrom the PLS loading and coefficients plot, and werealso capable of being directly manipulated. The ratioof Master batch to isocyanate (MB/I) was set to afixed value suggested by the supplier of the chem-icals. Ambient temperature (A_T) was considered as anoise variable that needed to be investigated andeventually controlled if possible.3.5. Response surface model (RSM) developmentIn general, the best way to develop a cause andeffect model and use it to find the optimum conditionsof the process is to design an appropriate set ofexperiments.A central composite RSM design was made inthe following four variables: the shot size (SS) andthe temperatures of Master batch (MB_T), isocya-nate (I_T), and mold. The mold temperature used inthe experiment was defined as a weighted averageof the profile of the core, sidewall, and preheattemperatures. The design consisted of a 24fullfactorial with three replicates of each condition, thenthe star points were added to complete a centralcomposite design. The main objective of runningsuch a design was to identify what variable inter-actions and curvature terms were important and tooptimize the process by plotting the response sur-face.By fitting a regression model to the data, thecoefficient of determination R2, which indicate howmuch variation is explained by the model, was 97.1%and 98.3% for the thermal conductivity and density,respectively. The response surface model resulted inFig. 5. Loading plot for the PLS between the presence of a fixture (x) and the quality variables (Ys).F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173323Fig. 6. t1t2scores from PCA between the presence of a fixture (x) and the process variables (Xs).Fig. 7. DmodX plot from PCA between the presence of a fixture (x) and the process variables (Xs).F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173324first order prediction equations for both thermalconductivity and density as follows:K ? factor 0:21 0:00064 MB?T ? 0:000778 SS? 0:00066 Mold?TDensity 1:775 ? 0:038 MB?T 0:0835 SS 0:04 Mold?TContour plots were then developed for the qualityvariables as shown in Figs. 11 and 12. As shown laterin Section 4, large shot size (SS) has an undesirableeffect on bimetallic bow and leads to a greater use ofchemicals. Therefore, shot size was maintained fixedat a relatively low value that was a compromise. Itwas also decided to keep the Mold_T at the lowestsetting as one way to improve energy consumption. Itis then obvious that to minimize k-factor and max-imize density, one should increase the master batchtemperature. These conditions were implemented andled to significantly improved panels.3.6. Multivariate monitoring (MSPC)The main objective of statistical process control(SPC) methods is to monitor the performance of aprocess over time to detect and identify out ofcontrol events.In multivariate SPC, control charts based onPCA or PLS scores, t, or a Hotellings T2basedon scores can be plotted to follow how the processbehaves over time based on the projection modeldeveloped 4,5. The models for monitoring need tobe built from normal process operating data whereonly common-cause variation is present. Targetvalues can be established, together with warninglimits that can reflect the current process capability.A DmodX plot of the residuals together withwarning limits provides the main chart for detectingany special or unusual event that may arise in theprocess.(i)A pilot trial was implemented in the manufactur-ing facility in order to evaluate the benefit ofmultivariate statistical process control on thisFig. 8. Loading plot for the PCA between the presence of a fixture (x) and the process variables (Xs).F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173325Fig. 9. t1u1scores from PLS between the quality variables (Ys) and the process variables (Xs).Fig. 10. Loading plot from PLS between the quality variables (Ys) and the process variables (Xs).F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173326process. A PCA model was developed formonitoring the spatial variation in density andk-factor. The normal variability of the process canbe modeled with two principal components thatexplain 79% of variation in the process. Figs. 13and 14 show the score and DmodX used tomonitor the process during this trial.(ii) A PLS model was also built from normaloperating data for monitoring the process andfor predicting the quality. This model used all theprocess variables (X) listed in Section 2.2 as wellas indicator variables for the fixtures. The qualityvariables (Y) included the void and leak variablesand all the k-factors and densities. The benefit ofusing such an approach based on processvariables x is one can reduce the number samplesthat are tested for the y values and consequentlysave money and time spent in testing. Anadditional benefit of using the PLS model withthe process variables is the ability to isolate/diagnose events on process upsets by usingcontribution plots to interrogate the underlyingmodel for the process variables that are mostcorrelated with the event over the period since itwas detected.4. Problem 2: minimizing bimetallic bowThe temperature variance between the steel paneland the ABS panel is the prime contributor to thewarping of the panel. In some instances, the temper-ature between the inner and outer panels, only a fewinches thick, can be approximately 55 jC. Unfortu-nately, there will always be thermal warping wherefoaming is being applied. The objective will be tominimize the degree of thermal warping 6.J. A. Hartsock derived a general equation to predictbimetallic bow due to the thermal effects which, in thecase of thin flat faces, can be reduced to the following7:B C2a1DT1? a2DT28D1Fig. 11. Response contour plot of K-factor. Settings: Temperatures of Master batch (MB_T), mold_T varied, and shot size (SS) isocyanate (I_T)fixed at their low levels.F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173327where B is the bow, a1and a2are the coefficients ofthermal expansion of the faces, DT1and DT2are thetemperature change of the faces, C is the length ofpanel, and D is the distance between the neutral axisof the tow faces.The process of foaming can also determine howextreme the outer case bow will be. The main focushas been on the time allowed for the foam to cure andthe over-packing of the units. Dimensions of theformed steel are also believed to contribute to surfacedeformation. Modern manufacturing practices havebeen able to reduce the number of over-packingoccurrences, but the time to cure is still a pressingissue. It is believed that bow would not occur if thepanels were able to remain in the mold fixture untilthe foam is completely cured 8,9. High productiondemands are making this task difficult to comply with.The importance of reducing the mean of the bow andminimize the standard deviation comes to play whenattaching panels to the refrigerator doors for cosmeticappearance. A high value of bow makes it difficult toattach panels.4.1. Principal component analysis to investigatespatial surface variationIn order to understand how the surface varies as aresult of foam expansion, the face was studied bymeasuring 180 points on 10 panels using a CoordinateMeasurement Machine (CMM), a precision measure-ment instruments that give the (x, y, z) coordinate ofall designated points on the surface of the panel. APCA model was then developed to model the spatialvariation over the surface patterns.The results of the PCA model, illustrated by theloading plot in Fig. 15, indicate that the processvariation can be modeled by two components thatexplains 87% of the process variation. Analysis ofthe loading plot shows that there are two mainclusters. A very interesting feature of the surfacevariation was revealed when relating the two clusterswith the corresponding points on the foamed parts. Itappears that up to 2 in. from the edges, the surface isflat, then it bows to the maximum and stays flatacross the surface as shown in the schematic pre-Fig. 12. Response contour plot of density. Settings: Temperatures of Master batch (MB_T), mold_T varied, and shot size (SS) isocyanate (I_T)fixed at their low levels.F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173328Fig. 13. t1t2scores from PCA model on the quality variables (Ys) for monitoring.Fig. 14. DmodX plot from PCA model on quality variables for monitoring.F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173329sented in Fig. 16. This analysis helped identify thesurface variation shape as well as establishing a moreefficient measuring technique using fewer points.The business benefit will be less time spent inmeasuring and same information.The maximum bow on the door surface was 0.54cm while the theoretical was calculated to be 0.15 cmby using Eq. (1), indicating that there is more roomfor improvement by optimizing the process.4.2. Principal component model of responses andprocess variablesTo investigate the correlation among the face andside bimetallic bow and 25 other process variables, aPCA model was built. Three components explained78% of the process variation. The score plot of t1vs.t2, shown in Fig. 17, reveals three different clusters ofobservations. The loading plot in Fig. 18 shows thatface and side bow are highly correlated as theirloadings are positioned on top of each other. In termsof process variables, demold time is negatively corre-lated with bimetallic bow, while shot size is positivelycorrelated. Cluster 1 is mainly dominated by longerdemold times and smaller shot sizes, while cluster 3has larger shot sizes and lower demold times. Thedimensions of the foamed parts expressed in terms oflength (L_*) and width (W_*) measured at threelocations are seen to have some correlation as wellwith the bimetallic bow.Fig. 15. Loading plot from PCA on the foam surface characteristics.Fig. 16. Schematic of the corresponding location of the two clustersin the foamed panels.F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173330Fig. 17. t1t2scores from PCA using both quality variables (Ys) and process variables (Xs).Fig. 18. Loading plot of PCA model using the quality variables (Ys) and the process variables (Xs).F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 1733314.3. Response surface modelIn order to investigate these effects further, and tominimize the bimetallic bow, a 22full factorialdesigned experiment was carried out using demoldtime and shot size as the controlled variables. The restof the process variables can be considered as uncon-trolled noise variables.The results from the DOE were analyzed using aregression model that explains 93% of the variation.Demold time, shot size, and the interaction betweenthese two variables proved to have significanteffects on the bow as illustrated by the followingequation:Bimetallic bow 0:213 2:45 shot size? 1:79 demold time 0:62 demold time ? shot sizeFig. 19 is a contour plot of the bimetallic bow as afunction of demold time and shot size. This plotbasically maps the direction that can be taken tominimize the bow: increase demold time anddecrease shot size. However, as shot size is re-duced, foam quality (density and k-factor) can beaffected and become not acceptable from a functionviewpoint. Thus, K-factor and density were meas-ured at each condition, and further qualificationtests had to be performed when finding an optimumsetting for shot size that minimized bimetallic bow.The increases in demold time also had to be bal-anced against the loss of production rate.Further improvement was done to control thefoamed door dimensions as it was observed fromthe PCA model that the length variables also had aninfluence on bow. This can be explained as longerdoors are inserted in the mold, the gap allowed forexpansion will become smaller and some deforma-tion to t