翻译原文_Analysis and optimization of a polyurethane reaction injection.pdf

Analysis and optimization of a polyurethane reaction injection molding (RIM) process using multivariate projection methods F. Yacoub, J.F. MacGregor* Chemical Engineering Department, McMaster University, 1280 Main Street West, JHE-374, Hamilton, ON, Canada L8S 4L7 Received 13 April 2002; received in revised form 20 August 2002; accepted 25 August 2002 Abstract Principal component analysis (PCA) and projection to latent structure (PLS) methods are used with industrial data to successfully diagnose several different problems arising in the manufacturing of rigid polyurethane foam insulation panels. The PCA and PLS models are used to reveal the spatial variation of quality variables throughout the foamed product, and their relations with the process variables. Designed experiments are performed in the key process variables identified from the PCA studies and the results are used to optimize the process. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Polyurethane; Reaction injection molding; Projection method 1. Introduction In the last two decades, chemical processes, like many other industries, have been going through a revolution in their data collection systems. Machine intelligence, immense data storage capacity, and high throughput data acquisition systems have driven the cost per data point down to a very low level. Masses of data are now available by measuring process variables as well as quality variables either on line or in quality control labs. Projection methods such as principal component analysis (PCA) and projection to latent structure (PLS) provide a way to handle the highly correlated data collected by these systems. In addition, they deal effectively with multiple response variables and with missing data, and they provide a good tool to extract and highlight the systematic variation in these multi- variate data sets. The most important property of projection methods isthecapabilitytoreducethemultivariatedimensionof a problem into a low-dimensional space, usually con- sisting of three to four dimensions. The SIMCA_P 8.0 software of Umetrics was used for the PCA/PLS analyses performed in this work. The focus of this study is the application of the multivariate projection methods for the diagnosis and analysis of a polyurethane reaction injection process. The main objectives of this research are to understand thespatial variation intheprocess,correctthecausesof this 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). Chemometrics and Intelligent Laboratory Systems 65 (2003) 1733 2. The mechanism of polyurethane formation The process of insulating refrigerators involves reaction injection molding (RIM) to form polyur- ethane foam. Each refrigerator cavity serves as a chemical reactor where two different sets of reactions take place simultaneously. One is the polymerization reaction, in which such bonds as urethane and urea may be formed. The other is the foaming reaction, which involves the evolution of carbon dioxide and the vaporization of blowing agent. Chemicals flow from day tanks through heat exchangers to control the temperature and then into the mix-head under high pressure to insure good mixing and then the mixture is injected inside the mold 1. In any reacting polyurethane foam, many physical and chemical changes occur, and these vary with time and extent of reaction as shown in Fig. 1. The temper- aturewithinthefoamrisesasthereactionproceedsand, because the foam is a good thermal insulator, temper- aturegradientsariseandcanresultinmanyproblemsas discussed laterinthepaper.Ingeneral,themanufacture of polyurethane rigid foam can be characterized by the following four stages 2. (I)Mixing step, where the Master batch which contain the polyol, a catalyst, a surfactant and a blowing agent is mixed under high pressure with the isocyanate in the mix-head. (II) Cream period, in which the temperature increase causedbytheexothermicchemicalreaction,issuf- ficienttopromotetheactivityoftheblowingagent. (III) Rise period, in which the blowing agent evapo- rates raising the foam until a sufficient rigidity is reached by either free rising or when the mold is filled. (IV) Post curing step, in which the polymer is treated by a high temperature for a certain time. The mechanical system consists of a rotary drum unit that has a six-station rotary frame. Foam fixtures are placed in each frame station. Refrigerator doors or other cavities to be foamed are placed inside the fix- tures where they are preheated, then injected with the reaction mixture in one position on the drum unit. Once foamed, the drum unit rotates the fixture through five other positions for curing, while the other positions are foamed, and eventually returns the fixture to the foam position. Each drum unit has two Fig. 1. Polyurethane foam formation. F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173318 polyurethane foam mix-head carriages. Each carriage foams a different door. 2.1. Problem description The instability of the foaming process and the complexity of controlling the quality variables created the need and motivation for this work. Two problems on this process are discussed separately as they arose at different times. The first project was to optimize the functionality of the polyurethane foam panels expressed by the spatial variation of its thermal conductivity and density. The insulation function of the foam, measured by thermal conductivity (k-factor), is considered as a vital variable to be controlled. It has a direct effect on the refrigerator performance and energy consumption. In theory, when the master batch is mixed with the isocyanate at a cer- tain temperature, the blowing agent boils, and creates a vapor that blows the foam and reduces the density. In rigid foam, the cells formed by the blowing agent redu- cethetransmissionofheat.Thelowerthek-factoris,the better the insulation and the refrigerator performance. Density, which is an indication of foam strength, is important in keeping the structural rigidity of the refrigerator. It is a result of the pressure that the vapor from the blowing agents exerts in the cell. The cell gas pressure 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 this paper is to minimize the distortion phenomena in the foamed panels known as Outer Bow (OB). Outer Bow is mainly caused by the movement restriction of the steel and ABS plastic panels. The panels are unable to expand or contract relative to each other since the distance separating them is relatively small. If move- ment is to occur, it will result in the warping of the panels or shear deformation. 2.2. Quality measurements Quality variables are measured off-line on a weekly basis in quality control labs. The upper specification limit of the thermal conductivity is based on energy calculations, and the lower specification limit of den- sity is defined as the minimum density to maintain structural strength. All measurements are performed at eight locations around the foamed panels.The criterion is to have all samples within the specified control limits. Thermal distortion is measured using a Coor- dinate Measuring Machine (CMM) by defining a plane that passes through points located in the corners of the panel and measures the deviation from this plane at several points across the panel surface to determine the shape and magnitude of surface bow. The following quality variables are measured: 2.3. Process variables Process variables were selected and retrieved from the database. The analysis was performed on six differ- entfixturesfromproductiontounderstandthevariation between fixtures and the effect of changes in the process variables. A summary of process variables used in the analysis and the corresponding nomencla- ture presented in the paper is given as follows: Time to testT_T Ambient temperatureA_T Master batch densityMB_D Master batch flowMB_F Isocyanate flowI_F Ratio between Master batch and isocyanateMB/I Isocyanate pressureI_P Master batch pressureMB_P Mix-head pressureMH_P Shot sizeSS Isocyanate temperatureI_T Master batch temperatureMB_T Isocyanate temperature at mix-headI_T_MH Master batch temperature at mix-headMB_T_MH Surfactant typeS Blowing agent typeB Fixture core temperatureCore_T Fixture sidewall temperatureSidewall_T Fixture preheat temperaturePreheat_T K*K-factor values at various spatial locations (18) D*Density values at various spatial locations (18) VoidsIdentified by sink marks in the outer steel LeaksIdentified visually Face bowMaximum warpage of the face foamed objects Side bowMaximum warpage of the side foamed objects F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173319 3. Problem 1: eliminating spatial variation in thermal conductivity and density 3.1. Principal component analysis on quality varia- bles (Ys) The main objectives behind fitting a PCA model on the Ys are to understand the spatial patterns and the correlation structure among the variables. Meas- urements made on a total of 64 sets of panels. Three principal components are significant by cross-validation 3 and they explain 76% of the variation. Some outliers are evident in the score plots and residual (DmodX) plots shown in Figs. 2 and 3, respectively. Outliers are considered very interesting observations that hold valuable information that can be understood using contribution plots. Further anal- ysis and interpretations of these outliers will be dis- cussed in a later section. The loading plot, shown in Fig. 4, reveals that there are two main groups. Ther- mal conductivity is positively correlated with leaks and negatively correlated with both density and voids. Furthermore, from the loading plot (Fig. 4), a pattern distribution of density and thermal conductiv- ity variation inside the cavity and in relation to the average value is evident. It is worth noting that at the injection side (locations 1 and 8) the density was higher and the k-factor was lower than around the edges of the mold. 3.2. Projection to latent structure (PLS) between fixtures and quality variables In order to understand the effect of the six fixtures used in production, a PLS model is built to relate the event of using a specific fixture to the quality variables. The X-matrix consisted of six indicator (0,1) variables indicating the presence or absence of any particular fixture during an injection. The Y- matrix consisted of the average K-factor, the average density, voids, and leaks for each of the 64 panels. The PLS model explained 72.5% the variation (Ry 2) in the Ys using only the information on which fixture was used for the molding process, implying that the Fig. 2. t1t2scores from PCA on the quality variables (Ys). F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173320 fixture differences were major contributors to the variation in quality. The PLS loading plot in Fig. 5 maps the relation between the six fixtures and the quality variables, and reveals some very interesting results. It is apparent that the presence of fixture 1 is highly correlated with high thermal conductivity and the occurrence of leaks while the presence of fixture 2 is negatively correlated with density and voids. It can be seen as well that the fixtures that have the best performance are fixtures 3 and 4. Both have low thermal conductivity and sufficiently high density, but not many voids. Fixtures 5 and 6 have low K- factor and high density but more voids. From this analysis, it was concluded that fixtures 1 and 2 provided unacceptable panel quality. Fixture 1 yields too high values for k-factor and leaks, while fixture 2 has low k-factor and leaks, but unacceptably low values of density. To understand the reasons for this, both PCA and PLS studies were performed to relate the fixtures and the quality variables to the process variables. 3.3. Principal component analysis (PCA) of fixtures and process variables A PCA model was build to map the structure between fixtures and process variables. The rationale behind building this model is to understand the correlation between the bad fixtures and certain proc- ess variables. In this model, six fixtures as well as process variables such as the temperatures of the chemicals and the fixtures (sidewall and core), and the preheat temperature were considered. The model yielded three latent variables that explain 68% of the variation (Rx 2) with a cross-vali- dated (Qx 2) value equal to 64%. The score plot in Fig. 6 identifies three main clusters. No outliers are observed 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 bad fixtures 1 and 2 have a different pattern. Fixture one has a higher preheat temperature than the other fixtures. 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) 173321 tion exists between high preheat temperature and high ratio between the master batch and isocyanate (MB/I). This observation can be explained by fact that as the preheat temperature rises, isocyanate which has a lower molecular weight will tend to evaporate and consequently the ratio of the master batch to isocya- nate reacting in the cavity will rise. It is worth noting that different operators had already observed that, in general, a high temperature resulted in a high k-factor. Fixture 2, on the other hand, exhibited a lower preheat, core, and sidewall temperature, in general, and higher isocyanate temperatures. Defective and faulty heaters in both the mix-head and the preheat station in fixture 2 were found to be the root cause of these correlations. 3.4. Projection to latent structure (PLS) between process and quality variables A PLS model was then built between the process variables 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% of the 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 strong relationship. The loading plot shown in Fig. 10 high- lights the important variables in the process and points to where the variability in the quality variables is coming 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 a positive correlation with k-factor and the occurrence of leaks while the isocyanate temperatures (I_T and I_T_MH) showed a negative correlation with k-factor as well as density. The above PLS model only reveals the correlation structure of the data during routine plant operation, and the observed correlation among the process and quality variables cannot be interpreted as causal Fig. 4. Loading plot on the quality variables (Ys). F. Yacoub, J.F. MacGregor / Chemometrics and Intelligent Laboratory Systems 65 (2003) 173322 relationships. However, the PLS loading plot in Fig. 10 reveals some very interesting relationships that needed to be explored further. Therefore, at this stage, it was decided to proceed with a designed experiment in order to establish causal relationships among the quality variables and some of the more interesting process variables arising from the PLS analysis. The process variables chosen were the ones that had a high correlation with the quality variables as discovered from the PLS loading and coefficients plot, and were also capable of being directly manipulated. The ratio of Master batch to isocyanate (MB/I) was set to a fixed value suggested by the supplier of the chem- icals. Ambient temperature (A_T) was considered as a noise variable that needed to be investigated and eventually controlled if possible. 3.5. Response surface model (RSM) development In general, the best way to develop a cause and effect model and use it to find the optimum conditions of the process is to design an appropriate set of experiments. A central composite RSM design was made in the following four variables: the shot size (SS) and the temperatures of Master batch (MB_T), isocya- nate (I_T), and mold. The mold temperature used in the experiment was defined as a weighted average of the profile of the core, sidewall, and preheat temperatures. The design consisted of a 24full factorial with three replicates of each condition, then the star points were added to complete a central composite design. The main objective of running such a design was to identify what variable inter- actions and curvature terms were important and to optimize the process by plotting the response sur- face. By fitting a regression model to the data, the coefficient of determination R2, which indicate how much variation is explained by the model, was 97.1% and 98.3% for the thermal conductivity and density, respectively. The response surface model resulted in Fig. 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) 173323 Fig. 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 (