ORIGINAL ARTICLE
An integrated parameter optimization system
for MISO plastic injection molding
Wen-Chin Chen&Min-Wen Wang&Chen-Tai Chen&
Gong-Loung Fu
Received: 30 June 2008 / Accepted: 6 November 2008 / Published online: 27 November 2008 # Springer-Verlag London Limited 2008
Abstract This paper presents the development of a parameter optimization system that integrates mold flow analysis, the Taguchi method, analysis of variance (ANOVA), back-propagation neural networks (BPNNs), genetic algorithms (GAs), and the Davidon–Fletcher– Powell (DFP) method to generate optimal process parameter settings for multiple-input single-output plas-tic injection molding. In the computer-aided engineering simulations, Moldex3D software was employed to determine the preliminary process parameter settings. For process parameter optimization, an L25 orthogonal
array experiment was conducted to arrange the number of experimental runs. The injection time, velocity pressure switch position, packing pressure, and injection velocity
were employed as process control parameters, with product weight as the target quality. The significant process parameters influencing the product weight and the signal to noise (S/N) ratio were determined using experimental data based on the ANOVA method. Exper-imental data from the Taguchi method were used to train and test the BPNNs. Then, the BPNN was combined with the DFP method and the GAs to determine the final optimal parameter settings. Three confirmation experi-ments were performed to verify the effectiveness of the proposed system. Experimental results show that the proposed system not only avoids shortcomings inherent in the commonly used Taguchi method but also produced significant quality and cost advantages.
Keywords Parameter optimization . Mold flow analysis . Taguchi method . ANOVA . GAs . DFP.
Plastic injection molding
1 Introduction
Determination of optimal process parameter settings is critical work that has a direct and dramatic influence on product quality and costs. In industry, trial-and-error processes and the Taguchi method are frequently employed to determine the initial process parameter settings for injection molding. The Taguchi optimization methodology uses the signal to noise (S/N) ratio approach to determine the initial process parameter settings. In previous studies, many researchers used the Taguchi method to determine the initial process parameter settings for an injection molding process. Tseng [1] determined statistically significant parameters, including effects from multiple interactions of the selected factors, through an W.-C. Chen
Graduate School of Industrial Engineering and System Management, Chung Hua University,
707 Wu Fu Rd., Sec. 2, Hsinchu 30012, Taiwan M.-W. Wang
Department of Mechanical Engineering,
National Kaohsiung University of Applied Sciences, 415 Chien Kung Road,
Kaohsiung 807, Taiwan C.-T. Chen
Department of Computer Science and Information Engineering, Ta Hwa Institute of Technology,
1 Tahwa Rd., Chiunglin, Hsinchu 307, Taiwan G.-L. Fu (*)
Department of Mechanical Engineering, Minghsin University of Science and Technology, 1 Hsin Hsing Rd.,
Hsinchu 30401, Taiwan e-mail: fu@must.edu.tw
analysis of variance (ANOVA) and the F test. Lin [2] examined the effectiveness of the Taguchi technique with regard to multiple performance characteristics by employ-ing cuttemploy-ing parameters. Shiou and Chen [3] examined optimal process parameters related to a Taguchi orthogo-nal array in the finishing operation of freeform surface plastic injection molding. Ghani et al. [4] described a Taguchi optimization methodology for finding a combi-nation of milling parameters using the S/N ratio approach and ANOVA. Yang et al. [5] employed an orthogonal array experiment to arrange 16 experimental runs. Melting temperature, injection speed, and injection pressure were adopted as the process control factors, and contour distortions were utilized as the quality index. However, the Taguchi method can only find the best set of specified process parameter level combinations which are discrete setting values of the process parameters. Application of the conventional Taguchi method is unreasonable when the variable of a process parameter is continuous, and it cannot help engineers obtain optimal initial process parameter setting results [6]. An unsuitable process parameter setting can cause many defective products and unstable product quality during the injection molding process. Therefore, efficient analytical methodologies and tools are necessary to efficiently and rapidly analyze process parameters and control product quality.
To deal with these problems, many researchers of injection molding processes have investigated the applica-tion of artificial neural networks (ANNs) on quality predictions [7–12]. The main reason for using ANNs is that neural networks have the ability to learn arbitrary nonlinear mappings between noisy sets of input and output data. When the quality predictor is precise, the quality controller can adjust the controllable parameters closer to the target values of the injection molding process, and an efficient model can be obtained. In finding the optimal parameter settings of injection molding processes, ANNs are frequently combined with genetic algorithms (GAs) [13, 14]. Ozcelik and Erzurumlu [13] employed an ANN model to validate the predictive capability and then interfaced with an effective GA to find optimum process parameter values. The most important parameters were determined using mold flow analytical results based on the ANOVA method. Upon optimization, it was seen that the genetic algorithm reduced the warpage that appeared in the initial samples. Shi et al. [14] presented an improved hybrid strategy for optimizing a plastic injection molding process. Numerical software simulation, a GA, and a back-propagation neural network (BPNN) were fused to optimize process parame-ters. Costly numerical calculations were avoided by creating an approximate model that used a BPNN. Kurtaran and Erzurumlu [15] integrated finite-element (FE) analysis, design of experimental method, response surface
method-ology, and a GA to effectively optimize warpage of thin-shell plastic parts. In considering product warpage, an ANOVA-based FE analysis can determine the most signif-icant process parameters. Optimum values for those process parameters can be determined through a predictive response surface model in conjunction with a GA. The above approaches used computer-aided engineering (CAE) simu-lations with an optimization technique that can determine the optimal process parameter settings for injection mold-ing. The main problem with previous studies was that CAE simulations are not practical since the molding environ-ments create other noises to the part quality; besides, the controllability, repeatability, and the precision of molding machines provide more noises that contribute to part quality in real molding. These noises are not considered in the optimization processes using CAE simulations. To resolve such problems, Chen et al. [16] integrated the Taguchi method, BPNNs, GAs, and engineering optimization con-cepts to optimize process parameters. A real-world plastic injection molding (PIM) experiment was performed, and an L25 orthogonal array experiment was conducted to arrange
the number of experimental runs. Experimental data from the Taguchi method were used to train and test the BPNN. Then, the BPNN was combined with GA to determine final optimal parameter settings. Their research results indicated that the BPNN–GA approach can effectively help engineers determine optimal process parameter settings. However, Chen et al. [16] used a standard testing slug; in the present study, we used a real-world housing piece which is better related to actual manufacturing experiences. In addition, the proposed parameter optimization system integrates mold flow analysis, the Taguchi method, ANOVA, BPNNs, GAs, and the DFP method to generate optimal process parameter settings for multiple-input single-output (MISO) plastic injection molding. The final optimal process parameter settings obtained from the proposed system should be more reliable and practical.
Previously, researchers showed that product weight is a critical quality attribute, and a good indicator of manufac-turing process stability for plastic injection molding. Yang and Gao [17] revealed that product weight is an important quality index for injection-molded products because the product weight has a closer relation to other quality properties (e.g., surface properties and mechanical proper-ties) and particularly dimensional properties (e.g., dimen-sions and thickness). They also claimed that the performance of a manufacturing process and its quality control can be monitored through product weight. Kamal et al. [18] showed that the control of injection-molded product weight is of great commercial interest and can produce great value for production management. Since injection molding is commonly used in the production of plastic housing components, product weight is a feasible single
quality characteristic that can be used for product quality control of plastic housing components.
Process parameter settings for plastic injection molding critically influence the quality of the molded products. An unsuitable process parameter setting inevitably causes a multitude of production problems: long lead times, many rejects, and substandard moldings. The negative impact on efficiency raises costs and reduces competitiveness. This research develops a process parameter optimization system to help manufacturers make rapid, efficient, preproduction setups for MISO plastic injection molding. The focus of this study was molded housing components, with attention to a particularly telling quality characteristic: weight. The optimization system proposed herein includes two stages. In the first stage, mold flow analysis was used to obtain preliminary process parameter settings. In the second stage, the Taguchi method with ANOVA was applied to determine optimal initial process parameter settings, and a BPNN was applied to build up the prediction model. Then, the BPNN was individually combined with the DFP method and with a GA to search for the final optimal process parameter settings. Three confirmation experiments were performed to verify the effectiveness of the final optimal process parameter settings. The final optimal process parameter settings are not limited to discrete values as in the Taguchi method and can determine settings for production that not only approach the target value of the selected quality characteristic more closely but also with less variation.
2 Optimization methodologies
The optimization methodologies including BPNNs, GAs, and the DFP method are briefly introduced as follows. 2.1 Back-propagation neural networks
Many researchers have mentioned that BPNNs have the advantage of fast response and high learning accuracy [19– 23]. A BPNN consists of an input layer, one or more hidden layers, and an output layer. The parameters for a BPNN include: the number of hidden layers, the number of hidden neurons, the learning rate, momentum, etc. All of these parameters have significant impacts on the performance of a neural network. In this research, the steepest descent method was used to find the weight and bias change and minimize the cost function. The activation function is a hyperbolic tangent function. In network learning, input data and output results are used to adjust the weight and bias values of the network. The more detailed the input training classification is and the greater the amount of learning information provided, the better the output will conform to the expected result. Since the learning and verification of
data for the BPNN are limited by the function values, the data must be normalized by the following equation: PN ¼ P Pmin
Pmax Pmin
Dð max DminÞ þ Dmin; ð1Þ
where PN is the normalized data; P is the original data; Pmaxis the maximum value of the original data; Pminis the
minimum value of the original data; Dmax is the expected
maximum value of the normalized data, and Dmin is the
expected minimum value of the normalized data. When applying neural networking to the system, the input and output values of the neural network fall in the range of [Dmin, Dmax].
According to previous studies [24,25], there are a few conditions for network learning termination: (1) when the root mean square error (RMSE) between the expected value and network output value is reduced to a preset value; (2) when the preset number of learning cycles has been reached; and (3) when cross-validation takes place between the training samples and test data. In this research, the first approach was adopted by gradually increasing the network training time to slowly decrease the RMSE until it was stable and acceptable. The RMSE is defined as follows:
RMSE¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 N XN i¼1 di yi ð Þ2 v u u t ; ð2Þ
where N, di, and yiare the number of training samples, the
actual value for training sample i, and the predicted value of the neural network for training sample i, respectively. 2.2 Genetic algorithms
GAs are a method of searching for optimized factors analogous to Darwin's survival of the fittest and are based on a biological evolution process. The evolution process is random yet guided by a selection mechanism based on the fitness of individual structures. There is a population of a given number of individuals, each of which represents a particular set of defined variables. Fitness is determined by the measurable degree of approach to the ideal. The“fittest” individuals are permitted to “reproduce” through a recom-bination of their variables, in the hope that their“offspring” will prove to be even better adapted. In addition to the strict probabilities dictated by recombination, a small mutation rate is also factored in. Less-fit individuals are discarded with the subsequent iteration, and each generation pro-gresses toward an optimal solution.
GAs consist of four main stages: evaluation, selection, crossover, and mutation [26]. The evaluation procedure measures the fitness of each individual solution in the population and assigns it a relative value based on the defining optimization (or search) criteria. Typically, in a
Comparisons of quality statistics between the Taguchi, BPNN–DFP, and BPNN–GA approaches are shown in Table9. In addition, comparisons of quality characteristics (weight) between the Taguchi, BPNN–DFP, and BPNN– GA approaches are shown in Fig. 5. According to the experimental results, the standard deviation of the Taguchi approach was 0.0071. That is approximately two times that of the BPNN–DFP approach (0.0035) and 3.5 times that of the BPNN–GA approach (0.0021). In the practical assess-ment, the process capability index is a major criterion for assessing the ability of a production process to make products that meet specifications. The practical minimum process capability index (Cpk) is 1.33 in many
manufactur-ing industries. If the process capability index (Cpk) is <1.33,
then manufacturers will not achieve a high yield rate and may produce many nonconforming products. Therefore, this research utilized the process capability index as the major criterion for the quality requirement. As the results in Table 9 show, the Cpk of Taguchi’s approach was 0.585;
which is roughly one third that of the BPNN–DFP approach (1.69) and one fifth that of the BPNN–GA approach (2.75). Consequently, the optimal process parameter settings generated by the proposed two approaches definitely produced better performances than the Taguchi method. Experimental results also revealed that the BPNN–GA approach produced the highest Cpk value and the
best-quality products. The BPNN–DFP approach did not perform quite as well but was still better than the original process parameter calculation method (the Taguchi meth-od). The main reason is that the BPNN–GA approach is a global search methodology for determining an optimal solution, whereas the BPNN–DFP approach is a local search methodology for finding an optimal solution. The Taguchi method can only find the best set of specified process parameter level combinations which comprises discrete setting values of the process parameters. The plastic injection molding industry produces myriad prod-ucts, and each product has its own optimal machine settings. An unsuitable process parameter setting can cause many defective products and unstable product quality during the injection molding process. In comparing the three methods to arrive at those parameters settings, the BPNN–GA search approach was clearly the best. There-fore, the proposed optimization system is practical and effective for parameter optimization in the plastic injection molding process.
5 Conclusions
Costs of production in plastic injection molding are directly affected by strategies for choosing parameter settings, especially when setting up production runs. Setup strategies
have traditionally relied on some combination of skilled trial and error, plus the Taguchi method. These traditional strategies, however, often produce less than optimal results. In seeking to alleviate some of those shortcomings, this research made use of the Taguchi method, adding back-propagation neural networks, genetic algorithms, the Davidon–Fletcher–Powell method, and engineering optimi-zation concepts to determine efficient strategies that optimize both the setup process and product quality. Test results showed that measurably better performance was obtained using a tailored combination of approaches than with the Taguchi method alone. Specifically, the Taguchi method with BPNN plus DFP and BPNN plus GA and statistical techniques optimally predicted process parameter settings for MISO plastic injection molding setup proce-dures. Application of these simple techniques produced dramatic improvements in productivity by: (1) improving the quality of the parts produced; (2) reducing the number of rejects produced; (3) reducing waste or the regrinding of rejects; (4) reducing inspection times required during production; and (5) improving the scheduling of produc-tion. Thus, the proposed system is a feasible and effective method for process parameter optimization of MISO plastic injection molding and can result in significant quality and cost advantages.
Acknowledgements The research was conducted as part of a project sponsored by CoreTech System Co., Ltd., Hsinchu, Taiwan.
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