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Step 3 Select an appropriate orthogonal array for arranging the experiment and acquiring the experimental treatments.
Step 4 Perform experiments for each treatment and collect the performance measurements of the responses.
Fig. 1 The flow chart of the proposed parameter optimization system
Step 5 Select an appropriate formulation for the S/N ratio and calculate the S/N ratio for each response under different treatments of the orthogonal array. The S/N ratio has three types: nominal-the-best, larger-the-better, and smaller-the-better.
Step 6 Implement the S/N ratio and ANOVA method to determine the initial parameter settings.
3.1 Experimental equipment and illustrative example
In this study, the experimental material used was polypropylene. The injection molding machine was a Nissei ES-400.
3.2 CAE simulations
The CAE simulations of the plastic part were carried out to identify the preliminary process parameter settings. The ranges of the parameters were set based on the material processing guide for the selected polypropylene. Simulations of the plastic part were performed to validate the processing windows using Moldex3D software. Simulation results indicated that the plastic part could be successfully filled with good weight repetitiveness inside the processing window. Figure 3 shows the simulation result at the end of filling with the molding parameter values shown in Table 1.
3.3 Implementation of the Taguchi method and BPNN quality predictor
The Taguchi method normally selects an appropriate formulation of the S/N ratio and calculates the S/N ratio for each treatment. There are three types of S/N ratios: nominal-the-best, larger-the-better, and smaller-the-better. Most engineers choose the highest S/N ratio treatment as the preliminary optimal initial process parameter setting. In this study, product weight was selected as the only response for a plastic injection-molded standard since it is easily monitored online, and weight is a critical quality attribute [17, 18]. The weight of the plastic injection-molded push-button housing piece was a nominal-the-best-type response. Prior to this research, the molder found that parts weighing 10.58 g had good and acceptable dimensions and mechanical qualities. So the target value of the push-button housing piece was set to 10.58 g, and the formula of the nominal-the-best is given as follows:
3.4 Hybrid BPNN-DFP and BPNN-GA search approaches to optimize the system To optimize the process parameter settings of the proposed optimization system, an effective GA was coupled with the BPNN model to yield a global optimal solution. In addition, the DFP method was combined with the BPNN model to produce a local optimal solution. Experimental data of the Taguchi method were used to effectively train and test the
BPNN model that finely maps the relationship between the input process control factors and the output response. In this application, the objective function of the DFP method and the fitness function of the GA were minimized by optimizing four independent process parameters, namely, the injection time, velocity pressure switch position, packing pressure, and injection velocity. Product weight was the target quality which was the output value of the BPNN model. The mathematical formulation of the objective function of the DFP method and the fitness function of the GA with the ranges of process parameters were the same and are given as follows [16]:
where X ¼ ðx1 ; x2 ; x3 is the process control param-eters; yo is the predicted value (weight); yt is the target value (weight); xi is the notation of process parameter i, and m is the total number of parameters. LSRi and USRi are the lower and upper search ranges of process parameter i, respectively. The method of setting LSRi and USRi is given as follows:
where PSni is the process parameter setting value of parameter i which generates the highest S/N ratio of the response n, and Di is the factor level’s equivalent range of parameter i in the Taguchi experiment. The initial values of parameter variables X(0) for both the hybrid BPNN–DFP search approach and the hybrid BPNN–GA search approach were the preliminary initial process parameter settings obtained from the Taguchi method.