Optimization of Process Parameters in Injection Moulding of FR Lever Using GRA and DFA and Validated by Ann

This study deals with the optimization of the injection moulding process parameters in the production of the FR (Forward Reverse) Lever, using the Grey Relational Analysis (GRA) and Desirability Function Approach (DFA) and the results are validated by ANN. The FR lever is used to control the direction of the rotation of spindles in conventional machines. Parameters such as injection pressure, injection speed and injection temperature, which influence the quality of the final product of the injection moulding process, are called the input parameters. Parameters such as Shrinkage and Surface Roughness, which are considered as the quality characteristics of this product, are called the output parameters. FR levers are produced using a fabricated Injection moulding tool, according to Taguchi’s experimental design and the response data are recorded. The recorded experimental data are analyzed and the optimum process parameters combinations have been found, by using the GRA and DFA. An ANN has been developed using the experimental data and the responses (output data) are predicted for the corresponding optimal parameters combination. Finally, the obtained optimum parameter combinations are tested by both ANN and the experiment and the results are found to be satisfactory.


INTRODUCTION
Many Engineers and researchers have done research on the optimization of the process parameters of Plastic Injection Moulding (PIM) for various thermoplastic materials and attempted to reduce the shrinkage, surface roughness and Warpage of plastic moulded products.Some authors have presented a few case studies on improving the Quality characteristics of surface roughness, shrinkage and Warpage, by applying the Taguchi technique, Artificial Neural Network (ANN), Fuzzy logic and combination methods.Pirc et al. (2008) introduced a practical methodology to optimize the position and the shape of the cooling channels in injection moulding processes and also Pirc et al. (2009) developed an iterative dual reciprocity boundary element method (DRBEM) to solve optimization of 3D cooling channels in injection molding.Gang et al. (2012) developed an experimentbased optimization system for the process parameter optimization of multiple-input multiple-output plastic injection molding process using particle swarm optimization algorithm.Huizhuo et al. (2010) presented a combination of artificial neural network and Design of Experiment (DOE) method is used to build an approximate function relationship between Warpage and the process parameters.Irene et al. (2010) presented a framework on a Multidisciplinary Design Optimization methodology, which tackles the design of an injection mold to achieve significant improvements.
In the present study, the Grey Relational Analysis and Desirability Functional Approach are applied for the optimization of the process parameters of Plastic Injection Moulding (PIM) for FR lever.The output responses are also predicted, using the developed Artificial Neural Network.App.Sci. Eng. Technol.,11(8)

MATERIALS AND METHODS
An Injection moulding tool for Forward and Reverse (FR) lever has been designed and discussed in detail in the previous research publication (Selvaraj and Venkataramaiah, 2012) of the same author.The 3D model of the FR lever is shown in Fig. 1a and the fabricated FR lever is shown in Fig. 1b.The parameters which influence the Injection moulding process and their levels, are shown in Table 1.The Taguchi experimental design L27 OA is selected, for conducting the experiments (Table 2) which conducted as per the experimental design.Nylon material is used for producing 27 FR levers, using the fabricated Injection moulding Tool (Fig. 2a).Two output parameters are measured, namely, shrinkage and surface roughness for all the 27 components of the FR lever.The shrinkages are calculated by using the procedures presented in the previous research publication (Selvaraj and Venkataramaiah, 2013) of the same author.The surface roughness values of the FR lever are measured using the Talysurf meter (Fig. 2b).

MATERIALS AND METHODS
An Injection moulding tool for Forward and designed and fabricated in the previous research publication (Selvaraj and Venkataramaiah, 2012) of the same author.The 3D model of the FR lever is shown in Fig. 1a and the fabricated FR lever is shown in Fig. 1b.The parameters which influence the Injection moulding ess and their levels, are shown in Table 1.The Taguchi experimental design L27 OA is selected, for conducting the experiments (Table 2) which are conducted as per the experimental design.Nylon-66 material is used for producing 27 FR levers, using the ricated Injection moulding Tool (Fig. 2a).Two output parameters are measured, namely, shrinkage and surface roughness for all the 27 components of the FR lever.The shrinkages are calculated by using the procedures presented in the previous research cation (Selvaraj and Venkataramaiah, 2013) of the same author.The surface roughness values of the FR lever are measured using the Talysurf meter (Fig. 2b).Grey relational coefficients of individual responses ----------------------------------------------------------------

RESULTS AND DISCUSSION
Optimization study: In this study, the influential parameters are optimized using two optimization techniques, the Grey Relational Analysis and Desirability Function Approach and also the Analysis Of Variance (ANOVA) is performed to find the influence of each process parameter on the responses.

Optimization steps in grey relational analysis:
Step 1: Normalization of the responses (Quality characteristics): The quality characteristics (experimental data) of the component are normalized ranging from zero to one.There are three different types of data normalization, according to the response requirement of the LB (lower-the-better), the HB (higher-the-better) and the NB (nominal-the-best).In this study, the lower-the-better (LB) criterion is considered for normalization, since surface roughness and shrinkage should be low and the values are calculated using Eq. ( 1) and tabulated in Table 3.
The preprocessing data ˲ * (k) can be calculated as follows: For i = 1:27, k = 1: 4, where k = number of quality characteristics and i=no of experiments: Step 2: Calculation of quality loss estimates (∆ 0i ): After normalizing the experimental data, the difference of the absolute value x 0 (k) i.e., 1 and the corresponding normalized values, x i (k) known as quality loss estimates (∆ 0i ) are calculated and furnished in Table 3.
Similarly all calculations are performed and are shown in Table 4: Step 3: Calculation of the individual grey relational grades: Individual grey relational coefficients: The Grey relational coefficient depends on quality loss estimates and distinguishing the coefficient ζ.Here ζ = 0.5 is considered.The grey relational coefficients are calculated by applying Eq. ( 2).
The greyrelation coefficient ξ C (k) for the k th performance characteristic in the i th experiment can be expressed as: 6861, 0.4735 and 0.9250) Similarly, all the coefficients are calculated, as shown in Table 4 Overall grey relational grade: The average value of the grey relational coefficients is the overall grey relational grade (Table 4).The grey relational grade is defined as follows: Similarly the grade values for all the 27 experimental runs are calculated in the same way as above and tabulated as in Table 4. Thus, the multiresponse optimization problem has been transformed into a single objective optimization problem, using the combination of the Taguchi method and grey relational analysis.Higher the value of grey relational grade, the closer the corresponding factor combination towards the optimal.
The optimal process parameter setting (A 3 B 3 C 3 D 1 E 1 F 1 G 1 H 3 I 3 J 1 ) has been found from Table 5, by choosing the higher average grade values of each parameter at different levels.Figure 3 shows the effect of the process control parameters on the multiperformance characteristics and the response graph of each level of the injection moulding parameters for the performance.
ANOVA for GRA results: The order of factors affecting the responses is determined, by performing Analysis of variance (ANOVA) as follows.

Analysis of variance for overall grey relational grade:
Grand total sum of squares: 2 +gg 26 2 +gg 27 2 ] = 10.535759 Total sum of squares: (Grand total sum of squares Sum of squares of mean) = 0.498939 moulding parameter levels using GRA The same procedure is used for calculating the 'mean of squares' for the remaining 9 parameters.
Mean squares due to error = (Sum of squares due to error)/(degree of freedom for error) = 0.0146356 Percentage of contribution: % injection speed = (Sum of squares due to injection speed)/(Total sum of squares) = 0.04317 The same procedure is used for calculating '% of contribution' for the remaining 9 parameters.
% contribution for error = (Sum of squares due to error)/(Total sum of squares) = 0.176000 Figure 4 indicates that the injection pressure has the most influence on the multi performance characteristics among all the parameters and also the influence of every controllable factor over performance characteristics can be obtained by examining these values (Table 6).

Optimization steps in Desirability Function
Approach (DFA): An optimal parametric combination for minimizing the surface roughness and shrinkage of the injection moulded component (FR lever) is determined, using DFA as follows.

Calculation of Individual desirability value:
Calculate the individual desirability The same procedure is used for calculating '% of contribution' for the remaining 9 parameters.um of squares due to error)/(Total sum of squares) = 0.176000 Figure 4 indicates that the injection pressure has the most influence on the multi performance characteristics among all the parameters and also the influence of every controllable factor over the multiperformance characteristics can be obtained by

Optimization steps in Desirability Function
An optimal parametric combination for minimizing the surface roughness and shrinkage of moulded component (FR lever) is

Calculation of Individual desirability value:
desirability value (ˤ ) using   Eq. ( 4).Here the lower-the-better is the suitable quality characteristic for both the responses.
= 0.4886 for R a Similarly the desirability values for R y , Rq and shrinkage are calculated (Table 7) as: ˤ $ = 0.7712, ˤ % = 0.4441 and ˤ % = 9594 The overall desirability is calculated for the experiment as follows: Similarly, the remaining values are calculated using the above formulae and the values are given in Table 7.

Optimal process parameters from DFA:
The optimal parameter combination is evaluated, based on the maximum composite desirability value.From Table 8 and Fig. 5, the optimal process parameters combination is A 3 B 3 C 3 D 1 E 1 F 2 G 1 H 3 I 3 J 1, by choosing the higher average composite desirability values of each parameter at different levels.

ANOVA for DFA results:
The ANOVA is performed as in the following, for the Composite Desirability values to find the order of the influencing parameters and the ANOVA results are shown in Table 9.

Mean squares:
Mean squares due to injection speed = (Sum of squares due to injection speed)/(degree of freedom for injection speed) = 0.085539 The same procedure is used for ca 'mean squares' for the remaining 9 other parameters.
Mean squares due to error = (Sum of squares due to error)/(degree of freedom for error) = 0.0465833 Percentage of contribution: % contribution for injection speed = (Sum of squares due to speed)/(Total sum of squares) = 0.09228 The same procedure is used for calculating the '% of contribution' for the remaining 9 other parameters.
Sum of squares due to error, SS E = SS T -SS F = Mean squares due to injection speed = (Sum of squares due to injection speed)/(degree of freedom for injection speed) = 0.085539.
The same procedure is used for calculating the 'mean squares' for the remaining 9 other parameters.
Mean squares due to error = (Sum of squares due to error)/(degree of freedom for error) = 0.0465833.contribution for injection speed = (Sum of squares due to injection speed)/(Total sum of squares) = 0.09228.
The same procedure is used for calculating the '% of contribution' for the remaining 9 other parameters.
% contribution for error = (Sum of squares due to error)/(Total sum of squares) = 0.150779.
Figure 6 shows that the injection pressure has more influence on the multi performance characteristics, among all the considered injection moulding parameters and the least effecting parameter is the clamping speed.

DEVELOPMENT OF ANN &PREDICTION OF RESPONSES
In the present work, an ANN has been developed (Fig. 7) to predict the surface roughness and shrinkage values, for the optimal parametric combination obtained from the Grey Relational Analysis (GRA) and Desirability Function Approach (DFA).Network features such as the number of neurons and layers are very important factors that determine the functionality and generalization capability of the network.In this work, a multilayer back-propagation neural network has been developed for the prediction of the sur roughness and shrinkage of forward injection moulding.The neural network has been designed using MATLAB.In order to design the best network architecture, the network is tested with different numbers of hidden layers and the number neurons in each hidden layer with different training algorithms and transfer functions in the hidden layer.Finally, the optimal network is designed to predict the output parameters.In this method, from the 27 experimental runs is ta responses are calculated by taking + 5% variation to train the NN and the values are tabulated in Table 10.The Table 10 gives both the input and output data for training.
Both the approaches are for the maximization of the multi objective function, but each having its own individual objectives.The GRA leads to reduce quality loss and the DFA to attain the highest desirability.Therefore, the result of optimization i.e., the optimal 6 shows that the injection pressure has more influence on the multi performance characteristics, among all the considered injection moulding parameters and the least effecting parameter is the clamping speed.

DEVELOPMENT OF ANN &PREDICTION OF
In the present work, an ANN has been developed (Fig. 7) to predict the surface roughness and shrinkage values, for the optimal parametric combination obtained from the Grey Relational Analysis (GRA) and Desirability Function Approach (DFA).Network s such as the number of neurons and layers are very important factors that determine the functionality and generalization capability of the network.In this propagation neural network has been developed for the prediction of the surface roughness and shrinkage of forward-reverse levers in injection moulding.The neural network has been designed using MATLAB.In order to design the best network architecture, the network is tested with different numbers of hidden layers and the number of neurons in each hidden layer with different training algorithms and transfer functions in the hidden layer.Finally, the optimal network is designed to predict the output parameters.In this method, the obtained data from the 27 experimental runs is taken and another 54 responses are calculated by taking + 5% variation to train the NN and the values are tabulated in Table 10.The Table 10 gives both the input and output data for Both the approaches are for the maximization of multi objective function, but each having its own individual objectives.The GRA leads to reduce quality loss and the DFA to attain the highest desirability.Therefore, the result of optimization i.e., the optimal   ------------------------------------------------------------------------------------------------------------------------Output data  -------------------------------------------------  setting determined by these two approaches differs.In the Desirability Functional Analysis (DFA), y max and y min are needed for each response, whereas in the Grey Relational Analysis (GRA) these are not needed.Two approaches have been found efficient.From Table 11, it is evident that the multi objectives are optimized, using both the GRA and DFA for surface roughness and shrinkage and efficiently minimized by Desirability Function Approach.

CONCLUSION
In the present work, two optimization techniques, the Grey Relational Analysis and the Desirability Function (DF) Approaches have been applied, for solving the multi-response optimization problem in Plastic Injection Moulding (PIM) and the optimum parameter combinations are determined.The Analysis of variance (ANOVA) is also performed on the overall grey relational grade, the composite desirability obtained from the GRA and DRA and it is revealed that injection pressure is the most influencing parameter.The developed ANN can predict the response (output) parameters reliably.Finally, it is found that the Desirability Function Approach (DFA) can effectively analyze the data in the determination of the optimal parameter setting.

Fig. 4 :
Fig. 4: Contribution of process parameters using GRAAnalysis of variance (ANOVA) of overall grey relational P-value 0.0107700 0.043170 0.0508950 0.204012 0.0303650 0.121718 0.0271915 0.108990 0.0230920 0.092564 0.0058725 0.023776 0.006542 0.026223 0.0022403 0.0089802 0.041619 0.166832 0.006975 0.027959 0.0146356 0.176000 1.0000 Sum of squares due to injection speed: 9 ∑ 3 i=1 procedure is used for calculating the the remaining 9 parameters.Sum of squares due to error, SS E = SS T -SS F = Mean squares due to injection speed = (Sum of squares due to injection speed)/(degree of freedom for injection speed) = 0.01077 The same procedure is used for calculating the the remaining 9 parameters.Mean squares due to error = (Sum of squares due to error)/(degree of freedom for error) = 0.0146356.tage of contribution: % contribution for injection speed = (Sum of squares due to injection speed)/(Total sum of squares) = 0.04317

Fig. 5 :
Fig. 5: Response graph for evaluation of optimal parametric

Fig. 5 :
Fig. 5: Response graph for evaluation of optimal parametric combination

Fig. 7 :
Fig. 7: Input and output parameters of the ANN model

Table 3 :
Preprocessing data of each performance characteristic

Table 5 :
Response table for the average grey relational grade

Table 6 :
Analysis of variance (ANOVA) of overall grey relational

Table 7 :
Evaluated individual desirability values and composite desirability

Table 8 :
Response table for the composite desirability

Table 10 :
Input and output data for training Input data -

Table 11 :
Results from ANN and confirmation experimentCriteria