## Abstract

Wire electrical discharge machining (WEDM) is a special form of electrical discharge machining that uses a small diameter wire as the electrode to cut a narrow kerf in the workpiece. Although it is a simple concept, the performance of the process is highly dependent on the operating parameters. The aim of this work is to optimize WEDM operating parameters with the objective of achieving a maximum material removal rate (MRR) and minimum surface roughness (SR) for an AISI 304 stainless steel workpiece. This work compares the performance of response surface methodology (RSM) and artificial neural network (ANN) based on the coefficient of determination, root mean square error, and absolute average deviation calculations. This is followed by implementing the fuzzy logic technique to get the optimal operating parameters. The results show that using both the RSM and ANN is more adequate and reliable in predicting the MRR and SR. In addition, it is shown that by increasing the peak current, the pulse on time, and by decreasing pulse off time, the resulting workpiece surface is rougher despite achieving a higher material removal rate. It is concluded that the optimal process parameters combination that achieves the maximum MRR and minimum SR is 25 µs pulse on time, 5 µs pulse off time, and 6 A peak current.

## Introduction

Wire Electrical Discharge Machining (WEDM) is a thermal non-traditional machining process. The electrical energy is used to generate an electrical spark of high thermal energy, which mainly helps in material removal. A series of discrete discharges occur between the wire and the workpiece in the presence of dielectric fluid. Hence, the workpiece surface is melted and removed due to the extremely high temperature occurs in the area where discharge takes place. The removed particles are flushed away by the flowing of the dielectric fluids. Of all the non-traditional machining processes, none has gained greater industry-wide acceptance than WEDM. It is mainly used to machine hard to be machined materials with very complex geometries [1].

Stainless steel materials have been applied in many modern industrial applications due to their outstanding characteristics such as high coefficient of work-hardening, high toughness, and low temperature conductivity, with anticorrosive, anti-oxidizing, and shiny surface features. Although all of these features, stainless steel is considered as hard to be machined material, which causes serious tool wear and a rough surface [2].

Many studies have been performed on the WEDM process. T. Ebisu, et al., simulated the debris movements and flow fields during corner shape cutting. Also, a structural analysis of wire deflection due to hydrodynamic force was illustrated. The results showed that at the corner the pressure and flow fields around the wire changed significantly. Furthermore, debris stagnation decreased temporarily at the area behind the wire just after the corner. Additionally, the wire deflection with the corner shape error was experimentally measured and compared to the analytical result [3]. Habib and Okada investigated the movement of the tungsten wire electrode by using the high-speed camera. The results showed that the machined kerf width and the wire electrode vibration amplitude decreased with the wire tension. Additionally, the amplitude perpendicular to the machining direction was a little smaller than that in the parallel one. Also, the wire vibration mode was analyzed depending on determining the optimal workpiece position, which led to smaller wire amplitude [4]. Okada et al. studied experimentally the effect of nozzle jet flushing on wire breakage. Furthermore, a numerical analysis was performed relating to the wire deflections, hydrodynamic stress distributions acting on the wire, flow fields, and debris residence time in the kerf. The experiments illustrated that wire breakage occurred at shorter kerf length. Relating to numerical analysis, the wire deflection due to jet flushing became larger and the debris easily accumulated in the gap at short kerf length, which caused higher wire breakage [5]. Durairaj et al. implemented the grey relational theory and Taguchi optimization technique for cutting parameters optimization to attain the minimum kerf width and the best surface quality. The performed analysis of variance resulted that the pulse on-time has a major influence on the surface roughness and kerf width [6]. Lingadurai et al. used the design of experiments approach to predict the optimal combination of parameters to achieve the best metal removal rate, kerf width, and surface roughness. The resulted analysis revealed that the pulse on-time significantly affected the kerf width and the wire feed rate affected the surface roughness, while the input voltage mainly affected the material removal rate [7]. Ramakrishnan and Karunamoorthy proposed a multi response optimization method using Taguchi’s robust design approach. An experimental confirmation was carried out to identify the effectiveness of this proposed method and a good improvement was obtained [8].

The aim of this work is to optimize the most influenced machining parameters, namely; pulse on time (Ton), pulse off time (Toff), and peak current (I), while cutting AISI 304 stainless steel by WEDM process. Additionally, studying the effect of each parameter on the resultant material removal rate (MRR) and surface roughness (SR) is performed. Response surface methodology (RSM) is implemented as it has been the most preferred statistical tool for optimizing. On the other hand, an artificial neural network (ANN) has been one of the most effective tools used for empirical modeling and optimization, especially for nonlinear equations. Thus, this study uses both RSM and ANN in optimizing to compare their performance. Additionally, the fuzzy logic technique is implemented to get the optimal process parameters combination to optimize the process, based on combining both the material removal rate and the surface roughness together as one variable.

## Experimental design

In order to assess the impact of the most important three process parameters on two responses, a large number of experiments need to be conducted. However, by implementing the experimental design based on the RSM, the number of experiments is reduced to a large extent and both effects of factors and their possible interactions can be analyzed. Equation 1 represents the quantitative form of the relationship between the desired response and the independent input parameter in RSM [9].

where the response parameter or output *y* depends on the controllable parameters or inputs *x*_{1}, *x*_{2},…, *x*_{k}, *f* is the response function or response surface, and *ε* represents the statistical error. Equation 2 represents the true relationship between *y* and the independent parameters, which is generally approximated by the lower order polynomial model.

where *β*’s are the unknown constants estimated by using regression analysis based on the statistical model [10].

As each process parameter is considered at three levels in this research as shown in Table 1, a face centered central composite design (FCCCD) is desirable to conduct the experiments, which is created from central composite design (CCD) by setting the axial distance *α* equal to one. The FCCCD is generated using MINITAB software. A total number of twenty experiments are carried out, where eight full factorial points with all combinations of parameters at two levels, six axial points at the face corresponding to α value of one and six central points are generated as illustrated in Table 2.

## Experimental setup

Figure 1 shows the used Kingred CNC wire cut EDM machine, found in the non-traditional machining laboratory, Faculty of Engineering – Mansoura University – Egypt. Molybdenum wire with a diameter of 0.18 mm is used as an electrode. Workpieces of AISI 304 stainless steel with 5 mm thickness are used while performing the experimental work. Figure 2a illustrates the cutting path performed during each experiment (Table 2). Machining time is measured during machining to calculate the MRR according to Eqs. 3, 4 and 5.

where *kw* is the kerf width, *t* is the workpiece thickness, and *v*_{c} is the cutting velocity. The kerf width can be estimated by adding wire diameter *w*_{d} to double of offset as illustrated in Fig. 2b. After performing all the experiments, the surface roughness is measured using a portable surftest SJ-210 series device, found in the Faculty of Dentistry – Mansoura University – Egypt. Table 2 shows the resultant MRR and the average of SR measurements per each experiment.

## Result and discussion

### Response surface methodology modeling results

MINITAB software is used during the RSM modeling. Equations 6 and 7 represent the predicted response equations for MRR and SR respectively. Figure 3 illustrates a statistical evaluation of the MRR and SR, which confirm the equation’s accuracy and good fitness between the experimental and predicted results.

### Artificial neural networks modeling results

In this study, a multilayer feed-forward artificial neural network (ANN) is trained [9]. Figure 4 illustrates the used ANN pattern, which consists of an input layer of three neutrons representing Ton, Toff and I, one hidden layer of 10 neurons, and an output layer of two neutrons representing MRR and SR. All the ANN calculations are performed using Neural Network Toolbox of MATLAB software. Figure 3 illustrates a statistical evaluation of the MRR and SR obtained by ANN, which shows good fitness between the experimental and predicted results of MRR and SR.

### Comparison of the performance of RSM and ANN modeling

The performance of RSM and ANN modeling are compared by calculating the coefficients of determination (*R*^{2}), root mean square error (RMSE) and absolute average deviation (AAD) for the MRR and SR, using Eqs. 8, 9 and 10 respectively [11].

where *n* is the number of experiments, *y*_{i} is the predicted value obtained from the ANN, *y*_{ai} is the actual value, and *y*_{m} is the average of the actual values. Table 3 presents the resultant *R*^{2}, RMSE, and AAD for both models. Although, both RSM and ANN models achieve higher quality predictions, however, higher values of R^{2} with lower values of RMSE and AAD showed that the RSM model can effectively predict the SR with higher estimation capabilities compared to ANN. On the contrary, the ANN model can effectively predict the MRR with higher estimation capabilities compared to RSM. The results show that using both the RSM and ANN is more adequate and reliable in predicting the MRR and SR. However, modeling by ANN using MATLAB software requires more experience to perform many training trails to achieve the most accurate prediction. While, modeling by RSM using MINITAB software can display prediction equations easily, so no experience is needed to predict the results under given conditions such as in the case of ANN modeling.

### Analysis of variance and response graphs

Tables 4 shows the analysis of variance (ANOVA) for the MRR and SR performed using MINITAB software. For the MRR and SR, it can be seen that all the independent variables have a significant effect on them (*P* value < 0.05).

The impact of every process parameter at different levels on the MRR and SR can be achieved by performing the response graphs shown in Fig. 5, based on calculating the output mean at each level using Eq. 11 [2].

where *M* is the mean of each output *L* (MRR or SR) at each level (1, 2 or 3) and *k* represents the number of experiments considering a specific level. It is clear that the longer the Ton, the more MRR in each sparking cycle. Also as the Toff is decreased, the gap voltage will slowly fall and the working current will rise, leading to the increase of the MRR and SR. Hence by increasing Ton and I and decreasing Toff, the produced surface is rougher and the heat-affected zone (HAZ) on the workpiece is deeper, although achieving higher MRR.

### Optimization by using fuzzy logic

When it comes to predicting the optimal process parameters combination that will achieve maximum MRR and Minimum SR together, not for each one only, fuzzy logic is the proper technique to perform the optimization procedure with multiple performance characteristics. Fuzzy logic can map two inputs space to only one output space considering both the MRR and SR together. Since the experimental values of the MRR and SR are in different ranges, normalization must be performed before applying a fuzzy logic technique. Equation 12 represents the used normalized equation [12].

where *N*_{p} is the normalized MRR or SR for every experiment number *p*, *x*_{p} is the MRR or SR for experiment number *p*, *x*_{max} and *x*_{min} are the maximum and minimum values of the MRR or SR for all experiments. Mamdani-type inference model is constructed using MATLAB software. For every experiment, the inputs for the inference system are the maximized normalized values of the MRR and the minimized normalized values of the SR, and the output is named the multiple performance characteristic index (MPCI). Three triangular membership function is assigned to every input, while five triangular curve membership function is assigned to the output. Nine IF/THEN fuzzy rules are performed for mapping between the inputs and the output. The centroid defuzzification method is used to convert the fuzzy value into the MPCI. Figure 6 shows the designed inference model while making optimization. Table 2 presents the resultant normalized values of MRR and SR for each experiment and the MPCI. From the resultant MPCI, experiment number 5 is considered to be the optimal process parameter combination as it achieves the highest MPCI. Therefore, the process parameter combination: Ton = 25 µs, Toff = 5 µs and I = 6 A can be considered as an optimal one. As the impact of every process parameter at different levels on the MPCI can be achieved easily by estimating the MPCI mean using Eq. 11, another optimal process parameters combination may be desided. Accordingly, Ton = 35 µs, Toff = 10 µs, and I = 3 A, may be considered as another optimal process parameters combination. As experiment number 5 achieved higher MRR and lower SR compared to that obtained from the centeral point's experiments (experiments number 15–20), it is better to consider it as the optimal one.

## Conclusion

The aim of this work is to optimize wire electrical discharge machining (WEDM) operating parameters with the objective of achieving a maximum material removal rate (MMR) and minimum surface roughness (SR) for an AISI 304 stainless steel workpiece. This work compares the performance of response surface methodology (RSM) and artificial neural network (ANN) based on the coefficient of determination, root mean square error, and absolute average deviation calculations. Both techniques are used to study the effect of independent process parameters on responses and develop predictive models. Additionally, this comparison is followed by implementing the fuzzy logic technique to get the optimal process parameters combination to optimize the process, based on merging both MRR and SR together as one variable. The results show that using both the RSM and ANN is more adequate and reliable in predicting the MRR and SR. In addition, it is obvious that by increasing the peak current, the pulse on time, and by decreasing pulse off time, the resulting workpiece surface is rougher despite achieving a higher material removal rate. Also, it is concluded that the optimal process parameters combination that achieves the maximum MRR and minimum SR is 25 µs pulse on time, 5 µs pulse off time, and 6 A peak current. This work helps many industrial applications relating to WEDM of AISI 304 stainless steel. As lower SR is achieved, less finishing processes are required after machining. Also, higher MRR contributes to lower machining time, which in turn reduces the net product cost.

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## Acknowledgements

The author would like to acknowledge the Faculty of Engineering – Mansoura University – Egypt for providing the required facilities in performing the experimental work. Also, she would like to acknowledge Shoman Company – Egypt for their valuable support in supplying the required workpiece specifications. Additionally, the author would like to acknowledge Assoc. Prof./Noha Abdel Mawla El-Wassefy – Faculty of Dentistry – Mansoura University – Egypt for her great help and patience during performing surface roughness measurements.

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El-Bahloul, S.A. Optimization of wire electrical discharge machining using statistical methods coupled with artificial intelligence techniques and soft computing.
*SN Appl. Sci.* **2, **49 (2020) doi:10.1007/s42452-019-1849-6

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### Keywords

- Wire electrical discharge machining
- Material removal rate
- Surface roughness
- Response surface methodology
- Artificial neural network
- Fuzzy logic technique