Optimization design for die-sinking EDM process parameters employing effective intelligent method

Abstract Electrical discharge machining (EDM) is a highly regarded method for producing ultra-precise mechanical parts. In this study, the process parameters of die-sinking EDM using copper electrodes and American Iron and Steel Institute (AISI) P20 tool steel workpieces are optimized for various output responses. The study surveys three input parameters, including Current (I), Pulse on Time (Ton), and Pulse Off Time (Toff). Some statistical methods, such as Taguchi and Analysis of Variance (ANOVA), are applied to find the optimal set of parameters for the output responses, consisting of Material Removal Rate (MRR), Electrode Wear Rate (EWR), and Surface Roughness (SR), and determine the most influential input factor. With the L9 Orthogonal Array (OA), the analytical results demonstrate the optimal parameter set for MRR is I = 6 A, Ton = 120 µs, and Toff = 30 µs, while those optimal values for EWR and SR are I = 2 A, Ton = 120 µs, and Toff = 90 µs and I = 2 A, Ton = 60 µs, and Toff = 30 µs, respectively. The study also indicates that input factor I has the most effect on the output responses, followed by Ton and Toff. Moreover, Grey relational analysis in the Taguchi method is also employed for multi-response optimization. The optimal parameter set for the three output factors is I = 6 A, Ton = 120 µs, and Toff = 60 µs, respectively. In this research, the microstructure and recast layer of the machined surfaces are investigated using optical microscopy as well.


Introduction
Electrical discharge machining (EDM) is an advanced and non-contact technique (Banu & Ali, 2016;Palanikumar & Davim, 2013;Rajmohan et al., 2012;Singh et al., 2004;Srivastava & Pandey, 2012).This machining method has been widely used to produce ultra-precise mechanical parts, aviation components, and so on (Amorim & Weingaertner, 2004;Bhowmick et al., 2023;Dewangan et al., 2023;Jagtap & Karande, 2023;Jeykrishnan et al., 2016;John et al., 2016;Korlos et al., 2016;Kumar et al., 2016Kumar et al., , 2021;;Mao et al., 2022;Patnaik et al., 2022;Phan et al., 2020;Pourasl et al., 2022;Singh et al., 2021aSingh et al., , 2021bSingh et al., , 2022aSingh et al., , 2022bSingh et al., , 2022cSingh et al., , 2022dSingh et al., , 2004;;Voisey, 2014;Zafar et al., 2022b).This method has been efficient for fabricating complex mold parts or drilling small/ultra-small holes with great depth in high-hardness materials that are difficult to obtain using conventional machining methods (Ho & Newman, 2003;Jeevamalar & Ramabalan, 2015;Wang et al., 2021).EDM employs a controllable discharge sequence in which the discharge process between an electrode and a workpiece in a dielectric fluid is continuously repeated (Banu & Ali, 2016).There is no mechanical contact between the electrode and the workpiece during EDM (Banu & Ali, 2016;Palanikumar & Davim, 2013;Rajmohan et al., 2012;Srivastava & Pandey, 2012).During discharge, a large amount of thermal energy is generated between the electrode and the workpiece.The generated temperature ranges between 8000°C and 12,000°C and can reach 20,000°C, resulting in the formation of molten metal puddles on both the electrode and workpiece surfaces.Due to the high temperature, some puddles will directly vaporize, while the remainder will become molten metal debris.The dielectric fluid flow will remove the debris from the space between the electrode and the workpiece (Srivastava & Pandey, 2012).For the EDM process, the electrode plays a vital role since it directly and significantly influences the accuracy of the machined parts, machining time, and the economics of the fabrication (Czelusniak et al., 2018).Thus, precise and high-quality electrodes for EDM machining are required.With outstanding properties, including high electrical and thermal conductivity, strong structural integrity, and excellent surface finishes, copper has been widely used as an electrode material in EDM (Banu & Ali, 2016).
The Taguchi method is one of the most common methods for optimizing the process of experiments in the engineering field (Chandrashekarappa et al., 2021;Liu et al., 2022;Nguyen et al., 2021;Sahu et al., 2013;Sharma et al., 2021;Vora et al., 2022;Yan et al., 2022;Zama et al., 2022;Zeng et al., 2021).This method identifies parameter settings that significantly improve the quality of the product or process to variations of noise factors (Rachman et al., 2021).Implementing the Taguchi design strategy helps reduce the number of experiments, saving time and money in the investigation (Rachman et al., 2021).Therefore, this method has been widely used to optimize the processing parameters in a recent report (Dewangan et al., 2023;Rahiman et al., 2022;Shah et al., 2023;Somani et al., 2022).For instance, by employing the Taguchi method, Dewangan and co-workers demonstrated the optimal set of operating current (I), pulse-on time (Ton), and pulse-off time (Toff) for achieving the maximum material removal rate (MRR) and minimum surface roughness (SR) when EDM machining D2 steel (Dewangan et al., 2023).In another report, the optimal set of I and Ton for obtaining the most favorable MRR and tool wear rate (TWR) in machining aluminum alloy 5083 was also optimized using the Taguchi design (Rahiman et al., 2022).Moreover, for having the best MRR, TWR, and SR during EDM processing of D2 tool steel, the most suitable set of I, Ton, and Toff was determined by the method (Somani et al., 2022).Recently, other techniques, such as the new method grey relational analysis (GRA), technique for order preference by similarity to an ideal solution (TOPSIS), and preference selection index (PSI), have been used together with the Taguchi method for multiobjective optimizations (Shah et al., 2023).To investigate the most influential input factor on the output responses, the ANOVA method has been extensively used.ANOVA is a statistical method for analyzing the variances in a set of data and separating them into groups according to the sources of those variations, according to the Taguchi approach (Barnabas et al., 2019;Hanif et al., 2019;Hussain & Khan, 2018;Jan et al., 2020;Kaushik et al., 2018;Muhammad & Jalal, 2023;Shaik et al., 2019).
In EDM, selecting processing parameters is critical for producing parts with good surface quality while saving processing time and costs (Jeevamalar & Ramabalan, 2015;Kumar et al., 2021;Rachman et al., 2021).As a result, many researchers have widely optimized the EDM processing parameters for a wide range of materials.For instance, using the Taguchi approach, Rachman et al. (Rachman et al., 2021) determined the optimal set of processing input parameters, including voltage (U) of 40 V, Ton of 250 µs, and Toff of 20 µs, for obtaining the lowest surface roughness (SR) during machine AISI P20 material.Kumar et al. (Kumar et al., 2021) presented an experimental investigation in which two EDM output responses, MRR and EWR, were considered for optimizing the input parameters for fabricating P20 tool steel.The results showed that for the highest MRR, the set of input parameters was I of 6 A, Ton of 100 µs, and Toff of 50 µs, while the set of input parameters for the lowest EWR was I of 4 A, Ton of 80 µs, and Toff of 50 µs.In another report (Zafar et al., 2022a), Zafar and co-workers evaluated MRR in EDM machining of AISI P20 steel.The results indicated that for the optimal MRR, the input parameters were I of 30 A, Ton of 1500 µs, and Toff of 12 µs.According to the above survey, many studies on optimizing input parameters for EDM processing on P20 steels using the Taguchi method have been done.However, it is hardly possible to find from the literature a report in which the three input factors, including I, Ton, and Toff, have been optimized for achieving multiple optimal output responses, such as MRR, EWR, and SR, during EDM machining of AISI P20 steel.Moreover, the topography of the machined surface of P20 steel has yet to be investigated.Thus, additional research into the EDM process in P20 tool steel is still necessary.
To fulfill the technical gaps, in this research, the EDM processing input parameters for machining AISI P20 steel with a copper electrode, including I, Ton, and Toff, were optimized using the Taguchi approach for individual output responses consisting of MRR, EWR, and SR.The Analysis of Variance (ANOVA) was utilized to determine the most influential input factor on the output responses.Moreover, Grey relational analysis was used together with the Taguchi method for obtaining the optimal parameter levels for the multiple output responses.The microstructure and recast layer of the machined surface were investigated using a microscope.For each parameter set, three machining operations were carried out.The mean values of the experimental results were used for optimization.
The outlay of this study is organized as follows.Section 2 introduces the materials and our proposed methods.Section 3 presents the experimental tests.The results and discussion will show in Section 4, and Section 5 will demonstrate the remarkable conclusion of this study.

Electrode
In this study, copper was chosen as an electrode material for the EDM process.Its shape and size shown in Figure 1 were selected based on the previous reports (Rafaqat et al., 2020(Rafaqat et al., , 2022)), which demonstrated that the electrode with a relief angle of 5° and land height of 1 mm can help reduce the machining time by ~ 50% and the hole taper.The detailed properties of copper material are presented in Table 1.

Workpieces
Preparing workpieces for the EDM process, an initial AISI P20 steel block was cut into nine samples with a dimension of 45 mm × 26 mm × 12.5 mm (length × width × height) using a wire cutter, as shown in Figure 2. The properties and chemical compositions are presented in Tables 2 and 3.

Taguchi method
Taguchi method uses the orthogonal array (OA) model to explore the fundamental control factors through a small number of experiments by dispensing the elements in a balanced manner and   converting the experimental results into signal-to-noise ratio (S/N) to investigate the optimal conditions.For optimization problems, there are three types of S/N ratio basically: "Larger the Better (LB)", "Nominal the Better (NB)", and "Smaller the Better (SB)".In this research, for minor surface roughness and low electrode wear rate, these two response factors were calculated using the SB formula.For the material removal rate, the LB type was used to calculate.

Larger the better
Smaller the better where -y u : the value of the u th measurement -n: Number of experiments in the orthogonal array

Experimental work
In this research, three input parameters in the EDM process, including I, Ton, and Toff, were chosen to find the optimal parameter set for individual output responses consisting of MRR, EWR, and SR.Three levels were selected for each input factor.With three factors and three levels, an L9 orthogonal array was used.For each parameter set, there were three machining performances on the same workpiece, so twenty-seven electrodes and nine workpieces were employed in the experiment.

Experimental setup
-EDM machine, dielectric fluid, and machining setup.An EDM machine, Accutex's DS-430S DM, was utilized for the experiment, and hydrocarbon oil was used as a dielectric fluid.The input parameters, including I, Ton, and Toff during machining, were set following selected levels.Other parameters were maintained according to the S-code 2 parameter set of the machine presented in Table 4.For machining, the workpiece was first adjusted and fixed on the EDM machine using a bench vice (Figure 3a).Then the copper electrode was clamped on the machine holder while maintaining its bottom surface parallel to the top workpiece surface (Figure 3a).After that, the EDM input factors, including I, Ton, and Toff, shown in Table 5, were set.Subsequently, the depth-cut was set at 12.6 mm to ensure that a through hole was obtained.When all required processing parameters were set, the dielectric fluid was allowed to be pumped into the tank.Until the workpiece completely sank into the fluid, the machine started machining.For each parameter set, three machined surfaces were performed (Figure 3b).The output responses for surveying are shown in Table 5.
-Roughness surface measurements.For the evaluation of the surface quality of the machined parts, surface roughness (Ra) was measured using a Mitutoyo SJ-201 roughness tester (Mitutoyo-Japan) with a cutoff length of 7.5 mm.For each machined surface, three  measurements were performed at different positions Figure 3(c-d).The average value was used for optimization.
-MRR and EWR calculations.For calculating MRR and EWR values, the samples before and after machining were weighed using an electronic scale (with an accuracy of 0.001 g), as shown in Figure 3(e-f).Their average weight was employed for calculation.

Selection of machining conditions
Three levels of each input factor and the range of these factors were chosen by referencing recent studies (Kumar et al., 2021;Phan et al., 2020).For instance, Le and Co-workers optimized the input parameters of the EDM process on machining SKD11 steel with variations of I, Ton, and Toff from 1 A to 5 A, 18 µs to 75 µs, and 9 µs to 37 µs, respectively (Phan et al., 2020).In another report (Kumar et al., 2021), these parameters in the range of 4-6 A, 80-120 µs, and 40-60 µs, respectively, were optimized during EDM machining of P20 steel.According to the survey, three levels of 2, 4, and 6 A were chosen for I, while 60, 90, and 120 µs and 30, 60, and 90 µs were for Ton and Toff, respectively (Table 5).The output responses used for optimizing are also presented in Table 5.

Measurement of response MRR, EWR, and SR
The MRR and EWR were calculated by dividing the difference in weights of the workpiece and electrode before and after machining by the machining time.
The MRR values, EWR values, and S/N ratio were calculated and filled in Table 6.SR (Ra) of each machined surface was measured three times, and the average value was calculated and used for optimization.For simplicity, noise factors were ignored in this study.

Determination of optimal EDM parameters for each response value
The average values of three output responses, including MRR, EWR, and SR, were calculated using Minitab 18 software.The S/N ratio of the responses and all the corresponding values are shown in Table 6.
In this study, the "smaller the better (SB)" type was chosen to obtain the S/N ratio for the EWR and SR responses, whereas the "larger the better (LB)" type was selected for the MRR.These average values of the S/N ratio for MRR, EWR, and SR (shown in Tables 7-9, respectively) were used to optimize the input parameters with their levels, as presented in Table 6.
The S/N ratio response of the MRR is shown in Table 7 with Delta being the variation between the maximum and the minimum value.The results indicate that the input factor I has the most significant influence on MRR (a Delta value of 17.747), followed by Ton (a Delta value of 4.101) and Toff (a Delta value of 2.599).Table 8 presents the Means of the S/N ratio for EWR.It also specifies that current is the most influential factor on electrode wear with a Delta value of 33.47, followed by Ton and Toff with a Delta value of 5.43 and 3.00, respectively.Table 9 displays the Means of the S/N ratio for SR.The results reveal that the Delta values of the input factors are not as immense as those for MRR and EWR.However, a similar influence tendency of the parameters on SR to those of MRR and WR is observed.The most influential parameter on surface roughness is the current (a Delta value of 9.025), followed by Ton (a Delta value of 2.357) and Toff (a Delta value of 0.398).The MRR results shown in Table 6 varied from 0.615 g/min to 7.125 g/min.It was found that increasing the current (I) led to the dramatic increase in MRR.In contrast, the effect of the Ton and Toff parameters on MRR strongly depended on the level of I.At a fixed I = 2 A, the minor change in the MRR was obtained with variations of the Ton and Toff values (Table 6).However, when the I value was set at 4 A and 6 A, increasing the Ton value led to a substantial increase in MRR (Table 6), while Toff had a minor effect.From Table 7 and Figure 4, it was found that the optimal parameters for the MRR were I = 6 A, Ton = 120 µs, and Toff = 30 µs.The results suggested that setting the higher input values of I and Ton together with the lower input value of Toff could faster remove the workpiece material during EDM machining.The obtained results were consistent with the findings in the recent reports (Kumar et al., 2021;Phan et al., 2020;Zafar et al., 2022b).For instance, Le and co-workers reported that the optimized input factors for multi-responses (material removal rate, tool wear rate, and surface roughness) in EDM machining of SKD11 steel were I = 5 A (level 5/highest level), Ton = 50 µs (level 4), and Toff = 18 µs (level 3) (Phan et al., 2020).The optimal set of processing parameters, including I = 6 A (level 3/highest level), Ton = 100 µs (level 2), and Toff = 50 µs (level 2), for MRR output response was demonstrated by Kumar and co-workers (Kumar et al., 2021).Moreover, in another report (Zafar et al., 2022b), authors also reported that an increase in the current value led to an increase in MRR, and the optimal set for MRR value was I = 30 A (level 3/highest level), Ton = 1500 µs (level 2), and Toff = 12 µs (level 2).
In the case of the EWR, the obtained results indicated that among the input parameters, the I had the major effect on the EWR.With an increase in I from 2 A to 6 A, the EWR increased from 0.0002 g/min to 0.0147 g/min, while at the same level of I, variations of Ton and Toff values caused a slight change in EWR value (Table 6).However, for optimizing EWR, the "smaller the better" type was used, thus, the optimal set of parameters for EWR was I = 2 A (level 1), Ton = 120 µs (level 3), and Toff = 90 µs (level 3) as shown in Figure 5.The setting lower value of I during machining resulting in the lower EWR is the same tendency with the recent report (Kumar et al., 2021).This study demonstrated that for the best EWR the optimal set of the parameters was I = 4 A (level 1/ lowest level), Ton = 80 µs (level 1), and Toff = 50 µs (level 2) (Kumar et al., 2021).Even though the similar range of I, Ton, and Toff and the same workpiece material were chosen for EDM optimizing, the maximum EWR value obtained in our research (0.0147 g/min) was much smaller than that reported by Kumar and co-workers (87.728 g/min) (Kumar et al., 2021).With variations of input parameters from the lowest to highest levels, the SR value increased from 2.121 µm to 7.985 µm (Table 6).Among these parameters, the discharge current (I) mainly affected on the SR value (Table 6).The optimal set of parameters for SR was I = 2 A, Ton = 60 µs, and Toff = 30 µs.The experimental results suggested that the lower values of input parameters provided a smaller SR value (Figure 6).Our finding is consistent with the recent study (Dewangan et al., 2023), which reported that the smallest SR value of 3.2 µm could be obtained when performing EDM on D2 steel with the lowest level of the input parameters such as I = 5 A (level 1), Ton = 10 µs (level 1), and Toff = 9 µs (level 1).

ANOVA for the response variable
ANOVA method was employed to investigate which EDM process parameter significantly affects EWR, MRR, and SR.The outcomes of the ANOVA for the output responses are shown in Tables 10-12, respectively.It demonstrated that factor A (current, I) had P-value and  contribution being less than 0.05 (at the 95% confidence level) and more than 92%, respectively, indicating that I had a statistically significant impact on MRR, EWR, and SR.Contrarily, factors B (Pulse on time, Ton) and C (Pulse off time, Toff) had P-values greater than 0.05 and/or contributions less than 5%, indicating that these parameters had a minor effect.

Results of the surface topography
The effect of EDM processing parameters on the machined surface topography was also investigated in this research.To do this, the microstructures of the surfaces obtained with different sets of input parameters, including Exp.No. 1 (I = 2 A, Ton = 60 µs, Toff = 30 µs), Exp.No. 5 (I = 4 A, Ton = 90 µs, Toff = 90 µs) and Exp.No. 9 (I = 6 A, Ton = 120 µs, Toff = 60 µs) (Table 6) were observed using a microscope (Figure 7).It was found that increasing I and Ton values from 2 A to 6 A and 60 µs to 120 µs, respectively, the surface roughness displayed in the microstructure images increased (Figure 7).This implied that I and Ton had major effect on the surface roughness of EDM machined parts, which is consistent with the outcome of the ANOVA analysis (Table S12).Moreover, these increases led to a significant increase in the thickness of recast layer, which is the outer layer of the heat affected zone and is derived from melted and resolidified workpiece material (Figure 8) (Amorim & Weingaertner, 2004).As reported, the enough thin-recast layer formed on the machined parts can help them improve their corrosion resistance during working (Hou et al., 2022).However, in the case of the thicker layers, high potential for many types of defects can be formed inside the layer such as scattered debris, inclusions, pockmarks, microcracks, globules, and pores (Goyal & Rahman, 2021;Karmiris-Obrata´nski et al., 2021;Muthuramalingam & Phan, 2021;Muthuramalingam et al., 2018;Selvarajan et al., 2023).Thus, the obtained results in this research indicated that machining the workpiece at higher values of I and Ton results in the lower surface quality of obtained products (Voisey, 2014).

Optimization multi-responses using grey relational analysis
To determine the optimal parameter set for multiple output responses, the Taguchi method combined with Grey relational analysis was used (Haq et al., 2008;Mausam et al., 2019;Priyadarshini et al., 2022).The optimal process was carried out in the following steps.
Step 1: Compute the S/N ratios for a given response and predict S/N ratios of the starting conditions using the Eq. ( 5).The result of S/N ratios for each quality characteristic is shown in Table 13.where n = number of replications y ij = observed response value where i = 1. 2. . ... n; j = 1. 2. . .k.
Step 2: Normalize the S/N ratio values by Eq. ( 6).The results are shown in Table 13.
Step 3: Calculate the grey relational analysis.From the data in Table 13, compute the grey relational coefficient for the normalized S/N ratio values by using Eq. ( 7).The value for ξΔmax is taken as 0.5 in Eq. ( 7).Given that each process parameter is equally weighted.The results are shown in Table 14.
where (1) j = 1.2. ..n; k = 1.2. ..m. n and m are the number of experimental data items and the number of responses.(2) y 0 k ð Þis the reference sequence (y 0 k (6) � is the distinguishing coefficient.It has a set range 0 � � � 1 (depending on how the system functions practically, the value might change).
Step 4: Next, the grey relational grade can be calculated by Eq. ( 8).The grades are finally taken into account for optimizing the multi-response parameter design problem.Table 14 the results.
where y i andkare the grey relational grade for the j th experiment and the number of performance characteristics.
Step 5: Based on the value of grey relational grade in Table 14 by using Eq. ( 9).The factor effects are presented in Figure 9, and the main effects are listed in Table 15.
Step 7: Using the grey grade value, ANOVA is formulated for identifying the significant factors.The results of ANOVA are given in Table 16.From ANOVA, it is clear that I (94.19%) is the most influent factor on AISI P20 steel in EDM, followed by Ton (2.79%) and Toff (1.62%).

Applications of the optimal input parameter set for fabricating complete parts
To investigate the potential of the obtained processing parameter sets for machining complex structures, the optimal set for SR value (I = 2 A, Ton = 60 µs, Toff = 30 µs) was used for machining the Apple logo, Tesla logo, and abbreviation for Ho Chi Minh City University of Technology and Education.To do this, the corresponding electrodes were prepared, as shown in Figure 10(a).It was found that these complex shapes were smoothly machined with this parameter set, and the machined surfaces were precise and of high quality (Figure 10b).The obtained results strongly strengthened the potential for employing the findings of this study in practical processes.

Remarkable conclusions
In this report, die-sinking EDM processing parameters, including current (I), Pulse On Time (Ton), and Pulse off Time (Toff), in the machining of AISI P20 steel were successfully optimized using Taguchi and ANOVA methods.It was found that the optimal sets of parameters for the shortest machining times (MRR value) and the minor electrode wear (EWR value) were I = 6  A (level 3), Ton = 120 µs (level 3), Toff = 30 µs (level 1) and I = 2 A (level 1), Ton = 120 µs (level 3), Toff = 90 µs (level 3), respectively, while that for achieving the minor surface roughness (SR value) was I = 2 A (level 1), Ton = 60 µs (level 1), Toff = 30 µs (level 1).The results also indicated that the Current (I) was the most influential parameter on MRR, EWR, and SR, contributing from ~92% to ~96%, followed by Ton and Toff, with contributions of ~2.5% to ~5% and ~0.8% to ~2.1%, respectively.The optimal parameter set for multi-responses was I = 6 A (level 3), Ton = 120 µs (level 3), and Toff = 60 µs (level 2).The microstructure images of the machined surfaces indicated that an increase in the level of input factors led to an increase in the thickness of recast layers, which caused a reduction in the quality of the machined surface.The outcomes of this study can be used as reference data for selecting EMD process parameters for machining AISI P20 steel to obtain the different output requirements.

Figure
Figure 1.(a) The design of copper electrode for the EDM process.(b) the fabricated copper electrode.

Figure
Figure 2. (a) The design of the AISI P20 steel workpiece for the EDM process.(b) the workpiece obtained using a wire cutter.

Figure 3 .
Figure 3. (A) AISI P20 steel workpiece was mounted on the EDM machine, (b) the obtained part after machining.(c (top view), d (front view)) the surface roughness of the machined surface was measured using a Mitutoyo SJ-201 roughness tester.An electronic scale used to weigh the workpiece before (e) and after machining (f).

Figure 4 .
Figure 4. Influence of EDM process parameters on MRR.

Figure 5 .
Figure 5. Influence of EDM process parameters on EWR.

Figure 6 .
Figure 6.Influence of EDM process parameters on SR.

Figure 9 .
Figure 9. Influence of EDM process parameters on the output responses.