1 Introduction

Despite long years of development, it remains difficult to achieve today’s desired precision using traditional manufacturing methods. The search to eliminate the boundaries and weaknesses of traditional machining methods has led to the emergence and development of unconventional manufacturing methods. Unconventional manufacturing methods, which generally involve the production of complex parts using different processing approaches, are in great demand due to the advantages they bring to design engineering [1]. One of the non-traditional manufacturing methods used in the machining industry is the electrical erosion processing method, also known as electric discharge machining (EDM). This widely used non-traditional production technique is based on the principle of material removal via a series of rapid and repeated electrical discharges between the workpiece and an electrode immersed in a dielectric fluid [2,3,4,5,6]. With a temperature of 8000–20,000°C, plasma is generated between the anode and the cathode [7]. The process helps in giving the accurate shape by using the electrode which is the replica of the cavity in the electrode governing the zone in which the spark erosion is occurring [8].

High conductivity heat resistance and high melting point are the main desired properties for EDM tool. The most common materials used in EDM tooling are copper, graphite, tungsten and tungsten carbide [9]. A suitable dielectric for EDM should be able to provide suitable conditions for initiation and maintain of good effective electric discharges, cool the electrodes and to carry away the debris from the spark gap. The most common dielectric mediums used are hydrocarbon oils such as Kerosene [10]. Surface integrity is one of the most important issues with EDM. Discharge current is one of the important factors that affect surface integrity. The surface roughness of the material increases with the increase in current and voltage. The crater size varies with pulse energy though it also depends on material properties [11].

In the EDM technique, the processing parameters and electrode selection significantly affect the machinability of the workpiece. Selection of the appropriate machining parameters and electrode usage directly affects the workpiece surface roughness (Ra), material removal rate (MRR) and tool wear rate (TWR). Payal et al processed EN-31 tool steel using the EDM technique with copper, brass and graphite electrodes. The highest MRR value in their study was obtained with the copper electrode, whereas the lowest Ra values were obtained with the brass electrode. Volcanic spills and cracks were observed on the surfaces treated with the graphite electrode because of the uneven distribution of heat [12]. Lee and Li processed tungsten carbide materials using graphite, copper and copper–tungsten electrodes. They stated that MRR increased with increasing discharge current and that the highest MRR value was obtained with the graphite electrode; however, the Ra value increased with the increase of the discharge current [13]. Son et al investigated the influence of the electrical pulse on machining characteristics in the EDM process and found that the pulse duration considerably affected MRR, TWR and surface accuracy [14]. A study was conducted by Gostimirovic et al on the effects of electrical processing parameters on die sinking EDM performance. In the machining of a manganese–vanadium tool steel workpiece using a graphite electrode, they found that the discharge current and pulse duration had highly influenced the MRR of the EDM process [15]. In the Khan study, aluminum material and mild steel were processed with copper and brass electrodes. Increased abrasion was seen on the electrodes when the discharge current was increased, with the brass electrode exhibiting more erosion than the copper electrode. This occurred because the thermal conductivity and melting point of the copper electrode were higher than those of the brass. The MRR increased in parallel with the discharge current, and the highest MRR was obtained in the processing of the aluminum material with the brass electrode [16]. In the study of Amorim and Weingaertner, AISI P20 tool steel was processed with copper and graphite electrodes in a sinker EDM machine. The highest MRR value was obtained using the graphite electrode with a negative polarity, while the graphite and copper electrodes exhibit similar performances in positive polarization. The researchers obtained the best Ra values under the test condition in which the copper electrode had a negative polarity [17]. Dewangan et al investigated the effect of electrodes on surface integrity using the EDM method. They used copper, brass and graphite electrodes in their experimental studies and obtained the best surface finish with the copper electrode. They stated that the discharge current was the most effective parameter on surface roughness [18]. Torres et al studied the influence of EDM parameters using a graphite electrode on an INCONEL 600 alloy. They evaluated the machining performances in terms of MRR, electrode wear, and surface roughness, and reported that better results were achieved with the graphite electrode having a negative polarity [19].

Previous studies show that, the use of mathematical modeling such as optimization and artificial neural networks is beneficial in terms of cost and time. Jung and Kwon used the Taguchi technique in experimental studies to investigate the effect of processing parameters on the experimental results. They stated in the conclusion of their study that the most effective processing parameter was the discharge current [20]. In another studies using the Taguchi method, Lin et al supported their work with analysis of variance (ANOVA) and noted that the discharge current and pulse duration increased the MRR, but had a negative effect on the Ra value [21]. Nikalje et al in their study, processed MDN 300 steel using EDM and found the most effective processing parameters to be the discharge current, pulse-on time, and pulse-off time. They stated that increasing the discharge current and pulse duration negatively affect the workpiece surface roughness [22]. The experimental investigation of Mohanty et al examined the machinability of Inconel 718 super alloy via the EDM process to identify the multiple performance characteristics of MRR, TWR, surface roughness, and radial overcut. Nonlinear regression analysis was conducted to develop a valid empirical model relating to the process parameters. They reported that the optimal levels of cutting parameters obtained for both the algorithms were validated through confirmation testing [23].

In the EDM technique, the determination of the machining parameters for the workpiece and electrode pair significantly affects the processing outputs. Determination of the appropriate levels of the processing parameters used is another important point in EDM. The Taguchi technique is often used to optimize processing parameters. The significance levels of the processing parameters on the process outputs can be determined using variance analysis ANOVA. The present study aimed to overcome the deficiency in the literature on the machinability of caldie cold work tool steel, widely used in mold production, using EDM. Thus, the study investigated its machinability using EDM with copper and graphite electrodes.

In this study, the investigation into the erosion process of caldie cold work tool steel using the EDM technique was carried out both experimentally and via mathematical modeling. In the experimental design, three levels of discharge current and three levels of pulse duration were used as the major process control parameters, with graphite and copper electrodes as the tools. The MRR and TWR were calculated using the results obtained from the experiments. Surface roughness, MRR and TWR were studied in depth using regression analysis. The most favorable machining parameters were determined for specified combinations of yield parameters via the Taguchi method. The role of the major process control parameters on the yield parameters was determined by ANOVA. The theoretical data were compared with the experimental data to validate the efficacy of the optimization. The data obtained in the experimental study were interpreted by scanning electron microscopy (SEM) images and supported by graphs.

2 Materials and methods

The experimental study was carried out on a FURKAN EDM M25A sinker electro erosion machining center. Caldie plastic mold tool steel was used as the workpiece. Caldie plastic mold steel is a non-standard cold work tool steel patented by Uddeholm Tooling, a Swedish tool steel manufacturer [24]. The chemical composition of caldie plastic mold tool steel is shown in table 1. The electrodes used were of graphite and copper, in dimensions of 15 × 15 × 100 mm. Table 2 shows the physical properties of the graphite and copper electrodes.

Table 1 Chemical composition of caldie plastic mold tool steel.
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Table 2 Physical properties of graphite and copper electrodes.
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The electrodes were prepared individually for each test condition. The surfaces of the electrodes were polished progressively using 200–1200 grid sandpaper. In the experiments, the processing time was kept constant at 1 h. The kerosene used as the dielectric medium fluid in the machinability tests was applied using lateral spraying. The surface roughness measurements were taken after the machining using the Mitutoyo SJ 410 device. The mean surface roughness (Ra) value was taken as the average of the values measured on three different areas of the treated surfaces. The Precisa XB200h precision scale with an accuracy of 1/10000 was used for weight measurements. Equations (1) and (2) were used to calculate MRR and TWR values. The experimental set-up is shown in figure 1.

Figure 1
figure 1

Experimental set-up.

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$$ MRR \left( {{\text{mm}}^{3} /{ \hbox{min} }} \right) = \frac{{\left( {W_{i} - W_{f} } \right)}}{\rho xt} $$
(1)
$$ TWR\left( {{\text{mm}}^{3} /{ \hbox{min} }} \right) = \frac{{\left( {T_{i} - T_{f} } \right)}}{\rho xt} $$
(2)

In these equations, \( W_{i} \) is the initial weight of the workpiece and \( W_{f} \) is the final weight, \( T_{i} \) is the initial weight of the electrode and \( T_{f} \) is the final weight, ρ is the density and \( t \) is the processing time.

3 Experimental design and optimization

In the studies conducted in the field of machinability, different statistical analysis methods have been used to optimize the cutting parameters and to determine their effect on the results. The most commonly applied of these are the Taguchi and ANOVA analyses [25,26,27]. Experimental set was prepared using the Taguchi method. Thus, the effect of the parameters on the test results can be calculated. The optimum test condition can also be determined using the Taguchi method. The ANOVA method is used to determine the relationship between inputs and outputs and the magnitude of the relationship. In experimental studies especially, it is very important in the interpretation of the test results to determine whether there is a relationship between the test parameters used and the experimental results. Regression analysis is one of the most frequently used subject areas of statistics. In case of multiple factors affecting an event, it is possible to investigate the cause–effect relationship via regression analysis.

Certain characteristics are used in the evaluation of test results obtained using the Taguchi method. One of these, “Smallest is better”, was selected for Ra and TWR in this study because Ra and TWR are required to be low during the electro erosion process. The “Smallest is better” approach of the Taguchi method is given in Eq. (3). The “Larger is better” approach, as shown in Eq. (4), was used for MRR. In Eqs. (3) and (4), yi is the performance response, i is the observation value and n is the number of tests in an experiment [28, 29].

$$ S/N = - 10\log \left[ {\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} y_{i}^{2} } \right] $$
(3)
$$ S/N = - 10\log \left[ {\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \frac{1}{{y_{i}^{2} }}} \right] $$
(4)

The signal/noise (S/N) ratio is based on both the mean values and the variability. The signal (S) factor refers to the real value obtained from the system, while the noise (N) factor refers to the factors which are not taken into consideration in the experimental design but have an effect on the test result. The sources that cause noise are all variables that result in a deviation from the intended value. Table 3 shows the test variables and their levels.

Table 3 Control factors and levels.
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In this study, two different electrodes, three different discharge current and three pulse duration current values were taken as control factors. The Taguchi L18 experimental design was used with Minitab software. Table 4 shows the design of the experiment determined by the Minitab package program and the test variables assigned in accordance with the matrix. Figure 2 shows the experimental procedure as a schematic diagram.

Table 4 Taguchi L18 orthogonal experimental design.
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Figure 2
figure 2

Experimental procedure.

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4 Results and discussion

4.1 Analysis of experimental results

Table 5 shows the Ra values of the surfaces processed using graphite and copper electrodes and the MRR, TWR values calculated using Eqs. (1) and (2). In table 5, the highest Ra value (10.36 µm) was obtained with the copper electrode during the test conditions using processing parameters of 25 A discharge current at 200 µs pulse duration. The highest Ra value with the graphite electrode was 9.38 µm.

Table 5 Experimental results.
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Figure 3 shows the effect of discharge current and pulse duration on the Ra. The graph shows that the increases in discharge current caused higher Ra values with both electrodes. In the graph, it can be seen that the Ra value was more adversely affected by the discharge current under processing with the copper electrode. Figure 3 shows that under equivalent experimental conditions, better Ra results were obtained in the trials with the graphite electrode.

Figure 3
figure 3

Effect of tool material, discharge current and pulse duration on Ra.

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Increase in discharge current results impulsive force acting on the workpiece high. This enhances formation of large and deep craters and consequently high material removal efficiency. Also increase in discharge current causes high material removal rate which deteriorates surface of workpiece. Hence an approximate increasing trend of Ra is observed with increase in discharge current. Figure 4 shows SEM images of surfaces processed using copper and graphite electrodes at 12 A discharge current and 200 µs pulse duration. Bubbles adversely affecting the Ra were formed due to rapid cooling and can be seen in the processing zone. The craters and micro-cracks on the surface likewise negatively affected the Ra [30, 31]. The topography of the graphite electrode treated surface in figure 4b is better than that seen in figure 4a.

Figure 4
figure 4

SEM surface images after machining at 12 A discharge current and 200 µs pulse duration: (a) copper electrode; (b) graphite electrode.

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Figure 5 shows the effect of the discharge current and pulse duration on MRR. It can be seen that an increase of discharge current increased the MRR under processing with both the graphite and the copper electrodes. The increase in the discharge current caused more material melting and evaporation of the workpiece surface in the unit time [32]. This led directly to the increase of the MRR.

Figure 5
figure 5

Effect of tool material, discharge current and pulse duration on MRR.

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Figure 6 shows the SEM image of a surface processed at 25 A discharge current and 200 µs pulse duration using the copper electrode. The highest MRR (13.55 mm3/min) was obtained under the current test condition. With the electro erosion process, the arcs coming from the electrode to the surface make pulses on the workpiece in an irratic manner. Therefore, the topography of the surface displays a varied form. Increased discharge current increased the intensity of the arc applied to the surface and caused deeper craters and pits. With the use of the dielectric liquid, larger particles were removed from the surface from these craters and pits and the processing was achieved. This situation enabled the MRR to reach high values. A longer duration of discharges applied to the workpiece surface also increased the amount of melted and vaporized material.

Figure 6
figure 6

SEM surface image after machining with copper electrode at 25 A and 200 µs.

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Figure 7 shows the effect of the discharge current and pulse duration on the amount of electrode wear formed after processing using the copper and graphite electrodes. Increase in discharge current results in higher degree of material erosion form the tool electrode. Therefore, with increase in discharge current, gradual increase in tool wear rate is observed. Figure 7 shows that the copper electrode was more eroded with the increasing discharge current. In the studies where the discharge current was increased to 25 A, the electrode was reported to have been more eroded. In the study in which the pulse duration and discharge current were high (24 A, 200 µs), the highest TWR value obtained was 1.32 mm3/min. As seen in figure 7, in the experiment using the graphite electrode, when the discharge current was increased, the amount of wear on the electrode also increased. Figure 7 shows that the copper electrode was more worn than the graphite electrode. The highest TWR with the graphite electrode was calculated as 1.196 mm3/min under the test conditions of 25 A discharge current and 200 µs pulse duration. The reason for this was that electrode materials with low melting temperatures are more subject to wear than electrode materials with high melting temperatures. The low melting temperature of the copper electrode compared to the graphite caused the TWR to be higher. The lower the TWR, the lower the electrode consumption and hence, the electrode production cost [33, 34].

Figure 7
figure 7

Effect of tool material, discharge current and pulse duration on TWR.

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4.2 Signal-to-noise (S/N) analysis

Using the Taguchi optimization technique, signal/noise (S/N) ratios were obtained for each combination of parameters in the orthogonal test sequence for Ra, MRR and TWR. The results obtained in the Taguchi experiments were converted to S/N ratios. In the S/N ratio results, the larger value is separated into the nominal value and the minimum value and analyzed by calculating it in that way. The highest S/N ratio according to the results shows the best performance. The calculated S/N ratios for Ra, MRR and TWR are shown in figure 8. The S/N ratios given in figure 8 show that the most effective factors on MRR and TWR were the discharge current, pulse duration and tool material, respectively.

Figure 8
figure 8

S/N ratios for machinability parameters.

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The S/N ratios shown in figure 8 are given in a chart form in table 6 for a better understanding of the effects of the machinability factors and levels on Ra, MRR and TWR. These values in table 6 show the effect of each factor level on changes of Ra, MRR and TWR. The most effective factors and levels on the parameters are given in bold in table 6. In the Taguchi method results the most effective factors and levels found for Ra were the tool material (1), discharge current (1) and pulse duration (1). The most effective factors and levels for MRR were the tool material (2), discharge current (3) and pulse duration (3) and for TWR they were the tool material (1), discharge current (1) and pulse duration (1).

Table 6 S/N ratios for Ra, MRR and TWR.
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4.3 ANOVA analysis

The ANOVA is used to determine the relationship between inputs and outputs and the magnitude of each relationship. In experimental studies especially, it is very important to determine the existence of a relationship between the test parameters used and the experimental results. The ANOVA was used in the statistical analysis of the experimental results using the Taguchi design. The difference of the group variables compared to the average performance was examined. This mathematical technique divides the total variability into its components by calculating values including the sum of squares, degree of freedom, variance, F-ratio and p-values [25]. Table 7 shows the ANOVA results at 95% confidence level for Ra, MRR and TWR.

Table 7 ANOVA results for Ra, MRR and TWR.
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According to the ANOVA results obtained in table 7, the effects of the factors on Ra, MRR and TWR are given in graphic form in figure 9. Figure 9 shows that the factors effective on Ra were the discharge current at 84.28%, pulse duration at 8.19% and tool material at 5.06%. Factors influencing the MRR were the discharge current at 89.48%, pulse duration at 6.84% and tool material at 3.32%. The ANOVA analysis of TWR results showed that the factors affecting TWR were the discharge current at 90.23%, pulse duration at 7.53% and tool material at 2.16%.

Figure 9
figure 9

Graphical representation of the ANOVA results: (a) Ra; (b) MRR; (c) TWR.

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The p-value determines the significance of the model and individual parameters. In general, a parameter having a p-value of less than 0.05 was considered to have a significant effect. Although the significance of each parameter was justified by its contribution factor, the F-test and probability values reconfirmed the significance of the process parameter. Table 7 shows higher discharge current F-values for Ra, MRR and TWR (i.e., 204.47; 1490.88 and 7169.39 respectively) and lower p-values (below 0.05), proving that the model was significant and could be used to optimize the machining parameters in the sinker electrical discharge machining of caldie plastic mold tool steel.

4.4 Regression analysis

Regression analysis is one of the most frequently used subject areas of statistics. In the case of multiple factors affecting an event, investigation of the cause–effect relationship is made possible by multiple regression analysis. A regression model consists of dependent and independent variables. The independent variable is the non-random variable used to describe the dependent variable. In general, multiple regression analysis is used to find the mean output values for the dependent variable [35,36,37].

The coefficient of determination, expressed as R2, indicates the reliability of the predicted model. In regression analysis results, the closer the R2 is to “1”, the better the independent variable explains the change in the dependent variable [35]. The regression analysis used the tool material, discharge current and pulse duration as the machining parameter variables to estimate the Ra, MRR and TWR.

For this, regression equations were formed for Ra, MRR and TWR by using statistical data obtained using the experimental data in table 5. The functional form of the simple linear regression model can be written in the form of Eq. (5) for a set. In this equation, y denotes the output, v1, v2 and v3 the variables and β represents the regression coefficient.

$$ y = \beta_{0} + \beta_{1} .v_{1} + \beta_{2} .v_{2} + \beta_{3} .v_{3} $$
(5)

The regression equations show the relationship between the input parameters and the outputs. Using data obtained experimentally under the machining conditions given in table 5, the regression equations of the system for Ra, MRR and TWR were generated as Eq. (6), (7) and (8) respectively.

$$ Ra\left( {\upmu{\text{m}}} \right) = 0.203 + 0.95*Tool\, material + 0.2441*discharge\,current + 0.00963*pulse\,duration $$
(6)
$$ MMR\left( {{\text{mm}}^{3} /{ \hbox{min} }} \right) = - 3.898 + 1.378\, Tool\,material + 0.4492*discharge\,current + 0.01577*pulse\,duration $$
(7)
$$ TWR\left( {{\text{mm}}^{3} /{ \hbox{min} }} \right) = - 0.2995 + 0.10556*Tool\, material + 0.042984*discharge\, current + 0.001579*pulse\,duration $$
(8)

In this study, the value of R2 was found to be 97.17% for Ra, 98.89% for MRR and 99.92% for TWR. A strong relationship (evaluated as close to “1”) was noted among the variables. The resulting R2 value indicated that the regression model was successful. Figure 10a–c shows that the correlation coefficient of the plots was greater than the critical value, indicating that the normal distribution of residuals was satisfied.

Figure 10
figure 10

Normal probability plot of the residuals: (a) Ra; (b) MRR; (c) TWR.

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4.5 Determination of optimum Ra, MRR and TWR

In order to test the accuracy of the optimum processing parameters obtained using the Taguchi technique, verification tests needed to be carried out. The optimum levels calculated for Ra, MRR and TWR in the verification experiments are shown in table 8. The optimum test conditions for Ra and TWR were A1B1C1. The optimum processing conditions for MRR were A2B3C3. Equations (9), (10) and (11) were used to calculate the optimum test conditions for Ra, MRR and TWR respectively.

Table 8 Mean S/N ratios.
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$$ R_{{a_{opt} }} = \left( {A_{1} - T_{{R_{a} }} } \right) + \left( {B_{1} - T_{{R_{a} }} } \right) + \left( {C_{1} - T_{{R_{a} }} } \right) + T_{{R_{a} }} $$
(9)
$$ MRR_{opt} = \left( {A_{2} - T_{MRR} } \right) + \left( {B_{3} - T_{MRR} } \right) + \left( {C_{3} - T_{MRR} } \right) + T_{MRR} $$
(10)
$$ TWR_{opt} = \left( {A_{1} - T_{TWR} } \right) + \left( {B_{1} - T_{TWR} } \right) + \left( {C_{1} - T_{TWR} } \right) + T_{TWR} $$
(11)

The values used in these equations (A1B1C1), (A2B3C3) and (A1B1C1) are the mean values of the S/N ratios shown in table 8, while the \( T_{{R_{a} }} \), \( T_{MRR} \) and \( T_{TWR} \) values are the mean values of the experimental test results.

The results of the validation test and the optimum variable levels were evaluated by taking into account the confidence interval \( CI \) value and calculated, respectively, using Eq. (12) and (13) [35].

$$ CI = \sqrt {F_{0.05} \left( {1,v_{e} } \right)V_{e} \left( {\frac{1}{{n_{eff} }} + \frac{1}{r}} \right)} $$
(12)
$$ n_{eff} = \frac{N}{{1 + v_{T} }} $$
(13)

The values F0.05 (1, ve) in the equations took into account the \( F \) (error degrees of freedom) in the table. Here, Ve refers to the error degrees of freedom, neff the number of experimental repetitions, r the number of validation experiments, \( N \) the total number of experiments and vT the sum of the degrees of freedom of the variables. The \( CI \) values calculated at a 95% reliability estimate using Eqs. (12) and (13) were found to be 0.723 for Ra, 0.493 for MRR and 0.021 for TWR are calculated as follows.

$$ \left( {Ra_{opt} - CI} \right) < R_{{a_{exp.} }} < \left( {Ra_{opt} + CI} \right) = \, 2.1 < 3.11 < 3.55 $$
$$ \left( {MRR_{opt} - CI} \right) < MRR_{exp.} < \left( {MRR_{opt} + CI} \right) = \, 12.57 < 13.55 < 13.56 $$
$$ \left( {TW - CI} \right) < TW_{exp.} < \left( {TW_{opt} + CI} \right) = \, 0.119 < 0.157 < 0.162 $$

As the results of Ra, MRR and TWR were measured within the confidence interval, the optimization study performed using the Taguchi method at a significance level of 0.05 was considered to be successful.

4.6 Experimental validation

Verification experiments were performed on the machining parameters to find optimum values for the best results and prediction model. Table 9 shows the results obtained by the Taguchi optimization and the regression equation. The regression model estimation values were closer to the experimental results than the Taguchi estimation results (table 9). Accordingly, these results demonstrate that the optimization study was successful.

Table 9 Experimental and prediction results.
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5 Conclusions

This study investigated the machinability of caldie plastic mold steel using different processing parameters with graphite and copper electrodes in a sinker EDM center. An optimization and estimation model was developed using experimental results. The results were examined experimentally and statistically and the findings are given below.

  • An increase in the discharge current negatively affected Ra and TWR, while the MRR was positively affected.

  • Under equivalent test conditions, lower Ra values were obtained with the graphite electrode compared to the copper electrode.

  • Using the same experimental parameters, higher MRR and TWR values were calculated with the copper electrode compared to the graphite electrode.

  • As a result of the Taguchi optimization, the optimum processing parameter levels for Ra and TWR were determined as A1B1C1, while levels for MRR were found to be A2B3C3.

  • As a result of the ANOVA, the tool material was effective by 84.28%, followed by the discharge current by 8.19%, and the pulse duration by 5.06%.

  • The effect rates of the parameters on MRR were 89.48% for the discharge current, 6.84% for the pulse duration and 3.32% for the tool material.

  • According to ANOVA results, the factors affecting TWR were calculated and ranked as discharge current (90.23%), pulse duration (7.53%) and electrode material (2.16%).

  • The values calculated for the experimental results and the estimated results were close, thus demonstrating the success of the optimization study.