Three-Stage Optimization of Surface Finish in WEDM of D2 Tool Steel via Taguchi Design and ANOVA Analysis

Abstract

Wire electrical discharge machining (WEDM) is a standard micro-manufacturing technology. In WEDM, surface roughness (SR), deviation dimension (DD), and machining time (MT) are critical requirements that impact machining quality and are affected by various input parameters. The workpiece often performs multiple machining steps (roughing, semi-finishing, and finishing) to achieve high accuracy. Each machining step directly affects the accuracy and machining time, and the preceding machining step influences the subsequent machining step parameters. Many input control parameters regulate WEDM’s performance. Thus, optimizing process control parameters at each step is essential to achieve optimal results. This study investigates the influence of input parameters, including pulse on time (Ton), pulse off time (Toff), and servo voltage (SV), on SR, DD, and MT when machining AISI D2 mold steel through rough, semi-finish, and finish cutting. Taguchi and Analysis of Variance (ANOVA) are applied to analyze and optimize this WEDM process. The results display that the optimal surface roughness values for rough, semi-finish, and finish-cut stages are 2.03 µm, 1.77 µm, and 0.57 µm, corresponding to the parameter set of Ton = 6 μs, Toff = 10 μs, and SV = 30 V; Ton = 3 μs, Toff = 15 μs, and SV = 60 V; and Ton = 21 μs, Toff = 45 μs, and SV = 60 V, respectively. In addition, in the finish-cut stage, the parameters for optimal DD of 0.001 mm (0.04%) are Ton = 3 μs, Toff = 15 μs, and SV = 40 V. In contrast, those values for optimal MT of 218 s are Ton = 3 μs, Toff = 30 μs, and SV = 40 V. All optimal input values are confirmed by the manufacturing mold and die parts.

1. Introduction

Using traditional techniques, electrical discharge machining (EDM) is frequently used to process hard materials and complex shapes that are difficult to machine. Wire EDM (WEDM) cutting has become a necessary equipment for tool, mold, manufacturing, automotive, and aerospace industries, etc. The advantage of this WEDM technique is that there is no direct contact between the wire and the workpiece during the machining process. Therefore, the high hardness of the workpiece poses no problem with machinability [1]. WEDM could create small, minimal radius angles with wires electrodes having a radius of 0.025–0.15 mm [2]. In WEDM, surface roughness (SR), deviation dimension (DD), and machining time (MT) are the criteria to evaluate the machining quality [3].

There are many input parameters, such as pulse on time (Ton), pulse off time (Toff), waveform, and servo voltage (SV), that could impact the WEDM quality. Optimizing the process parameters for some popular materials is critical to improve the WEDM technique [4]. Many authors have reported optimization when applying WEDM to Ti6Al4V, aluminum composite, AISI P20 steel, SKD61 steel, EN41B steel, Al₂O₃–TiC composite, and Al 2219 alloy [5,6,7,8,9,10,11]. Rana et al. [12], for instance, reported the optimization of the cutting speed of the WEDM process for Al 2219 alloy by controlling Ton, Toff, and SV. They applied Box-Behnken design (BBD) experimentation combined with the Response Surface Methodology (RSM) technique. It was discovered that cutting speed varies directly with pulse on time and spark gap voltage but inversely with pulse off time. Wang et al. [13] indicated that the discharge current wave forms such as rectangular, triangular, and trapezoidal can impact the machining quality. The triangular waveform has the highest material removal rate (MRR), followed by the trapezoidal one. The result showed that the SR and residual stress of the triangular wave form are also higher than those of the other forms. Zhou et al. [14] increased EDM efficiency by applying a gap servo voltage during machining. By adaptively controlling the gap servo voltage to change the gap distance, arcing ratios were compelled to adhere closely to an arcing ratio expectation with little deviation. Thus, it is possible to achieve both stabilized and efficient machining simultaneously. Comparable tests showed that EDM performance significantly increased, with the machined depth being almost three times better than traditional EDM.

AISI D2 material is utilized in various practical applications, including producing punching tools, mandrels, mechanical press forging dies, plastic molds, die casting dies, aircraft landing gear, helicopter rotor blades, and shafts [15]. Many studies have investigated optimizing input parameters when machining D2 material, such as V. Singh et al. [15] optimized five numbers of machining parameters (pulse on time, pulse off time, peak current, servo voltage, and wire feed) of WEDM of AISI D2 steel (workpiece) with five numbers of performance parameters (gap current, cutting rate, gap voltage, MRR, and SR) and compare the results through Taguchi, RSM, and ANOVA optimization techniques. S. Sharma et al. [1] investigated various input process parameters (Ton, Toff, Ip, Tw) on the response characteristics (MRR, gap voltage, MT) by using a Taguchi L9 orthogonal array. Signal-to-noise ratio and ANOVA were employed in the study of response parameters. S. Kumar Chaubey et al. [16] observed the effect of peak current (IP), pulse on time (Ton), wire tension (WT), and wire feed rate (WF) on the material removal rate (MRR) and the surface roughness (SR). A. Kumar et al. [17] used Taguchi L16 array experimental design for four process input control parameters, wire speed, flushing pressure, gap voltage, and current, which are investigated for MRR and surface roughness. ANOVA and Signal-to-Noise based analysis show that MRR is influenced by these input parameters in the order of current, followed by gap voltage, wire speed, and flushing pressure. S. A. Afridi et al. [18] employed the Taguchi approach to experimental design to conduct cutting experiments at varying levels of pulse on time, pulse on time, servo voltage, and wire tension (L16). Experimental results were optimized using ANOVA and Grey Relational Analysis to refine the process inputs and achieve performance measures that minimize surface roughness, power consumption, and kerf width while maximizing material removal rate.

Besides the processing parameter optimization, many investigations report the surface integrity improvement [19,20,21], the effects of wave discharge current [13,19], and analysis of inaccuracies in cutting angles [17]. There are many optimization methods used, such as the Analytic Hierarchy Process, the PROMETHEE Method [22], TOPSIS, the Analytical Hierarchy Process (AHP) [23,24], deep learning neural networks, and supervised machine learning [3,25]. However, the study [26] demonstrated the advantages of using the Taguchi method, such as the simplicity of use and the ability to reduce variations when using an outer array. The Taguchi approach is less quick and efficient than Response Surface Methodology [27]. One advantage of the Taguchi method is that it enables researchers and engineers to identify which factors most significantly affect the response variable, even with limited statistical knowledge and resources [28]. To optimize the processing parameter, Taguchi method and Analysis of Variance (ANOVA) [29,30,31,32], Japanese statistician Genichi Taguchi [33] developed the Taguchi method to address the multi-factor modeling issue. By recognizing and lessening the impact of disturbances, the Taguchi method’s basic idea is to ascertain the inputs required to attain maximum efficiency [34]. An input variable known as “Credit” is a helpful signal that influences the outcome in two ways: it moves the outcome closer to the target. When using statistical methods, one way to verify calculation results is to apply the variance analysis, or ANOVA method. This approach is frequently employed in numerous domains [34]. ANOVA examines whether variations exist between various experiments. Notable values from an ANOVA include the p-value, sum of squared deviations (SS), and degrees of freedom (D.O.F.), where P stands for the testing process’s reliability. The baseline and S/N data were subjected to ANOVA to identify significant and non-significant variables and to determine how they affected the response characteristics [35].

After a comprehensive study of the existing literature, several gaps have been noted in optimizing WEDM process parameters. The studies above primarily focus on determining the optimal input parameters to achieve accuracy for different materials within a single machining stage. They have not comprehensively evaluated the machining process to achieve accuracy and minimize machining time. Meanwhile, modern machine parts have increasingly high accuracy requirements. To meet these demands, EDM-machined parts are often processed in multiple steps (roughing, semi-finishing, and finishing), where dimensional deviation and surface roughness are crucial parameters affecting machining accuracy. Additionally, machining time is a key factor in determining accuracy and production efficiency. The machining conditions of a previous step can influence the results of a subsequent machining step. However, despite numerous studies optimizing machining parameters for D2 steel using WEDM, these studies have only focused on one stage, with few studies investigating the influence of technological parameters on the overall machining process concerning accuracy and machining time. To analyze the ambiguous problem, the Taguchi method is used in this study to optimize the WEDM processing input parameters, such as Ton, Toff, and SV, for the individual output responses, such as DD, SR, and MT, for D2 material. The study results could provide novel insight into the WEDM technique and the product quality.

2. Materials and Methods

2.1. Workpiece and Wire Electrode

The AISI D2 steel is used as a workpiece material for the experiment. AISI D2 is a high-carbon, high-chromium tool steel alloyed with molybdenum and vanadium (with chemical composition and material properties shown in

Table 1. Chemical composition of D2 (%).

Element	C	Mn	Si	P	S	Cr	Mo	V
Content (%)	1.4–1.6	0.6	0.4	0.03	0.03	11–13	0.8–1.2	0.2–0.5

and

Table 2. Mechanical, thermal, and processing properties of AISI D2 steel.

Properties	Values
Rockwell Hardness	58–62 HRC
Strength	600–700 MPa
Yield Strength	400 MPa
Elastic Modulus	190–210 GPa
Density	7700 kg/${\mathrm{m}}^3$
Electrical Resistivity	54.8 μOhm-cm at 21 °C
Elongation at Break	4–10%
Poisson Ratio	0.27–0.30
Melting Point	1510 °C

) [10,25]. It has varied practical applications such as manufacturing plastic molds, tools, metal dies, etc. It was bought by Nguyen Phuong Steel Company (Binh Duong, Vietnam) with dimensions 78 mm × 180 mm × 12 mm, as shown in Figure 1a. After drilling, the workpiece is quenched to obtain 60–62 HRC (Figure 1b). Subsequently, every sample is cut out and assigned a specific number (Figure 1c). The workpiece is fixed in the fixture during manufacturing, as shown in Figure 2. An electrode brass wire with a diameter of 0.25 mm was purchased from Viet Phat Company (Dong Nai, Vietnam) with the parameters.

2.2. Machine

Wire EDM machine is used Accutex GE 43S (Taichung, Taiwan) with the following parameters: AC380V, 50 Hz, 400 × 300 × 215 table dimension, ion resin with 80–100 KΩ in ion level, pure water with 2 kg/cm² in pressure. The machine’s components are shown in Figure 2.

2.3. Input Parameters

The experiment process is shown in Figure 3. Each sample was cut into three positions. Each position was repeated three times as follows: the rough-cut stage was optimized to obtain the input parameter for roughness, the semi-finish-cut stage was optimized to obtain the input parameter for semi-roughness cut using the rough-cut stage’s optimization level, and the finish-cut stage was optimized to obtain input parameter using the parameters from both the first and semi-finish-cut stages. Three factors are observed: pulse on time (Ton), pulse off time (Toff), and servo voltage (SV). Data were collected and analyzed by using Minitab 19. In the first study, the workpiece was cut with the roughness parameter (rough-cut stage) using a square hole with a dimension of 8 mm. Then, the optimization value of the rough-cut stage was used for the second research. In the second study, this workpiece was cut twice, during the semi-finish-cut stage, using two rounds of square holes of 10 mm in size. The optimization value of the rough-cut stage was used in the first round, and the semi-roughness parameter (semi-finish-cut stage) was used in the second round. After that, the optimization value of the rough-cut and semi-finish-cut stages was used for the finish-cut stage. In the third study, this workpiece was cut three times, the finish-cut stage using three rounds of square holes with a size of 12 mm. In the first and second rounds, the optimization input parameters of the rough-cut stage and semi-finish-cut stage were used to cut for the first and second rounds, and the finish-cut stage was used as an input parameter.

Table 3. Input parameter for the rough-cut, semi-finish-cut, and finish-cut stages.

Parameter	Rough-Cut Stage	Semi-Finish-Cut Stage	Finish-Cut Stage
NO	1	2	3
IP	10	9	7
TON	variable	variable	variable
TOFF	variable	variable	variable
SV	variable	variable	variable
OV	15	16	20
AON	08	03	01
AOFF	12	07	10
WT	12	13	14
WF	6	8	9
WA	07	01	01
FR%	100	100	100
F	11.4	16	30
FT	M90	M90	M90
SG	6	25	16
H1	0.158	-	-

displays the input parameters. The parameters in the machine’s catalog are used to choose additional secondary settings. To guarantee that every experiment has the same conditions, these parameters will not change during the experiment.

2.4. Experiment Process

Table 4. Factor and experimental level for the first, second, and finish-cut stages.

No.	Factors	Unit	Rough-Cut Stage			Semi-Finish-Cut Stage			Finish-Cut Stage
			Experimental Level			Experimental Level			Experimental Level
			1	2	3	1	2	3	1	2	3
1	Ton	μs	6	10	14	3	10	17	3	12	21
2	Toff	μs	10	14	18	5	10	15	15	30	45
3	SV	V	30	40	50	40	50	60	40	50	60

shows the factors and experimental levels for the first, second, and finish-cut stages. There were three factors: pulse on time (Ton), pulse off time (Toff), and servo voltage (SV), and each one had three levels. Using the array selector, the appropriate orthogonal array was L9 in Taguchi for each stage.

Each measurement was repeated three times. The roughness surface is measured by Mitutoyo SJ-201 (Kawasaki, Japan) as shown in Figure 4. The dimension length is measured by Mitutoyo Dial Bore Gauge CG-S10/2109SB-10 with 0.001 mm (Kawasaki, Japan). The deviation dimension was calculated in Equation (1):

Deviation length = (measurement length − standard length) × 100/2

(1)

The problem form specifies three ways to compute the S/N ratio:

+The Larger the better:

$${\displaystyle \frac{S}{N}}\left(\mathrm{L}\mathrm{B}\right)=-10{\mathrm{l}\mathrm{o}\mathrm{g}}_{10}\left({\displaystyle \frac{1}{\mathrm{n}}}\sum _{\mathrm{u}=1}^{\mathrm{n}}{\displaystyle \frac{1}{{\mathrm{y}}_{\mathrm{u}}^2}}\right)$$

(2)

+Smaller the better:

$${\displaystyle \frac{S}{N}}\left(\mathrm{S}\mathrm{B}\right)=-10{\mathrm{l}\mathrm{o}\mathrm{g}}_{10}\left({\displaystyle \frac{1}{\mathrm{n}}}\sum _{\mathrm{u}=1}^{\mathrm{n}}{\mathrm{y}}_{\mathrm{u}}^2\right)$$

(3)

+Nominal the best:

$${\displaystyle \frac{S}{N}}\left(\mathrm{S}\mathrm{B}\right)=10{\mathrm{l}\mathrm{o}\mathrm{g}}_{10}\left({\displaystyle \frac{{\overline{y_u}}^2}{{\mathrm{s}}_{\mathrm{u}}^2}}\right)$$

(4)

$$\overline{y}={\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{u}=1}^{\mathrm{n}}{\mathrm{y}}_{\mathrm{u}}^2$$

(5)

$$s^2={\displaystyle \frac{1}{\mathrm{n}-1}}{\sum }_{\mathrm{u}=1}^{\mathrm{n}}{{(y}_u-\overline{y })}^2$$

(6)

where y_u is the value of the uth measurement, s is the standard deviation, and n is the number of experiments in the orthogonal array. The optimization objective for all kinds of problems is always to maximize the S/N ratio.

3. Results and Discussion

3.1. Determination of Optimal WEDM Parameters for SR in the Rough-Cut Stage

Based on the experiment results, the Taguchi method is calculated via Minitab software version 20.1.

Table 5. Level factor and S/N scale in the rough-cut stage.

Number of Experiments	Level in the Rough-Cut Stage
	Ton	Toff	SV	SR	S/N Scale
1	6	10	30	2.03 ± 0.048	−6.14319
2	6	14	40	2.25 ± 0.031	−7.03094
3	6	18	50	2.38 ± 0.016	−7.52575
4	10	10	40	2.52 ± 0.01	−8.02812
5	10	14	50	2.42 ± 0.025	−7.69450
6	10	18	30	2.38 ± 0.012	−7.53776
7	14	10	50	2.59 ± 0.014	−8.27170
8	14	14	30	2.81 ± 0.034	−8.96405
9	14	18	40	2.58 ± 0.03	−8.23259

,

Table 6. Signal-to-Noise ratio for surface roughness in the rough-cut stage.

Level	Ton	Toff	SV
1	−6.900	−7.481	−7.548
2	−7.753	−7.896	−7.764
3	−8.489	−7.765	−7.831
Delta	1.589	0.415	0.282
Rank	1	2	3

and Table S1 and Figure 5 show the level factor, Signal-to-Noise (S/N) ratio for surface roughness, and S/N scale and influence of WEDM process parameters on the surface in the rough-cut stage. The results indicate that Ton was the most influential factor to the SR of D2 material in WEDM, followed by Toff and SV. When Ton increased, surface roughness decreased. It could be explained that the material removal rate (MRR) increased when Ton increased in Equation (7):

Wt = E × I × t

(7)

where Wt, E, I, and t denote the energy of material removal, the voltage, current, and the time, respectively.

In addition, the smaller the value of Toff and SV, the better the surface quality. Because the value of SV was significant, the wire movement speed would also be slower, combined with the current small Toff value, which will cause many shots to concentrate on a small length, causing “craters”, and “fire” gets bigger and deeper, causing the surface quality to deteriorate. The results were consistent with the findings in the recent reports by Mahapatra and Patnaik’s study [36]. It can be seen that Ton and Toff have significant similarities in both experiments. SV had a small influence on this experiment.

ANOVA can figure out the contribution of each factor during the WEDM process.

Table 7. ANOVA for surface roughness in rough-cut stage (DoF: Degrees of freedom, SS: Sum of squares, MS: Mean square (SS/DoF), F value: Fisher’s value (SS/SSE)).

Factors	DoF	SS	MS	F-Value	p-Value	Contribution (%)
Pulse On Time (μs)	2	1.75578	0.877891	83.16	0.000	73.11
Pulse Off Time (μs)	2	0.11574	0.057869	5.48	0.007	4.82
Servo Voltage (V)	2	0.03403	0.017013	1.61	0.210	1.42
Error	47	0.49615	0.010556	-	-	20.66
Total	53	2.40170	-	-	-	100

shows the ANOVA for surface roughness in the rough-cut stage. The findings show that the p-values for the pulse on and off times are less than 0.05. This indicates that at the 95% confidence level, each parameter has a statistically significant impact on rough machined surface roughness. However, this parameter has little effect on surface roughness during rough machining because the servo voltage p-value is greater than 0.05. When comparing the F-value of the pulse on time and pulse off time, it is shown that both are greater than F0.05, 2.53 = 3.15, indicating that the rough machined surface roughness is affected by these parameters. Servo voltage has a lower significance than the other two parameters because its F-value is less than 3.15. The most significant factor influencing surface roughness during rough-cut staging is pulse on time (73.11%), followed by pulse off time (4.82%) and servo Voltage (1.42%). Besides the impact ranking of each factor, the impact contribution of all aspects can be calculated via a regression equation:

Regression equation is SR = 1.652 + 0.05521 × Ton + 0.00833 × Toff + 0.00297 × SV

(8)

Based on the result in Figure 5 and Table S4, in the rough-cut stage, Ton = 6, Toff = 10, and SV = 30 are a set of parameters for optimization of SR with SR = 2.03 µm (coincides with experiment 1) and MT = 649 s.

Research results for AISI D3 material by A. Ramaswamy et al. [37] also indicate that surface roughness increased with an increase in current. The SR ranges from 2.51 to 2.18 µm [38]. For AISI H13 material, research results by M. Deshwal et al. [39] show that the surface roughness amplifies with a rise in Ton and diminishes with an increase in voltage and Toff. The optimum value of surface coarseness is 1.420 μm [40].

3.2. Determination of Optimal WEDM Parameters for SR in the Semi-Finish-Cut Stage

In the semi-finish-cut stage, the SR is better than in the rough-cut stage. Figure 6 and

Table 8. Level factor and S/N scale in the semi-finish-cut stage.

Sample	Level in the Semi-Finished-Cut Stage
	Ton	Toff	SV	SR	S/N Scale
1	3	5	40	2.23 ± 0.07	−6.9547
2	3	10	50	2.08 ± 0.04	−6.3475
3	3	15	60	1.77 ± 0.06	−4.9628
4	10	5	50	3.07 ± 0.06	−9.7338
5	10	10	60	3.16 ± 0.05	−9.9941
6	10	15	40	3.13 ± 0.05	−9.9253
7	17	5	60	3.83 ± 0.05	−11.6643
8	17	10	40	4.15 ± 0.05	−12.3505
9	17	15	50	4.07 ± 0.04	−12.1884

and Table S2 show the influence of WEDM process parameters on surface roughness and the level factor and S/N scale in the semi-finish-cut stage. Remarkably, because of the increase in material removal energy as Ton increases, surface roughness decreases with increasing Ton value. The expression for this increase in ablation energy is given by Formula (7). T and Wt have a proportionate relationship in the formula, and Ton is equivalent to the T value. Therefore, the discharge time and material removal energy decrease with a smaller Ton value. The regression equation is calculated as follows:

SR = 2.304 + 0.14214 × Ton − 0.00500 × Toff − 0.01244 × SV

(9)

Equation (9) indicates that the surface quality is directly correlated with the Ton value, which means that a higher Ton value corresponds to a lower surface quality. This is demonstrated by the regression function above. Surface quality is inversely correlated with Toff and SV values. Therefore, a higher value for Toff and SV indicates a higher quality surface. Additionally, this outcome is comparable to the study [41].

Evaluating the impact ranking and the contribution of the input factors can help improve the machining quality.

Table 9. Signal-to-Noise ratio for surface roughness in semi-finish-cut stage.

Level	Ton	Toff	SV
1	−6.088	−9.451	−9.743
2	−9.884	−9.564	−9.423
3	−12.068	−9.025	−8.874
Delta	5.979	0.539	0.870
Rank	1	3	2

and

Table 10. ANOVA for surface roughness in the semi-finish-cut stage.

Factors	DoF	SS	MS	F-Value	p-Value	Contribution (%)
Pulse On Time (μs)	2	35.7636	17.8818	2637.58	0.000	97.13
Pulse Off Time (μs)	2	0.1706	0.0853	12.59	0.000	0.46
Servo Voltage (V)	2	0.5657	0.2828	41.72	0.000	1.54
Error	47	0.3186	0.0068	-	-	0.87
Total	53	36.8186	-	-	-	100

present the Signal-to-Noise ratio for surface roughness in the semi-finish-cut stage and ANOVA for surface roughness in the semi-finish-cut stage. Notably, similar to the result in Table 8, the impact ranking of these factors is reduced in the following order: Ton, Toff, and SV. Ton is also the most critical factor of the SR in a semi-finished-cut stage. Moreover, in semi-finished cutting, the most significant factors affecting surface roughness are pulse on time (97.13%), servo voltage (1.54%), and pulse off time (0.46%).

Based on the result in Figure 6 and Table S5, in the semi-finish-cut stage, Ton = 3, Toff = 15, and SV = 60 are a set of parameters for optimization of SR with SR = 1.77 µm (coincides with experiment 3) and MT = 383 s.

3.3. Determination of Optimal WEDM Parameters for SR, DD, and MT in the Finish-Cut Stage

a

Minimize surface roughness in the finish-cut stage

In the semi-finish-cut stage, the MRR is lower, but the SR is better than in the rough-cut stage. Figure 7 and

Table 11. Level factor and S/N scale in the finish-cut stage.

Sample	Level in the Finish-Cut Stage
	Ton	Toff	SV	Value of Experiment			S/N Scale
				SR (µm)	DD (%)	MT (s)	SR	DD	MT
1	3	15	40	0.67	0.04	254	3.49773	27.0504	−48.0854
2	3	30	50	0.64	0.237	343	3.87357	12.5031	−50.6975
3	3	45	60	0.67	0.430	625	4.10311	7.3244	−55.9130
4	12	15	50	0.64	0.283	395	3.92045	4.9214	−51.9394
5	12	30	60	0.61	0.348	631	4.36420	9.1527	−56.0053
6	12	45	40	0.63	0.295	264	3.98973	10.6027	−48.4502
7	21	15	60	0.58	0.358	686	4.70591	8.9124	−56.7265
8	21	30	40	0.65	0.158	235	3.71935	15.9655	−48.4346
9	21	45	50	0.63	0.170	356	4.19721	15.3636	−51.2599

and Table S3 show the influence of WEDM process parameters on surface roughness, as well as the level factor and S/N scale in the finish-cut stage. The difference from semi-finished is that in the rough-cut stage, the surface roughness increases with decreasing input value. This could be the case because there is not much difference in the roughness values obtained from this fine-cutting process, meaning that the response value does not accurately reflect the results. Since the experiment has just completed semi-finishing cutting using the ideal roughness parameters, the surface quality is already good. The higher the values of Toff and SV, the better the surface roughness. This result is also similar to the study by V. Singh et al. [15], where the SR decreases with the increase in pulse off time and servo voltage. With increasing SV values, the machine’s controller keeps a larger distance between the workpiece and tool, providing more space for the removal and flushing of particles, thereby maintaining surface quality. Additionally, the increased gap reduces the intensity of the sparking action, thereby enhancing surface quality [18]. Consequently, a considerable SV value indicates a slower wire movement speed, which, when paired with a large spacing between discharges, helps to prevent the “craters” from becoming too close together.

Table 12. Signal-to-Noise ratio for surface roughness in the finish-cut stage.

Level	Ton	Toff	SV
1	3.825	4.041	3.736
2	4.091	3.986	3.997
3	4.207	4.097	4.391
Delta	0.383	0.111	0.655
Rank	2	3	1

and

Table 13. ANOVA for surface roughness in the finish-cut stage.

Factors	DoF	SS	MS	F-Value	p-Value	Contribution (%)
Pulse On Time (μs)	2	0.007078	0.003539	15.75	0.000	18.36
Pulse Off Time (μs)	2	0.000633	0.000317	1.41	0.254	1.64
Servo Voltage (V)	2	0.020278	0.010139	45.12	0.000	52.60
Error	47	0.010561	0.000225	-	-	27.40
Total	53	0.038550	-	-	-	100

show the Signal-to-Noise ratio for surface roughness in the finish-cut stage and ANOVA for surface roughness in the finish-cut stage. Surprisingly, the finish-cut stage has a slight difference between the affected Ton to the surface roughness of the rough-cut stage and the semi-finish-cut stage. The SV parameter has changed the influence ranking to become the factor that matters most. This change indicates that Ton and Toff have a much smaller influence on surface roughness when finishing cutting because the machining residual is too small. In addition, servo voltage (52.6%) is the factor that affects surface roughness the most after finishing cutting; pulse on time (18.36%) is the second-most important factor, and pulse off time (18.36%) is the third factor (1.64%) that affects surface roughness. Besides the contribution of each factor, the total impact of all factors can be calculated via a regression equation:

Regression Equation: SR = 0.7695 − 0.001512 Ton − 0.000167 Toff − 0.002361 SV

(10)

Based on the result in Figure 7 and Table S6, in the finish-cut stage, Ton = 21, Toff = 45, and SV = 60 are a set of parameters for optimization of SR with confirmed SR = 0.57 µm.

b

Minimize dimension deviation in the finish-cut stage

In finishing cutting, the dimensional error increases with increasing Toff value. An excessively long interval between shots will result in uneven and sporadic bombardment of the surface, along with increased machining residue. Size tends to be smaller than nominal size because optimal surface quality parameters were used during the semi-finished cutting process. The deviation dimension after finishing cutting increases with increasing SV value. This is because a large SV value will result in a slower wire speed and more bombardments on a smaller area of a larger size. It grows bigger than the stated size this time as well, a shown in Figure 8. A comparison reveals that SV parameters in this experiment and other fine-cutting experiments significantly impact this step.

Table 14. Signal-to-Noise ratio for dimension deviation in the finish-cut stage.

Level	Ton	Toff	SV
1	15.626	13.628	17.873
2	8.226	12.540	10.929
3	13.414	11.097	8.463
Delta	7.400	2.531	9.410
Rank	2	3	1

illustrates how much the cutting parameters affect the size when machining. SV plays the most important role, followed by Ton. The Toff factor has the lowest impact rank compared to other factors. Additionally, servo voltage (36.59%) is the factor that affects size error the most after finishing cutting; pulse on time (28.77%) is the second most important factor, and pulse off time (4.2%) is the third most important factor, as shown in

Table 15. ANOVA for dimension deviation in the finish-cut stage.

Factors	DoF	SS	MS	F-Value	p-Value	Contribution (%)
Pulse On Time (μs)	2	0.29312	0.146562	17.96	0.000	28.77
Pulse Off Time (μs)	2	0.04280	0.021400	2.62	0.086	4.2
Servo Voltage (V)	2	0.37275	0.186377	22.84	0.000	36.59
Error	38	0.31002	0.008158	-	-	30.43
Total	44	1.01870	-	-	-	100

. In addition, the impact contribution of all factors can be calculated via this regression equation:

Dim = −0.345 − 0.00039 Ton + 0.00238 Toff + 0.01072 SV

(11)

Based on the result in Figure 8 and Table S7, in the finish-cut stage, Ton = 3, Toff = 15, and SV = 40 are a set of parameters for optimization of DD (coincides with experiment 1) with DD = 14.001mm (0.04%).

c

Minimize machining time in the finish-cut stage

In the finish-cut stage, the machining time is usually higher for a similar cutting volume due to the lower cutting velocity.

Table 16. Signal-to-Noise ratio for machining time in the finish-cut stage.

Level	Ton	Toff	SV
1	−51.57	−52.25	−47.99
2	−52.13	−51.38	−50.97
3	−51.47	−51.54	−56.21
Delta	0.66	0.87	8.22
Rank	3	2	1

and Figure 9 show the influence of WEDM process parameters on machining time and Signal-to-Noise ratio for machining time in the finish-cut stage. The results reveal that the Ton value increases, and the machining time increases. Because the machining residual is small, the removal energy does not need to be large. Machining time will increase if the Toff value is small or large. The machining time increases with increasing SV value because a higher SV value causes the wire to move more slowly, which slows down the machining speed. This outcome corresponds to the research in [16].

Table 17. ANOVA for machining time in the finish-cut stage.

Factors	DoF	SS	MS	F-Value	p-Value	Contribution (%)
Pulse On Time (μs)	2	2525	1263	2.21	0.136	0.32
Pulse Off Time (μs)	2	10,390	5195	9.08	0.002	1.32
Servo Voltage (V)	2	761,837	380,918	665.91	0.000	96.90
Error	20	11,441	572	-	-	1.46
Total	26	786,193	-	-	-	100

shows that the impact ranking on the machining time in the finish-cut stage follows the order SV, Toff, and Ton. SV appears to be the most impactful factor during this stage. Table 17 shows that servo voltage is the factor that affects machining time the most when finishing cutting, accounting for 96.90% of the total. Pulse on time comes in second, with 1.32% of the total influence, and third after the time of machining (0.32%). The regression equation of the MT value is as follows:

MT = −537.3 + 0.42 Ton − 1.378 Toff + 19.82 SV

(12)

Based on the result in Figure 9 and Table S8, in the finish-cut stage, Ton = 3, Toff = 30, and SV = 40 are a set of parameters for optimization of MT with confirmed MT = 218 s.

An atomic force microscopy (AFM) study of the surface nanomorphology of the EDM machined surface was conducted to assess the surface measurement results. The AFM technique can effectively assess the surface roughness created on the EDM surface and make a three-dimensional image at the nanoscale. AFM observes the surface morphology of some samples to clarify the study results, as shown in Figure 10. In the AFM image, the pits show a dark contrast, and the variation in contrast (dark and bright regions) indicates roughness [42,43]. The results showed that the surface roughness of sample 1 is 0.55 µm, which is consistent with the other measurements.

Overall, the optimal input parameter set with confirmation test and value of responses are represented as follows in

Table 18. Optimal input parameters and value responses in the experiment.

		Pulse On Time	Pulse Off Time	Servo Voltage	Predict Value	Confirmation Test	Benchmark with
Surface roughness (SR)	Rough-cut stage	6 μs	10 μs	30 V	2.15 µm	2.03 µm	2.66 μm [22] 2.8 µm [20] 3.034–6.677 µm [1] 1.369–3.206 µm [18]
	Semi-finish-cut stage	3 μs	15 μs	60 V	1.91 µm	1.77 µm
	Finish-cut stage	21 μs	45 μs	60 V	0.59 µm	0.57 µm
Deviation dimension in the finish-cut stage (DD)		3 μs	15 μs	40 V	0.197%	0.04%
Machining time in the finish-cut stage (MT)		3 μs	30 μs	40 V	215.42 s	218 s

. Figure 11 shows the confirmation test of the optimal input parameter in manufacturing. The result indicates the efficiency of the Taguchi and ANOVA methods.

4. Conclusions

Based on the result, the conclusion can be written as follows:

-

These results would improve the machine’s surface properties and productivity while lowering machining costs, errors, and operation time.

-

The quality of the machine part from D2 tool steel in the WEDM belongs to the input parameter. In each cutting step, the degree of influence of the factors will be different.

-

In the rough-cut stage

The results indicate that Ton was the most influential factor to the SR, then Toff and SV. The most significant factor influencing surface roughness during rough-cut staging is pulse on time (73.11%), followed by pulse off time (4.82%) and servo voltage (1.42%). The parameter sets of Ton = 6 μs, Toff = 10 μs, and SV = 30 V are the optimal values with SR = 2.03 µm.

-

In the semi-finished-cut stage

A higher Ton value corresponds to a lower surface quality. Surface quality is inversely correlated with Toff and SV values (a higher value for Toff and SV indicates a higher quality surface). Pulse on time (97.13%), servo voltage (1.54%), and pulse off time (0.46%) affect surface roughness. Ton = 3 μs, Toff = 15 μs, and SV = 60 V are the set of optimal parameters with SR = 1.77 µm.

-

In the finish-cut stage

Minimize surface roughness in the finish-cut stage

The higher the values of Toff and SV, the better the surface roughness. Servo voltage (52.6%) is the factor that affects surface roughness the most after finishing cutting; pulse on time (18.36%) is the second-most important factor, and pulse off time (18.36%) is the third factor (1.64%) that affects surface roughness. SR = 0.57 µm with Ton = 21 μs, Toff = 45 μs, and SV = 60 V.

Minimize dimension deviation in the finish-cut stage

Servo voltage (61.95%) is the factor that affects size error the most after finishing cutting; pulse on time (10.01%) is the second most important factor, and pulse off time (6.87%). The parameters for optimal DD of 0.04% are Ton = 3 μs, Toff = 15 μs, and SV = 40 V.

Minimize machining time tasks in the finish-cut stage

Servo voltage is the factor that affects machining time the most when finishing cutting, accounting for 96.90% of the total. Pulse on time comes in second, with 1.32% of the total influence, and third after the time of machining (0.32%). The optimal value of MT is 218 s, with Ton = 3 μs, Toff = 30 μs, and SV = 40 V.

The results of the optimized parameter set have been verified through experimental cutting and AFM inspection. This research provides a basis for optimizing other factors for each machining step to improve accuracy and reduce machining time.

5. Future Recommendations

The research not only evaluated the effects and found optimal roughness parameters for different machining steps but also successfully identified optimal parameters for dimensional deviation and machining time during the finishing of D2 material using WEDM. Future studies should further investigate the relationship between machining accuracy and machining time to ensure both high precision and efficient production. There is also potential to expand this work to other materials or to explore hybrid optimization approaches.