As shown in Section 3, two-electrode EDM performed better in terms of edge wear than one-electrode EDM. However, for the two-electrode cases, the MDS approach was no better the SDS approach in terms of edge wear, surface roughness, or machining time. We used a Box-Behnken design (one of the most popular second-order RSM) to optimize the roughing and finishing currents of the MDS and the roughing gap.
4.1 Experimental plan
The process parameters and their respective levels are shown in Table 2. We considered three parameters: the discharge current differences in the roughing and finishing stages, and the roughing gap. In the MDS approach, a high discharge energy during the first step saves machining time, and a low discharge energy during the third step ensures a good surface finish. Therefore, in the roughing stage, the discharge current is increased in the first step by an amount equivalent the roughing current difference (RCD), fixed to 14 A during the second step and decreased during the third step by an amount equivalent to the RCD. The RCD was set to 0, 2, or 4 A. The minimum RCD was 0 A (equivalent to that of the SCD approach), the intermediate RCD was 2 A (equivalent to the MDS approach before RSM optimization) and the maximum RCD was double the intermediate value. During finishing, the discharge current was increased, fixed, and then decreased in the first, second, and third steps, respectively. The finishing current difference (FCD) was set to 0, 1, or 2 A, using a method similar to that applied to derive the RCDs. The roughing gap distance W is the clearance between the workpiece and electrode. The gap was set to 0.04, 0.07, or 0.10 mm. The intermediate level is the same as that of the SDS and MDS before RSM; i.e., 0.03 mm away from both the minimum and maximum levels.
Table 2
Parameters and their levels for the MDS experiment
Parameters
|
Unit
|
Level 1
|
Level 2
|
Level 3
|
RCD
|
A
|
0 (14→14→14)
|
2 (16→14→12)
|
4 (18→14→10)
|
FCD
|
A
|
0 (5→5→5)
|
1 (6→5→4)
|
2 (7→5→3)
|
Gap
|
mm
|
0.04
|
0.07
|
0.10
|
Table 3 shows the BBD matrix and measurement data, where the edge wear is the wear of the electrode after the finishing stage, and the machining time is the sum of the roughing and finishing times.
Table 3
Box-Behnken design matrix and data for MDS
Std
order
|
Run
order
|
RCD
(A)
|
FCD
(A)
|
Gap
(mm)
|
Roughness
(µm)
|
Wear
(mm)
|
Time
(min)
|
5
|
1
|
0
|
1
|
0.04
|
3.81
|
0.071
|
12.53
|
1
|
2
|
0
|
0
|
0.07
|
4.36
|
0.065
|
11.58
|
12
|
3
|
2
|
2
|
0.1
|
3.50
|
0.061
|
11.15
|
10
|
4
|
2
|
2
|
0.04
|
3.20
|
0.060
|
11.90
|
15
|
5
|
2
|
1
|
0.07
|
3.93
|
0.072
|
13.05
|
3
|
6
|
0
|
2
|
0.07
|
2.97
|
0.067
|
12.33
|
2
|
7
|
4
|
0
|
0.07
|
4.63
|
0.088
|
13.47
|
8
|
8
|
4
|
1
|
0.1
|
3.73
|
0.076
|
12.18
|
6
|
9
|
4
|
1
|
0.04
|
3.68
|
0.14
|
16.02
|
4
|
10
|
4
|
2
|
0.07
|
4.31
|
0.096
|
13.25
|
13
|
11
|
2
|
1
|
0.07
|
4.01
|
0.067
|
13.05
|
14
|
12
|
2
|
1
|
0.07
|
4.11
|
0.070
|
11.77
|
7
|
13
|
0
|
1
|
0.1
|
3.95
|
0.082
|
14.55
|
11
|
14
|
2
|
0
|
0.1
|
7.64
|
0.045
|
9.14
|
9
|
15
|
2
|
2
|
0.04
|
4.60
|
0.063
|
10.81
|
4.2 Analysis of surface roughness
Analysis of variance (ANOVA) was performed to draw a model with significant terms. Using the adjusted R2 as the criterion of model adequacy, the model with the largest adjusted R2 was selected. Equation (3) is the regression equation for the average surface roughness (Ra) with respect to the FCD ΔIf and gap W in the coded units estimated from the experimental data:
Ra = 2.43 – 0.7 ΔIf + 37.7 W – 22.9 ΔIf ∙W (3)
As the roughing stage is followed by the finishing stage, the Ra should be unaffected by the RCD. ANOVA revealed that the R2 of the fitted model was 62.51%, and the adjusted R2 was 52.28. Thus, 62.51% of the surface roughness variation is attributable to linear effects of the FCD, the gap, and their interaction. The smaller R2 value may reflect surface roughness variations among the milled electrodes, and errors when measuring inclined surfaces. Fig. 7 shows the estimated Ra, with respect to FCD ΔIf and gap W when RCD is fixed at 2 A. The FCD had a greater influence on Ra. When the FCD increased, Ra tended to decrease to a minimum. The graph also shows that the gap had less effect on Ra when the FCD increased by up to 2 A.
Figure 8 shows the surface finish improvement of the MDS approach using FCD 2 A compared to the conventional SDS approach using a single discharge current when the average discharge current is set to 5 A. The average surface roughness Ra was improved to 3.2 µm by increasing the discharge current at the first step and decreasing it at the third step, compared with 4.6 µm by the conventional approach.
4.3 Analysis of edge wear
The edge wear EW of the finishing electrode is influenced by three parameters. Equation (4) shows their effects. The coefficient of determination R2 and adjusted R2 were 96.97% and 93.95%, respectively.
EW = 0.05 + 0.0069 ΔIr + 0.0175 ΔIf + 0.175 W + 0.0055ΔIr2 – 0.0129 ΔIf2 – 0.3125 ΔIr∙W
+ 0.1583 ΔIf∙W (4)
Figure 9(a) shows the estimated response surface of edge wear with respect to the RCD and FCD when the gap remains constant at the intermediate value of 0.07 mm. The edge wear tended to be smallest when the RCD was set to 1.5 A and the FCD to either 0 or 2 A. Figure 9(b) shows the estimated response surface in terms of the RCD and gap when the FCD was set to 1 A. The edge wear of the finishing electrode tends to be smallest when the RCD is 1 A and largest when the RCD is 4 A, showing that the roughing parameters are linked to edge wear in the finishing stage. Figure 9(c) shows the estimated response surface of edge wear in view of the FCD and the roughing gap. Edge wear tended to decrease as the gap increased. The FCD exerted a quadratic effect on edge wear.
4.4 Analysis of machining time
Machining time (MT) is influenced by three parameters, as shown in Equation (5), with R2 = 93.85% and an adjusted R2 = 89.23%.
MT = 9.35 + 0.114 ΔIr + 3.579 ΔIf + 28.0 W + 0.462ΔIr2 – 1.628 ΔIf2 – 24.04 ΔIr∙W (5)
Figure 10(a) shows the estimated response surface of the machining time with respect to the RCD and FCD when the gap is fixed at its intermediate value of 0.07 mm. The machining time is shortest when the RCD is 2 A and the FCD is 0 or 2 A. The effects of the RCD and gap are shown in Figure 10(b). When the FCD is set to the intermediate value of 1, the machining time is minimized if the RCD is 2 A and the gap is 1 mm. The estimated response surface of the machining time with respect to the FCD and roughing gap is shown in Figure 10(c). The machining time decreased as the gap increased to 0.1 mm and the FCD was either 0 or 2 A. The response surface of the machining time exhibited a trend similar to that of the edge wear of the finishing electrode, indicating that a long machining time increases edge wear.
4.5 Optimal conditions
The desirability function approach is implemented to optimize the three response variables affected by the three process parameters [36]. The desirability function approach is most often employed to optimize multiple responses simultaneously [35]. This approach searches for parameter settings that jointly optimize multiple responses by satisfying the requirements for each response under consideration. In this approach, the estimated response values of each response are transformed to scale-free desirability between 0 and 1. The individual desirability (d) for each response to be minimized is obtained by specifying the target value and upper bound required for the response. If the response is larger than the upper bound, d is set at 0. If the response is smaller than the upper bound, d increases from 0 to 1 as the response variable comes closer to the target value. If the response is smaller than the target value, d is determined to be 1. A weight factor, which determines the desirability function shape for each response, is then assigned to each response. Weight can be given as a value between 0.1 and 10. When the weight is 1, the desirability function is linear. When the response needs to be smaller than the upper bound, a weight less than 1 is determined. If the response should be close to the target value, weight is set at a value greater than 1. In general, if the weight factor is not mentioned, it is set at 1 [35].
The individual d are combined into an overall desirability D, which is the geometric mean of the individual d. When the response variables vary in terms of importance, D is the weighted geometric mean of the individual d. The relative importance of response variables are reflected by the ‘importance values’. The optimal compromise among multiple responses is achieved by maximizing D [36]. The desirability function approach was employed to simultaneously minimize the average surface roughness Ra, the edge wear of the finishing electrode, and the machining time simultaneously. The target values and upper bounds were 3 and 6 µm for Ra, 0.05 and 0.1 mm for edge wear, and 10 and 15 min for the machining time, respectively. As it is more important that the surface roughness and machining time are lower than their upper bounds than that they reach the importance target values, their weights were set to 0.5. Moreover, edge wear was considered to be twice as important as surface roughness and machining time, and was thus assigned an importance value of 2.
Using the response optimizer in Minitab, the optimal parameter combination was shown to be (RCD, FCD, Gap) = (0.580, 2.0, 0.04) (Fig. 11). These conditions optimize the three responses simultaneously. The estimated Ra was 3.50 µm, the edge wear of the finished electrode was 0.052 mm, and the machining time was 10.78 min. As the RCD is controlled in integral increments, we performed additional experiments at RCDs of 0 A and 1 A.
4.6 Confirmation experiment
The optimal conditions (subsection 4.5) were (RCD, FCD, Gap) = (0.58 A, 2 A, 0.04 mm). As the current can be controlled only in integral units, we tested two conditions [(0 A, 2 A, 0.04 mm) and (1 A, 2 A, 0.04 mm)] three times, and compared the data (Table 4). The three responses were optimized when the RCD was 1 A.
Table 4
Comparing two conditions for optimal parameter settings
No.
|
RCD: 0A
|
RCD: 1A
|
Roughness
(µm)
|
Wear
(mm)
|
Time
(min)
|
Roughness
(µm)
|
Wear
(mm)
|
Time
(min)
|
1
|
3.55
|
0.065
|
11.53
|
3.27
|
0.047
|
12.33
|
2
|
3.50
|
0.069
|
12.23
|
3.24
|
0.057
|
12.25
|
3
|
3.42
|
0.069
|
12.70
|
3.27
|
0.053
|
11.82
|
Avg.
|
3.49
|
0.067
|
12.16
|
3.26
|
0.052
|
12.13
|
SD
|
0.066
|
0.0023
|
0.589
|
0.017
|
0.005
|
0.274
|
Table 5
Comparative experimental conditions and results with two electrodes
EDM approaches
|
RCD
(A)
|
FCD
(A)
|
Gap
(mm)
|
Roughness
(µm)
|
Wear
(mm)
|
Time
(min)
|
SDS
|
0
|
0
|
0.07
|
4.27
|
0.065
|
10.65
|
MDS before RSM
|
2
|
1
|
0.07
|
4.01
|
0.072
|
12.11
|
MDS after RSM
|
1
|
2
|
0.04
|
3.26
|
0.052
|
12.13
|
4.7 MDS optimization results
The comparisons in Section 3 showed that the two-electrode MDS approach was somewhat inferior to the two-electrode SDS approach (Fig. 6). In this section, we used an RSM to optimize the RCD, FCD, and gap in terms of edge wear, surface roughness, and machining time. Fig. 12 shows the average values of the three responses for the two-electrode SDS and two-electrode MDS approaches, before and after RSM.
RSM for the Two-electrode MDS approach contributed to the improvement of edge wear and surface roughness. Through RSM optimization for the MDS approach, the edge wear of the finishing electrode was improved from 0.072 mm to 0.052 mm, and the average surface roughness was reduced from 4.01 to 3.27. The RSM optimized MDS approach has reduced edge wear by 20% and average surface roughness by 24% compared to the SDS approach. However, the machining time of the MDS approach has increased by 15% compared to the SDS approach, where the discharge current is not changed. The machining time of the MDS is longer than that of the SDS because the time saved from the high discharge current in the first step is smaller than the time increased from the low discharge current in the third step. Overall, the Two-electrode MDS approach with RSM shows better performance than the Two-electrode SDS approach.
The RSM of the two-electrode MDS approach improved edge wear and surface roughness. RSM optimization improved the edge wear of the finishing electrode from 0.072 to 0.052 mm, and reduced the Ra from 4.01 to 3.27. The RSM-optimized MDS approach reduced edge wear by 20%, and the Ra by 24%, compared to the SDS approach. However, the machining time of the MDS approach increased by 15% compared to the that of SDS approach (where the discharge current does not change). The MDS machining time is longer than that of SDS because the time saved by using a high discharge current in the first step is less than the extra time required by the low discharge current in the third step. Overall, the two-electrode RSM-optimized MDS approach performed better than the two-electrode SDS approach.