Since it is always advantageous to minimize the surface roughness, the S/N ratio was applied to determine the optimum cutting parameters for a good surface finish quality in WEDM of Ti-6242 titanium alloy. Accordingly, Minitab statistical software is employed in all the analysis plots and designs. The response tables for S/N ratio and means on surface roughness of Ti-6242 titanium alloy are given in Tables 5 and 6, respectively. In Figure 4 and 5 are plotted the main effects for S/N ratio and means on surface roughness (Ra) versus all the input factors, respectively.
The Figures 4-a, b, c, and d demonstrate the influence of the four input factors (U, Ton, S and P) on the mean S/N ratios, respectively. It can be observed that the lines joining data points of different levels have different slopes for servo voltage (U), pulse on time (Ton), feed rate (S) and flushing pressure (p) input factors. Hence, the levels influence differently the surface roughness. Table 5 and figure 4 are obtained according to STB criterion. The level with the greatest S/N ratio is considered the optimal level of the machining parameters. The better combination of input factors can be now selected from graph of Figure 4 (see also Table 5 (smaller is best)). It can be observed that the best combination is formed by the levels (L2, L2, L1, L1) for input factors (U, Ton, S and P), respectively. Therefore, the lowest surface roughness (Ra) is achieved at the values 100V, 0.9 µs, 29mm/min and 60 bar for U, Ton, S and p, respectively in WEDM of Ti-6242 titanium alloy by brass wire and deionized water.
Table 5. Response Table for Signal to Noise Ratios (Smaller is better)
Control factor
|
Mean ƞ by factor level (dB)
|
Delta
|
Rank
|
|
L1
|
L2
|
L3
|
|
|
U(V)
|
-7.987
|
-6.642
|
-11.889
|
5.247
|
1
|
Ton(µs)
|
-9.177
|
-7.586
|
-9.755
|
2.168
|
3
|
S(mm/min)
|
-7.837
|
-8.229
|
-10.451
|
2.614
|
2
|
P(bar)
|
-8.365
|
-9.405
|
-8.748
|
1.039
|
4
|
Response Table for Signal-to-noise
Figure 5-a shows that when the voltage U increases from 80 to 100V, the mean of surface roughness (Ra) decreases slightly, however, the increase in servo voltage from 100 to 120V results in significant rise in the mean of surface roughness. It can be seen also from the graph of Figure 5-c that mean of surface roughness increases at first with the increase in advanced speed S from 29 to 36, thereafter it leaps as S rises from 36 to 43mm/min.
On the other hand, it can be observed from Table 6 that the effect of machining parameters U and S on mean of surface roughness (Ra) in WEDM of Ti-6242 alloy using brass wire and deionized water dominates the effect of Ton and P. Indeed, the higher the slope values in the main effects plot, the higher the values of delta in the response table for means. The rank directly represents the level of input factor effect based on the values of delta. Herein, the effects of various input factors (according to the ranks of response tables given in Tables 5 and 6) in sequence of their effect on Ra are servo voltage U, feed rate S, pulse on time Ton, and flushing pressure p. This means that flushing pressure p affects the Ra at lowest level, however, servo voltage U affects it at highest level.
Table 6: Response Table for Means
Control factor
|
Mean factor level
|
Delta
|
Rank
|
L1
|
L2
|
L3
|
U (V)
|
2,560
|
2,150
|
4,035
|
1,885
|
1
|
Ton (µs)
|
3,170
|
2,427
|
3,148
|
0,743
|
3
|
S (mm/min)
|
2,490
|
2,692
|
3,563
|
1,073
|
2
|
P (bar)
|
2,725
|
3,227
|
2,793
|
0,502
|
4
|
3.2 Analysis of variance (ANOVA)
3.2.1 ANOVA for surface roughness Ra
Hereafter, analysis of variance (ANOVA) is performed to assess the contribution of different input factors (U, Ton, S, and P) on response variable Ra. Table 7 shows the analysis results by ANOVA which approves that machining voltage U, injection pressure p, wire feed rate S and pulse on time Ton are significant machining settings for surface roughness Ra because their P-value is less than 0.05. Larger F-Value signifies that the variation of the machining setting (U, S, Ton and P) results in a significant variation in the machining characteristics (Ra).
According to Ftest analysis, it can be confirmed that the highly significant parameters in deceasing order in terms of the effect on surface roughness (Ra) are servo voltage U, feed rate S, pulse on time Ton and flushing pressure p. However, the percent contributions of the machining parameters on Ra are shown in table 7 and figure 6. Startup voltage U is found to be major factor affecting the Ra (62.94%), the percent contribution of feed rate S, pulse on time Ton, and flushing pressure p on the Ra are 20.84%, 11.46%, and 4.74% respectively.
Table 7: Results of ANOVA for Ra
Process parameter
|
DF
|
Seq SS
|
Adj SS
|
Adj MS
|
F-value
|
P-value
|
Contribution %
|
U
|
2
|
11.7939
|
11.7939
|
5.89695
|
11413.45
|
0.000
|
62.94
|
Ton
|
2
|
2.1476
|
2.1476
|
1.07382
|
2078.35
|
0.000
|
11.46
|
S
|
2
|
3.9050
|
3.9050
|
1.95252
|
3779.06
|
0.000
|
20.84
|
P
|
2
|
0.8882
|
0.8882
|
0.44412
|
859.58
|
0.000
|
4.74
|
Error
|
9
|
0.0046
|
0.0046
|
0.00052
|
|
|
0.02
|
Total
|
17
|
18.7394
|
|
|
|
|
100.00
|
S
|
R-sq
|
R-sq(adj)
|
R-sq(pred)
|
|
|
|
|
0.0227303
|
99.98%
|
99.95%
|
99.90%
|
|
|
|
|
3.2.2 ANOVA for regression model of Ra
In Figure 7 are presented the residual plots for surface roughness (Ra) using 18 experimental runs. We realized 9 experiments, but the roughness is tested twice for each experiment. The graphs of figure 7 demonstrates that residues found are independent while displaying a randomized dispersion. Moreover, Figure 7 shows that the variable follows the normal distribution, and the residuals are distributed roughly in a straight line, displaying a good relationship between the analytically predicted values for all Ra performances and experiment. The results presented in Table 8 are obtained with Minitab Software using ANOVA analysis. The percentage of variation in the response displayed in Table 8 is very high (R-sq(adj) >99%), thereby, the model fits well the data.
Table 8: Result of ANOVA for Regression model of Ra
Source Regression
|
DF
|
Seq SS
|
Adj SS
|
Adj MS
|
F-Value
|
P-Value
|
Contribution %
|
Regression
|
8
|
18.7348
|
18.7348
|
2.34185
|
4532.61
|
0.000
|
99.98%
|
U
|
1
|
6.5269
|
4.5964
|
4.59643
|
8896.33
|
0.000
|
34.83
|
Ton
|
1
|
0.0014
|
2.1475
|
2.14754
|
4156.54
|
0.000
|
0.01
|
S
|
1
|
3.4561
|
0.3190
|
0.31895
|
617.33
|
0.000
|
18.44
|
P
|
1
|
0.0140
|
0.8857
|
0.88566
|
1714.18
|
0.000
|
0.07
|
U2
|
1
|
5.2670
|
5.2670
|
5.26702
|
10194.24
|
0.000
|
28.11
|
T2on
|
1
|
2.1462
|
2.1462
|
2.14623
|
4153.98
|
0.000
|
11.45
|
S2
|
1
|
0.4489
|
0.4489
|
0.44890
|
868.84
|
0.000
|
2.40
|
P2
|
1
|
0.8742
|
0.8742
|
0.87423
|
1692.05
|
0.000
|
4.67
|
Error
|
9
|
0.0046
|
0.0046
|
0.00052
|
|
|
0.02
|
Total
|
17
|
18.7394
|
|
|
|
|
100.00
|
S
|
R-sq
|
R-sq(adj)
|
R-sq(pred)
|
|
|
|
|
0.0227303
|
99.98%
|
99.95%
|
99.90%
|
|
|
|
|
The quadratic model proposed to predict surface roughness (Ra) can be expressed based on response surface analysis (RSA) as a function of U, Ton, S and P in regression Equation (2):

Figure 8 shows a contrast between surface roughness Ra measured experimentally and predicted analytically based on the model equation Eq.2. It can be seen that the forecasted values of Ra are very close to experiment, thereby, highly promising the model described by Equation 2 in predicting the surface roughness (Ra) in WEDM of Ti-6242 using brass wire and deionized water.
Figures 9 a, b, c, d, e and f show the contour plots for surface roughness Ra: S vs p, Ton vs p, Ton vs S, U vs p, U vs S and U vs Ton, respectively. It's clear that the dark blue zone of each graph represents the optimal cutting parameters ensuring a good surface finish quality. Figure 9-a shows that the increase in flushing pressure had not significant effect on surface roughness for minimal feed rate values. However, when flushing pressure converges to 80 bar, the excessive increase in feed rate S results in the highest surface roughness. Once more, if this critical value of flushing pressure is reached for lower values of pulse on time, the surface finish quality decreases significantly (Figure 9-b). Figure 9-c indicates that the excessive increase in servo voltage U results in a bad surface finish quality practically regardless the amount of flushing pressure p (for p less than 96 bar). But, for extreme values of servo voltage U, surface roughness reaches its maximum again when flushing pressure converges to 80 bar.
Hence, it can be concluded that to obtain good surface finish the value 80 bar of flushing pressure should be avoided for highest amounts of servo voltage U and feed rate S along with for lower levels of pulse on time Ton. In fact, this finding could be supported by Figure 4-d which demonstrates that the mean S/N ratio goes down and achieves a minimum at the flushing pressure of 80 bar. However, at the same level of flushing pressure, surface roughness mean was the highest predicted as given in Figure 5-d.
Moreover, it can be observed from Figures 9-d and 9-e that a very poor surface roughness is highly expected with excessive decrease in pulse on time Ton if attended by an important increase in each of servo voltage and feed rate. Finally, Figure 9-f demonstrates that the extreme surface roughness or rougher machined surface are obtained for a greater feed rate S and a higher servo voltage U.