# Optimization of Machining Parameters for Corner Accuracy Improvement for WEDM Processing
## 3 Experiment and Discussion
### Optimization  
After conducting the experiment for different parameters and obtaining the corner error, machining time data, and relationship between each parameter to corner error, these data were analyzed by using the Box-Behnken RSM response surface method for optimization. The process optimization involves estimation of coefficients, prediction of responses, and verifying the developed model. In terms of quality, the value of the corner error and processing time are minimum value. The quadratic equation for predicting the optimum value was obtained according to the Box-Behnken design and input variables. Furthermore, the relationship between the independent variable and the response can be presented as follows. \[ \begin{array}{ll}\text{Error}_{(30)}=&1.043+0.01259\;\text{ON}-0.02993\; \text{OFF}-0.01148\;\text{OV}-0.0555\;\text{SV}+\\ &0.03325\;\text{WT}+0.01393\;\text{WA}-0.000654\;\text{ON}\times\;\text{ON}+0.00 1264\\ &\text{OFF}\times\;\text{OFF}+0.000585\;\text{OV}\times\;\text{OV}+0.000743\; \text{SV}\times\;\text{SV}-0.001704\\ &\text{WT}\times\;\text{WT}\\ &\\ \text{Error}_{(60)}=&1.673-0.00265\;\text{ON}-0.01569\;\text{OFF}-0.01248\; \text{OV}-0.0839\;\text{SV}+\\ &0.01677\;\text{WT}+0.000585\;\text{OFF}\times\;\text{OFF}+0.000236\;\text{ OV}\times\;\text{OV}+0.001110\\ &\text{SV}\times\;\text{SV}-0.000759\;\text{WT}\times\;\text{WT}+0.000477\; \text{ON}\times\;\text{OV}+0.000314\\ &\text{OFF}\times\;\text{OV}\\ &\\ \text{Error}_{(90)}=&0.684+0.001092\;\text{ON}-0.000547\;\text{OFF}-0.00443\; \text{OV}-0.03774\;\text{SV}+\\ &0.00977\;\text{WT}+0.001204\;\text{WA}+0.000242\;\text{OV}\times\;\text{OV}+0.00 0551\;\text{SV}\times\;\text{SV}\\ &-0.000295\;\text{SV}\times\;\text{WT}\\ \text{CutSpeed}=&18474-306.5\;\text{ON}+202.4\;\text{OFF}-79.0\;\text{OV}-672.7 \;\text{SV}-268.5\;\text{WT}-\\ &309.9\;\text{WA}+17.354\;\text{ON}\times\;\text{ON}-1.396\;\text{OFF}\times \;\text{OFF}+12.354\;\text{OV}\times\;\text{OV}+\\ &11.323\;\text{SV}\times\;\text{SV}+10.635\;\text{WT}\times\;\text{WT}+43.17 \;\text{WA}\times\;\text{WA}-15.531\\ &\text{ON}\times\;\text{OFF}+12.750\;\text{ON}\times\;\text{OV}-7.266\;\text{ ON}\times\;\text{SV}-7.594\;\text{OFF}\times\;\text{OV}+\\ &4.281\;\text{OFF}\times\;\text{SV}+3.56\;\text{OFF}\times\;\text{WA}-9.031\; \text{OV}\times\;\text{SV}-1.84\;\text{OV}\times\;\text{WA}\end{array}  \tag{6}\]  
where \(\text{Error}_{(30)}\) is the corner error prediction for the 30\({}^{\circ}\) corner, \(\text{Error}_{(60)}\) is the corner error prediction for the 60\({}^{\circ}\) corner, \(\text{Error}_{(90)}\) is the corner error prediction for the 90\({}^{\circ}\) corner, and CutSpeed is the machining time prediction. As a function of two factors, 3D surface plots and their corresponding 2D contour graphs are helpful in understanding both main and interaction effects of two factors. The two parameters with the greatest influence were chosen for confirmation. The effects of interaction with the ON and WT parameters on corner error are depicted in Figures 4-6. It can be seen, when the parameter pulse-on time (ON) was 8 and wire tension (WT) was 14, that the smaller corner error was obtained. Meanwhile, the effect of interaction with the ON and OFF parameters on machining speed is shown in Figure 7. It is seen that the faster machining time was obtained with the setting parameter pulse-on time (ON) of 12 and pulse-off time (OFF) of 8. The Minitab response optimizer tool was used for setting the highest desirability, and different numerical combinations were looked for in maximizing the model functions. As shown in Figure 8a, the optimal conditions of the maximum response for the 30\({}^{\circ}\) corner were obtained at ON:8, OFF:10, OV:10, SV:37, WT:14, and WA:2. The maximum response for the 60\({}^{\circ}\) corner was obtained at ON:8, OFF:11, OV:9, SV:38, WT:14, and WA:2 (Figure 8b). Similarly, the maximum response for the 90\({}^{\circ}\) corner was obtained at ON:8, OFF:12, OV:11, SV:38, WT:14, and WA:2 (Figure 8c).