# Optimization of Machining Parameters for Corner Accuracy Improvement for WEDM Processing
## 2 Methodology
### Response Surface Methodology  
Response surface methodology (RSM) is an advanced experimental design method that combines mathematics and statistics that are helpful for analyzing the problem and fitting the model with a lot of independent parameters to control the dependent parameter. The response surface contour map is used to represent the relationship between the influencing factors and the quality characteristics. The first step of the response surface method (RSM) is to find out the mathematical model relationship between the response variables and the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{3}{c}{**Level (Code)**} & \multirow{2}{*}{**Code Level/Value Range**} \\  & **Low** & **Mid** & **High** & \\ \hline OV & 9 & 11 & 13 & 1–32 (level)/50–140 V \\ ON & 8 & 10 & 12 & 1–24 (level)/50–1200 ns \\ OFF & 8 & 10 & 12 & 4–50 (level)/4–50 μs \\ SV & 36 & 38 & 40 & 16–75 (level)/16–75 V \\ WT & 10 & 12 & 14 & 1–20 (level)/300–2200 g \\ WA & 2 & 3 & 4 & 1–8 (level)/increase or decrease proportionally \\ \hline \hline \end{tabular}
\end{table}
Table 1: Machining parameters with three levels.  
Figure 2: Flowchart of experiment.  
independent variables. Usually, a low-order polynomial with independent variables within a set range is used, which is a first-order regression model, as shown in Equation (1) [25].  
\[\mathrm{Y}=\phi(X_{1},X_{2},X_{3},\ldots\ldots,X_{i},\ldots\ldots,X_{k}) \tag{1}\]  
where \(Y\) is the performance characteristic of the system, \(\phi\) is the performance of function, \(X_{i}\) is the independent parameter \(i\), and \(k\) is the number of parameters.  
If the correlation between variables is nonlinear, a higher-order polynomial must be used, such as a second-order model, as shown in Equation (2).  
\[Y=d_{0}+\sum_{i=1}^{k}d_{i}X_{i}+\sum_{i=1}^{k}d_{ii}X_{i}^{2}+\sum_{i=1}^{k-1 }\sum_{j=i+1}^{k}d_{ij}X_{i}X_{j} \tag{2}\]  
where \(d_{i}\), \(d_{ii}\), and \(d_{ij}\) are the regression coefficients.  
When the experiment is close to the region near the optimal response value, the second-order model is usually used to analyze the second-order response surface, and the optimal response value can be determined.  
The Box-Behnken design approach was used in this study. The Box-Behnken design method is an experimental design method in RSM that can be efficiently used for developing second-order polynomial models to solve problems. To fit a second-order regression model (quadratic model), the Box-Behnken design only requires three levels for each factor, rather than the five levels in central composite design. The design points fall at combinations of the high and low factor levels and their midpoints [26]. Moreover, the Box-Behnken design uses face points, which is relatively more practical rather than the corner points in central composite design. Since the Box-Behnken design has fewer design points, it needs a smaller number of experimental runs. In this study, the Box-Behnken design was developed using Minitab for optimizing six different independent process parameters as shown in Table 1. Table 2 shows the experimental design using Box-Behnken RSM by Minitab.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**OV** & **ON** & **OFF** & **SV** & **WT** & **WA** \\ \hline  
\hline \end{tabular}
\end{table}
Table 2: Experiment design based on Box–Behnken RSM.