## 3 Experimental Process and Analysis
### Experimental Data  
After determining the experimental variables, the appropriate range of values was selected for the response surface experiment. There are four optimization variables in this experiment, so \(\alpha\)=2. The design and combination of the experimental sample points were carried out by the CCD method, as shown in Table 5. Table 6 is the experimental data results of the sample points which were obtained by calling each other between ANSYS and MATLAB.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Run**} & \multicolumn{4}{c}{**Actual/mm**} & \multicolumn{4}{c}{**Coded**} & \multicolumn{2}{c}{**\(E_{\text{max}}\)**} & \multicolumn{2}{c}{**Number of**} \\ \cline{2-10}  & \(R_{1}\) & \(h\) & \(s\) & \(w\) & \(\overline{x}_{1}\) & \(\overline{x}_{2}\) & \(\overline{x}_{3}\) & \(\overline{x}_{4}\) & **/(V/mm)** & **Elements** & **DOFs** \\ \hline
1 & 6 & 10 & 5 & 40 & \(-1\) & \(-1\) & 1 & \(-1\) & 10,909.89 & 2074 & 3958 \\
2 & 24 & 15 & 3.5 & 45 & 1.571 & 0 & 0 & 0 & 9154.23 & 2125 & 4038 \\
3 & 13 & 15 & 0.5 & 45 & 0 & \(-2\) & 0 & 11,831.83 & 2528 & 4700 \\
4 & 20 & 10 & 5 & 40 & 1 & \(-1\) & 1 & \(-1\) & 8599.39 & 2081 & 3967 \\
5 & 6 & 20 & 5 & 50 & \(-1\) & 1 & 1 & 1 & 11,053.85 & 2080 & 3962 \\
6 & 6 & 10 & 2 & 50 & \(-1\) & \(-1\) & \(-1\) & 1 & 12,416.88 & 2133 & 4047 \\
7 & 13 & 15 & 3.5 & 45 & 0 & 0 & 0 & 0 & 9664.49 & 2090 & 3981 \\
8 & 13 & 15 & 3.5 & 45 & 0 & 0 & 0 & 0 & 9664.49 & 2090 & 3981 \\
9 & 20 & 20 & 5 & 50 & 1 & 1 & 1 & 1 & 8870.22 & 2080 & 3957 \\
10 & 13 & 15 & 6.5 & 45 & 0 & 0 & 2 & 0 & 9328.45 & 2087 & 3983 \\
11 & 13 & 5 & 3.5 & 45 & 0 & \(-2\) & 0 & 0 & 10,048.23 & 2131 & 4060 \\
12 & 20 & 20 & 5 & 40 & 1 & 1 & 1 & \(-1\) & 8243.91 & 2082 & 3963 \\
13 & 6 & 20 & 2 & 50 & \(-1\) & 1 & \(-1\) & 1 & 11,789.22 & 2140 & 4057 \\
14 & 6 & 10 & 2 & 40 & \(-1\) & \(-1\) & \(-1\) & \(-1\) & 11,656.15 & 2128 & 4044 \\
15 & 13 & 15 & 3.5 & 45 & 0 & 0 & 0 & 0 & 9664.49 & 2090 & 3981 \\
16 & 13 & 25 & 3.5 & 45 & 0 & 2 & 0 & 9151.81 & 2129 & 4035 \\
17 & 17 & 15 & 3.5 & 55 & 0 & 0 & 0 & 2 & 10,380.85 & 2088 & 3973 \\
18 & 6 & 10 & 5 & 50 & \(-1\) & \(-1\) & 1 & 1 & 11,564.39 & 2076 & 3959 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Experimental data.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **EE** & **Proportion (\%)** \\ \hline \(R_{1}\)/mm & 325,162.8862 & 25.0 \\ \(\theta_{1}\)/mm & 20,294.4814 & 1.6 \\ \(h\)/mm & 140,533.0000 & 10.8 \\ \(s\)/mm & 655,163.7245 & 50.3 \\ \(w\)/mm & 160,650.0366 & 12.3 \\
**Total** & 1,301,804.1290 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Influence proportion of the optimized parameters on \(E_{\text{max}}\).  
The last two columns of Table 6 are the number of elements and nodes (degrees of freedom) of the local finite element model in Figure 1b. According to statistics, it took only 61.8 seconds to complete the above 30 CCD experiments. Without the CCD method, 625 ISM experiments would be required. Thus, by using CCD method, the optimization efficiency was greatly improved.  
Referring to the above data, the coefficients of the response surface model were obtained by Equation (5). We can get the initial response surface model from Table 7.