# Optimization Design of the Lower Rocker Arm of a Vertical Roller Mill Based on ANSYS Workbench
## 3 Optimum Design of Response Surface Analysis Method
### Optimization of the Response Surface  
(1) Response surface analysis  
The response surface offers high accuracy and good prediction performance, and can study the interaction between several random variables [13; 14]. Optimize the experimental design through the steps outlined in the Design of Experiments section; the design scope is shown in Table 1. After setting the parameters, 25 groups of experimental design points are updated, and the response results of the experimental design points are shown in Table 2[15]. Parameter P1 corresponds to \(x_{1}\), P5 corresponds to \(x_{5}\), P6 corresponds to \(x_{6}\), and P7 corresponds to \(x_{7}\). Parameter P8 is the total mass of the lower rocker arm, P9 is the maximum stress, and P10 is the maximum displacement. After updating 25 groups of experimental points, the standard response surface-full second-order polynomial was selected to fit the response surface model [15]. After fitting, the relationship between the input variable and the target variable of the response surface was obtained; that is, the mathematical relationship between the four input variables and the mass, the maximum displacement, and the maximum stress of the lower arm [16; 17]. The Kriging was used to generate 2D curves between parameters P1, P5, P6, P7,P8, P9, and P10, respectively. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name** & **P1/mm** & **P5/mm** & **P6/mm** & **P7/mm** \\ \hline Initial value & 142 & 777 & 100 & 182 \\ Constraint range & [127.5, 155.8] & [705, 849.4] & [94.5, 107.0] & [163.8, 200.2] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Constraint range of design variables. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**P1/mm** & **P5/mm** & **P6/mm** & **P7/mm** & **P8/kg** & **P9/MPa** & **P10/mm** \\ \hline
141.70 & 777.21 & 100.75 & 182.00 & 6552.52 & 1.08 & 116.29 \\
127.53 & 777.21 & 100.75 & 182.00 & 6468.43 & 1.10 & 117.92 \\
155.87 & 777.2  
The relationship between the four input variables of the lower arm and the mass of the lower arm is shown in Figure 8. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**P1/mm** & **P5/mm** & **P6/mm** & **P7/mm** & **P8/kg** & **P9/MPa** & **P10/mm** \\ \hline
131.72 & 726.36 & 96.35 & 169.18 & 6662.58 & 1.10 & 116.65 \\
151.68 & 726.36 & 96.35 & 169.18 & 6769.89 & 1.07 & 121.33 \\
131.72 & 828.06 & 96.35 & 169.18 & 6301.74 & 1.14 & 121.14 \\
151.68 & 828.06 & 96.35 & 169.18 & 6428.00 & 1.11 & 125.95 \\
131.72 & 726.36 & 105.15 & 169.18 & 6664.81 & 1.09 & 119.11 \\
151.68 & 726.36 & 105.15 & 169.18 & 6772.20 & 1.08 & 120.06 \\
131.72 & 828.06 & 105.15 & 169.18 & 6303.89 & 1.12 & 116.16 \\
151.68 & 828.06 & 105.15 & 169.18 & 6430.20 & 1.11 & 120.12 \\
131.72 & 726.36 & 96.35 & 194.82 & 6672.33 & 1.09 & 120.10 \\
151.68 & 726.36 & 96.35 & 194.82 & 6779.55 & 1.08 & 120.43 \\
131.72 & 828.06 & 96.35 & 194.82 & 6313.55 & 1.12 & 116.71 \\
151.68 & 828.06 & 96.35 & 194.82 & 6439.76 & 1.11 & 108.72 \\
131.72 & 726.36 & 105.15 & 194.82 & 6674.57 & 1.09 & 118.98 \\
151.68 & 726.36 & 105.15 & 194.82 & 6781.86 & 1.08 & 109.79 \\
131.72 & 828.06 & 105.15 & 194.82 & 6315.70 & 1.12 & 125.58 \\
151.68 & 828.06 & 105.15 & 194.82 & 6441.96 & 1.11 & 125.87 \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 8: Relationship between the mass of the lower rocker arm and the four input variables: (**a**) relationship curve between P8 and P1; (**b**) relationship curve between P8 and P5; (**c**) relationship curve between P8 and P6; (**d**) relationship curve between P8 and P7. It can be seen from Figure 8 that P8 increases with the increase of input variables P1, P6 and P7, and decreases with the increase of input variable P5. The reason for this rule is that the wall thickness of the lower rocker arm decreases with the increase of P5. The thinner the wall thickness, the lighter the total mass of the lower rocker arm.