# Optimization Design of the Lower Rocker Arm of a Vertical Roller Mill Based on ANSYS Workbench
## 4 Conclusions  
(1) The static analysis of the lower rocker arm was carried out by using ANSYS Workbench. The results show that the maximum equivalent stress occurred at the transition between the casting at the front end of the lower rocker arm and the web welding, and the maximum displacement occurred at the pull ring at the tail of the lower rocker arm. The maximum equivalent stress and maximum displacement meet the design requirements. Furthermore, the stress distribution of the lower rocker arm was small, which means that the strength margin was large and that, consequently, there is space for lightweight design.  
(2) Taking the minimum mass of the lower rocker arm as the optimization objective, the structural size of the internal cavity as the input variable, and the maximum equivalent stress and maximum displacement as less than the allowable value as the constraint condition, the mathematical model of the optimization design was established (Formula (10)).  
(3) Combined with the response surface optimization module and multi-objective genetic algorithm in the workbench, the structural size of the internal cavity of the lower rocker arm was optimized. The first group of data in the three groups of optimal parameter combinations was selected as the optimization design point, and static analysis was carried out (Table 3). The results show that in order to meet the strength and deformation requirements, the mass of the optimized lower rocker arm was reduced from the original 6552.5 kg to 6206.2 kg, and the optimization goal of reducing the mass by 5.29% was achieved. The structural optimization method of the lower rocker arm can provide a reference for the structural optimization of other mechanical devices with complex geometry and bearing complex loads.  
Figure 13: Displacement distribution before and after the lower rocker arm optimization: (**a**) displacement distribution before the lower rocker arm optimization; (**b**) displacement distribution after the lower rocker arm optimization.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & **Value before** & **Initial Value after** & **Actual Value after** & **Amplitude of** \\  & **Optimization** & **Optimization** & **Optimization** & **Change** \\ \hline P8/kg & 6552.5 & 6206.2 & 6206.2 & \(-\)5.285\% \\ P9/MPa & 116.29 & 119.86 & 119.18 & +2.485\% \\ P10/mm & 1.0802 & 1.1469 & 1.1475 & +6.230\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of response surface optimization results.  
**Author Contributions:** Conceptualization, W.W. and J.S.; methodology, W.W. and H.Y.; software, J.S. and H.Y.; validation, B.C.; formal analysis, B.C.; investigation, J.S. and W.W.; resources, Y.W.; data curation, H.Y.; writing--original draft preparation, J.S. and H.Y. and W.W.; writing--review and editing, W.W.; visualization, B.C.; supervision, W.W.; project administration, W.W. and Y.W.; funding acquisition, W.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was financially supported by the Jiangsu Key Laboratory of Precision and Micro-Manufacturing Technology (2019), the Jiangsu \"Six Talent Peak\" Project (JXQC-022), and the Jiangsu University Students' Practice Innovative Training Project (202010298054Z).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
**Conflicts of Interest:** The authors declare no conflict of interest.