## 4 Conclusions  
As the main bearing part of the mobile pump truck, it is of great significance to study the strength of the frame to improve the safety and reliability of the whole vehicle. In this paper, the static characteristics of the frame model under classical working conditions were obtained via the numerical simulation of four working conditions of the frame: full load bending, full load torsion, emergency turning, and emergency braking. The main conclusions are as follows:  
1. Through the analysis of displacement nephogram and stress nephogram under four working conditions, it can be obtained that the maximum displacement in the frame is not more than 3 mm and the maximum stress is not more than 80 MPa under the three working conditions of the frame: full load bending, emergency turning, and emergency braking. The frame can meet the strength design requirements, and there is a certain margin in the strength of the frame, which can be designed to be lightweight while ensuring the structural strength of the frame.
2. The deformation and stress of the frame under torsion conditions are large, the maximum displacement is 18.18 mm, and the maximum stress is 352.68 MPa, but both are far below the yield strength limit of the material, and can meet the design requirements of the frame strength. However, as the most dangerous condition of the frame, the torsion condition should be avoided as far as possible in real life.
3. Through the displacement and stress monitoring of the axle, beam, and longitudinal beam, this paper can clearly reflect the displacement and stress changes in the main parts of the body under various working conditions of the frame, and more accurately predict the structural performance of the mobile pump truck. The analysis results can provide a reference for the subsequent design of the mobile pump truck frame.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Full Load Bending** & **Full Load Torsion** & **Emergency Turning** & **Emergency Braking** \\ \hline Safety factor & 10.94 & 2.23 & 9.85 & 10.48 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Safety factor under four typical working conditions.  
**Author Contributions:** Conceptualization, S.-P.L. and Y.-L.Z.; methodology, Y.-L.Z.; software, H.-B.L.; validation, H.-B.L. and L.C.; formal analysis, L.C.; investigation, S.-P.L.; resources, Y.-L.Z.; data curation, L.C.; writing--original draft preparation, H.-B.L.; writing--review and editing, Y.-L.Z.; visualization, L.C.; supervision, Y.-L.Z.; project administration, S.-P.L.; funding acquisition, Y.-L.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The research was financially supported by the \"Pioneer\" and \"Leading Goose\" R&D Program of Zhejiang (grant no. 2022C03170), Science and Technology Project of Quzhou (grant no. 2022K98), Zhejiang Provincial Natural Science Foundation of China (grant no. LZY21E060001), and Science and Technology Project of Zhejiang (grant no. LGC21E050001).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.  
**Conflicts of Interest:** The authors declare no potential conflict of interest with respect to the research, authorship, and/or publication of this article.