## 4 Conclusions  
In this paper, the physical parameters of L-HM46 hydraulic oil at different temperatures are obtained. The model of the external gear pump is established. A numerical calculation method is developed based on the obtained hydraulic oil parameters, and the method is verified by a control experiment. The influence of the cavitation thermodynamic  
Figure 10: Temperature drop at P2 (**a**), P3 (**b**), and P4 (**c**).  
effect at different temperatures on cavitation in a gear pump is investigated. The main conclusions are as follows:  
(1) In the cases presented in this article, the gear pump forms a cavitation vortex in the outlet bridge area. This phenomenon is a result of the rapid changes in chamber volume during rotation, leading to a substantial pressure difference and the emergence of swift leakage flow within the narrow gear gaps. Vortex cavitation is observed in the outlet bridge area. As the two teeth gradually move apart, the low-pressure region within the cavitation area increases. Consequently, cavitation diminishes and eventually disappears. The cavitation undergoes periodic development and alterations during the gear pump's rotation.  
(2) Comparing the result at 303 K, under the same cavitation number, the gas volume fraction decreased, and the pressure coefficient increased at 363 K, owing to the inhibitory impact of the thermodynamic effects.  
(3) Thermodynamic effects cause a temperature drop, and the temperature drop becomes more pronounced as the temperature increases. However, the opposite phenomenon is observed in the calculation example: the temperature drop of the calculation example for 303 K is less than that of 363 K, which is due to the physical properties of the lubricant, and the density of the lubricant decreases as the temperature rises. In the same space in the 363 K case, the total amount of vaporization is only half of 303 K. This difference in mass results in a difference in heat release, ultimately showing a decrease in temperature drop as the temperature increases.  
The realistic application of this study manifested in multiple aspects. As for the optimization of industrial machinery, this innovation can enhance the gear pump to improve its resistance to cavitation and ensure stable performance under varying operating conditions. Moreover, the decline in temperature will help reduce damage to the surface of the road. In another aspect, the principle of this study can be applied in the design of a temperature regulator, which can be used in industrial manufacturing to yield benefits for the maintenance of materials. In addition, this research can also be further deepened to study the environmental influence of cavitating flow to learn how to release the negative impact of this phenomenon.  
Conceptualization, X.W. and T.C.; methodology, X.W., X.Y. and T.C.; software, Y.L. and Z.L.; validation, X.W., Y.L. and Z.L.; formal analysis, X.W., Y.L., Z.L. and X.Y.; investigation, Y.L.; resources, Z.L.; data curation, X.Y.; writing--original draft preparation, X.W. and X.Y.; writing--review and editing, X.W. and Y.L.; visualization, X.W. and X.Y.; supervision, T.C.; project administration, T.C.; funding acquisition, T.C. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Aviation Science Foundation (20230023072001) and the Technology Innovation Program of Beijing Institute of Technology (2023 CX11004).  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.