# Research on Temperature Field Analysis Method of High-Speed Bearing Chamber-Bearing System
## 2 Model and Method
### Geometric Models of Bearing Chambers  
The overall structure of the bearing chamber-bearing system is intricate, comprising five distinct bearing chambers, as illustrated in Figure 2. To effectively decouple the calculation of the oil-air two-phase flow within the bearing chamber from the temperature \begin{table}
\begin{tabular}{c c} \hline \hline
**Structure Parameters** & **Value** \\ \hline Outer race diameter & 75 mm \\ Inner race diameter & 45 mm \\ Pitch diameter & 60 mm \\ Width & 15 mm \\ Contact angle & 33\({}^{\circ}\) \\ Ball diameter & 9.525 mm \\ Number of balls & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Structure parameters of the ball bearing. Figure 1: Geometric model of the bearing chamber–bearing system. field analysis of the entire bearing chamber-bearing system, this article adopts a strategy that involves analyzing the oil-air two-phase flow and heat transfer process within each individual bearing chamber separately. By doing so, the convective heat transfer coefficients associated with the chamber walls are determined and used as thermal boundary conditions for the subsequent steady-state temperature field analysis of the entire system. This approach allows for a more focused and manageable analysis of the complex interactions occurring within each chamber, which is crucial for accurately predicting the thermal behavior of the system as a whole. Given the symmetrical nature of Chamber 2 and Chamber 4, both of which are situated between ball bearings, the convective heat transfer coefficients for the walls in Chamber 2 are calculated. These results are then applied to Chamber 4, leveraging the symmetry to avoid redundant calculations. Chamber 3, positioned at the center of the overall system and located behind the oil supply surfaces of the two ball bearings, has a smaller volume compared to the other bearing chambers. Consequently, there is a minimal amount of lubricating oil entering Chamber 3. Due to this, two-phase flow and heat transfer calculations for Chamber 3 are not performed. Instead, the convective heat transfer coefficient obtained from the calculation of Chamber 2 is adapted and used as the boundary condition for the walls in Chamber 3. In the case of Chamber 1 and Chamber 5, which exhibit significant structural differences, we performed separate two-phase flow and heat transfer calculations for each chamber to accurately determine the convective heat transfer coefficients of the chamber walls for these distinct configurations. These coefficients are then utilized as thermal boundary conditions for the thermal analysis of the entire structural assembly. The names of the chamber walls are depicted in Figure 3 for reference. There are a total of 12 surfaces inside Bearing Chamber 1, 4 surfaces inside Bearing Chamber 2, and 17 surfaces inside Bearing Chamber 3. Taking the shaft rotation surface contained in the chamber as the starting surface, the wall surfaces of each bearing cavity are named in counterclockwise order. Taking Bearing Cavity 2 as an example, the shaft rotation surface is named 2-1 surface, the wall surface near bearing No. 1 is named 2-2 surface, the rotating wall surface inside the bearing cavity is named 2-3 surface, and the wall surface  
Figure 2: Five bearing chambers of the bearing chamber–bearing system. near bearing No. 2 is named 2-4 surface; the naming method of the wall surfaces of Bearing Cavities 1 to 5 is followed in an analogous manner. The simplified model of Bearing Chambers 1, 2, and 5 retains static chamber walls, an oil-air two-phase flow fluid domain, and a rotating shaft section. The oil inlet of all bearing chambers is simplified as an annular clearance between the bearing's outer ring and cage. The oil outlet configuration for Chamber 1 features 11 axial circular tubes positioned on the right-hand side of the chamber. In contrast, the outlet for Bearing Chamber 2 is designed as a square outlet located at the base of the chamber.