# Research on Temperature Field Analysis Method of High-Speed Bearing Chamber-Bearing System
## 2 Model and Method
### Numerical Method of Oil-Air Two-Phase Flow in Bearing Chamber  
For oil-air two-phase flow numerical calculations in Bearing Chambers 1, 2, and 5, the fluid-structure interaction (FSI) method is used to obtain the convective heat transfer coefficients on chamber walls. The boundary conditions are as follows: the main shaft solid domain is set to rotate, and the inlet boundary is set as a velocity inlet condition, with specified axial and circumferential velocities to simulate oil splashing led by bearing rotating. The axial velocity is the inlet velocity of lubricating oil, and the circumferential velocity is the angular velocity of the bearing cage. The outlet boundary is set as a pressure outlet. The outer wall of the bearing chamber housing and the inner wall of the main shaft are maintained at a constant temperature of 20 \({}^{\circ}\)C. The effect of gravity is taken into account during calculation, with its direction set vertically downwards and with a value of 9.81 m/s\({}^{2}\). The material of the main shaft is 1 Cr11 Ni2w2 MoV, and the material of the chamber shell is 15 CrMnMoVE. The type of lubricating oil is Mobil Jet Oil II. Operating conditions are detailed in Table 2. The total heat generation of each bearing in the bearing chamber-bearing system and the oil outlet temperature calculated based on the given operating conditions are presented in Table 3.  
At initialization, the air phase volume fraction of the bearing chamber fluid region is set to 1, and the oil phase volume fraction is set to 0. The SIMPLE algorithm is used for pressure-velocity coupling of the two-phase flow inside the bearing chamber. The pressure \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Operating** \\ **Condition** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Rotate** \\ **Speed (rpm)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Oil Supply** \\ **Temperature** \\ (°C)** \\ \end{tabular} } & \multicolumn{4}{c}{**Bearing 1, Bearing 4**} & \multicolumn{4}{c}{**Bearing 2, Bearing 3**} \\ \cline{3-8}  & & & **Radical** & **Axial** & **Oil Flow** & **Radical** & **Axial** & **Oil Flow** \\  & & (°C) & **Load (N)** & **Load (N)** & **Rate (L/min)** & **Load (N)** & **Load (N)** & **Rate (L/min)** \\ \hline \(1\) & 40,000 & 85 & 600 & 2000 & 1.3 & 600 & 1500 & 0.8 \\ \(2\) & 40,000 & 85 & 900 & 2000 & 1.3 & 900 & 1500 & 0.8 \\ \(3\) & 40,000 & 85 & 950 & 2000 & 1.3 & 950 & 1500 & 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Operating conditions. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Operating Condition** \\ \end{tabular} } & \multicolumn{4}{c}{**Bearing 1, Bearing 4**} & \multicolumn{4}{c}{**Bearing 2, Bearing 3**} \\ \cline{2-5}  & \multirow{2}{*}{**Heat Generation (W)**} & \multicolumn{2}{c}{**Oil Outlet**} & \multirow{2}{*}{**Heat Generation (W)**} & \multicolumn{2}{c}{**Oil Outlet**} \\  & & & **Temperature (°C)** & & **Temperature (°C)** \\ \hline \(1\) & 3691.32 & 165.41 & 3629.47 & 219.34 \\ \(2\) & 3689.65 & 165.37 & 3627.37 & 219.26 \\ \(3\) & 3688.81 & 165.35 & 3626.41 & 219.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Heat generation of bearings. term uses the PRESTO! format, and the momentum, turbulent kinetic energy, and turbulent dissipation rate are discretized using the upwind scheme. During calculation, the inlet and outlet mass flow rates and the average oil phase volume fraction in the bearing chamber are monitored. The calculation is considered to have converged when the difference between the inlet and outlet mass flow rates is approximately 1% and the average oil phase volume fraction in the chamber remains essentially unchanged. At this point, the calculation is stopped, and the results are read for further analysis. This convergence criterion ensures that the simulation has reached a stable state, providing reliable results for the analysis of the bearing chamber's two-phase flow.