## 2 Model Establishment
### Problem Analysis  
Based on the calculation method of heat generation and convective heat transfer coefficient in Section 2.2, the transient temperature field of a 6311 ball bearing was analyzed under durability experiment conditions (radial load 2400 N, bearing speed 5800 r/min). At the same time, a bearing durability experiment was carried out on the bearing lubrication experiment bench of a high-speed traction motor under the same working condition, and the transient temperature changes on the inner surface of the inner ring and outer surface of the outer ring were recorded.  
The overall block diagram and the experimental device on the bearing lubrication experiment bench for a high-speed traction motor are shown in Figure 2. The inner and outer ring temperature sensors measure the temperature of the inner and outer ring bearing surfaces. The loading device applies radial and axial loads to the bearings, and the motor drives the bearings to rotate through the belt. The control cabinet loads the experiment conditions, including settings and control of load and speed, and the recorder records the temperature data of different positions of the bearing in real time. The comparison curve of the durability experiment and transient temperature field simulation temperature of the ball bearing are shown in Figure 3. It can be seen from the comparison curve that the inner and outer ring temperatures of the bearing simulated by the Section 2.2 theory are more than five times higher than the experimental temperatures, and there is a large deviation between the heat generation and convection heat transfer coefficient of the bearing calculated directly by the approximate empirical formula and the actual values.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Base-Oil Type** & **Kinematic Viscosity** & **Thermal Conductivity** & **Prandtl Number** \\ \hline Synthetic oil & 88.74 \(mm^{2}/s\) & 0.1324 \(W\cdot m^{-1}\cdot K^{-1}\) & 1532.44 \\ \hline \end{tabular}
\end{table}
Table 4: Performance parameters of lubricant grease.  
The calculation method for Palmegren bearing heat generation is derived from experiments [5]. Limited by the experimental conditions and detection devices, the empirical formula is only applicable for the calculation of bearing heat generation for medium-low speeds and medium-small torques. Meanwhile the rolling bearing of a high-speed EMU traction motor operates at a high velocity, carries enormous load, and works under complex working conditions, with its actual running speed above 6000 rpm and a radial load of up to 3000 N. Therefore, the Palmegren formula requires further correction before it is applied to heat calculation for a rolling bearing in the traction motor of a high-speed EMU. In addition, the convective heat transfer coefficient of lubricant inside the bearing is approximately obtained from the surface heat transfer coefficient of a flat plate in laminar flow. The rolling bearing in the traction motor of the high-speed EMU is lubricated with grease. A thin oil film takes shape during the bearing operation on the inner surface of the outer ring, outer surface of the inner ring, cage surface and roller surface, which can help lubricate and cool. Despite its theoretical mathematical significance, the approximate empirical formula is not precise enough to calculate the convective heat transfer coefficient completely. Therefore, there is a wide disparity between the temperature distribution of rolling bearings based on these mathematical model formulas and the experimental data.  
Figure 3: Temperature contrast curve between the durability experiment and the transient temperature field simulation.  
Figure 2: Overall block diagram and the experimental device on the bearing lubrication experiment bench for a high-speed traction motor. (**a**) Overall block diagram; (**b**) Experimental device.