## 1 Introduction  
The rolling element bearing is a critical part supporting the rotating components of the mechanical system and provides additional damping to stabilize the system. In comparison to plain bearings, it is more difficult to model the rolling bearing as a whole due to the complicated coupling between the interactions of components (i.e., rolling elements, cages, and rings) of rolling bearings [1]. [PERSON] et al. [2] proposed a conventional quasi-static analysis to determine the internal load distribution, the bearing stiffness, and the fatigue life of rolling bearings. [PERSON] et al. [3] investigated the influences of different traction models on the dynamic behavior of a cylindrical roller bearing under radial loads, and calculated the cage rotational speed for a wide range of rotational speeds and bearing loads. Nowadays, the problem of the excessive friction heat and the resulting failure of rolling bearing has become more prominent. Therefore, research on the heating mechanism, heat transfer process, and temperature distribution of bearings is very necessary. There are a number of researchers who have made remarkable contributions to this subject. [PERSON] [4] proposed a method for calculating the friction heat generation of a rolling element bearing based on the integral method, which is suitable for medium- and low-speed and sufficient lubrication conditions. However, this method underestimates the total friction heat generation of bearings in high-speed working conditions. Therefore, the actual friction heat of the bearing cannot be estimated accurately. [PERSON] et al. [5]proposed an empirical formula for calculating the friction heat of high-speed roller bearings, which involved the dynamic viscosity and flux of the lubricant. [PERSON] et al. [6] studied the thermal characteristics of the steel bearing and ceramic ball bearing through experiments. [PERSON] et al. [7] calculated the friction power loss caused by the roller, cage, and inner ring and outer ring raceways of a cylindrical roller bearing. Their model assumes that each element of the bearing is a cylinder rotating at a certain angular velocity inside the viscous fluid. The model has certain limitations for various kinds of contact friction heat in the bearing. Based on the quasi dynamics method, the friction power loss in the contact pairs between the parts of the rolling bearing, the friction power loss of the flange caused by the cage and inner (outer) ring guide, the friction power loss between the roller and cage pocket, and the oil churning of the roller were studied by [PERSON] [8]. [PERSON]'s approach is an approximation based on the assumption of laminar flow. SKF [9] proposed a more accurate algorithm for calculating friction torque, but it has not been widely used because of the calculation process complexity and the mass of unknown parameters involved in the calculation. [PERSON] et al. [10,11] regarded lubricating oil as a non-Newtonian fluid, and applied thermal elastohydrodynamic lubrication to the thermal analysis of the rolling bearing. [PERSON] et al. [12] studied the heat transfer characteristics between inner and outer rings of the angular ball bearing. [PERSON] et al. [13] applied the thermal resistance network method for the thermal analysis of double-row tapered roller bearings. [PERSON] et al. [14] developed a simulation method to determine the effects of non-uniform loading on bearing thermal performance under different preloads. [PERSON] et al. [15] studied the thermal characteristics of double-row tapered roller bearings used in a high-speed locomotive. At present, the main theoretical methods for calculating the temperature field of a bearing assembly are the finite element method, heat flow network method, and thermal elastohydrodynamic lubrication method. [PERSON] et al. [16] obtained the instantaneous temperature distribution of a rolling bearing under different loads and speeds. [PERSON] et al.