## 1 Introduction
### Problem Description  
(1) The necessity of thermal behaviors prediction: Addressing the demands of predictive maintenance in industrial equipment and thermal failure risks under extreme operating conditions, this study focuses on grease-lubricated rolling bearings for high-speed railway traction motors. Due to the frequent start-stop operational patterns inherent to railway systems, these bearings endure full-lifecycle service characterized by multi-stage acceleration-deceleration dynamics and frequent switching between light and heavy loads. Such operational complexities result in differences in grease degradation states and bearing microscale surface, both critically influencing bearing temperature evolution. Conventional thermal models exhibit limited capability in resolving transient heat transfer characteristics across these dynamically shifting operational stages. As illustrated in Figure 1, the deep groove ball bearings for the traction motors of high-speed trains were subjected to a multi-stage discontinuous long-term durability test spanning 2778 h. During each stage, the bearing speed was ramped from 0 to 5600 rpm while maintaining a constant radial load of 2650 N, simulating actual operating conditions of traction motors. Post-experimental analysis revealed grease carbonization phenomena in both internal bearing components and chamber surface, induced by sustained frictional heating during testing. The surface morphology characterization of bearing assemblies demonstrated burning marks on the cage and ball surfaces, accompanied by a microscopic crack in the ball surface structure. These observations confirm the critical temperature-dependent degradation mechanisms affecting both bearing surface integrity (particularly smoothness) and lubricant performance. The identified microscopic crack in the final stage implies potential mechanical risks, including abnormal vibration spectra, should the bearing continue operating under such thermally compromised conditions. Conversely, a comparative analysis of temperature rise characteristics on the inner surface of the inner ring and outer surface of the outer ring during the initial, mid, and final stages reveals that the degradation of metal surface smoothness and lubricant effectiveness dynamically alters the frictional heat generation and bearing cooling efficiency. This thermal phenomenon manifests as significant fluctuations in the temperature curves of both surfaces during the final stage, deviating from their theoretically stable thermal progression. The initial stage exhibited higher temperatures compared to the mid-stage, attributable to incomplete grease homogenization. This demonstrates that transient comparisons of bearing temperature rise across different operational stages can effectively reflect both the grease lubrication status and the surface topographical characteristics of bearing components. Consequently, in order to avoid various problems caused by mechanical thermal failures, implementing real-time thermal monitoring and conducting predictive studies on bearing thermal behaviors are essential during long-term durability operation. (2) The application conditions relying solely on the thermal modeling of the Virtual Model Layer (VML) are limited. Traditional thermal modeling methodologies struggle to obtain accurate computational parameters throughout the entire lifecycle due to variations in grease properties and mechanical wear. Precise bearing thermal modeling relies on calculations of heat sources, thermal resistances (TRs), and heat capacity, particularly real-time varying contact TRs and internal convective TRs dependent on rotational speed and applied loads. Although certain TRs equivalent methods demonstrate satisfactory computational accuracy and simulation efficacy [24; 25], thermal calculations require continuous support from extensive oil-air mixture state data and material property parameters (includingviscosity, diffusion coefficient, and Prandtl number of oil-air mixtures) [26] (see Section 3).