## 3 Construction of LPTN-Based VML  
### Bearing LPTN Model  
The time it takes for a bearing to roll for one cycle is much shorter than the time it takes for heat to diffuse along the circumferential direction of the raceway. Therefore, assuming that the transient temperature of the bearing is symmetrically distributed along the axis, the 3D heat transfer problem is transformed into a 2D problem [23]. The selection of nodes, calculation of heat sources, and TRs are key conditions for constructing the LPTN model, which has evolved from the initial simple three-node model to a multi-node thermal model that considers the rheological properties of lubricants, thermal expansion, and the influence of retaining frames [28]. Under the lumped mass assumption, the LPTN model for the traction motor's deep groove ball bearing and its house is configured with 14 nodes, as illustrated in Figure 5, with detailed node description provided in Table 1.  
In order to solve the LPTN model, it is necessary to set initial and boundary conditions. In this study, the initial temperature of the T1-T13 temperature nodes was set to 22.6 \({}^{\circ}\)C to match the experimental environment. The T14 temperature node is set as a boundary condition, i.e., the temperature of the surrounding environment, ignoring its changes over time, and is also set to 22.6 \({}^{\circ}\)C. The time step for solving is set to 60 s.  
Critical analysis reveals that the investigated bearing, primarily subjected to radial loads, generates heat dominantly through three mechanisms: frictional heating at rolling/stationary component interfaces, viscous power dissipation within the lubricant, and auxiliary frictional losses from other elements. During thermal transients, non-uniform thermal expansion of solid materials, induced by temperature gradients and geometric constraints, alters initial interference fits and introduces thermally induced loads [43]. Concurrently, temperature-dependent variations in grease kinematic viscosity induce time-varying friction torque fluctuations at contact interfaces, thereby modifying global heat generation patterns. Notably, certain parameters in heat source calculations derived from empirical formulations exhibit strong dependencies on bearing type, operational loads, rotational speeds, and initial conditions. While the existing literature provides nominal value ranges for these parameters [44], their precise quantification under transient operational states remains unresolved. Furthermore, heat transfer between nodes primarily occurs through contact conduction and convective heat transfer mechanisms [45]. Temperature variations exhibit negligible influence on the thermal conductivity of solid materials, while thermal expan  
Figure 4: Influence of input parameters on bearing temperature of reference nodes. sion effects on conduction TRs related to bearing dimensions are considered insignificant. Consequently, conduction TRs of solid components remain essentially invariant and are categorized as constant TRs. Conversely, Hertzian contact TRs within bearing clearances and ball/roller-cage gaps, as well as TRs induced by grease-oil-air mixtures, demonstrate strong dependencies on rotational speeds and applied loads [46]. Additionally, grease's physical properties (e.g., kinematic viscosity, thermal conductivity, and density) exhibit working conditions-dependent behavioral patterns [47], classifying these resistances as variable TRs. The precise quantification of such resistances necessitates complex computational procedures involving initialization protocols and nonlinear problem-solving, where calculation accuracy directly governs the fidelity of thermal analysis and temperature prediction results. As established in Section 1.2, the investigated bearing undergoes multi-stage operational states characterized by dynamic speed transients and frequent load switching