Numerical thermo-mechanical modeling of tread braking systems under ultra-long downhill constant-speed conditions with coupled time-dependent heat partition coefficients

Abstract

During constant-speed braking of freight trains on long downhill ramps, friction between the wheel and brake shoe generates significant thermal loads, causing the tread temperature to rise continuously. This leads to microstructural evolution, thermally induced residual stresses, and various surface damages, thereby posing serious risks to operational safety. The heat partition coefficient is a critical parameter that governs the distribution of frictional heat flux between the wheel and brake shoe, directly influencing temperature evolution, thermal stress fields, and fatigue damage predictions. However, existing numerical methods typically simplify this coefficient as a constant, neglecting its temperature-dependent, dynamically evolving nature, which limits their ability to accurately capture the true heat flux distribution during prolonged braking. To address this issue, this study proposes a thermo-mechanical coupled numerical modeling framework for wheel–brake shoe systems under ultra-long downhill (50 km) constant-speed braking conditions, developed through secondary programming in Matlab and Ansys APDL. The model incorporates the temperature-dependent thermal properties of the wheel and brake shoe and couples a time-varying heat partition algorithm to assess its impact on the evolution of tread temperature and thermal stress. Simulation results reveal that the heat partition coefficient initially increases, then decreases, and eventually fluctuates around a nearly constant value. The maximum variation amplitude is only 0.004 % for high-friction composite brake shoes, whereas it reaches 0.517 % for cast iron shoes due to their higher sensitivity to temperature-dependent thermal properties. Although the coefficient theoretically evolves dynamically with temperature, during long-duration braking, limited variations in thermal diffusivity restrict changes in heat flux distribution, making its overall impact on temperature and thermal stress predictions negligible. These findings indicate that assuming a constant heat partition coefficient can maintain modeling accuracy while improving computational efficiency under ultra-long ramp constant-speed braking conditions. Nonetheless, dynamic characteristics should be considered for materials with strongly temperature-sensitive thermal properties. The proposed modeling framework is also applicable to other braking components, such as brake discs, providing a theoretical basis and numerical tool for investigating frictional heat generation mechanisms, thermal stress prediction, and safety assessment in freight train braking systems.