Fast non-Hertzian wheel-rail thermal contact models integrated with tread brake in train dynamic simulations

Tread braking induces significant transient thermal loads at the wheel-rail interface. Conventional thermal models often rely on Hertzian contact assumptions and treat the rail as an isothermal boundary, neglecting contact patch fidelity and the evolving thermal state of the rail during extended braking. This paper presents an integrated numerical framework that overcomes these limitations, bridging advanced contact mechanics with operational-scale thermal simulation. The non-Hertzian ANALYN algorithm determines the contact patch geometry to improve the rail chill prediction, providing a physics-based representation of heat partitioning at the interface. A train-synchronised moving-grid 2D rail thermal model (vertical-longitudinal) captures cumulative heating from successive wheel passages, enabling simulation of braking scenarios exceeding 50 km of track. The wheel and brake block are represented by a computationally efficient 1D radial model, calibrated and assessed against an experimentally validated 2D axisymmetric reference, with more than 85% reduction in computation time. Parametric analysis reveals that interfacial thermal power exchange is predominantly governed by contact patch size, with secondary sensitivity to shape and position, a finding with direct implications for modelling local heat flux densities relevant to wear and fatigue assessments. The 1D model preserves thermal accuracy while reducing computational cost, making it suitable for integration into Longitudinal Train Dynamics (LTD) frameworks for braking events lasting several minutes. By concurrently resolving non-Hertzian contact mechanics and rail thermal history, the framework delivers a robust, efficient tool for simulating realistic thermal conditions in railway tread braking applications, supporting improved assessment of thermally assisted damage mechanisms and informed maintenance strategies.