Augmented simplified modelling of elastic pole shoe–rail frictional sliding contact in magnetic track brakes

The magnetic track brake, widely used as an emergency brake in railway vehicles, generates additional braking force through direct conformal contact with the rail. While finite element simulations can accurately reproduce this interaction, their computational cost is prohibitive for many applications. This work introduces an augmented contact model that extends a previously reported simplified elastic half-plane approach by additionally accounting for small overall elastic deformations while maintaining favourable computational efficiency. A two-step iterative scheme is employed, in which first contact resolution and then elastic deformations are handled in succession. The contact between a single pole shoe and the rail is simulated and compared with prior studies and reference results in the commercial finite element software Abaqus . The proposed model achieves good agreement with the reference solutions while preserving low computational cost. These findings establish the method as an efficient, reliable, and practical tool for pole shoe–rail contact analysis in both academic and engineering contexts.