This paper deals with the geometric issue of the contact between a wheel and a rail joint. A new model in this field is proposed. Actually, the wheel and rail elasticity is introduced in order to overcome the singularity of the contact force that is met in the classical approaches. The coordinates of the bicontact zone are calculated from nonlinear set equations derived from the Hertz's theory. This model will allow to simulate more realistic the dynamic behavior of the passing wheel over a rail joint.

Dry friction dampers are widely used in railway vehicle suspensions due to their simplicity, robustness, and cost-effectiveness compared to hydraulic alternatives. However, accurately modelling their behaviour remains challenging because of the discontinuous nature of friction forces. This paper presents a comparative study between two modelling approaches: continuous (regularized) models, which smooth out discontinuities, and discontinuous (switch-based) models, which explicitly capture stick–slip transitions. Using a two-degree-of-freedom suspension system, both models are implemented and analyzed under steady-state and transient conditions. Results show that while continuous models are easier to implement and integrate numerically, they fail to capture key physical phenomena such as zero relative velocity intervals and force discontinuities. In contrast, discontinuous models offer superior physical fidelity and significantly better computational efficiency, especially during static friction phases. This study highlights the trade-offs between modelling simplicity and accuracy, providing valuable insights for the simulation and design of railway suspension systems. The findings support the use of discontinuous models in safety-critical simulations and suggest avenues for hybrid modelling strategies.

The use of high-power railway vehicles requires enhanced control of wheel-rail adherence. The aim of the present work is to prove the appropriateness of non-smooth models in the study of the axle torsional stick-slip vibrations which may occur when traction vehicles are set into motion. The model is simple, observes the main friction characteristics and provides the basis for efficient dynamics simulation. A set-valued friction law is accounted for and the motion equations are formulated as a switch model. Numerical integration is done by an event-driven algorithm. Application examples are presented. An experimental setup comprising a reduced-scale wheel set is analysed to validate the model proposed. The friction parameters are then identified using the proposed force-creepage relationship. Validation and verification are further carried out in frequency domain. Related problems may be solved using the present method, as it is pointed out in the paper.