A geometric approach to wheel–rail contact accounting for non-prismatic rails in turnouts

Journal article, 2025

This work introduces a comprehensive methodology for solving the geometric wheel–rail contact problem, applicable to both mainline tracks and turnouts. The approach accurately identifies all contact areas, computes the contact plane and determines distances between undeformed surfaces. Unlike traditional nonlinear methods that may miss critical contact points, this method ensures full intersection detection through an analytical closed-form solution between conical frustums (wheels) and linear segments (rails or turnout surfaces). The formulation supports parallel computation on CPUs or GPUs. The geometric model is coupled with the Variational Theory to address the elastic contact problem, enabling the calculation of approaches, potential contact zones and traction distributions. Principal Component Analysis defines the contact plane, while mapping techniques handle the representation of successive turnout profiles. Static simulations of wheelset positions at crossings reveal key phenomena, such as sudden shifts in contact locations, variations in overall contact stiffness and wheel radius differences that increase creepage and localised wear. These findings are crucial for improving the understanding of vehicle dynamics through turnouts and enhancing the design and maintenance of railway infrastructure.