A linear wheel–crossing interaction model

Abstract

This paper presents the derivation of a linear model for wheel–rail interaction kinematics at railway crossings. The purpose of this model is to demonstrate the fundamental constraints imposed on a crossing geometry if it should be compatible with a given range of wheel profile shapes. In this model, the contact point locations on the wing rail and on the crossing nose are described using linear functions, and the wheel profiles are modelled as conical. Based on these assumptions, a method is developed to adjust the vertical position and longitudinal inclination of the wing rail and the crossing nose in order for the crossing geometry to be compatible with a given range of equivalent wheel profile cone angles. In particular, an expression is derived for the average impact angle. The derived relation highlights the potential of tailoring crossing geometries for a given spread in wheel profile shapes in traffic for minimized loading and damage. Further, the properties of the model are compared to the results of quasi-static multibody simulations for a range of wheel profiles.