Transient wheel–rail rolling contact theories

This paper provides an overview of different theories to analyse unsteady rolling contact phenomena between wheel and rail: the exact formulation by Kalker, the simplified model based on the Winkler approximation, and the recent two-regime model. The classic solution to the transient problem derived by Kalker using the complete theory of elasticity is first recalled. The more involved situation of combined creepages and spin is analysed using Kalker's simplified model. Analytical solutions are reported in integral form concerning the time-varying and constant creepages. Qualitative results are additionally provided for the case of a time-varying contact patch. Finally, a novel theory, which describes the transient evolution of the force-creepage characteristics using a system of ordinary differential equations (ODEs), is introduced.