The influence of contact modelling on simulated wheel/rail interaction due to wheel flats

• The effect of contact modelling on impact forces due to wheel flats is studied.
• Newly formed and rounded wheel flats are considered.
• The 2D and Hertzian contact models give rather similar results to the 3D model.
• For the Hertzian contact model, the wheel trajectory needs to be pre-calculated.
• The longitudinal flat geometry is more important than the type of contact model.

Most available wheel/rail interaction models for the prediction of impact forces caused by wheel flats use a Hertzian spring as contact model and do not account for the changes in contact stiffness due to the real three-dimensional wheel flat geometry. In the literature, only little information is available on how this common simplification influences the calculation results. The aim of this paper is to study the influence of contact modelling on simulated impact forces due to wheel flats in order to determine the errors introduced by simplified approaches. For this purpose, the dynamic wheel/rail interaction is investigated with a time-domain model including a three-dimensional (3D) non-Hertzian contact model based on Kalker's variational method. The simulation results are compared with results obtained using a two-dimensional (2D) non-Hertzian contact model consisting of a Winkler bedding of independent springs or alternatively a single non-linear Hertzian contact spring. The relative displacement input to the Hertzian model is either the wheel profile deviation due to the wheel flat or the pre-calculated vertical wheel centre trajectory. Both the 2D model and the Hertzian spring with the wheel centre trajectory as input give rather similar results to the 3D model, the former having the tendency to slightly underestimate the maximum impact force and the latter to slightly overestimate. The Hertzian model with the wheel profile deviation as input can however lead to large errors in the result. Leaving aside this contact model, the correct modelling of the longitudinal geometry of the wheel flat is actually seen to have a larger influence on the maximum impact force than the choice of contact model.