Comparisons between beam and continuum models for modelling wheel-rail impact at a singular rail surface defect

A singular rail or wheel surface irregularity, such as a squat, insulation joint or wheel flat, can cause large wheel-rail impact force. Both the magnitude and frequency content of the impact force need to be correctly modelled because they are closely related to the formation, deterioration and detection of such irregularities. In this paper, we compare two types of commonly used wheel-track interaction models for wheel-rail impact problems, i.e., a beam and a continuum finite element model. We first reveal the differences between the impact forces predicted by the two models due to a typical rail squat using a time-frequency analysis. Subsequently, we identify the causes for the differences by evaluating the effects of different model assumptions, as well as different model parameters. Results show that the impact force consists of a forced vibration peak M1 followed by free vibration related oscillations with three dominant frequencies: f(1) (340 Hz), f(2) (890 Hz) and f(3) (1120 Hz). Compared with the continuum model, the beam model with a Hertzian contact spring overestimates the M1 peak force. The discrepancy can be reduced by using a Winkler bedding contact model. For the track model, the beam model is comparable to the continuum model up to about 800 Hz, beyond which the track damping starts to deviate. As a result, above 500 Hz, the contact forces dominate at f(2) for the beam while at f(3) for the continuum model. Finally, we show that the continuum model is more accurate than the beam model by comparing to field observations. The effects of stress wave propagation on the differences are also discussed.