Abstract: Hertzian spring is widely used today in many dynamics models of high frequency wheel-rail interaction, but its applicability to high speed railways has not been validated. For cases of Hertz contact, two multi-body dynamics based models, a wheel-track coupled dynamics model and a vehicle dynamics model, are developed, in which Hertzian springs are employed to represent the normal contact. Meanwhile, a 3-D transient rolling contact model is developed for reference using the explicit finite element method, in which the rolling contact is solved by a surface-to-surface algorithm in the consideration of actual contact geometries. High-frequency normal contact forces calculated at 150-500 km/h and in the presence of typical corrugation (wavelength 20-140 mm and depth 0.01-0.20 mm) show that significant difference exists among the contact forces predicted by the three models, but for relatively shallow corrugation (no contact loss occur) a linear relationship has been obtained between the corrugation depth and the amplitude of the contact force by all three models. In detail, the normal contact forces predicted by the wheel-track coupled dynamics and the vehicle dynamics models are significantly higher than those by the transient rolling contact model, their maximum over-estimations are 39.2% and 88.4% of the static load, respectively, and the obtained critical depths, at which wheel and rail lose contact during rolling, deviate significantly with the employed models, being greater than 0.2 mm, 0.14 mm and 0.05 mm for the three model, respectively, when the wavelength of 30 mm is taken. In a word, significant errors exist in predictions of high-speed and high frequency wheel-rail interactions if the traditional Hertzian spring is employed.

Key words: high-frequency wheel-rail dynamic interaction, explicit finite element method, surface-to-surface contact algorithm, multi-body dynamics, hertz spring, rail corrugation