An equivalent ellipse model for wheel-rail contact with applications to vehicle-track coupled dynamics

Purpose In vehicle-track coupled dynamics, the wheel-rail contact model is particularly important because its accuracy and stability determine the effectiveness and reliability of the vehicle-track coupled model. The aim of this article is to propose a model that can satisfy the efficiency and accuracy of the dynamics. Design/methodology/approach This article proposes an equivalent ellipse model (EEM) that considers non-Hertz geometry gaps. Using CONTACT as a reference, the accuracy and stability of the model are validated in both static contact and dynamic applications. Findings The results show that in static contact, EEM exhibits higher accuracy in both the normal and tangential directions, compared to the Hertz theory. In dynamic applications, two specified cases are considered: straight track with lateral irregularity and curved track. The Hertz theory exhibits instability in the curved track compared to the EEM. The critical speed calculated by EEM is also closer to CONTACT than that of Hertz theory, showing great accuracy. Finally, as a rapid algorithm, EEM exhibits computational efficiency comparable to the Hertz theory, being several times faster than CONTACT. Originality/value The novelty of this method is that it uses the ratio of length and width obtained from KP method to re-solve the Hertz theory. At the same time, this is different from the Hertz theory, which uses the curvature of the contact point as the input and avoids the error caused by excessive curvature changes near the contact point.