Methods to calculate accurate wheel/rail contact positions and static contact stress levels

The key requirement to calculate the fatigue and wear levels of wheels and rails is to establish a method that can accurately represent the wheel/rail contact stress. Wheel and rail surfaces are composed of a series of surfaces each with a different curvature, which makes research on wheel/rail contact very difficult. In this paper, a wheel from a passenger train with a LM-type worn tread profile and a 60 kg/m rail are taken as the research objects in a study on the contact positions and static contact stress. An analytical model for accurately finding the contact position is established by building and solving wheel and rail profile equations. Furthermore, a slice-based model is established to calculate the contact stress of a contact point, especially for points on the profiles near the junction of two surfaces with different curvatures. The error created by using the slice-based model is corrected so as to make the calculation more accurate. An example, in which the axis load is 18 t, is analyzed. The maximum contact stress, deformation and contact spot size are calculated, and some useful conclusions are obtained. The research presented in this paper can provide a reliable foundation for future research on wheel and rail fatigue, friction and wear.