Determination of the wheel rail contact patch in semi-Hertzian conditions

This paper deals with the subject of the semi-Hertzian contact, which is a way to represent the wheel rail contact in railways or roller bearing applications. The method is based on the interpenetration of the two underformed bodies' profiles. The first step deals with the problem of the shape ratio; it is proposed to compensate the two main curvatures to obtain the good ratio in Hertzian conditions. Then, Hertz and Kalker's equations are used to establish the stresses at the level of a strip. These stresses expressions are used directly in a contact model discretized in strips and tabulated as a function of the lateral displacement between the wheel and the rail. The validation is made by comparison to the previous multi-Hertzian model of the VOCOLIN software. A first test shows identical results in Hertzian conditions; a second one shows only a small difference in semi-Hertzian conditions like S1002/UIC60 1:40.