Study on the improvement of semi-Hertzian wheel/rail contact algorithms

The normal stress distribution of the contact patch is the base for wheel/rail dynamic analysis as well as the wheel wear calculation. When the wheel polygonalization appears on the worn-type wheel tread of the high-speed trains, the lateral and longitudinal relative wheel/rail curvature around the contact patch will vary with the change of wheel circumferential position. In such a case, the commonly used Hertzian contact method cannot meet the calculation precision, while even the non-Hertzian method has relatively high precision, but its calculation efficiency cannot meet the demand of engineering application. A non-Hertzian method was introduced to analyze the influence of the wheel polygonalization on the contact patch. By studying the shape and the pressure distribution of the contact patches at different contact positions, it is found that when the wavelength of the wheel polygonalization is larger than 65 mm, the results of the improved semi-Hertzian method can agree well with the non-Hertzian method with reasonable computing time. Besides, to ensure that the calculation result can meet the accuracy requirement when the wheelset yaw motion occurs, the trace method is used to improve the semi-Hertzian method and verified by the contact method. © 2025 Periodical Offices of Chang’an University