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A Hybrid Method to Obtain the Wheel–Rail Contact Point at Extreme Positions

When conducting a numerical simulation of a train’s derailment and post-derailment, it is necessary to continuously observe the relative position of the wheel and rail, which is of great significance for the correct evaluation of train safety. In this paper, a non-analytic method is proposed to extend the search range and improve the accuracy of the classical semi-analytical method, i.e. the contact locus method. Based on the point cloud convex hull, a high-density wheel contact locus vertical profile is obtained by projecting the chamfer and internal zone of the flange onto the rail cutting plane. To obtain maximum compression in the normal direction and avoid singularities on both rail head sides in the Cartesian coordinate system the rail surface is interpolated with the polar spline curve. Compared with the classical method used to describe the wheel contact locus, in the proposed hybrid method, potential contact points are provided. Finally, the proposed hybrid method and the classical methods are applied to the wheel track coupling simulation. Numerical results demonstrate the high reliability and effectiveness of the proposed method.