Calculation Method of Hertz Normal Contact Stiffness

Elastic contact deformation between the wheel and rail is pivotal in the computation of the wheel-rail contact force in the vehicle-track coupled dynamics. Based on the Hertz contact theory, the nonlinear contact stiffness is used to depict the relation of the wheel-rail normal contact force and their relative compression. The current empirical formulas of the Hertz contact stiffness for the wheel-rail contact are based on the work of British Railway in 1970 s, and are classified into two categories, i.e., coned profile and worn profile. However, they are restricted to specific wheel radii and rail profiles. In this work, based on Hertz contact theory, the general formulas of the elastic normal contact stiffness are deduced, which can satisfy the Hertz contact conditions. According to the characteristics of the wheel-rail geometry, the dimension of wheel-rail contact spots and contact stiffness parameters are tabulated and determined. Finally, an example of LM wheel profile and CN60 rail profile is used to compare the results of the empirical formulas and those of the proposed formulas. The results show that the Hertz contact parameter table formed by the proposed contact formula makes up the absence of the contact stiffness in the current ones, and can be used directly in elastic contact calculation. When the circle around the nominal center of the wheel profile and the central circle of the rail head are in contact, the results calculated by empirical formulas have less error in the contact stiffness deviation of the worn tread, which varies in 0.40% − 0.44%. Otherwise, there is a significant difference between the results of empirical formulas and those of the proposed formulas, the range of which is −25.97% −131.42%.