Comparison and Verification of Vertical Wheel-Rail Contact Models

In the coupling vibration of vehicle-track system, Hertz nonlinear wheel-rail connect model precisely describes the normal wheel-rail forces. Because of the nonlinear wheel-rail relationship, the vehicle-track system can only be solved iteratively with very small time step, which leads to a slow computation process. To simplify the calculation of wheel-rail force, the secant linear model and the tangent linear model are put forward and their vertical wheel-rail stiffness, additional stiffness matrix, and additional force vector of the vehicle-track system by the vertical wheel-rail forces are deduced. To prove the two linear-approximation wheel-rail connect models, the CRTS-II slab ballastless track is taken for example and the vertical wheel rail forces of the vehicle-track system under the three vertical wheel-rail contact models are compared when an individual vehicle passes the track at a speed of 250 km/h. The results show that the time-variant wheel-rail stiffness of Hertz nonlinear wheel-rail connect model is different from that of secant linear model or tangent linear model. However, the excitation of vehicle-track system is essentially the rail irregularity and the static wheel load. With constant rail irregularity and static wheel load, when the vertical wheel-rail stiffness is different, the vertical wheel-rail relative displacement is changed to meet almost the same of the vertical wheel-rail force.