Critical speed of high-speed trains considering wheel-rail contact

The maximum speed of a high-speed train is limited to its critical speed. In this study, the definition of critical speed is reviewed. The relationship between creepage and creep force and the effects of the parameters of the first and second suspension systems are also studied using a bogie model to increase the critical speed. Kalker’s linear creep theory and its modification of Wormey’s saturation constant are reviewed. The nonlinear creep force of Vermeulen’s creep theory, Polach’s calculation, and the newly calculated longitudinal and lateral creep forces using strip theory from wheel-rail contact pressure are investigated for the critical speed. Flange contact is also considered when lateral displacement exceeds the dead band between wheel flange and rail. Direct numerical integration and a shooting algorithm are devised to calculate the response, especially for the limit cycle. Results show that as speed increases, the equilibrium point becomes unstable and creates a limit cycle through a Hopf bifurcation. The unstable fixed point can be a critical speed. The critical speed increases as the creep curve becomes stiff before saturation, which is more effective than the variation in suspension parameters. The consideration of flange contact can also increase the critical speed.