Kinematics modelling and numerical investigation on the hunting oscillation of wheel-rail nonlinear geometric contact system

In the research of the wheelset's hunting oscillation, it is found that if the wheel-rail geometric contact is nonlinear, the wheelset oscillation will produce the high-order odd harmonic frequencies (HOHFs) besides the hunting fundamental frequency. In the existing literature, the HOHFs are rarely discussed. Based on the Klingel's linear model, the kinematics model of a wheel-rail nonlinear geometric contact system is established, and equation analysis proves that there are only odd harmonics in the hunting oscillation without even harmonics. The HOHFs energy is concentrated in the strongly nonlinear zone of wheel-rail geometric contact, which is an important manifestation of the wheel-rail hunting impact. The numerical simulations of an isolated wheelset model and a complete vehicle model are conducted to study the HOHFs performance on the vibration of the wheelset and bogie frame. The results show that the HOHFs can produce the lateral vibration responses of the bogie frame, such as the 3rd harmonic, and track irregularity and primary suspension can disturb or restrain the HOHFs vibration response, such as the 5th and 7th harmonics. The wheel-rail nonlinear kinematics model proposed in this paper is an extension to the classical Klingel's linear model. Like the hunting fundamental frequency, the HOHFs perform as the sources of the self-excited oscillation in rail vehicles, which is of great significance to the research of the train hunting instability and its condition monitoring methods.