Parametric excitation of railway car body sway induced by nonlinear air spring stiffness

Aiming at the phenomenon of low-frequency lateral car body sway still occurring in railway vehicles when operating below the critical speed, this paper investigates the phenomenon of parametrically excited vibration of the car body sway by considering the nonlinear characteristics of the air spring. The study first established a vertical dynamic model of the air spring based on air thermodynamics, and then a quadratic polynomial was used to describe the nonlinear stiffness characteristics obtained by polynomial fitting of the dynamic stiffness. Building upon this foundation, a 3-DOF vehicle dynamics model was established, encompassing car body bounce, rolling, and lateral motions. The research employed the method of multiple scales for the analytical solution of the simplified system equations, and the fourth-order Runge-Kutta method was used for numerical solution to verify the accuracy of the analytical method. The analysis results indicate that when the vertical excitation frequency of the bogie frame is twice the natural frequency of the system's sway motion, the car body’s lateral sway motion will be excited. The critical threshold for exciting the vehicle’s lateral vibration is related to the vehicle's structural and suspension parameters, and its magnitude is positively correlated with the secondary suspension damping and the natural frequency of the vehicle system's sway motion. By comparing with the 10-DOF vehicle dynamics model, it was found that the phase difference caused by the track wavelength weakens the amplitude of the car body's bounce motion, thereby attenuating the car body's lateral vibration. The conclusion suggests that since the frequency band for the parametric resonance phenomenon is narrow, it can be avoided by modifying the vehicle’s structural or suspension parameters.