Non-Linear Analysis of Disc Brake-Induced Vibrations for Railway Vehicles

Abstract

In this article, a two-degree-of-freedom model for the disc brake system is set up by considering the vertical motion of the brake unit and the pitch motion of the bogie frame, and the sliding friction interface between the brake lining and disc is included in the model. Using the Hurwitz determinants, an algebraic criterion for determining the Hopf bifurcation point of the system is proposed. The vehicle speed at the Hopf bifurcation point is defined as the critical speed where the equilibrium position of the disc brake system loses stability and the limit cycle emerges. In order to investigate the stability of the disc brake system, parametric studies are undertaken. It is shown that the mass of brake unit, vertical damping of primary suspension, friction coefficient, and brake normal force between the lining and disc have significant influences on the critical speed. The instability of the system may not occur if the parameters are properly designed. The limit cycle arisen due to the loss of stability of the equilibrium position is studied using the numerical integration method. It is found that once the brake system loses its stability at a certain speed, the stick—slip motion occurs and the limit cycle oscillation will last until the vehicle comes to a standstill. It is also known that the frequency of limit cycle is significantly affected by the mass and suspended stiffness of the brake unit but is not related to the vehicle speed in the braking process.