Dynamics Analysis Of Stability, Bifurcation, And Chaos Of Vehicle Brake Groan At Low Speeds

Brake groan at low speed is one of the tough problems that have been always puzzling in the automotive industry, and one of the theory contributes it to a self-excited stick-slip vibration that induced by the negative correlations between friction and velocity (Stribeck characteristic). Numerous scholars have conducted many researches and established different dynamic models to simulate and study these phenomena. However, most of their research achievements concentrate on the periodic stick-slip vibration, and leave the bifurcation and chaos of stick-slip vibration seldom reported. The main content of this paper are as follows:(1) A new dynamic model of disc brake that comprehensively considers the pad tangential vibration and disc torsional vibration was established. Then, a stability analysis is conducted by applying a smoothed exponential dry friction model, and found the instability of brake system is induced by Hopf bifurcation. Moreover, the numerical calculation determined that the vibration mode could mainly divide into two stages:1. the system vibration could easily maintains in the stable limit cycle within a relatively wide range of low angular velocity; 2. the vibration mode is easy to change by decreasing the angular velocity to lower, and the period doubling bifurcation and chaos will occur. Finally, the feasible periodic vibration region was optimized by using the maximum Lyapunov exponent diagram.(2) A disc brake dynamic model of a pad with two layer structure was established based on the above model. First, a stability analysis is conducted to study the effects of mass distribution and joining stiffness of pad on system stability. Then, a numerical calculation was conducted to optimize the up layer amplitude by selecting proper mass distribution and joining stiffness at low angular velocity; also, the two parameters are optimized to reduce chaotic vibration at lower angular velocity.(3) Some numerical calculations were conducted based on the first brake system model with several friction models that have different function forms, and the results show that the bifurcation and chaos are independent to the function form of friction model. Then, a random friction model was proposed, and the effects of friction coefficient boundary on system vibration are studied basically.