Bifurcation and Chaotic Behaviors of Vehicle Brake System Under Low Speed Braking Condition

Purpose The coupling system of brake disc and brake sub-system responds in a variety of nonlinear dynamics manner under low-speed braking condition. In this article we aim to obtain the bifurcation and chaotic behavior of vehicle brake system under this condition. Methods We established a pure brake condition 4-DOF differential equations of torsional vibration in this paper based on Crowther's model, which predicts the existence of chaotic stick-slip vibration. Based on this model, by means of numerical methods, we have calculated firstly the low-speed bifurcation characteristics of the brake disc and brake sub-system angular velocity difference relative to vehicle speed, and secondly the effects of system parameters on the bifurcation. Material Metal type, semi-metallic type, non-metallic type friction material. Results The results showed that: brake disc and brake sub-system angular velocity difference exhibits chaotic vibration in the low-speed zone. With the increase of inertia ratio of brake sub-system and brake disc, system vibrations changed from periodic doubling bifurcation to chaos, then inversed back to doubling period and single period stick-slip motions. With the increase of ratio of the kinetic friction coefficient and the static friction coefficient, system vibrations changed from chaotic stick-slip motions to single period stick-slip motions. With the increase of brake pressure, the system stick-slip vibrations changed from doubling bifurcation to chaos, which worsened the vehicle chatter. Conclusions The results can provide theoretical guidance for parameter design, which can optimize the chaos interval, but we need further experiments to explore and study.