Stochastic Bifurcation and Behavior Analysis of 4WID Vehicle Disc Brake With Driving Torque Control

Abstract The driving force of each wheel in a four-wheel independent drive (4WID) vehicle can be independently controlled, which provides a new approach for controlling the brake chatter. Since the model simplification, parameter errors can lead to significant uncertainty in the dynamic model of the brake chatter, making it difficult to select control parameters. Hence, a stochastic dynamic model of 4WID vehicle disc brake with stiffness uncertainty of brake pad is proposed, the control algorithm of the driving torque is designed by using the proportional-derivative control method. Then, the stochastic averaging method is used to solve the averaged Itô differential equation, the stochastic stability of the brake system for different control parameters is discussed by means of the boundary type of the one-dimensional energy process. Furthermore, the Fokker Planck Kolmogorov equation is derived, the dynamic bifurcation boundary and phenomenological bifurcation boundary of control parameters are analytically obtained by using the bifurcation coefficient. Meanwhile, the influences of the noise intensity, equivalent lateral damping, and brake pressure of the brake pad on the bifurcation boundary are discussed. The results indicate that the increase of the equivalent lateral damping and the decrease of the noise intensity and brake pressure are effective measures to expand the stability region of control parameters. Finally, the energy probability density and joint probability density are numerically simulated to verify the analytical analysis of the stochastic stability and bifurcation characteristics, which provides technical supports for optimizing control parameters of the brake chatter.