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

Abstract

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. The dynamic model of the brake chatter exhibits significant uncertainty due to model simplification and parameter errors, which makes it difficult to select control parameters. Hence, a stochastic dynamic model of 4WID vehicle disk brake with stiffness uncertainty of brake pad is proposed, and 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, and 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 (FPK) equation is derived, and 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 support for optimizing control parameters of the brake chatter.