Dynamic response and stability analysis of brake chatter with stochastic parameter perturbation

The parameter perturbation makes it difficult to analyze the dynamic mechanism of the brake chatter with the help of an ideal deterministic model. Hence, a stochastic dynamic model of brake chatter with the uncertainty of the torsional stiffness of the brake disc is established, the Stribeck model is used to describe the friction characteristic between the brake pad and brake disc. Then, the Itô stochastic differential equation is solved by means of the stochastic averaging method, the boundary type of the one-dimensional energy process is identified to discuss the stochastic stability of the brake system. Furthermore, the Fokker Planck Kolmogorov equation is derived, the dynamic bifurcation and phenomenological bifurcation are analytically proven, the influences of parameters, such as noise intensity, brake pressure, and friction coefficient, on bifurcation characteristics are revealed. The results show that the noise intensity, brake pressure, and friction coefficient difference need to be reduced to improve the system stability. Finally, the probability density function of the brake system is used to validate the analytical analysis. The relevant results provide a theoretical basis for better suppressing the brake chatter.