Bifurcation Analysis for Brake Squeal

This article presents a perturbation approach for the bifurcation analysis of MDoF vibration systems with gyroscopic and circulatory contributions, as they naturally arise from problems involving moving continua and sliding friction. Based on modal data of the underlying linear system, a multiple scales technique is utilized in order to find equations for the nonlinear amplitudes of the critical mode. The presented method is suited for an algorithmic implementation using commercial software and does not involve costly time-integration. As an engineering example, the bifurcation behaviour of a MDoF disk brake model is investigated. Sub- and supercritical Hopf-bifurcations are found and stationary nonlinear amplitudes are presented depending on operating parameters of the brake as well as of tribological parameters of the contact.