An improved brake squeal source model in the presence of kinematic and friction nonlinearities

The goal of this paper is to investigate the source characteristics of brake squeal. An improved model is suggested where a point mass is in contact with a belt moving at constant velocity. First, the governing equations with kinematic and friction nonlinearities are formulated. The kinematic nonlinearities arise from an arrangement of the springs that support the point mass, as well as from a loss of contact between the belt and the mass (due to its vertical motion). Second, the nonlinear equations are numerically solved, and a wide range of dynamic responses are observed. Results show that some assumptions made in prior articles, where a linearized model was utilized, are not valid. Third, the nonlinear equations are simplified by ignoring the contact loss nonlinearity, and then linearized about an operating point for stability considerations. Instability regimes are then obtained for a set of parameters. Further, coupled modes are found even though some contradictions between the model assumptions and linearized system solutions are observed. It is concluded that the contact loss nonlinearity is crucial, and it must not be ignored for squeal source investigation.