Brake squeal instability: linear and nonlinear numerical approaches

“Brake squeal” groups a large set of high-frequency sound emissions from brake systems. They are generated during the braking phase and are characterized by a harmonic spectrum. The onset of squeal is due to an unstable behaviour occurring in linear conditions during the braking phase, and a general approach used by several authors to determine the system instabilities is the complex eigenvalues analysis. When the brake begins to squeal, the response of the system reaches a new limit cycle where the linear models cannot be used anymore. This paper presents the integration of two different numerical procedures to identify the mechanism bringing to squeal instability and to analyse its dynamics. The first approach is a finite element modal analysis of the brake system and is used to identify its eigenvalues and to relate them to the squeal occurrence. The second one is a specific finite element programme, Plast3, appropriate for nonlinear dynamic analyses in the time domain and is particularly addressed to study contact problems with friction between deformable bodies. This programme computes the contact stresses and permits to determine the dynamics of the system along the contact surface, both in the linear and nonlinear fields. The two models are compared and the onset of squeal is predicted both in the frequency domain by the linear model and in the time domain by the nonlinear one. The instability predictions, obtained by the two models, are discussed. To simplify the dynamics of its components, the study is carried out on a simple model, made of a disc, a small friction pad and a beam supporting the pad. The geometry of the model is related to an experimental set-up used to validate the models and to compare the numerical results with the experiments.