Noise and vibration for a self-excited mechanical system with friction

This work proposes a complete characterization of brake squeal from the calculation of the non-linear vibration to the calculation of the associated sound pressure. A simplified finite elements brake system model composed of a disc and a pad is investigated. The contact is modelled by introducing several local contact elements at the friction interface and a cubic contact law is used to describe the contact force. The classical Coulomb law is applied to model friction and the friction coefficient is assumed to be constant. The stability analysis of this system provides two classical cases of instabilities which are single and multi-instabilities. For one and two unstable modes, non-linear time integrations and spectrum analysis are performed to detect all the harmonic components in the velocity spectrum. In this paper, the decomposition by harmonic components of the velocity is used to calculate the acoustic radiation by applying the boundary element method for each contributions. The sound pressure radiated is calculated for the two cases under study and a comparison in terms of levels and directivity is provided. It can be noted that the two unstable modes case presents significantly higher levels of acoustic pressure. In near field, directivity patterns for both cases are composed of four main lobes with different orientations. Moreover, over others observation plan, the multi-instabilities case presents a more complex directivity pattern due to the participation of two modes in the time response. Finally, the study of the influence of the truncation shows that for both cases, the first two harmonic components are enough to describe to global pressure field with a good accuracy.