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 multiinstabilities. 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.

The acoustic response associated with squeal noise radiations is a hard issue due to the need to consider non-linearities of contact and friction, to solve the associated nonlinear dynamic problem and to calculate the noise emissions due to self-excited vibrations. In this work, the focus is on the calculation of the sound pressure in free space generated during squeal events. The calculation of the sound pressure can be performed by the Boundary Element Method (BEM). The inputs of this method are a boundary element model, a field of normal velocity characterized by a unique frequency. However, the field of velocity associated with friction-induced vibrations is composed of several harmonic components. So, the BEM equation has to be solved for each frequencies and in most cases, the number of harmonic component is significant. Therefore, the computation time can be prohibitive. The reduction of the number of harmonic component is a key point for the quick estimation of the squeal noise. The proposed approach is based on the detection and the selection of the predominant harmonic components in the mean square velocity. It is applied on two cases of squeal and allows us to consider only few frequencies. In this study, a new method will be proposed in order to quickly well estimate the noise emission in free space. This approach will be based on an approximated acoustic power of brake system which is assumed to be a punctual source, an interpolated directivity and the decrease of the acoustic power levels. This method is applied on two classical cases of squeal with one and two unstable modes. It allows us to well reconstruct the acoustic power levels map. Several error estimators are introduced and show that the reconstructed field is close to the reference calculated with a complete BEM.