Transient non-linear dynamic analysis of automotive disc brake squeal – On the need to consider both stability and non-linear analysis

This paper outlines the non-linear transient and stationary dynamics due to friction-induced vibrations in a disc brake model. Using a finite element model and the Continuous Wavelet Transform, the contributions of fundamental frequencies and harmonic components in non-linear transient and stationary dynamics are investigated for disc brake system subjected to single and multi-instabilities. Results from these non-linear analyses demonstrate the complexity of the contributions of different harmonic components in transient friction-induced vibrations with the coexistence of multi-unstable modes. One of the most important contributions of this study is to illustrate the limitation of stability analysis related to transient and stationary non-linear behaviors. Stability analysis around an equilibrium point can only be used as the first step in providing information on the onset and increase of self-excited disc brake vibrations. Consequently, a complete non-linear analysis is necessary to fully predict non-linear vibration and the contribution of unstable modes. This study shows that an under-estimation of the unstable modes observed in the non-linear time simulation can be calculated by the stability analysis. During transient vibrations, an additional unstable mode can appear. This instability is not predicted by the complex eigenvalues analysis due to the fact that linear conditions (i.e. the linearized stability around an initial equilibrium point) are not valid during transient and stationary oscillations. So new fundamental frequencies (linked to the appearance of the new unstable mode) can emerge in the signals due to the non-linear contact and loss of contact interactions at the frictional interface. Therefore, non-linear transient and stationary self-excited vibrations can become very complex and include more unstable modes than those predicted by a linearized stability analysis around a non-linear equilibrium point.