Instability analysis of friction oscillators with uncertainty in the friction law distribution

Abstract

Despite substantial research efforts in the past two decades, the prediction of brake squeal propensity, as a significant noise, vibration and harshness (NVH) issue to automotive manufactures, is as difficult as ever. This is due to the complexity of the interacting mechanisms (e.g. stick-slip, sprag-slip, mode coupling and hammering effect) and the uncertain operating conditions (temperature, pressure). In particular, two major aspects in brake squeal have attracted significant attention recently: nonlinearity and uncertainty. The fugitiveness of brake squeal could be attributed to a number of factors including the difficulty in accurately modelling friction. In this paper, the influence of the uncertainty arising from the tribological aspect in brake squeal prediction is analysed. Three types of friction models, namely the Amonton-Coulomb model, the velocity-dependent model and the LuGre model, are randomly assigned to a group of interconnected oscillators which model the dynamics of a brake system. The complex eigenvalue analysis, as a standard stability analysis tool, and the friction work calculation are performed to investigate the probability for instability arising from the uncertainty in the friction models. The results are discussed with a view to apply this approach to the analysis of the squeal propensity for a full brake system.