The Role of Nonlinearity and Uncertainty in Assessing Disc Brake Squeal Propensity

Despite significant progress made in the past 20 years in discovering some of the mechanisms of brake squeal, it remains difficult to predict the underlying friction-induced instabilities reliably. Most numerical analyses are based on linear deterministic analyses of structural vibrations such as the complex eigenvalue analysis (CEA). However, nonlinear multi-scale processes govern friction contact with high sensitivities to operating and/or environmental conditions. In addition, uncertainties in the material properties and boundary conditions such as contact and friction laws are rarely considered. Hence, it is quite common to underpredict or overpredict the number of instabilities and extensive brake noise dynamometer tests are still required in industry to ensure acceptable brake noise performance. In this paper, simplified finite element brake models are used to illustrate the role of nonlinearity in brake squeal. By using nonlinear time series analyses, forced response calculations, dissipated friction work and acoustic radiations, unstable pad modes have been found to be responsible for the instantaneous mode squeal which, although observed experimentally, cannot be predicted with the traditional linear CEA. By considering coupled spring-mass-damper oscillators representing a pad on a sliding plate, the role of uncertainties of contact stiffness and friction laws in brake squeal is examined using probabilities of the positive real part of complex eigenvalues and positive friction work. The implications of nonlinearity and uncertainty for brake squeal predictions are discussed. Suggestions on how the new insights gained into nonlinearities and uncertainties can be exploited for practical brake squeal analyses in industry are proposed.