On the potential of uncertainty analysis for prediction of brake squeal propensity

Brake squeal is a source of significant warranty-related claims for automotive manufacturers because it is annoying and is often perceived by customers as a safety concern. A brake squeal analysis is complex due to changing environmental and operating conditions, high sensitivity to manufacturing and assembly tolerances as well as the not so well understood role of nonlinearities. Although brake squeal is essentially a nonlinear problem, the standard analysis tool in industry is the linear complex eigenvalue analysis (CEA) which may under-predict or over-predict the number of unstable vibration modes. A nonlinear instability analysis is more predictive than CEA but is still computationally too expensive to be used routinely in industry for a full brake finite element model. Also, although the net work analysis of a linearised brake system has shown potential in predicting the origin of brake squeal, it has not been extensively used. In this study, the net work of an analytical viscously damped self-excited 4-dof friction oscillator with cubic contact force nonlinearity is compared with the instability prediction using the CEA and a nonlinear instability analysis. Results show that both the net work analysis and CEA under-predict the instability because of their inability to detect the sub-critical Hopf bifurcation. Then, the uncertainty analysis is applied to examine if it can improve instability prediction of a nonlinear system using linear methods and its limitations. By applying a variance-based global sensitivity analysis to parameters of the oscillator, suitable candidates for an uncertainty analysis are identified. Results of uncertainty analyses by applying polynomial chaos expansions to net work and CEA correlate well with those of the nonlinear analysis, hence demonstrating the potential of an uncertainty analysis in improving the prediction of brake squeal propensity using a linear method.