Stability Analysis and Improvement of Uncertain Disk Brake Systems With Random and Interval Parameters for Squeal Reduction

Stability analysis and improvement of disk brake systems for squeal reduction have been investigated by automotive manufacturers for decades. However, most of the researches have not considered uncertainties. For this case, a practical approach for analyzing and improving the stability of uncertain disk brake systems is proposed in this paper. In the proposed approach, a hybrid uncertain model with random and interval parameters is introduced to deal with the uncertainties existing in a disk brake system. The parameters of brake pressure, densities of component materials, and thickness of back plate are treated as random variables; whereas the parameters of frictional coefficient and Young's modulus of component materials are treated as interval variables. Attention is focused on stability analysis of the disk brake system for squeal reduction, and the stability is investigated via complex eigenvalue analysis (CEA). The dominant unstable mode is extracted by performing CEA based on a linear finite element (FE) model, and the negative damping ratio corresponding to the dominant unstable mode is selected as the indicator of system stability. To improve the efficiency of analysis, response surface methodology (RSM) is used to replace the time-consuming FE simulations. Based on RSM and CEA, the stability analysis model of the disk brake system is constructed, in which reliability analysis, hybrid uncertain analysis and sensitivity analysis are applied to deal with the uncertain problems. The analysis results of a numerical example demonstrate the effectiveness of the proposed approach, and show that the stability and robustness of the uncertain disk brake system can be improved effectively by increasing the stiffness of back plate.