A universal approach to squeal analysis of the disc brakes involving various types of uncertainty
On the basis of fuzzy random variables, a universal approach to squeal analysis of the disc brakes involving various types of uncertainty is proposed in this paper. In the proposed approach, first, the brake stability analysis function related to reliability is constructed with fuzzy random variables. Next, the fuzziness represented by fuzzy random variables is decomposed into interval uncertainties by using a level cut strategy. Then, the expectations and the variances of the brake stability analysis function are approximately solved by the random moment method at different cut levels, and the lower bounds and the upper bounds of the expectations and the variances are calculated by using a first order Taylor expansion and a subinterval analysis. Finally, by combining the different interval solutions with the corresponding cut levels, the fuzzy solutions of the brake stability analysis function are obtained, which can be employed to evaluate the brake squeal instability. The proposed approach provides a universal framework for dealing with various types of uncertainty that may exist in automotive brakes. The universality, the accuracy and the efficiency of the proposed approach to the squeal instability analysis of the brakes involving various types of uncertainty are verified by the analysis results from nine different numerical examples.