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.
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