A universal approach to squeal analysis of the disc brakes involving various types of uncertainty

Abstract

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.

An optimization method for brake instability reduction with fuzzy-boundary interval variables

“…An automotive disk brake is depicted in Figure 3, which has been studied in our earlier work. 7 This brake is made up of several key components: a brake disk, a pair of brake pads, a bracket, a calliper, two guide pins, a hydraulic actuation system, and so on. Each brake pad is constituted by a lining and a back plate.…”

“…For this brake, a critical unstable frequency has been predicted at around 7.4 kHz by performing complex eigenvalue analysis and transient dynamic analysis. 7 Based on the critical unstable eigenvalue and response surface methodology, a brake instability index has been constructed as a function of system parameters in Lü et al 7 In this study, the brake instability index is defined as the absolute value of the damping ratio of critical unstable eigenvalue. To reduce brake squeal potential, it is very common to set a target value for the brake instability index in the literature.…”

“…Over the past few decades, the issues of uncertainty analysis and optimization have attracted more and more attention in scientific fields, such as the fields of material science, 2 structural mechanics, 3,4 and automotive engineering. 5–7…”

A study of the influence of heterogeneous friction coefficient and heterogeneous contact stiffness on the generation of squeal

“…The squeal uncertainty was analyzed when system parameters such as average friction coefficient, Young modulus of the disc, densities of key components were treated as interval variables, random variables, fuzzy variables and so on. 47–51…”

“…The squeal uncertainty was analyzed when system parameters such as average friction coefficient, Young modulus of the disc, densities of key components were treated as interval variables, random variables, fuzzy variables and so on. [47][48][49][50][51] Besides, some methods are proposed to improve the calculation efficiency of braking squeal uncertainty. Sarrouy et al 52 applied piecewise polynomial chaotic to process stochastic eigenvalue problems efficiently.…”