Analysis of vibration and squeal noise of a brake rotor using a simplified model

Abstract

Brake squeal is a very notorious noise phenomenon which occurs during the process of vehicle braking. Even now, consentaneous explanation of such phenomenon still evades researchers due to its fugitive nature and the complex physical interactions between different components involved in a brake system, among which the brake rotor is the most crucial one. This study proposes a simplified brake rotor model with an attempt to deepen the understanding on the generation of brake vibration and the high-frequency sequel noise. More specifically, structural analysis, response/stability analysis and sound radiation of the brake rotor system are investigated. The proposed brake rotor model is a combination of an annular plate and a cylindrical shell segment connected together by distributed artificial springs. This model is believed to be representative enough for high-frequency squeal noise problem on the one hand, and simple enough to be handled using a semi-analytical approach on the other hand. Compared with other existing models and simulation approaches, one of the obvious advantages of such a simplified model resides in the flexibility it offers to carry out various analyses. Based on a three-dimensional elasticity theory, a numerical procedure is established using variational principle and Rayleigh-Ritz method. Modal analyses show the existence of three types of modes, classified as plate-dominant-modes, shell-dominant-modes and strongly-coupled-modes. Each mode of the combined structure is also decomposed into a linear combination of the individual sub-structure modes, such providing a direct and systematic means to carry out modal classification and quantification. The dynamic interaction between the brake rotor and the pad is investigated based on a parametric excited vibration system, i.e. the combined structure under the excitation of a rotating spring-damper -mass (SDM) system. Time domain responses of the system are simulated through Green's function with results validated using Finite Element simulation data. The effects of various parameters on the response feature are thoroughly investigated through comparative studies among various excitation configurations. Such a model is shown to be able to predict the occurrence of instability in the brake rotor, which is mainly responsible for the generation of the high- frequency brake squeal. A comprehensive stability analysis is performed using Valeev's method when the excitation involves only a spring component. It is shown that instability occurs when the rotation speed and the natural frequencies of the system satisfy a certain condition. The general understanding on the vibration feature and the previously developed model are further used to study the sound radiation of the system. The radiation surface of the brake rotor is assumed to be rigidly baffled. Based on Rayleigh's formula, the modal radiation properties and modal coupling effect on sound radiation of the combined structure are discussed, and the time history of the sound power of the parametric excited vibration system is worked out. At last, the effect of the radiation damping incurred by the structure/fluid interaction is taken into account in the analysis. It is shown that structure/sound coupling may have a stabilization effect on this parametric excited system.