Prediction and suppression of chaotic instability in brake squeal

Paul A Meehan

doi:10.1007/s11071-021-06992-1

Abstract

Chaotic instability in a vibration phenomenon, known as brake squeal, is investigated including the combined effects of falling friction, sprag-slip and mode coupling. Brake squeal is a high-pitched noise that occurs sometimes when a vehicle is decelerated using disc brakes. The equations of motion for the two dominant coupled modes of the brake system reduce to two autonomous coupled nonlinear second-order systems. The mode coupling instability via friction causes limit cycle behaviour via a supercritical Hopf bifurcation. This limit cycle is shown to break up into chaotic motion characterised by a Poincare map with a less than one-dimensional attractor, similar to that found in a forced dry friction oscillator. For the first time, conservative analytical conditions for brake squeal chaos are developed and verified numerically over a range of sprag angles and brake pressures for fundamental and real brake systems. The predictive model is then used to identify and quantify means to suppress brake squeal chaos to unlikely, excessive friction levels. The results provide predictive insight into conditions under which brake squeal chaos occurs and its suppression.

Highlights

Brake squeal is an annoying high-pitched tonal noise that occurs during braking of a vehicle using disk brakes
The mode coupling instability via friction causes limit cycle behaviour via a Hopf bifurcation. This limit cycle is shown to break up into chaotic motion characterised by a phase space with an approximate one-dimensional attractor, similar to that found in a forced dry friction oscillator
Comparisons of the full numerical solutions and the conservative analytical criteria derived in section 2.3 were performed and used to identify conditions under which chaotic instability occurs and its suppression over a range of friction coefficients, modal damping constants, sprag angles and brake pressures

Summary

Introduction

Brake squeal is an annoying high-pitched tonal noise that occurs during braking of a vehicle using disk brakes. There have been several specific mechanisms of brake squeal investigated, as reviewed in [2], including; falling friction, spragging [3][4] and mode coupling [8][9]. Spurr [3] first suggested the ‘sprag-slip’ mechanism for the instability of brake squeal He found a semi-rigid strut inclined to a moving surface could ‘sprag’ or dig into the moving surface and dynamically slip based on the static friction and the sprag angle [4]. North [8] identified the mechanism of mode coupling in automotive brake squeal, analogous to ‘binary flutter’, and Hoffman [9] performed a reduced model numerical analysis to provide important mechanistic insight and the effects of damping [10][21]. A closed form prediction for the occurrence, growth and amplitude of brake squeal was identified [18], but chaos was not investigated

Objectives

Methods

Results

Conclusion