Prediction and Suppression of Chaotic Instability in Brake Squeal

Chaotic instability in a vibration phenomenon, known as brake squeal, is investigated including the combined effects of falling friction and mode coupling. Brake squeal is a high-pitched noise that occurs sometimes when a vehicle is decelerated using disk 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 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. 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.