Suppression of Friction-Induced Oscillations through Use of High-Frequency Dither Signals
Michaux, Michael Andre
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Friction-induced oscillations occur in many engineering systems, often resulting in noise, vibration, and excessive or uneven wear. This research addresses the suppression of such oscillations, especially with application to braking systems, through the use of high-frequency dither signals. Brake squeal is an annoying and elusive problem too often present in braking systems of automobiles, trucks and aircraft. In previous work, the effectiveness of high-frequency dither to eliminate squeal in an automotive disc brake assembly was demonstrated experimentally. The main features of the dither-squeal cancellation system was the application of a high frequency variation in the brake pressure force accomplished by means of a piezoelectric stack placed behind one of the brake pads. This thesis contains a theoretical and numerical treatment of the application of dither to frictional systems. Two types of systems are investigated. The first is a classic, mass-on-a-moving belt problem, which experiences friction-induced oscillations similar to those encountered in brake applications. The system is first studied using an analytical technique based on the method of averaging. It is shown that, depending on the system, friction, dither-waveform, and belt-speed parameters, dither can stabilize an unstable system. However, in some cases, dither can destabilize an initially stable system. These results are verified numerically using time integration. The second type of system analyzed in this thesis is an annular plate with a rotating frictional device. The method of multiple scales is used to predict subcritical regions of instability; the results are validated using Floquet theory. The thesis treats both tangential and normal dither, the latter being closer to the brake application. It is found that normal dither, in addition to being harder to analyze, is much less effective than tangential dither.