Chaos Control in Attitude Dynamics of Automotive Disc Brake System Based on Synchronization

基於同步化應用於車輛碟式煞車系統之渾沌控制

張舜長(Shun-Chang Chang)

《中國機械工程學刊》 39卷5期 (2018/10) Pp. 443-450

摘要

Disc brake squeal is a nonlinear transient phenomenon of the friction-induced self-excited instability of an automotive brake system. In most situations, decreasing this squeal noise to some extent during braking is very important for the comfort of passengers, which is dependent on an absence of chaos; consequently, suppressing chaos becomes quite important. Therefore, this study aims to confirm chaotic motion and apply synchronization to control chaos for an automotive disc brake system. Rich dynamics of the disc brake system were studied using a bifurcation diagram, phase portraits, a Poincaré map, frequency spectra, and Lyapunov exponents. First, the largest Lyapunov exponent was estimated using synchronization to identify periodic and chaotic motions. Next, complex nonlinear behaviors were thoroughly observed for a range of parameter values in the bifurcation diagram. Finally, a continuous feedback control method based on synchronization characteristics was proposed to eliminate chaotic oscillations, improve the performance of the automotive disc brake system, and prevent brake squeal noise from occurring. Numerical simulations were utilized to verify the feasibility and efficiency of the proposed control technique.

關鍵字

disc brake ； bifurcation ； chaos ； Lyapunov exponent ； synchronization

並列摘要

車輛碟式煞車所產生的尖銳聲音是由摩擦力導致的一種非線性現象。，降低在煞車時的尖銳聲 對乘客舒適性而言是很重要的，而此現象造成因素是煞車系統產生渾沌運動所致。因此，本文旨在探討碟式煞車系統的非線性動態。藉由分歧圖、相圖、龐克映相圖、頻譜圖及李亞譜諾指數來呈現其非線性行為。利用最大的李亞譜諾指數來驗證系統是否有存在渾沌行為。最後，採用同步化法及連續控制法去控制渾沌運動，並經由數值模擬結果顯示，所提出的控制方式皆能有效地控制煞車系統渾沌行為的發生並能將之轉換為穩定的周期運動，以抑制煞車時產生的尖銳聲。