受限颗粒体对制动系统非线性振动的影响

制动系统在工作时，往往受到沙粒、尘土以及磨屑等受限颗粒体的影响，这些受限颗粒体在摩擦副中的高度分布具有较强的随机性，一定程度诱发了制动系统的非线性振动. 本文中基于制动片切向振动模型，引入了新的受限颗粒体摩擦模型，提出了用波动系数来描述受限颗粒体高度分布随机性的强弱. 发现在特定参数下，当此系数为0时，制动片切向振动为周期运动；但是当此系数不为0时，制动片切向振动呈现拟周期或混沌运动，此时的切向振动分岔特性图的稳定轨道也会出现数量或分布的变化，甚至表现出混沌特性. 同一时变信号内，受限颗粒体引发制动片切向非线性振动包括发散、收敛以及拟周期运动等多种形式. 

Influence from Confined Particles on the Nonlinear Vibration of Brake System

In tribological research, confined particle refers to the particle which is confined by the roughness of surfaces. The influence by confined particles, e.g. sand particles, dust and wear particles, is inevitable in brake system. The height distribution of these confined particles is of strong randomness, which induces the nonlinear vibration of brake system more or less. This paper introduced a new confined particle frictional model, and a fluctuation parameter was proposed to describe the strength of randomness of height distribution of confined particles based on tangential vibration model of brake pad. The mechanism of this coefficient influence brake system can be explained as follow. The height of all confined particles followed a certain distribution C. These particles can be divided into N group, and the height of particles in each group followed a certain distribution C_i (i=1~N). It was assumed that the mean values of C_i (i=1~N) were constant during the frictional process, but the deviations changed with a fluctuation ?σ following a distribution N (0, σ*σ_i) in every time step, and σ* was the fluctuation parameter which determined the strength of randomness. The friction force-velocity relation was determined by a stribeck-type frictional model. The friction force between particle and surfaces was calculated according to a hard-particle contact model. The tangential vibration of pad and angular vibration of disk were studied in both time and frequency domains. It was found that when fluctuation parameter was 0, the tangential vibration of pad was a periodic motion under certain condition. When fluctuation parameter turned to 0.001, the tangential vibration was quasi-periodic. When fluctuation parameter turned to 0.01 or 0.03, the tangential vibration was chaotic, and some parts of the time varying signals of disk angular displacement showed divergence characteristic. The non-zero value of fluctuation parameter may induce many vibration forms including divergence, convergence and quasi-periodic motions in a single time-varying signal. By studying the friction coefficient and the ratio of friction force from particle-surface contact to total friction force over time, it was found that the friction coefficient and the ratio of particle-surface friction force were constants over time when fluctuation parameter was 0. The friction coefficient and the ratio showed obvious fluctuation, and the friction coefficient nearly increased over time and finally reached a stable value when fluctuation parameter turned to non-zero value. The bifurcation characteristic of pad vibration using angular velocity of disk as bifurcation parameter was studied. It was found that the bifurcation diagram had clear single-period region, transition regions and four-period region in w=0.88~0.97 under a certain condition. While the number of stable orbits, the number and position of transition region may change when the fluctuation parameter turned to non-zero value. When the fluctuation parameter was large enough, the periodic characteristic can hardly be observed.