模态耦合及摩擦系数速度斜率与黏滑运动的关系

Relationship among Mode Coupling, Friction velocity Slope and Stick slip Motion

摘要:

摩擦尖叫的理论目前主要有摩擦系数速度负斜率、模态耦合、黏滑运动和锁滑理论，但没有一种理论可以完全解释摩擦尖叫等现象.因此，深入探讨各个理论之间的内在联系对于统一摩擦振动和噪声机理的认识至关重要.以摩擦系数及其速度特性为切入点，基于考虑摩擦系数及其速度斜率的单点接触集总参数柔体刚体组成的二自由度非线性摩擦振动动力学模型，通过理论推导和数值计算研究摩擦系数速度斜率对模态耦合不稳定的影响，并根据摩擦系数及其速度斜率的符号形成4个区域,分析了4个区域的黏滑运动的特点和极限环及工况依赖性，并指出在摩擦系数速度正斜率情况下系统参数改变会导致Hopf分岔.

关键词:摩擦尖叫; 摩擦系数速度斜率; 模态耦合; 黏滑运动; Hopf分岔

Abstract:

Till now, four main frictional squeal mechanisms are highlighted including negative frictionvelocity slope theory, mode coupling theory, spragslip motion theory and stickslip motion theory. However, none of them can explain various frictional squeal phenomena fully. So it is very important to make clear the relationship among various mechanisms in order to unify the realization of friction induced vibration and noise. A nonlinear friction induced vibration lamped parameter model with two degree of freedoms is established, to simulate the friction induced vibration behaviour between a flexible body and a rigid body frictional pairs with singlepoint contact based on friction coefficient and frictionvelocity slope. By deduction and calculation, effect of friction coefficient and frictionvelocity slope on mode coupling instability is studied, according to which instability characteristics are summarized in four areas. For each area, stickslip motion, limit cycle and their dependence on working conditions are investigated. At the same time, it is pointed out that the change of system parameters result in the occurrence of Hopf bifurcation under the condition of positive frictionvelocity slope.

Key words:friction induced squeal; frictionvelocity slope; mode coupling; stickslip motion; Hopf bifurcation