二维耦合干摩擦振子黏滑运动分析

针对工程中广泛存在的二维干摩擦问题,通过引入斜弹簧建立一种可考虑x,y两个方向耦合的振子模型。定义摩擦力方位角来描述动、静摩擦力矢量分量,并考虑振子振动过程中可能出现黏滞,提出了一种分析二维耦合干摩擦振子黏滑运动的方法,给出了二维耦合干摩擦振子黏滑运动的复杂边界条件。基于指数型动态摩擦模型对二维耦合干摩擦振子的黏滑运动进行了数值仿真,给出了x方向和y方向相同激振频率相同相位角、相同激振频率不同相位角、不同激振频率不同相位角3种工况下的仿真结果及系统解随激振频率和相位角的变化规律。仿真结果表明,二维耦合摩擦振子运动中可能出现黏滑状态转换;当x方向和y方向的激励频率和相位角均不相等时,与前两种工况相比,质量块的运动轨迹、系统相图均为更加复杂的平面曲线,同时一个周期内系统可出现多次黏滑转换;两个方向激振频率相同时,改变激振频率和激励相位角,系统的解均没有出现次谐波,振子为周期运动。所提出的方法可为进一步研究二维耦合干摩擦振子的动力学特性及运动稳定性提供参考。

Stick-slip motion of a two-dimensional coupled dry friction oscillator

In view of the widely existed two-dimensional friction problems in engineering, an oscillator model which considers the coupling of and direction is established by introducing oblique springs. With the concept of the friction force direction angle being defined to determine the components of the static and kinetic friction force vector, and considering that stick-slip motion may occur when the oscillator is vibrating, a method for analyzing stick-slip motion of a two-dimensional coupled dry friction oscillator is proposed, and complex stick-slip transition boundaries of the two-dimensional coupled dry friction oscillator are given. Based on an exponential-type dynamic friction model, numerical simulation is carried out for stick-slip motion of the two-dimensional coupled dry friction oscillator, with the simulation results and the law of the system solution changing with excitation frequency and phase angle under three different working conditions at x direction and y direction, namely the same excitation frequency and phase angle, the same excitation frequency and different phase angle, and different excitation frequency and phase angle, are provided. Numerical results indicate that transition of stick-slip state may occur in the motion of the two-dimensional coupled dry friction oscillator; in comparison with the first two conditions, when frequencies and phase angle of and direction of the excitation are not equal, trajectory of the mass is a more complicated plane curve, the system can have multiple stick-slip transitions in one cycle at the same time; with the same frequency of and direction, the response of the oscillator has no fractional frequencies and is periodic by altering the frequency and phase angle. The proposed method can provide reference for further study of dynamics and motion stability of a two-dimensional coupled dry friction oscillator.