两自由度减振镗杆系统的安全盆侵蚀与分岔

Erosion and bifurcation of the safe basin of a two-degree-of-freedom damping boring bar system

建立了考虑橡胶圈和阻尼液非线性因素的两自由度减振镗杆系统的动力学模型,研究了系统的安全盆侵蚀与分岔过程。用数值方法得到初值对系统安全性的影响以及系统参数对安全盆侵蚀演变的影响。在一定的参数条件下,系统安全盆出现了边界分形侵蚀和边界光滑侵蚀两种不同的侵蚀过程。根据系统安全盆在侵蚀过程中的最大Lyapunov指数分析了安全盆边界分形侵蚀与边界光滑侵蚀的区别。结果表明,当安全盆出现边界分形侵蚀时,其相应最大Lyapunov指数大于零,系统出现混沌运动;而当安全盆出现边界光滑侵蚀时,其相应最大Lyapunov指数始终小于零,系统在安全盆侵蚀过程中并没有出现混沌运动,只是振动幅值增大并跳出安全区域。研究结果对减振镗杆系统的参数选择具有一定的指导意义。

The dynamic model of a two-degree-of-freedom damping boring bar system was established considering the nonlinear factors of rubber ring and damping fluid. The erosion of the safe basin and bifurcation process of the system were studied. The influences of initial values on the system security and the evolution of the system parameters during the safe basin erosion were examined by numerical methods. Under the condition of certain parameters, two kinds of erosion processes of the safe basin mamely the fractal boundary erosion and smooth bound-ary erosion would occur in the system. The difference between the fractal boundary erosion and smooth boundary erosion was analyzed by the Top Lyapunov Exponent of the system during the erosion process of the safe basin. The results show that the Top Lyapunov Exponent of system will be more than zero, and the chaotic motion of the system will occur when the fractal boundary erosion appears. When the smooth boundary erosion appears, the corresponding Top Lyapunov Exponent will be always less than zero, and the chaotic motion of the system does not occur in the process of the safe basin erosion, however, the amplitude of the system vibration will increase and finally jump out of the safe area. The results are helpful to select the system parameters.