非线性刚度转子系统振幅突变控制策略的分析

Analysis on Amplitude Catastrophe Control Strategy for Rotor System with Nonlinear Stiffness

利用平均法推导了非线性刚度转子系统的频率响应方程，结合突变理论求出了转子系统振幅突变的突变流形和分叉集，根据突变流形和分叉集确定了非线性刚度参数、激励频率和偏心距等引起转子系统振幅突变的影响因素，讨论了激励频率和非线性刚度参数的取值范围，提出了利用电磁辅助支撑装置产生的非线性刚度参数控制转子系统振幅突变的技术方案，给出了动态激励频率和综合非线性刚度参数的取值范围，得到了线性和非线性电磁支撑刚度参数的设计准则，奠定了非线性刚度转子系统振幅突变控制的理论基础．

The frequency response equation of the rotor system with nonlinear stiffness was deduced by using the averaging method, and the amplitude catastrophe manifold and bifurcation set were also calculated by means of the catastrophe theory. The non-linear stiffness coefficient, the excitation frequency and the eccentricity that caused the amplitude catastrophe of the rotor system were determined, with the help of the amplitude catastrophe manifold and bifurcation set. At the same time the scope of the nonlinear stiffness coefficient and the excitation frequency was provided. The control scheme that the nonlinear stiffness coefficient which produced by a auxiliary electromagnetic support device using to control amplitude catastrophe of the rotor system was proposed. According to the value range of the excitation frequency and the nonlinear stiffness coefficient, the design guidelines were given for linear and nonlinear electromagnetic support stiffness coefficient, and the theoretical basis of amplitude catastrophe control for rotor system with the non-linear stiffness coefficient was established.