非线性转子系统稳定性量化分析方法

转子轴承系统是一类多自由度非线性动力系统，广泛应用于工程实际．设计观念和维修体制的变革提出了稳定性量化分析的要求．本文利用轨线保稳降维方法提出了转子系统稳定性的量化分析方法．首先，对高维非线性非自治转子系统进行数值积分，将n维空间的轨线映射为一系列一维的映象轨线，并将各自由度的运动方程中除该自由度外的所有状态变量用积分结果代换，得到n个互相解耦，含有多个时变参数的单自由度方程．然后，在一维观察空间的外力位移扩展相平面上定义了动态中心点，研究转子系统中常见的几种运动的动态中心点动能差序列的特点，给出了上述典型运动形式的轨线稳定裕度的定量评估指标，应用灵敏度分析技术快速有效地预测周期运动的倍周期分岔点和Hopf分岔点．以一个具有非线性支承的滑动轴承柔性转子模型为例，证明了该方法的有效性．

Quantitative Methodology for the Stability Analysis of Nonlinear Rotor Systems

Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom.Modern concepts on design and maintenance call for quantitative stability analysis.Using trajectory based stability-preserving,dimensional-reduction, a quantitative stability analysis method for rotor systems is presented. At first,a n-dimensional nonlinear non-autonomous rotor system is decoupled into n subsystems after numerical integration.Each of them has only one-degree-of-freedom and contains time-varying parameters to represent all other state variables. In this way, n dimensional trajectory is mapped into a set of one-dimensional trajectories. Dynamic central point (DCP) of a subsystem is then defined on the extended phase plane, namely force-position plane. Characteristics of curves on the extended phase plane and the DCP's kinetic energy difference sequence for general motion in rotor systems are studied. The corresponding stability margins of trajectory are evaluated quantitatively. By means of the margin and its sensitivity analysis, the critical parameters of the period doubling bifurcation and the Hopf bifurcation in a flexible rotor supported by two short journal bearings with nonlinear suspensionare determined.