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QUANTITATIVE METHODOLOGY FOR STABILITY ANALYSIS OF NONLINEAR ROTOR SYSTEMS

机译:非线性转子系统稳定性分析的定量方法

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Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom. Modem concepts on design and maintenance call for quantitative stability analysis. Using trajectory based stability-preserving and dimensional-reduction, a quanttative stability analysis method for rotor systems is presented. At first, an n-dimensional nonlinear non-autonomous rotor system is decoupled into n subsystems after numerical integration. Each of them has only onedegree-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 beatings with nonlinear suspensionare are determined.
机译:在工业上广泛应用的转子轴承系统是具有多个自由度的非线性动力学系统。有关设计和维护的现代概念要求进行定量稳定性分析。利用基于轨迹的稳定性保持和降维,提出了一种转子系统的定量稳定性分析方法。首先,在数值积分后,将n维非线性非自治转子系统解耦为n个子系统。它们每个都只有一个自由度,并且包含随时间变化的参数来表示所有其他状态变量。以此方式,将n维轨迹映射到一组一维轨迹。然后,在扩展的相平面(即力位置平面)上定义子系统的动态中心点(DCP)。研究了转子系统中一般运动的扩展相平面上的曲线特征和DCP的动能差序列。定量评估相应的轨迹稳定裕度。通过余量及其灵敏度分析,确定了由两个带有非线性悬架的短轴颈跳动支撑的挠性转子中周期倍增分叉和霍普夫分叉的关键参数。

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