Jeffcott转子系统分岔点预测

首先简述了一种用于转子轴承系统的稳定性量化分析方法,即首先利用数值积分对高维非线性转子系统进行解耦,将Rn轨线映射为一系列R1映像轨线,然后在R1观察空间中定义轨线的稳定裕度,根据轨线稳定裕度利用灵敏度技术预测动力系统的分岔点。最后,对一个单跨转子模型试验台建立了动力学方程,并利用上述方法通过2个算例预测了系统发生分岔的参数值和分岔特性。预测结果与直接数值积分法在庞加莱截面得到的分岔参数值基本一致,但由于该方法利用了灵敏度技术,所以其分岔点的搜索过程比直接数值积分法中的试探法要快得多。

Bifurcation prediction of Jeffcott rotor system

The quantitative methodology for the stability analysis of nonlinear rotor systems is briefly described in this paper.At first,an n-dimensional nonlinear non-autonomous rotor system is decoupled into n subsystems after numerical integration.In this way,n-dimensional trajectory is mapped into a set of one-dimensional trajectories.The corresponding stability margin and its trajectory are evaluated quantitatively in one-dimensional observation space.By means of the margin and its sensitivity analysis,the critical parameters of bifurcation in nonlinear rotor systems are determined.This method is applied in stability analysis of a single span rotor system supported by lubricated bearings through two cases to predict the bifurcational parametric value and corresponding bifurcational characteristic.The study shows that the method mentioned in this paper obtains the same results as direct numerical integration,moreover it is faster than numerical calculation in the trial-and-error way in determining the critical parameter of bifurcation.