转子-轴承系统稳定性的非线性动力学分析

Research on Stability, Bifurcation and Chaos in RotorBearings

利用修正的短轴承理论模型对转子轴承系统进行了稳定性、分岔与混沌特性分析。结果表明：系统平衡失稳时产生滞后超临界Ｈｏｐｆ分岔，由于滞后的存在，使得滞后区内系统拓扑结构的等价性在大扰动下可能破坏，因此，线性理论无法解释该区段内的动态行为；不平衡量较小时，系统失稳时产生拟周期分岔、倍周期分岔并可以导致混沌振动；较大不平衡量时，系统始终呈现同频周期运动，这表明较大的不平衡量反而有助于增稳作用。这些结果为控制转子的稳定运行状态提供了依据，为油膜失稳故障的监测与诊断提供了有益的启发。

In this paper, stability, bifurcation and chaos of rotorbearings are analyzed with the modified short bearing approach method. The result of the calculation shows: linear instability belongs to hysteric supercritical Hopf bifurcation, because to hysteresis, the topological equivalent may be wrecked in large disturbance, hence the system dynamics can not be analyzed with linear analysis method; lower unbalance resulted doubling period bifurcation, almost periodic motion and chaotic motion; when unbalance is higher, the motion is synchronous, hence the conditions achieved during operation at the lower values of unbalance are more dangerous than the ones characterizing running at higher values, and can be ascribed to instability. The analysis results of this paper provide the theoretical bases for qualitatively controlling the stable operating state of rotors, and contribute to oil instability fault detection and diagnosis.