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Non-periodic and chaotic response of three-multilobe air bearing system

机译：三多瓣空气轴承系统的非周期性和混沌响应

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摘要

The dynamic response of a three-multilobe air bearing (TMAB) system is investigated for various values of the rotor mass and bearing number using a hybrid numerical scheme consisting of the differential transformation method (DTM) and the finite difference method (FDM). The validity of the numerical scheme is demonstrated by comparing the results obtained for the rotor center orbit under typical operating conditions with those obtained from the traditional FDM approach and a perturbation method, respectively. The dynamic behavior of the rotor center is then investigated for rotor mass values in the range of 1.0 ≤ m_r ≤ 16.0 kg and bearing number values in the range of 1.0 ≤ Λ ≤ 5.0. The phase trajectories, power spectra, bifurcation diagrams, Poincaré maps and maximum Lyapunov exponents show that the TMAB system exhibits a complex dynamic behavior consisting of periodic, quasi-periodic and chaotic motion at certain values of the rotor mass and bearing number. In general, the numerical results obtained in this study provide a useful insight into the dynamic response of TMAB systems. In particular, the results indicate the operating conditions which should be avoided in order to achieve a desirable periodic motion of the system.
机译：使用由微分变换法（DTM）和有限差分法（FDM）组成的混合数值方案，研究了三多瓣空气轴承（TMAB）系统的动态响应，以求出转子质量和轴承数量的各种值。通过比较典型工作条件下转子中心轨道的结果与分别从传统FDM方法和扰动方法获得的结果进行比较，证明了数值方案的有效性。然后研究转子中心的动态行为，转子质量值在1.0≤m_r≤16.0 kg范围内，轴承数量在1.0≤Λ≤5.0范围内。相轨迹，功率谱，分叉图，庞加莱图和最大Lyapunov指数表明，TMAB系统在转子质量和轴承数量的某些值下表现出复杂的动力学行为，包括周期性，准周期性和混沌运动。通常，本研究中获得的数值结果为TMAB系统的动态响应提供了有用的见解。特别地，结果指示了为了实现系统的期望的周期性运动而应当避免的操作条件。

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