Abstract The application of active magnetic bearings (AMBs) enables turbomachinery to increase power density, controllability and resilience to external disturbances. However, due to the limited load capacity of AMBs, base shock excitations may result in contact between the rotor and the touchdown bearings (TDBs), which can seriously damage the machine. This paper presents a dynamic analysis of a rotor-AMB-TDB system experiencing strong base shocks while the AMBs are operating. The contacts between the rotor and the TDBs, and the rolling-ball contacts within the TDBs are modeled based on the Hertzian contact theory. A PD controller is designed, considering saturation. The dynamic equations were solved numerically, and the results showed three different rotor motion modes after base shocks. FFT spectra, STFT spectra, Poincare maps and bifurcation diagrams were used for the dynamic analysis. Unsuitable system parameters, including unbalance eccentricity, radial clearance, equivalent stiffness and damping ratio, may lead to complex behaviors including periodic, KT-periodic, and quasi-periodic responses as well as jump phenomena. This study reveals the mechanism of nonlinear responses, provides a method for predictions, and helps with controller designs for rotor re-levitation.

中文翻译：

---

转子-AMB-TDB系统在强基础激波激励下的非线性动力学仿真与参数分析

摘要 主动磁轴承 (AMB) 的应用使涡轮机械能够提高功率密度、可控性和对外部干扰的恢复能力。然而，由于 AMB 的负载能力有限，基座冲击激励可能会导致转子和接地轴承 (TDB) 之间发生接触，从而严重损坏机器。本文介绍了转子-AMB-TDB 系统在 AMB 运行时经历强基础冲击的动态分析。转子和 TDB 之间的接触以及 TDB 内的滚球接触基于赫兹接触理论建模。考虑到饱和，设计了 PD 控制器。对动力学方程进行了数值求解，结果显示了基础冲击后三种不同的转子运动模式。FFT 谱、STFT 谱、庞加莱图和分岔图用于动态分析。不合适的系统参数，包括不平衡偏心率、径向间隙、等效刚度和阻尼比，可能导致复杂的行为，包括周期、KT 周期和准周期响应以及跳跃现象。这项研究揭示了非线性响应的机制，提供了一种预测方法，并有助于转子重新悬浮的控制器设计。