The present study is devoted to investigate the oscillatory behaviors of the 16-pole rotor active magnetic bearing system. A controllable electromagnetic force generated via a conventional proportional-derivative controller is utilized to stabilize the system lateral oscillations that excited by the rotating disk eccentricity when the spinning speed ($\Omega$) is close to or equal the system linear natural frequency ($\omega$). The nonlinear dynamical equations governing the controlled system lateral vibrations at constant stiffness coefficients are derived in this article for the first time. Then, four nonlinear autonomous first-order differential equations to describe the considered system oscillation amplitudes and the corresponding phase angles are obtained applying the asymptotic analysis. Bifurcation behavior of the system periodic motions under varying the different control parameters is explored. The main acquired results confirm that the 16-pole rotor-AMB system at constant stiffness coefficients can exhibit one of three oscillatory motions that are periodic, quasiperiodic, or chaotic motions depending on the derivative gain coefficient. Moreover, the system may respond with one-stable solution, bi-stable solutions, tri-stable solutions, or quadri-stable solutions depending on the proportional gain coefficient. Numerical simulations for different system motions are validated via the system time response, Poincare map, orbit plot, and frequency spectrum that are showed an excellent agreement with the obtained analytical results.

本研究致力于研究16极转子主动磁轴承系统的振动行为。通过传统的比例微分控制器产生的可控电磁力可用来稳定系统横向振荡，当旋转速度为（$\Omega$）接近或等于系统线性固有频率（$\omega$）。本文首次得出了以恒定刚度系数控制受控系统横向振动的非线性动力学方程。然后，通过渐近分析，获得了四个非线性自治一阶微分方程来描述所考虑的系统振荡幅度和相应的相角。探索了在不同控制参数下系统周期运动的分叉行为。获得的主要结果证实，在恒定刚度系数下的16极转子AMB系统可以根据导数增益系数呈现周期性，准周期性或混沌运动三种振荡运动之一。此外，系统可能会以单稳态解决方案，双稳态解决方案，三稳态解决方案，或四稳态解取决于比例增益系数。通过系统时间响应，庞加莱图，轨道图和频谱图对不同系统运动的数值模拟进行了验证，这些模拟结果与所获得的分析结果高度吻合。