On the nonlinear dynamics of constant stiffness coefficients 16-pole rotor active magnetic bearings system

Abstract

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 (Ω) is close to or equal the system linear natural frequency (ω). 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.