Radial Versus Cartesian Control Strategies to Stabilize the Nonlinear Whirling Motion of the Six-Pole Rotor-AMBs

Abstract

Rotor active magnetic bearings system is the most efficient supporting technique of high-speed rotating machinery. This work aims to explore the dynamical behaviors of the 6-pole rotor active magnetic bearings system for the first time. Two different control strategies are introduced to mitigate the considered system lateral vibrations and the corresponding whirling motions. The first control technique (Radial control) is suggested such that the attractive magnetic force in each pole is proportional to both the radial displacement and radial velocity of the rotating disk toward that pole. The second control strategy (Cartesian control) is proposed such that the controlled magnetic force in each pole is designed to be proportional to both the cartesian displacement and cartesian velocity of the rotating disk in two perpendicular directions. Based on the proposed control strategies, two nonlinear dynamical models are derived and then analyzed by applying perturbation methods. Different response-curves and bifurcation diagrams are plotted utilizing the disk spinning-speed and the disk eccentricity as bifurcation control parameters. The main obtained analytical and numerical results illustrated that the considered system can perform a circular forward whirling motion only under the first control technique, while four whirling modes (that are forward whirling , backward whirling, both forward and backward whirling, and oscillation along a straight line) are noticed in the second control method depending on the disk spinning speed. Moreover, it is found that the radial control method is robust against the system instability than the cartesian control one, especially at large disk eccentricity. However, the cartesian control method could exhibit a vibration suppression efficiency higher than the radial control one at small disk eccentricity.

Experimental Comparison of the Known Hypotheses of the Lateral Buckling for Semi-Slender Pinned Columns

“…Next (Saeed, 2020) did an analysis of the steady-state forward and backward whirling motion of the asymmetric nonlinear rotor system and (Saeed et al, 2020a) did a nonlinear dynamic analysis of the six-pole rotor-AMB system under two different control configurations. Later (Saeed et al, 2020b) executed an analysis of radial versus Cartesian control strategies to stabilize the nonlinear whirling motion of the six-pole rotor-AMBs and (Saeed et al, 2020c) an analysis of periodic, quasi-periodic and chaotic motions diagnose a crack on a horizontally supported nonlinear rotor system. Next, (Saeed et al, 2021a) made a sensitivity analysis and vibration control of asymmetric nonlinear rotating shaft system utilizing 4-pole AMBs as an actuator and (Saeed et al, 2021b) did an analysis of the rub-impact forces between a controlled nonlinear rotating shaft system and the electromagnet pole legs.…”

Rub‐Impact Force Induces Periodic, Quasiperiodic, and Chaotic Motions of a Controlled Asymmetric Rotor System

“…Ishida and Inoue [18] applied a nonlinear active vibration absorber to control the lateral vibrations of a vertically suspended rotating shaft. Saeed et al [19][20][21][22] applied different active control strategies utilizing the active magnetic bearings as an actuator. Saeed and Kamel [19] employed a nonlinear combination of both the position and velocity controllers to control the vibrations of the nonlinear Jeffcott rotor model supported horizontally via four electromagnetic poles.…”

“…Saeed et al [20] proposed a combination of both the nonlinear and linear proportional-derivative controllers to mitigate the nonlinear vibrations of the asymmetric rotor system that is supported vertically. Saeed et al [21,22] introduced six electromagnetic poles to control the rotating disk vibrations utilizing PD controller. ey explored two control configurations that are the Cartesian and radial control schemes.…”

Technical Buckling, Stress and Strain Simplified Analysis of Semi-Slender Thin-Walled Cylindrical Pinned Column

“…Saeed (2019) did an analysis of vibration behavior and motion bifurcation of a nonlinear asymmetric rotating shaft. Next Saeed (2020) did an analysis of the steady-state forward and backward whirling motion of the asymmetric nonlinear rotor system and Saeed et al (2020a) did a nonlinear dynamic analysis of the six-pole rotor-AMB system under two different control configurations. Later Saeed et al (2020b) executed an analysis of radial versus Cartesian control strategies to stabilize the nonlinear whirling motion of the six-pole rotor-AMBs and Saeed et al (2020c) an analysis of periodic, quasi-periodic and chaotic motions diagnose a crack on a horizontally supported nonlinear rotor system.…”

“…Next Saeed (2020) did an analysis of the steady-state forward and backward whirling motion of the asymmetric nonlinear rotor system and Saeed et al (2020a) did a nonlinear dynamic analysis of the six-pole rotor-AMB system under two different control configurations. Later Saeed et al (2020b) executed an analysis of radial versus Cartesian control strategies to stabilize the nonlinear whirling motion of the six-pole rotor-AMBs and Saeed et al (2020c) an analysis of periodic, quasi-periodic and chaotic motions diagnose a crack on a horizontally supported nonlinear rotor system. Next, Saeed et al (2021a) made a sensitivity analysis and vibration control of asymmetric nonlinear rotating shaft system utilizing 4-pole AMBs as an actuator and Saeed et al (2021b) did an analysis of the rub-impact forces between a controlled nonlinear rotating shaft system and the electromagnet pole legs.…”