Nonlinear Dynamics and Motion Bifurcations of the Rotor Active Magnetic Bearings System with a New Control Scheme and Rub-Impact Force

• Main Authors: Nasser A. Saeed, Emad Mahrous, Emad Abouel Nasr, Jan Awrejcewicz
• Format: Article
• Language: English
• Published: MDPI AG 2021-08-01
• Series: Symmetry
• Subjects: rotor-AMBS; stability; rub-impact force; periodic, quasiperiodic and chaotic vibration; frequency spectrum; Poincare map
• Online Access: https://www.mdpi.com/2073-8994/13/8/1502

This article is dedicated to investigating the nonlinear dynamical behaviors of the 8-pole rotor active magnetic bearing system. The rub and impact forces between the rotating disc and the pole-legs are included in the studied model for the first time. A new control scheme based on modifying the 8-pole positions has been introduced. The proposed control methodology is designed such that four poles only are located in the horizontal and vertical directions (i.e., in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>+</mo><mi>X</mi><mo>,</mo><mo>+</mo><mi>Y</mi><mo>,</mo><mo>−</mo><mi>X</mi><mo>,</mo><mo>−</mo><mi>Y</mi></mrow></semantics></math></inline-formula> directions)<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>,</mo></semantics></math></inline-formula> while the other four poles are inserted in a way such that each pole makes 45° with two of the axes <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>+</mo><mi>X</mi><mo>,</mo><mo>+</mo><mi>Y</mi><mo>,</mo><mo>−</mo><mi>X</mi><mo>,</mo><mo>−</mo><mi>Y</mi></mrow></semantics></math></inline-formula>. The control currents in the horizontal and vertical poles are suggested to be proportional to both the velocity and displacement of the rotor in the horizontal and vertical directions, respectively, while the control currents in the inclined poles are proposed to be dependent on the combination of both the displacement and velocity of the rotor in the horizontal and vertical directions. Accordingly, the whole-system mathematical model is derived. The derived discontinuous dynamical system is analyzed employing perturbation methods, Poincare maps, bifurcation diagrams, whirling orbits, and frequency spectrum. The obtained results demonstrated that the controller proportional control gain can play a significant role in changing the vibratory behaviors of the system, where the proposed control method can behave either as a cartesian control strategy or as a radial control one depending on the magnitude of the proportional gain. In addition, it is found that the rotor system can vibrate with periodic, periodic-n, quasiperiodic, or chaotic motion when the rub and/or impact forces occur. Moreover, it is reported for the first time that the rotor-AMB can oscillate symmetrically in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>X</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>Y</mi></semantics></math></inline-formula> directions either in full annular rub mode or quasiperiodic partial rub mode depending on the impact stiffness coefficient and the dynamic friction coefficient.