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Nonlinear Dynamics

, Volume 78, Issue 4, pp 2439–2457 | Cite as

Vibration suppression of a time-varying stiffness AMB bearing to multi-parametric excitations via time delay controller

  • M. Eissa
  • M. Kamel
  • A. Al-Mandouh
Original Paper

Abstract

The applications of active magnetic bearings are growing in industry due to its amazing advantages in reducing friction losses. In this research, the vibration of a two-degree-of-freedom rotor, active magnetic bearings system is suppressed via a nonlinear time delay controller at the confirmed worst resonance case. The selected resonance case is the simultaneous primary and sub-harmonic resonance case. The main aim of this paper was to study the effects of the nonlinear, time delay controller on the behavior of the vibrating system. The multiple time scale perturbation technique is applied to obtain an approximate solution to the second-order approximation. The steady-state solution is obtained around the worst resonance case. The stability of the system is studied applying both frequency response equations and phase-plane method. The worst resonance case is confirmed applying numerical technique. The effects of the different parameters on the steady-state response of the vibrating system are investigated. The obtained approximate solution is validated numerically. Some recommendations are given regarding the design of such system. At the end of the work, a comparison is made with the available published work.

Keywords

Rotor–active magnetic bearings (AMB)-control Time delay Multi-parametric excitation Stability Resonance cases Perturbation method 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Engineering Mathematics, Faculty of Electronic EngineeringMenoufia UniversityMenoufEgypt
  2. 2.Faculty of Science in TureifNorthern Border UniversityArarKingdom of Saudi Arabia

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