Journal ArticleDOI
Stability and multi-pulse jumping chaotic vibrations of a rotor-active magnetic bearing system with 16-pole legs under mechanical-electric-electromagnetic excitations
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In this paper, the stability and Shilnikov-type multi-pulse jumping chaotic vibrations are investigated for a nonlinear rotor-active magnetic bearing (AMB) system with the time varying stiffness and 16-pole legs under the mechanical-electric-electromagnetic excitations.Abstract:
The stability and Shilnikov-type multi-pulse jumping chaotic vibrations are investigated for a nonlinear rotor-active magnetic bearing (AMB) system with the time varying stiffness and 16-pole legs under the mechanical-electric-electromagnetic excitations. The ordinary differential governing equation of motion for the rotor-AMB system is given by a two-degree-of-freedom nonlinear dynamical system including the parametric excitation, quadratic and cubic nonlinearities. The averaged equations of the rotor-AMB system are obtained by using the method of multiple scales under the cases of 1:1 internal resonance, primary parametric resonance and 1/2 subharmonic resonance. Some coordinate transformations are employed to find the type and number of the equilibrium points for the averaged equations. Using the global perturbation method developed by Kavacic and Wiggins, the explicit sufficient conditions near the resonance are obtained for the existence of the Shilnikov-type multi-pulse jumping homoclinic orbits and chaotic vibrations. This implies that the Shilnikov-type multi-pulse jumping chaotic vibrations may occur for the rotor-AMB system in the sense of Smale horseshoes. Numerical simulations are presented to verify the analytical predictions by using the fourth-order Runge-Kutta method. The Shilnikov-type multi-pulse jumping chaotic vibrations can exist in the rotor-AMB system with the time varying stiffness and 16-pole legs under the mechanical-electric-magnetic excitations.read more
Citations
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Journal ArticleDOI
Control Performance, Stability Conditions, and Bifurcation Analysis of the Twelve-Pole Active Magnetic Bearings System
Sabry M. El-Shourbagy,N. A. Saeed,Magdi Kamel,Kamal R. Raslan,Mohamed K. Aboudaif,Jan Awrejcewicz +5 more
TL;DR: In this article, the effect of the magneto-electro-mechanical nonlinearities on the oscillatory motion of the twelve-pole system controlled via a proportional derivative controller was investigated.
Journal ArticleDOI
Integral Resonant Controller to Suppress the Nonlinear Oscillations of a Two-Degree-of-Freedom Rotor Active Magnetic Bearing System
TL;DR: In this paper , two integral resonant controllers are proposed to mitigate the system lateral oscillations in the horizontal and vertical directions, which can force the rotor system to respond as a linear one with a single periodic attractor when the control parameters are designed properly.
Journal ArticleDOI
On the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System
Sabry M. El-Shourbagy,N. A. Saeed,Magdi Kamel,Kamal R. Raslan,Emad Abouel Nasr,Jan Awrejcewicz +5 more
TL;DR: In this article, the performance of a nonlinear position-velocity controller in stabilizing the lateral vibrations of a rotor-active magnetic-bearings system (RAMBS) is investigated.
Single-pulse chaotic dynamics of functionally graded materials plate
TL;DR: In this paper, a homoclinic Silnikov was used to construct a subspace for the purpose of subspace subspaces, which is called subspace subspace subspace.
Journal ArticleDOI
Analytical modeling and experimental validation of the six pole axial active magnetic bearing
B.M. Sikora,Adam Pilat +1 more
TL;DR: In this article, an analytical magnetic bearing model was developed to provide the axial magnetic induction distribution in 3D, which utilizes magnetic vector potential formulation and Schwarz-Christoffel mapping.
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