Nonlinear Vibration of a Rotor-Active Magnetic Bearing System With 16-Pole Legs

2017 ◽  
Author(s):  
Ruiqin Wu ◽  
Wei Zhang ◽  
Ming Hui Yao
Keyword(s):  
Parametric Excitation ◽  
Multiple Scales ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Dynamical Response ◽  
Time Varying ◽  
Chaotic Motions ◽  
Dimensionless Equation ◽  
Amb System ◽  
Bearing System

In this paper, the nonlinear dynamics of a rotor-active magnetic bearing system with 16-pole legs and the time varying stiffness is investigated. The magnetic forces are obtained through an electromagnetic theory. The motion governing equation is derived by using Newton law. The resulting dimensionless equation of motion for the rotor-AMB system with 16-pole legs and the time varying stiffness is presented with the two-degree-of-freedom system including parametric excitation, the quadratic and cubic nonlinearities. The averaged equations of the rotor-AMB system are obtained by using the method of multiple scales under the case of the primary parametric resonance and 1/2 sub-harmonic resonance. The numerical results show that there exist the periodic, quasi-periodic and chaotic motions in the rotor-active magnetic bearing system. Since the weight of the rotor effect the system, it is also found that there are the different shapes of motion on the two directions of the rotor-AMB system. The parametric excitation, or the time-varying stiffness produced by the PD controller has great impact on the system. Thus, the complicated dynamical response in the rotor-AMB system can be controlled through adjusting the parametric excitation.

Multi-Pulse Chaotic Motions of a Rotor-Active Magnetic Bearing With Time-Varying Stiffness

2005 ◽  
Author(s):  
Wei Zhang ◽  
Ming-Hui Yao ◽  
Xue-Ping Zhan ◽  
Li-Lai Bai
Keyword(s):  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Time Varying ◽  
Chaotic Motions ◽  
Dimensionless Equation ◽  
System A ◽  
Averaged Equations ◽  
Asymptotic Perturbation Method ◽  
Amb System ◽  
Asymptotic Perturbation

In this paper, we investigate the Shilnikov type multi-pulse chaotic dynamics for a rotor-active magnetic bearings (AMB) system with 8-pole legs and the time-varying stiffness. The stiffness in the AMB is considered as the time varying in a periodic form. The dimensionless equation of motion for the rotor-AMB system with the time-varying stiffness in the horizontal and vertical directions is a two-degree-of-freedom nonlinear system with quadratic and cubic nonlinearities and parametric excitation. The asymptotic perturbation method is used to obtain the averaged equations in the case of primary parametric resonance and 1/2 subharmonic resonance. It is found from the numerical results that there are the phenomena of the Shilnikov type multi-pulse chaotic motions for the rotor-AMB system. A new jumping phenomenon is discovered in the rotor-AMB system with the time-varying stiffness.

NONLINEAR BEHAVIOR OF TUNED ROTOR-AMB SYSTEM WITH TIME VARYING STIFFNESS

2011 ◽  
Vol 21 (01) ◽  
pp. 195-207 ◽  
Author(s):  
M. EISSA ◽  
M. KAMEL ◽  
H. S. BAUOMY
Keyword(s):  
Steady State ◽  
Multiple Scales ◽  
Primary Resonance ◽  
Nonlinear Behavior ◽  
Steady State Solution ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Practical Case ◽  
Time Varying ◽  
Amb System

A rotor-active magnetic bearing (AMB) system with a periodically time-varying stiffness subjected to tuned and external excitations is studied and solved. The tuned excitation represents an imposed noise on the external excitation to simulate the practical case. The method of multiple scales is applied to analyze the response of the system two modes near the simultaneous combined and primary resonance cases. The stability of the steady state solution near this resonance case is studied applying Lyapunov's first method. The system exhibits many typical nonlinear behaviors including multiple-valued solutions, jump phenomenon, softening nonlinearity and saturation. The presence of the tuned excitation increased the steady state amplitudes and produced a chaotic system. The effects of the different parameters on the steady state solutions are investigated and discussed. Comparison with previous work is reported.

Analysis of Nonlinear Dynamics of a Rotor-Active Magnetic Bearing System With 16-Pole Legs

2017 ◽  
Author(s):  
Ruiqin Wu ◽  
Wei Zhang ◽  
Ming Hui Yao
Keyword(s):  
Nonlinear Dynamics ◽  
Perturbation Method ◽  
Primary Resonance ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Chaotic Motions ◽  
Dimensionless Equation ◽  
Asymptotic Perturbation Method ◽  
Amb System ◽  
Asymptotic Perturbation

In this paper, we use the asymptotic perturbation method to analyze the nonlinear dynamics of a rotor-active magnetic bearing (AMB) system with 16-pole legs. The motion governing equation is derived by using classical Newton law. The resulting dimensionless equation of motion for the system is expressed as a two-degree-of-freedom system including the parametric excitation, quadratic and cubic nonlinearities. The asymptotic perturbation method is used to obtain the averaged equation when the primary resonance and 1/2 sub-harmonic resonance are taken into consideration. From the averaged equations obtained, numerical simulations are presented to investigate the modulation of vibration amplitudes of the rotor-AMB system. Based on a specific set of parameters, it is found that there exist the periodic, quasi-periodic and chaotic motions in the modulated amplitude of the rotor in the system.

scholarly journals Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom

2020 ◽  
Vol 2020 ◽  
pp. 1-29 ◽  
Author(s):  
W. Zhang ◽  
R. Q. Wu ◽  
B. Siriguleng
Keyword(s):  
Perturbation Method ◽  
Electromagnetic Force ◽  
Nonlinear Vibrations ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Time Varying ◽  
Asymptotic Perturbation Method ◽  
Amb System ◽  
Asymptotic Perturbation ◽  
Quadratic And Cubic Nonlinearities

The asymptotic perturbation method is used to analyze the nonlinear vibrations and chaotic dynamics of a rotor-active magnetic bearing (AMB) system with 16-pole legs and the time-varying stiffness. Based on the expressions of the electromagnetic force resultants, the influences of some parameters, such as the cross-sectional area Aα of one electromagnet and the number N of windings in each electromagnet coil, on the electromagnetic force resultants are considered for the rotor-AMB system with 16-pole legs. Based on the Newton law, the governing equation of motion for the rotor-AMB system with 16-pole legs is obtained and expressed as a two-degree-of-freedom system with the parametric excitation and the quadratic and cubic nonlinearities. According to the asymptotic perturbation method, the four-dimensional averaged equation of the rotor-AMB system is derived under the case of 1 : 1 internal resonance and 1 : 2 subharmonic resonances. Then, the frequency-response curves are employed to study the steady-state solutions of the modal amplitudes. From the analysis of the frequency responses, both the hardening-type nonlinearity and the softening-type nonlinearity are observed in the rotor-AMB system. Based on the numerical solutions of the averaged equation, the changed procedure of the nonlinear dynamic behaviors of the rotor-AMB system with the control parameter is described by the bifurcation diagram. From the numerical simulations, the periodic, quasiperiodic, and chaotic motions are observed in the rotor-active magnetic bearing (AMB) system with 16-pole legs, the time-varying stiffness, and the quadratic and cubic nonlinearities.

Nonlinear Oscillation of a Rotor-AMB System With Time Varying Stiffness and Multi-External Excitations

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Kamel ◽  
H. S. Bauomy
Keyword(s):  
Steady State ◽  
Order Approximation ◽  
Nonlinear Differential Equations ◽  
Steady State Solution ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Multiple Time ◽  
Time Varying ◽  
The Stability ◽  
Amb System

The rotor-active magnetic bearing system subjected to a periodically time-varying stiffness having quadratic and cubic nonlinearities is studied and solved. The multiple time scale technique is applied to solve the nonlinear differential equations governing the system up to the second order approximation. All possible resonance cases are deduced at this approximation and some of them are confirmed by applying the Rung–Kutta method. The main attention is focused on the stability of the steady-state solution near the simultaneous principal resonance and the effects of different parameters on the steady-state response. A comparison is made with the available published work.

Analysis of Nonlinear Dynamics for a Rotor-Active Magnetic Bearing System With Time-Varying Stiffness: Part I — Formulation and Local Bifurcations

2003 ◽  
Author(s):  
Wei Zhang ◽  
Jean W. Zu
Keyword(s):  
Nonlinear Dynamics ◽  
Steady State ◽  
Transient State ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Time Varying ◽  
Quasiperiodic Solutions ◽  
Local Bifurcations ◽  
Averaged Equations ◽  
Amb System

In this two-part paper, we investigate nonlinear dynamics in the rotor-active magnetic bearings (AMB) system with 8-pole legs and the time-varying stiffness. The model of parametrically excited two-degree-of-freedom nonlinear system with the quadratic and cubic nonlinearities is established to explore the periodic and quasiperiodic motions as well as the bifurcations and chaotic dynamics of the system. The method of multiple scales is used to obtain the averaged equations in the case of primary parameter resonance and 1/2 subharmonic resonance. In Part I of the companion paper, numerical approach is applied to the averaged equations to find the periodic, quasiperiodic solutions and local bifurcations. It is found that there exist 2-period, 3-period, 4-period, 5-period, multi-period and quasiperiodic solutions in the rotor-AMB system with 8-pole legs and the time-varying stiffness. The catastrophic phenomena for the amplitude of nonlinear oscillations are first observed in the rotor-AMB system with 8-pole legs and the time-varying stiffness. The procedures of motion from the transient state chaotic motion to the steady state periodic and quasiperiodic motions are also found. The results obtained here show that there exists the ability of autocontrolling transient state chaos to the steady state periodic and quasiperiodic motions in the rotor-AMB system with 8-pole legs and the time-varying stiffness.

An anti-windup control strategy to actuator saturating input voltage for active magnetic bearing system

2016 ◽  
Vol 35 (3) ◽  
Author(s):  
Avadh Pati ◽  
Richa Negi
Keyword(s):  
Control Strategy ◽  
Pid Control ◽  
Input Voltage ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Region Of Attraction ◽  
Control Scheme ◽  
Amb System ◽  
Voltage Saturation ◽  
Bearing System

Purpose The active magnetic bearing is highly nonlinear and unstable system. In general most of physical systems, conventional PID control strategies are employed for their stable operation but the dynamics of the system are influenced by input voltage saturation that degrades the performance of the system. The conventional PID control scheme does not work properly alone. In such a situation, PID faces windup phenomenon that leads to instability in the system. To overcome this problem, an anti-windup control scheme leads to stable and smooth operation of active magnetic bearing system. Design/methodology/approach The proposed anti-windup control strategy is based on dynamic output feedback that is applied on linearized active magnetic bearing (AMB) system to stabilize and avoid the input voltage saturation effect in the actuator. Findings An anti-windup controller is designed for active magnetic bearing system in presence of input voltage saturation. The stability of AMB system with anti-windup controller is derived in sense of Lyapunov and expressed as linear matrix inequality problem for AMB system and the designed anti-windup controller also enlarges the region of attraction of considered AMB system. Originality/value T-S fuzzy technique is used for obtaining local linear model of nonlinear active magnetic bearing system for easy and simple implementation of anti-windup control scheme. In proposed methodology the region of attraction for anti-windup compensator is also discussed. The effectiveness of proposed method is verified by the numerical simulation results for considered active magnetic bearing system and domain of attraction or stability region of closed loop AMB system are also calculated using Eigen Value Optimization technique for both the cases such as with and without anti-windup controller. The comparative result and the contribution of proposed control strategy are also discussed.

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