Bifurcation Behavior of a Rotor Supported by Active Magnetic Bearings

Ji, Jinchen; Yu, Lie; Leung, A.Y.T.

doi:10.1006/jsvi.2000.2916

Cited by 70 publications

(42 citation statements)

References 8 publications

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“…Introducing the small perturbation parameter e, Eqs. (13) and (14) can be expressed as: € x þ eðl À 3a 5 x 2 À 3a 6 x _…”

Section: Perturbation Analysismentioning

confidence: 99%

“…The obtained results show that AMB system is capable of auto-controlling transient state chaos to steady state periodic motion. Ji et al [6] studied numerically the non-linear oscillations and the Hopf bifurcation in rotor-AMB system. They indicated that the steady state solutions lose their stability by either the saddle-node bifurcation or the Hopf bifurcation.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear study of a rotor–AMB system under simultaneous primary-internal resonance

Kamel

Bauomy

2010

Applied Mathematical Modelling

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a b s t r a c tA rotor-active magnetic bearing (AMB) system subjected to a periodically time-varying stiffness with quadratic and cubic non-linearities under multi-parametric excitations is studied and solved. The method of multiple scales is applied to analyze the response of two modes of a rotor-AMB system with multi-parametric excitations and time-varying stiffness near the simultaneous primary and internal resonance. The stability of the steady state solution for that resonance is determined and studied using Rung-Kutta method of fourth order. It is shown that the system exhibits many typical non-linear behaviors including multiple-valued solutions, jump phenomenon, hardening and softening non-linearities and chaos in the second mode of the system. The effects of the different parameters on the steady state solutions are investigated and discussed also. A comparison to published work is reported.

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“…Introducing the small perturbation parameter e, Eqs. (13) and (14) can be expressed as: € x þ eðl À 3a 5 x 2 À 3a 6 x _…”

Section: Perturbation Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear study of a rotor–AMB system under simultaneous primary-internal resonance

Kamel

Bauomy

2010

Applied Mathematical Modelling

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“…Equation (7) does not have Z 2 ⊕ Z 2 symmetry. Other papers [10][11][12][13] do not consider the influence of the weight of the rotor on the electromagnetic force resultants.…”

Section: Nonlinear Electromagnetic Forces Of Amb Systemmentioning

confidence: 99%

“…Wang and Nosh [11] utilized a numerical method to investigate nonlinear responses and chaotic dynamics of a rotor landed on safety auxiliary bearings in active magnetic bearings. Ji et al [12] numerically studied nonlinear oscillations and the Hopf bifurcation in a rotor-AMB system. They indicated that the steady state solutions lose their stability by either the saddle node bifurcation or the Hopf bifurcation.…”

Section: Introductionmentioning

confidence: 99%

Periodic and Chaotic Motions of a Rotor-Active Magnetic Bearing with Quadratic and Cubic Terms and Time-Varying Stiffness

Zhang

Zhan

2005

Nonlinear Dyn

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In this paper, we use the asymptotic perturbation method to investigate nonlinear oscillations and chaotic dynamics in 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. Because of considering the weight of the rotor, the formulation on the electromagnetic force resultants includes the quadratic and cubic nonlinearities. The resulting dimensionless equations of motion for the rotor-AMB system with the time-varying stiffness in the horizontal and vertical directions are 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 that there exist period-3, period-4, period-6, period-7, period-8, quasiperiodic and chaotic modulated amplitude oscillations in the rotor-AMB system with the time-varying stiffness. It is seen from the numerical results that there are the phenomena of the multiple solutions and the soft-spring type and the hardening-spring type in nonlinear frequency-response curves for the rotor-AMB system. The parametric excitation, or the time-varying stiffness produced by the PD controller is considered to be a controlling force which can control the chaotic response in the rotor-AMB system to a period n motion.

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“…When the rotor weight was taken into account [4], the parameters were investigated by semi-analytical methods to "nd regimes of non-linear behavior such as jump phenomenon and subharmonic motion. A local bifurcation of codimension two of rotor motion was investigated on the center manifold near the double-zero degenerate point by using center manifold theory and the normal form method [5]. Saddle-node bifurcation, Hopf bifurcation and saddle-connection bifurcation were found in the reduced normal form equations.…”

Section: Introductionmentioning

confidence: 99%