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.

Multi-pulse chaotic motions of a rotor-active magnetic bearing system with time-varying stiffness

Magnetic bearings use magnetic forces to support various machine components. Because of the non-contact nature of this type of suspension, magnetic bearing technology offers a number of significant advantages over conventional bearings, such as rolling element and fluid film bearings. An active magnetic bearing basically consists of an electromagnetic actuator, position sensors, power amplifiers, and a feedback controller. All of these components are characterized by nonlinear behavior and therefore the entire system is inherently nonlinear. However, in simulations of the dynamic behavior of magnetic bearing systems, the nonlinearities are usually neglected to simplify the analysis and only linear models are used. Moreover, many control techniques currently used in magnetic bearing systems are generally designed by ignoring nonlinear effects. The main reason for simplification is the intractability of the complexity of the actual model. In fact, the inherent nonlinear properties of magnetic bearing system...

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Nonlinear Dynamics of Magnetic Bearing Systems

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A theoretical model for analyzing the dynamic behavior of a misaligned rotor with active magnetic bearings

The dynamical behavior of a parametrically excited simple rigid disk-rotor supported by active magnetic bearings (AMB) is investigated, without gyroscopic effects. The principal parametric resonance case is considered and studied. The motion of the rotor is modeled by a coupled second-order nonlinear ordinary differential equations. Their approximate solutions are sought applying the method of multiple scales. A reduced system of four first-order ordinary differential equations are determined to describe the time variation of the amplitudes and phases of the vibration in the horizontal and vertical directions. The steady-state response and the stability of the solutions for various parameters are studied numerically, using the frequency response function method. The numerical results show that the system behavior includes multiple solutions, jump phenomenon, and sensitive dependence on initial conditions. It is also shown that the system parameters have different effects on the nonlinear response of the rotor. Results are compared to previously published work.

Dynamic Behavior of an AMB/Supported Rotor Subject to Parametric Excitation

This paper is concerned with the effect of a thrust active magnetic bearing (TAMB) on the stability and bifurcation of an active magnetic bearing rotor system (AMBRS). The shaft is flexible and modeled by using the finite element method that can take the effects of inertia and shear into consideration. The model is reduced by a component mode synthesis method, which can conveniently account for nonlinear magnetic forces and moments of the bearing. Then the system equations are obtained by combining the equations of the reduced mechanical system and the equations of the decentralized PID controllers. This study focuses on the influence of nonlinearities on the stability and bifurcation of T periodic motion of the AMBRS subjected to the influences of both journal and thrust active magnetic bearings and mass eccentricity simultaneously. In the stability analysis, only periodic motion is investigated. The periodic motions and their stability margins are obtained by using shooting method and path-following technique. The local stability and bifurcation behaviors of periodic motions are obtained by using Floquet theory. The results indicate that the TAMB and mass eccentricity have great influence on nonlinear stability and bifurcation of the T periodic motion of system, cause the spillover of system nonlinear dynamics and degradation of stability and bifurcation of T periodic motion. Therefore, sufficient attention should be paid to these factors in the analysis and design of a flexible rotor system equipped with both journal and thrust magnetic bearings in order to ensure system reliability.

Effect of Thrust Magnetic Bearing on Stability and Bifurcation of a Flexible Rotor Active Magnetic Bearing System

This paper investigates the rotor dynamic coefficients of a thrust active magnetic bearing when runner tilt is taken into account. The influence of runner tilt upon the load capacity and the dynamic forces and moments of a thrust active magnetic bearing is analysed. A total of 24 rotor dynamic coefficients are defined to describe the dynamic behaviour of the thrust active magnetic bearing. A general method is presented to calculate these coefficients, which can be used conveniently for the coupled dynamic analysis when a rotor is supported by both radial and thrust magnetic bearings.

Rotor dynamic coefficients of a thrust active magnetic bearing considering runner tilt

This paper is concerned with the stability and bifurcation of a rigid rotor support by journal and thrust active magnetic bearing (TAMB). The system is modelled as a five-axis controlled active magnetic bearing-rotor system (AMBRS), and the system equations are formulated by combining the equations of motion of the rotor and the equations of the decentralized proportional-integral-derivative controllers. For this AMBRS, the magnetic forces of the journal and TAMB are strongly non-linear with respect to control current and shaft displacement. This study focuses on the influence of non-linearities on the stability and bifurcation of T periodic motion of the AMBRS subjected to the influence of TAMB and mass eccentricity. In the stability analysis, only periodic motion is investigated. The periodic motions and their stability margin are obtained by shooting method and path-following technique. The local stability and bifurcation behaviours of periodic motions are obtained by the Floquet theory. The re...

Y. S. Ho

Papers

Effect of Thrust Magnetic Bearing on Stability and Bifurcation of a Flexible Rotor Active Magnetic Bearing System

Rotor dynamic coefficients of a thrust active magnetic bearing considering runner tilt

Stability and bifurcation of a rigid rotor-magnetic bearing system equipped with a thrust magnetic bearing