Application of active magnetic bearings in flexible rotordynamic systems - A state-of-the-art review

Chaos prediction in MEMS-NEMS resonators

Study of nonlinear dynamics and chaos in MEMS/NEMS resonators

The non-linear dynamic behavior of a rigid disc-rotor supported by active magnetic bearings (AMB) is investigated, without gyroscopic effects. The rotor-AMB system is subjected to a periodically time-varying stiffness. The simultaneous primary resonance case is considered and examined. The vibration of the rotor is modeled by a coupled second-order non-linear ordinary differential equations with quadratic and cubic non-linearities. Their approximate solutions are sought applying the method of multiple scales. The steady-state response and the stability of the system at the simultaneous primary resonance case for various parameters are studied numerically, applying the frequency response function method. It is found that different shapes of chaotic motion exist, which are determined using phase-plane method. It is also shown that the system parameters have different effects on the non-linear response of the rotor. For steady-state response, however, multiple-valued solutions, jump phenomenon, hardening and softening non-linearity occur. Results are compared to previously published work.

Resonance behavior of a rotor-active magnetic bearing with time-varying stiffness

Nonlinear dynamics near resonances of a rotor-active magnetic bearings system with 16-pole legs and time varying stiffness

Homoclinic bifurcation and chaos control in MEMS resonators

Dynamic behavior of an AMB supported rotor subject to harmonic excitation

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 nonlinear oscillations and dynamic behavior of a rigid disk-rotor supported by active magnetic bearings (AMB), without gyroscopic effects. The nonlinear equations of motion are derived considering a periodically time-varying stiffness. The method of multiple scales is applied to obtain four first-order differential equations that describe the modulation of the amplitudes and the phases of the vibrations in the horizontal and vertical directions. The stability and the steady-state response of the system at a combination resonance for various parameters are studied numerically, applying the frequency response function method. It is shown that the system exhibits many typical nonlinear behaviors, including multiple-valued solutions, jump phenomenon, hardening, and softening nonlinearity. A numerical simulation using a fourth-order Runge-Kutta algorithm is carried out, where different effects of the system parameters on the nonlinear response of the rotor are reported and compared to the results from the multiple scale analysis. Results are compared to available published work.

Usama H. Hegazy

Papers

Homoclinic bifurcation and chaos control in MEMS resonators

Resonance behavior of a rotor-active magnetic bearing with time-varying stiffness

Dynamic behavior of an AMB supported rotor subject to harmonic excitation

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

A Time-Varying Stiffness Rotor Active Magnetic Bearings Under Combined Resonance