| An active magnetic bearing is an electro-mechanical system that has no friction and for which the bearing stiffness and damping can be changed by varying the feedback controller's gains. They are used for compressors, turbines, vacuum pumps, flywheels, and are being developed for artificial hearts (pumps). While the currently available magnetic bearing systems have proven to be quite reliable, confidence on this new technology may be improved through developing simple models for bearing nonlinearities and studying their theoretical effects on steady state rotordynamics.; The radial active magnetic bearing considered has four pole-pairs and uses a linear current feedback control. The controller's proportional gains that result in either hardening or softening spring characteristics are obtained. A one-dimensional model of magnetic flux is developed to predict bearing force coupling of rotor motion in two perpendicular directions. The effects of this geometric coupling on linearized bearing force coefficients are determined.; The forced response of a two-degrees-of-freedom rigid rotor in one magnetic bearing for one-frequency harmonic excitation is studied. The parameters i.e. rotor unbalance eccentricity, speed, gravity load, and bearing geometric coupling are investigated to find regimes of nonlinear behavior such as jumps, bifurcation from harmonic to subharmonic or quasiperiodic motion. The nonlinear dynamics is demonstrated using frequency response curves, bifurcation diagrams, Poincare maps, and rotor orbits. Stable periodic and quasiperiodic motions are obtained using numerical integration, while coexisting stable and unstable periodic motions are obtained using the semi-analytical trigonometric collocation method. The periodic motion's local stability and bifurcation behavior are obtained using Floquet theory.; A simple piecewise linear model of magnetic material's flux saturation is obtained. Then, the effects of flux saturation on rotordynamics are investigated. Finally, the effects of bearing nonlinearities on the dynamics of a simple flexible rotor are determined. |
