Abstract
The equations of motion of a two-degrees-of-freedom mass in a magnetic bearing are non-linear in displacement, with geometric coupling of the magnetic bearing coupling the horizontal and vertical components of rotor motion. The non-linear forced response is studied in two ways: (1) using imbalance force; (2) using non-imbalance harmonic force. In the forced response, only periodic motion is investigated here. Stable periodic motion is obtained by numerical integration and by the approximate method of trigonometric collocation. Where unstable motion coexists with stable motion after a bifurcation of periodic motion, the unstable motion is obtained by the collocation method. The periodic motions' local stability and bifurcation behavior are obtained by Floquet theory. The parameters i.e., rotor speed, imbalance eccentricity, forcing amplitude, rotor weight, and geometric coupling are investigated to find regimes of non-linear behavior such as jumps and subharmonic motion.
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