Nonlinear dynamic simulation of an active magnetic bearing system with non-symmetric coordinate coupling forces
Equations of motion are presented for a two degree of freedom system representing a rotor suspended with an active magnetic bearing. The rotor is subjected to both a rotating unbalance force and a steady load, which is balanced by differential bias in the vertical magnet pair. A coupling between the coordinate directions resulting from the spatial arrangement of magnets is included in the equations of motion, which renders them nonlinear even though the closed loop control on each axis is linear. Results of a path-following analysis of the equations show that the addition of a steady load has several effects. Compared with previous results for an unloaded system, the response is now asymmetric due to unequal stiffnesses, and the region of unacceptable high amplitude response extends over a larger frequency range. In addition, the frequency ranges over which multiple stable solutions coexist is expanded. New results for the unloaded case are also presented that show domains of attraction to large amplitude stable response due to an applied impulse. There is a strong dependence of the domains of attraction on the timing of the impulse.
