STABILITY AND BIFURCATION OF ROTOR MOTION IN A MAGNETIC BEARING

The equations of motion of a two-degrees-of-freedom mass in a magnetic bearing are non-linear in displacement, with geometric coupling of th e 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 t he forced response, only periodic motion is investigated here. Stable periodic motion is obtained by numerical integration and by the approx imate method of trigonometric collocation. Where unstable motion coexi sts with stable motion after a bifurcation of periodic motion, the uns table motion is obtained by the collocation method. The periodic motio ns local stability and bifurcation behavior are obtained by Floquet th eory. The parameters i.e., rotor speed, imbalance eccentricity, forcin g amplitude, rotor weight, and geometric coupling are investigated to find regimes of non-linear behavior such as jumps and subharmonic moti on. (C) 1998 Academic Press.