Design of Magnetic Bearings for Rotor Systems With Harmonic Excitations

Abstract

This paper presents a method for calculating the control forces and the bearing stiffness and damping coefficients to control the response of multi-mass flexible rotor systems mounted on magnetic bearings and subjected to unbalance or harmonic excitation forces. The capability for inclusion of hydrodynamic bearings is retained to model seal effects or to permit the design of magnetic bearings for hybrid systems. Control forces at the magnetic bearing locations are evaluated based on the desired shaft response specified by the modal coordinates. These forces are determined such that the error between the desired response and the achieved response is minimized in a least-square sense. Equivalent bearing coefficients are calculated from the control forces and the achieved response which when superimposed on the nominal bearing coefficients yield the resultant magnetic bearing coefficients required for control. An example case is presented where control of rotor response has been attempted at the first and the second unbalance critical speeds. The results demonstrate appreciable improvement in response using magnetic bearings.