Stability of Magnetic Bearing-Rotor Systems Having a Central Support Backup Bearing

Abstract

The unperturbed (fully nonlinear) stability of a magnetic bearing-rotor system having a single central backup bearing near the middle of the shaft is analyzed under conditions of magnetic bearing(s) failure for zero gravity using the Lyapunov second (direct) method; these results are shown to apply with gravity, based on observed similiaries of the nonlinear Lagrangian equations. These are completely general stability criteria for practical values of system parameters and conditions of system operation and failure. It turns out that the center-backup bearing configuration has some considerable advantages over conventional designs: in addition to known results for stability and instability, the system can be stable when one or both magnetic bearings fail (has negative stiffness). This “temporary stability” depends upon inherent gyroscopic forces and may be lost when dissipative forces are introduced. The results are applicable to other gyroscopic systems.