Quasiperiodic Vibration of a Rotor in a Magnetic Bearing with Geometric Coupling

This paper develops a one-dimensional model of the magnetic flux to estimate the magnetic forces by including the pole face curvature. Accounting for the pole face curvature results in a normal force that is perpendicular to the principal force; this causes geometric coupling of forces. The non-dimensional equa- tions of motion are derived for a point mass rotor in one magnetic bearing with P D current feedback and geometric coupling. The steady-state nonlinear vibrations are then investigated. The rotor-bearing system has the softening spring type nonlinearity and exhibits characteristic jumps and hysteresis. When speed is increased, the presence of geometric coupling increases the rotor displacement be- f ore the jump and decreases the displacement beyond the jump. Geometric coupling also causes quasiperiodic vi- bration of the rotor. The (a)periodicity of the rotor mo- tion is discussed using Poincare maps and bifurcation di- agrams. Increasing the differential gain of the controller could not damp the quasiperiodic motion to a periodic one .