Bifurcation behavior of a rotor supported by active magnetic bearings

The non-linear dynamics of a rigid rotor levitated by active magnetic bearings is investigated. The vibrations in the horizontal and vertical directions are analyzed on the center manifold near the double-zero degenerate point by using normal-form method. The resulting normal forms in the horizontal and vertical directions are different due to the effect of rotor weight. It is shown that the vibratory behavior in the vertical direction can be reduced on the center manifold to the Bogdanov-Takens form. For the autonomous case, there exist saddle-node bifurcation and Hopf bifurcation for local analysis, and a saddle-connection bifurcation for global analysis. For non-autonomous case, the Melnikov technique is used to determine the critical parameter at which the homoclinic orbits intersect transversally. For the vibrations in the horizontal direction, the essential non-linear terms of the truncated normal form are third order. The behaviors of zero solutions are given. Finally, numerical simulations are performed to verify the analytical predictions.