Bifurcation behavior of a rotor supported by active magnetic bearings

The non-linear dynamics of a rigid rotor levitated by active magnetic beari ngs is investigated. The vibrations in the horizontal and vertical directio ns are analyzed on the center manifold near the double-zero degenerate poin t by using normal-form method. The resulting normal forms in the horizontal and vertical directions are different due to the effect of rotor weight. I t is shown that the vibratory behavior in the vertical direction can be red uced on the center manifold to the Bogdanov-Takens form. For the autonomous case, there exist saddle-node bifurcation and Hopf bifurcation for local a nalysis, and a saddle-connection bifurcation for global analysis. For non-a utonomous case, the Melnikov technique is used to determine the critical pa rameter at which the homoclinic orbits intersect transversally. For the vib rations 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 analytica l predictions. (C) 2000 Academic Press.