Stability of a 4 degree of freedom rotor on electrodynamic passive magnetic bearings

Electrodynamic bearings exploit repulsive forces due to eddy currents to produce positive stiffness by passive means without violating the Earnshaw stability criterion. This remarkable characteristic makes this type of bearing a suitable alternative to active magnetic bearings in fields such as kinetic energy storage flywheels, turbo pumps, high speed compressors, among others. However, the suspension can become unstable due to rotating damping. To obtain deeper understanding of this instability phenomenon this paper presents the analysis of stability of a four degree of freedom (4dof) rotor supported by electrodynamic bearings. The 4dof rotor model is coupled to the dynamic model of the eddy current forces generated by the electrodynamic bearing and the stability of the complete system is analyzed. This model is used to study the stability of both cylindrical and conical whirling motion of the rotor. In addition to the well known cylindrical whirl instability the possible occurrence of conical instability is demonstrated. Finally the effects of two stabilization strategies are analyzed