This paper deals with the theoretical study of a horizontal shaft, partially levitated by a passive magnetic bearing, impacting its stator. Rigid body dynamics are utilised in order to describe the governing nonlinear equations of motion of the shaft interacting with a passive magnetic bearing and stator. Expressions for the restoring magnetic forces are derived using Biot Savart law for uniformed magnetised bar magnets and the contact forces are derived by use of a compliant contact force model. The theoretical mathematical model is verified with experimental results, and shows good agreements. However, the simulated contact forces are higher in magnitude compared to the experimental results. The cause of this disagreement is addressed and shows that the formulation of the theoretical contact force model slightly overestimates the forces acting during a full annular backward whirl motion.
Journal of Sound and Vibration, 2013, Vol 332, Issue 24, p. 6359-6376