A simple kinematic model for the behavior of a magnetically levitated rotor operating in overload regime

Currently, the use of magnetic levitation systems has incremented in lieu of the many advantages they present respect to conventional systems. They provide frictionless operation and thus, a wearless life, eliminate the need for lubricants and allow for active vibration control. However, there are some limitations to their use, the dynamic load capacity is restricted by the magnetic properties of the materials used in their constructions and, therefore, their tolerance to large dynamic loads, such as in the case of blade loss or similar sudden failures, is small. For these cases, as well as for the case of bearing power loss, all commercial magnetic suspensions contain a safety backup system, usually consisting of roller bearings that avoid contact between stationary and rotating parts. The present work analyses the behavior of a rotor supported by a magnetic radial bearing on the non-drive end, which is operated in an overload regime. In this regime, a series of impacts occurs between the rotor and the backup bearing, which results on a highly non-linear system that might become unstable depending on the geometry, the control algorithm, the speed and excitation conditions. A non-linear model is proposed. The equations are separated into two regimes, one when the rotor is levitated and one during contact with the backup bearings; the contact is modeled by kinematic conditions. The magnetic bearing forces are estimated using a non-linear model and a PID algorithm is considered as a system's control strategy. Rigid body theory for planar collision is considered for description of impacts between the backup bearing and the rotor.