Forces in Magnetic Journal Bearings: Nonlinear Computation and Experimental Measurement

A method of calculating forces between magnets and shaft in an active magnetic journal bearing is presented. The method is based on two-dimensional finite element modelling of a region including both metals and free space for the determination of magnetic flux density. It includes nonhnear, single-valued magnetization functions for the metals in the magnets and shaft. The force is determined by the virtual work principle applied to the change of energy stored in the magnetic field as a function of shaft position within the clearance space. The extent of magnetic saturation in the metals is examined as a function of coil current and shaft position, and effects of one type of geometric error in magnet pole faces is considered. Results indicate that there is a coupling between coordinate directions for each magnet, and that the magnitude of coupling is strongly influenced by saturation and pole face geometry. Forces are also measured in an experimental apparatus with geometry similar to an actuator for an active magnetic journal bearing. The measurement of forces in the steady current case is based on deflection of a calibrated beam held in clamped-clamped supports. Force as a function of position and coil current from a single magnet in the principal attractive direction is measured, as well as force in the direction normal to the principal axis. The measurements indicate that the ratio of normal force to principal force is approximately a linear function of the shaft eccentricity in the normal direction. Force from a pair of opposed magnets of equal strength is also measured, to simulate the effect of a strongly biased magnetic bearing. Since the resultant principal force is small, the ratio of the normal component of force to the principal component is large, exceeding 5 at large eccentricities and small currents. Results of the measurements and calculations imply that significant coordinate coupling may be present in magnetic bearings and that control strategies for flexible rotor systems including active magnetic journal bearings should account for such coupling.