A 2D-Based Analytical Method for Calculating Permanent Magnetic Ring Bearings with Arbitrary Magnetization and its Application to Optimal Bearing Design

This paper investigates the optimal design of passive permanent magnetic bearings in terms of maximum stiffness per magnet volume ratio. Examining the influence of design parameters on maximum material utilization, we present general conclusions regarding cross-section dimension, type of magnetization, and magnetic pole number. Further, we provide generalized design plots for selected configurations, which can be used for rapid dimensioning of bearings with adequate raw material utilization. The analytical computation method used for all calculations is based on the interaction energy of elementary magnetic dipoles and thus supports any kind of magnetization, including when strength and direction may vary within the cross-section of the magnetic rings. Although the design problem is three-dimensional and the analytical method two-dimensional, the resulting error is negligible for most practical applications.