Generalized three-dimensional mathematical models for force and stiffness in axially, radially, and perpendicularly magnetized passive magnetic bearings with "n" number of ring pairs

This work deals with generalized three-dimensional (3D) mathematical model to estimate the force and stiffness in axially, radially, and perpendicularly polarized passive magnetic bearings with "n" number of permanent magnet (PM) ring pairs. Coulombian model and vector approach are used to derive generalized equations for force and stiffness. Bearing characteristics (in three possible standard configurations) of permanent magnet bearings (PMBs) are evaluated using matlab codes. Further, results of the model are validated with finite element analysis (FEA) results for five ring pairs. Developed matlab codes are further utilized to determine only the axial force and axial stiffness in three stacked PMB configurations by varying the number of rings. Finally, the correlation between the bearing characteristics (PMB with only one and multiple ring pairs) is proposed and discussed in detail. The proposed mathematical model might be useful for the selection of suitable configuration of PMB as well as its optimization for geometrical parameters for high-speed applications.