This article deals with the generalized procedure of designing and optimizing multi-ring radial and thrust permanent magnet bearings (PMBs) with an axial air gap for maximum force and stiffness per volume of the magnet. Initially, the procedure of determining optimized design variables in both the configurations is presented using the MATLAB codes written for solving the three dimensional (3D) equations of force and stiffness in PMB having `n' number of rings on the stator and rotor. The maximized results of the forces in both radial and thrust multi-ring PMBs are validated with the values obtained using finite element analysis (FEA). Then, the correlation between the optimized parameters and the air gap is obtained, and curve fit equations for the same are proposed in terms of stator outer diameter. Further, curve fit equations establishing the relationship between the maximized bearing features, and the aspect ratio (L/D4) of the bearing are expressed for different values of air gap in both the radial and thrust bearings. Finally, the generalized method of designing and optimizing the multi-ring PMB is demonstrated with a specific application. A designer can use the presented curve fit equations for optimizing design variables and calculating maximized bearing features in multi-ring radial and thrust PMBs easily just by knowing the bearing features for a single ring pair.
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