Optimization of Stiffness per Magnet Volume Ratio of Discrete and Continuous Halbach Type Permanent Magnetic Bearings

To optimize stiffness per magnet volume ratio, whichs major intentions are to reduce the costs and to preserve material resources, an energy based analytical calculation method of the radial stiffness for permanent magnetic bearings with arbitrary magnetization is introduced. To simplify the calculations the stiffness is calculated from a planar model, what means that the annular ring magnets are treated as infinitely long parallel bars. The error made by neglecting the curvature effect is investigated and shows to be negligible for reasonable designs. Using this calculation method, optimal geometries for permanent magnetic ring bearings with Halbach type magnetization are presented. Thereby, discrete Halbach stacking, i.e. several stacked rings with rotating magnetization from axial to radial and so on, and continuous Halbach magnetization, i.e. one magnet that is magnetized sinusoidal, is distinguished. To show the possible improvement of stiffness per magnet volume ratio, also the characterizing values for standard single ring bearings and standard stacked structures are calculated.