Exploring the Physical Limits of Axial Magnetic Bearings Featuring Extremely Large Vertical Levitation Distances

This work provides an analytical method, based on the Ampèrian model of permanent magnets (PM), for a fast calculation of the magnetic flux density in three-dimensional space applying Biot–Savart law, and the calculation of the forces using Lorentz's law. The applied approach enables the characterization regarding forces, torques, and stiffnesses of the levitating PM for any arbitrary position in space. Furthermore, it permits the extension of the investigation to any shape and configuration of ironless magnetic bearings (MB). In order to demonstrate the simple use of the analytical model, in this article, the dimensions of an ironless axial MB employing PMs are optimized with a multiobjective Pareto analysis, which reveals the physical limits concerning maximum achievable levitation height with respect to given constraints on, e.g., the required force and tilting stiffnesses, and the MB robustness defined by the maximum allowable payload on the levitating magnet. Moreover, the optimized axial MB and a corresponding test bench are realized to validate the proposed model with experimental results. For the sake of completeness, it should be mentioned that in a later stage, the optimized MB can also be scaled with simple scaling laws if the demanded specifications, e.g., concerning desired maximum levitation height or payload capability, would have changed.