Angle-dependence of the levitation force from a frustum-shaped magnet and recessed superconducting bulk

The widespread application of superconducting magnetic levitation bearings is limited by their relatively low stiffness. Recently we investigated a novel thrust bearing geometry comprised of a conical frustum (or truncated cone) shaped permanent magnet levitating inside a matching tapered hole machined into a high-temperature superconductor bulk. This configuration was found to produce superior restoring forces and stiffness compared to the conventional cylindrical magnet and superconductor arrangement. Here, using H-formulation finite-element simulations, we evaluate the angle-dependence of the frustum on the levitation force. We find that the optimal angle is not universal, but depends on the mode of displacement as well as the frustum dimensions. Correlations with the incident magnetic flux are identified for estimating the angle best suited to the operating regime of the bearing.