Superconducting magnetic bearings (SMBs)^{[1]} generally consist of a rotor containing permanent magnets or magnetic materials and a stator containing bulk superconductors. Since the pinning effect levitates the rotor, there is no mechanical contact. Therefore, the use of this structure in flywheels^{[2]}, cryogenic pumps^{[3]}, and bearings for satellites^{[4]} is being considered. We are particularly interested in bearings for onboard satellites.

The bearings for satellites are about 400 mm in diameter and are expected to operate at 72 rpm, and the allowable heat generation is minimal (4 mW). We have proposed an SMB structure consisting of a rotor composed of ring-shaped segmented permanent magnets and an iron yoke, and a stator composed of ring-shaped segmented bulk superconductors. The permanent magnets are parallel magnetized. Electromagnetic losses occur in such a structure. First, a magnetic field is generated on the rotor side. Next, a superconducting current flows in response to the magnetic field on the stator side. At this time, superconducting losses occur on the stator side. A magnetic field created by the superconducting current is generated. This magnetic field generates eddy currents. At this time, eddy current loss and iron loss are generated on the rotor side. To optimize the design of SMBs to suppress these electromagnetic losses, it is important to investigate their rotation loss characteristics.

We developed a FEM analysis model of the SMB and analyzed the rotational loss for various levitation forces. We used a model that combines the H-φ formulation and A-V formulation as a three-dimensional electromagnetic field analysis. The φ formulation is used to calculate the magnetic field generated by the rotor, the H-φ formulation to calculate the current induced in the superconductor of the stator, and the A-V formulation to calculate the eddy currents induced in the stator by the magnetic field due to the superconducting current. The analysis is performed using COMSOL Multiphysics, a general-purpose physics simulation software, and an n-value model for the superconductor's current-voltage characteristics. This study is mainly concerned with the electromagnetic interpretation of eddy current losses.

**References**

[1] J. R Hull, Superconducting Science and Technology, Vol. 13, No. 2 (2000), pp. R1-R15.

[2] K. Demachi, et al., Physica C: Superconductivity, Vol. 426-431, Part 1 (2005), pp. 826-833.

[3] Q. Lin, et al., IEEE Transaction on Applied Superconductivity, Vol. 22, No. 3 (2012).

[4] M. Hazumi et al., Proc. of SPIE, Space Telescopes and Instrumentation 2020: Optical, Infrared, and Millimeter Wave, Vol. 11443 (2020), 114432F.

[5] A. Arsenault et al., IEEE Transactions on Applied Superconductivity, Vol.31, No.2 (2021).

Keywords: Superconducting magnetic bearing, Rotational loss, Finite Element Analysis