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• Based on H - ϕ formulation combined with moving mesh to establish full 3D models. • Using Halbach array rotors to improve levitation force and stiffness. • Optimized rotor produces larger area of flux penetration and shielding current. • Superconducting bulks coupled with optimized rotor maintains thermal stability. The superconducting flywheel system exploiting the magnetic coupling between the bulk high temperature superconductors (HTSs) and permanent magnets (PMs) exhibits excellent performance of self-stable levitation, and is promising for power applications. In this paper, we use the H - ϕ formulation combined with moving mesh to establish a full 3D model for the thrust type and journal type bearings in the HTS flywheel system. We then proposed different Halbach schemes to enhance the magnetic flux density of the rotor and thus the coupling, and investigated the levitation force, relaxation characteristics, electromagnetic transient distribution, and temperature characteristics of the bearings. Results show that, under axial zero field-cooled (ZFC) condition, the optimized PM rotor scheme can significantly improve the maximum levitation force and stiffness by 4.0 and 2.3 times respectively for the thrust type bearing, and the maximum levitation force of journal type bearing can be improved by a factor of 5.5. Under the radial ZFC condition, the maximum levitation force and stiffness of the journal type bearing have been increased by 4.9 times and 2.9 times. For the relaxation of both bearings during operation, the optimized PM rotors lead to relatively greater attenuation of levitation force. The proximity of the optimized PM rotors intensifies the magnetic flux movement of the HTS bulks but only brings about a limited temperature rise, and the superconductors still maintain a good low-temperature working environment. This study provides an effective methodology for analyzing the HTS bearing systems and good references for the optimal design of compact HTS flywheel energy storage systems (FESSs). [ABSTRACT FROM AUTHOR]