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In this paper, we propose a novel structure of permanent-magnet-biased axial hybrid magnetic bearing. It has four segments of poles to control three degrees of freedom (3-DOF). Based on the inner and outer air gaps in conventional axial magnetic bearings, a novel air gap, called the subsidiary air gap, is constructed between the permanent magnet and the stator poles. This air gap separates the bias flux paths from the control flux paths. As a result, lower power loss of the axial magnetic bearing can be achieved due to lower magnetic reluctance of the control flux paths. Furthermore, by means of the equivalent magnetic circuit method and the 3-D finite-element method (FEM), we analyze and model the 3-DOF axial hybrid magnetic bearing. Experimental results show that the presented axial magnetic bearing has good control performance and little coupling among X, Y, and Z directions. However, the rotational power loss will be large at high speed because of the alternating flux density in the thrust plate produced by four segments of stator poles. Therefore, we propose a novel stator, named the parallel-slot stator, and novel thrust plate to reduce the rotational power loss effectively, which is assembled by DT4 and nanocrystalline materials. Meanwhile, we have designed and assembled an axial hybrid magnetic bearing prototype with the novel stator and thrust plate, which is applied in the five-degrees-of-freedom reaction flywheel system with angular momentum of 15 Nms at 5000 r/min. It is validated by the experimental results.