Improving Rotational Stability of Radial Permanent Magnetic Bearings for Compact Rotors via Axial Offset and Optimal Sizing

Permanent magnetic bearings (PMBs) provide a passive, contactless alternative to mechanical bearings, yet their inherent instability complicates their adoption in small-scale rotating machinery. While axial instability is well-known for radially stable PMBs, rotational instability can arise when the bearing radius exceeds the lever arm between the bearing center and the rotor’s center of rotation. This study addresses this limitation by introducing an axial offset between magnets to improve rotational stability, enabling the integration of large-diameter PMBs in flat-profile rotors and enhancing overall system compactness. A semi-analytical model for calculating bearing stiffness is employed to investigate how bearing offset and other geometric parameters can be used to tailor stiffness characteristics. Parametric analysis reveals that a positive axial offset effectively increases rotational stability at the expense of reduced radial stiffness. The low computational cost of the model enables further optimization of the bearing dimensions. An optimization strategy is proposed to size single-layer radial PMBs for compact rotors, tuning both radial and rotational stiffness while minimizing volume. The design approach is extendable to multi-layer topologies. Additionally, a practical expression is derived to estimate the theoretical upper bound of radial stiffness based on bearing outer radius and clearance.