A 2½-D Linear Magnetic Analysis For Parallel-Airgap Radial Magnetic Bearings

This paper provides methods for investigating the design of a class of radial magnetic bearings in which axial MMF is provided in each one of a set of flat, uniform-thickness circular discs arranged in alternation such that every second disc is mechanically attached to the rotor and the interleaving discs are fixed to the stator. The axial MMF in the rotor discs is a sinusoidal function of angle and is taken to be independent of radius. Similarly, the axial MMF in the stator discs varies sinusoidally with respect to angle and is invariant with respect to radius. Provided that both the numbers of pole-pairs of rotor and stator discs differ by 1, a net transverse force can be produced. Many questions arise with regard to the design of radial bearings of this configuration. A particular motivation behind these bearings is to achieve a high specific load capacity. This paper sets out a linear magnetic analysis for providing a first-cut approximate assessment of the force which can be generated from such bearings. The analysis proceeds using the assumption that lines of magnetic flux remain in concentric cylinders. Then for each radius, the problem of predicting the distribution of magnetic flux reduces to a 2D problem. This 2D problem is addressed using linear superposition. The flux field due to the MMF on the stator-discs is computed assuming that the rotor-discs contribute no MMF. Then the flux field due to the MMF on the rotor-discs is computed assuming that the stator-discs contribute no MMF. When these two fields are added, it is possible to compute Maxwell stresses at every position in the airgap. The net transverse components of force due to flux in a thin-walled cylindrical volume are computed and then integrated with respect to radius to produce a prediction of the total transverse flux in the bearing. This paper investigates three different arrangements. In Class I: both rotor and stator discs are considered to be made up of permanent magnet materials and the necessary MMF is generated by the distribution of permanent magnet materials in the discs. Class I is a hypothetical case only since the net force produced between rotors is a known function of the relative rotation of the two components and cannot be controlled. In Class II: the rotor is considered to be made of permanent magnet and stator is wound. In Class III: both rotor and stator are wound. Results have been shown for the Class I & II in this paper.