Magnetic circuit coupling characteristics of axial gimballing magnetic bearing biased with permanent magnet for magnetically suspended flywheel

To satisfy the requirements of the high precision vernier-gimballing function of a magnetically suspended flywheel, an axial magnetic bearing biased with a permanent magnet, i.e., the axial gimballing magnetic bearing (AGMB) is presented, with the capacity of controlling the 3 degrees of freedom rotor motion including axial translation and radial tilt. The concepts of bias-flux coupling degree and control-flux coupling degree are introduced and defined. Based on the coupling degree analytical expression of AGMB and the traditional radial magnetic bearing biased with a permanent magnet (called radial gimballing magnetic bearing applied for vernier-gimballing, RGMB for short) from an equivalent magnetic circuit, the quantitive relationship between the magnetic circuit model and the coupling degree is constructed, and the coupling degree influence on the magnetic bearing performance, such as its bias-force change rate, current stiffness change rate, and maximal loading ability, is obtained to further decide flywheel vernier-gimballing performance. This opens a theoretical path for the analysis and evaluation of magnetic flux coupling and magnetic bearing performance. It is verified by magnetic-circuit analysis and finite element (FE) simulation that the coupling degree and bias-force change rate, current stiffness change rate of AGMB are nearly one order less than those of RGMB, and the maximal gimballing moment of flywheel is 2.7 times larger. As a result, a 50 N·m·s flywheel based on AGMB has the large and high precision gimballing capacity of 0.5° maximal gimballing angle, 8.1 N·m maximal gimballing moment, and less than 15% of bias-force change rate and current stiffness change rate over all the statues.