Honor Paper: Ambient- Temperature Passive Magnetic Bearings: Theory and Design Equations

As described previously (R. F. Post, D. D. Ryutov, J. R. Smith, and L. S. Tung, Proc. of MAG '97 Industrial Conference on Magnetic Bearings, p. 167), research has been underway at the Lawrence Livermore National Laboratory on ambient-temperature passive magnetic bearings for a variety of possible applications. In the approach taken the limitations imposed by Eamshaw's theorem with respect to the stability of passive magnetic bearing systems are overcome by employing special combinations of elements, as follows: Levitating and restoring forces are provided by permanent-magnet elements that provide positive stiffnesses for selected displacements (i.e., those involving translations or angular displacement of the axis of rotation). As dictated by Eamshaw's theorem, bearing systems thus constructed will be statically unstable for at least one of the remaining possible displacements. Stabilization against this displacement is accomplished by using periodic arrays ("Halbach arrays") of permanent magnets to induce currents in close-packed inductively loaded circuits, thereby producing force derivatives stabilizing the system while in rotation. Disengaging mechanical elements stabilize the system when at rest and when below a low critical speed. The paper discusses theory and equations needed for the design of such systems.