| Magnetic repulsion can be produced by several mechanisms: (1) the interaction of two permanent magnets of like polarity (electromagnetic repulsion), (2) the interaction of a dc magnet and a superconductor (diamagnetic repulsion), and (3) eddy current induction in a conductor which is either moving through a non-uniform dc flux field, or stationary in an ac flux field (motional and ac eddy current repulsion, respectively). Despite the fact that they utilize repulsive force, devices based on permanent magnet repulsion, according to Earnshaw's theorem, are inherently unstable. It may be possible, however, to control the instability using either of the latter two repulsive mechanisms. Designs for magnetically levitated vehicles based on motional eddy current repulsion, and passive magnetic bearings based on both diamagnetic and eddy current repulsion concepts are currently under consideration. One of the main impediments to the development of these devices, however, is the difficulty in analyzing them. Analytical solutions are available for only a few simple one- and two-dimensional geometries. Consequently, developers of passive electrodynamic devices, have relied heavily on diamagnetic limit approximations, which for a conventional conductor means infinite speed, and, of course, experimentation.; During the 1980s, numerical techniques were first applied to Maxwell's equations. Finite element codes became widely accepted, and software packages with capabilities for static, transient, and non-linear magnetic analysis appeared on the market. None of these codes, however, tackled the problem of motionally induced eddy currents. The reason is twofold. First, motionally induced eddy currents are negligible in many electromechanical devices. Their behavior is described either by static field equations or dynamic equations with ac current sources. Secondly, introduction of the velocity term in Maxwell's equations presents numerical difficulties. Numerical oscillations associated with the solution of competing diffusion and convection problems are well known. Recently, the upwinding technique, which has its origins in finite difference fluid flow, has been applied in electrodynamic finite element codes. This development, which was motivated primarily by the emergence of maglev technology worldwide, facilitates the analysis of high speed electrodynamic phenomena. The ability to analyze complex 3-D devices at high speed promises a revolution in the development of passive repulsive devices.; In this research, current numerical capabilities for the analysis of motional eddy current devices are assessed. Three levels of complexity are investigated: low speed 3-D, high speed 2-D, and high speed 3-D. Two rotating devices are analyzed. The first is comprised of an axial flux magnet array spinning above a circular conductive disk. The device can provide braking or coupling at low speeds, and axial stability for a magnetic bearing at high speeds. The second device is a passive eddy current bearing comprised of a nonmagnetic stator carrying an array of radial flux magnets, and a cylindrical conductive rotor. Centering force is provided by the imbalance in repulsive forces as rotor and stator become eccentric. Experimental, analytical, and numerical results for these devices are compared. Numerous parametric studies are undertaken, and design recommendations are forwarded. The effectiveness of numerical techniques is assessed, and strategies for effective finite element modeling are discussed. (Abstract shortened by UMI.)... |
