This article reviews levitation devices using superconductors and magnets. Device concepts and their applications such as noncontact bearings, flywheels, and momentum wheels are discussed, following an exposition of the principles behind these devices. The basic magneto–mechanical phenomenon responsible for levitation in these devices is a result of flux pinning inherent in the interaction between a magnet and a type II superconductor, described and explained in this article by comparison with behavior expected of a perfect conductor or a nearly perfect conductor. The perfect conductor model is used to illustrate why there is a difference between the forces observed when the superconductor is cooled after or before the magnet is brought into position. The same model also establishes the principle that a resisting force or torque arises only in response to those motions of the magnet that changes the magnet field at the superconductor. A corollary of the converse, that no drag torque appears when an axisym...

Superconductor and magnet levitation devices

The theory and applications of eddy currents induced in conducting materials by time-varying magnetic fields are reviewed. The mathematical methods employed in solving the relevant problems are presented. Both analytical and numerical methods are described. Applications based on effects arising from eddy currents are discussed in detail. These applications are to magnetic levitation, electromagnetic launching, hyperthermia treatment of cancer, and nondestructive testing. >

Eddy currents: theory and applications

When a conductive material is subjected to a time-varying magnetic flux, eddy currents are generated in the conductor. These eddy currents circulate inside the con- ductor generating a magnetic field of opposite polarity as the applied magnetic field. The interaction of the two magnetic fields causes a force that resists the change in magnetic flux. However, due to the internal resistance of the conductive material, the eddy currents will be dissipated into heat and the force will die out. As the eddy currents are dissipated, energy is removed from the system, thus producing a damp- ing effect. There are several different methods of inducing a time-varying magnetic field, and from each method arises the potential for a different type of damping system. There- fore, the research into eddy current and magnetic damping mechanisms has led to a diverse range of dampers, many of which are detailed in this paper. The majority of the research in eddy current damping has taken place in the area of mag- netic braking. A second topic that has received significant interest is the use of eddy current dampers for the suppres- sion of structural vibrations. However, much of this research is not concentrated in one area, but has been applied to a variety of different structural systems in a number of distinct ways. In this paper, we review the research into various types of eddy current damping mechanisms and we discuss the future of eddy currents with some potential uses that have not yet been studied.

Eddy Current Damping in Structures

The force on a rectangular current‐carrying coil moving above and parallel to a conducting plate of arbitrary thickness is investigated. Expressions are developed for the lift and drag forces on the coil as a function of speed. Numerical calculations are made for a very thick plate and for plates with thickness of the order of the skin depth. Thick‐plate results are compared with experimental measurements of lift and drag on a superconducting coil suspended above a rotating aluminum wheel.

Force on a Rectangular Coil Moving above a Conducting Slab

This review summarizes and assimilates the results of work reported in the literature over the past 25 years that pertains to understanding those factors that influence the dynamic stability of repulsive-force magnetic levitation (maglev) suspension systems. The review includes summaries of the results of representative tests of large-scale vehicles on linear test tracks and of analytical and laboratory-scale investigations of stability and dynamics of electrodynamic suspension systems. Research needs are also addressed.

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Review of dynamic stability of repulsive-force maglev suspension systems

Baseline specifications for a magnetically suspended vehicle capable of 300 mi/h (483 km/h) operation are given. The magnetic forces (lift, drag, and lateral) on a superconducting coil moving over an aluminum guideway are shown. The basic features of the associated cryogenics are presented along with a discussion of the cryogenic refrigeration requirements. Vehicle dynamics and the resultant ride quality over roadbeds of various roughnesses are analyzed. Thrust requirements for the propulsion system are specified, and both the linear induction motor and the linear synchronous motor are considered. Several guideway configurations are suggested and the significant properties of each are noted.

Baseline specifications for a magnetically suspended high-speed vehicle

This paper deals with eddy currents in bounded plane conductors. Specifically, we are concerned with the semi‐infinite plane sheet and a conducting disk. The eddy‐current distribution in a perfectly conducting sheet or disk due to a magnetic monopole source is obtained by a technique due to Sommerfeld. Sommerfeld's analysis for the disk is incomplete, but we have completed the derivation for this geometry. The eddy‐current decay in a semi‐infinite sheet of finite conductivity is solved by an approximate technique. The results are used to calculate lift, drag, and transverse forces on a magnetic monopole moving parallel to the edge of a semi‐infinite sheet of finite conductivity.

Eddy Currents in Finite Conducting Sheets

To study the motion of a magnetically suspended high‐speed vehicle, a simple example (the long wire above a thin conducting plate) is considered in detail. The lift and drag forces on the magnet (long wire) are derived for arbitrary motion above the plate. The stability of the system is analyzed for typical parameters (velocity = 300 mph, height = 0.1 m). By using a Laplace‐transform technique, it is shown that two types of modes occur (in the linearized equations of motion). One mode is a vertical oscillation with an amplitude that grows slowly in time. The other mode is an unbounded increase in the horizontal velocity error. This latter instability results from the fact that the drag force decreases with increasing velocity at high speeds. In this connection, an error is pointed out in a recent publication in which it was claimed that the system is stable. Detailed consideration of the effects of horizontal acceleration and vertical velocity on the magnetic forces is given. The effects of aerodynamic dr...

Analysis of Motion of Magnetic Levitation Systems: Implications for High‐Speed Vehicles

The report examines certain critical problem areas relative to magnetic suspension of high-speed vehicles and develops a baseline design for a TMLRV (tracked magnetically levitated research vehicle). Both types of magnetic suspension, the repulsive-force suspension and the attractive-force suspension, are considered. The present study has not turned up any problems serious enough to completely eliminate one of these competing suspensions. Areas considered in the report include propulsion systems and their compatibility with magnetically-levitated high-speed vehicles, aerodynamic effects, fairlure modes, studies of ride quality, and criteria for maximum allowable track roughness. In regard to the repulsive-force suspension, experiments have been carried out to measure ac loss in the superconducting magnets and an assessment of the magnetic shielding requirement has been made. Two model electromagnets for the attractive-force suspension, and their feedback control systems, were built and tested during the present study.

L. C. Davis

Papers

Force on a Rectangular Coil Moving above a Conducting Slab

Baseline specifications for a magnetically suspended high-speed vehicle

Eddy Currents in Finite Conducting Sheets

Analysis of Motion of Magnetic Levitation Systems: Implications for High‐Speed Vehicles

Preliminary design studies of magnetic suspensions for high speed ground transportation. Final report on tasks 2/3, Feb 72--Mar 73