Electrodynamic suspension

thumb|right|Jumping rings lift when an AC current energises a coil and electrodynamic forces push the rings upward against gravity

Electrodynamic suspension (EDS) is a form of magnetic levitation in which there are conductors which are exposed to time-varying magnetic fields. This induces eddy currents in the conductors that creates a repulsive magnetic field which holds the two objects apart.

These time-varying magnetic fields can be caused by relative motion between two objects. In many cases, one magnetic field is a permanent field, such as a permanent magnet or a superconducting magnet, and the other magnetic field is induced from the changes of the field that occur as the magnet moves relative to a conductor in the other object.

Electrodynamic suspension can also occur when an electromagnet driven by an AC electrical source produces the changing magnetic field, in some cases, a linear induction motor generates the field.

EDS is used for maglev trains, such as the Japanese SCMaglev. It is also used for some classes of magnetically levitated bearings.

Types

Many examples of this have been used over the years.

Bedford levitator

In this early configuration by Bedford, Peer, and Tonks from 1939, an aluminum plate is placed on two concentric cylindrical coils, and driven with an AC current. When the parameters are correct, the plate exhibits 6-axis stable levitation.

Levitation melting

In the 1950s, a technique was developed where small quantities of metal were levitated and melted by a magnetic field of a few tens of kHz. The coil was a metal pipe, allowing coolant to be circulated through it. The overall form was generally conical, with a flat top. This permitted an inert atmosphere to be employed and was commercially successful. No feedback control is necessarily needed.

Repulsive systems have a major downside as well. At slow speeds, the current induced in these coils by the slow change in magnetic flux with respect to time is not large enough to produce a repulsive electromagnetic force sufficient to support the weight of the train. Moreover, the energy efficiency for EDS at low speed is low. For this reason the train must have wheels or some other form of landing gear to support the train until it reaches a speed that can sustain levitation. Since a train may stop at any location, due to equipment problems for instance, the entire track must be able to support both low-speed and high-speed operation. Another downside is that the repulsive system naturally creates a field in the track in front and to the rear of the lift magnets, which act against the magnets and create a form of drag. This is generally only a concern at low speeds; at higher speeds the effect does not have time to build to its full potential and other forms of drag dominate.

where N is the number of turns of wire (for a simple loop this is 1) and ΦB is the magnetic flux in webers through a single loop.

Since the field and potentials are out of phase, both attractive and repulsive forces are produced, and it might be expected that no net lift would be generated. However, although the EMF is at 90 degrees to the applied magnetic field, the loop inevitably has inductance. This inductive impedance tends to delay the peak current, by a phase angle dependent on the frequency (since the inductive impedance of any loop increases with frequency).

:<math>K = R + i \omega L \,</math>

where K is the impedance of the coil, L is the inductance and R is the resistance, the actual phase lead being derivable as the inverse tangent of the product ωL/R, viz., the standard phase lead evidence in a single-loop RL circuit.

But:

:<math> \mathcal{E} = I K</math>

where I is the current.

Thus at low frequencies, the phases are largely orthogonal and the currents lower, and no significant lift is generated. But at sufficiently high frequency, the inductive impedance dominates and the current and the applied field are virtually in line, and this current generates a magnetic field that is opposed to the applied one, and this permits levitation.

However, since the inductive impedance increases proportionally with frequency, so does the EMF, so the current tends to a limit when the resistance is small relative to the inductive impedance. This also limits the lift force. Power used for levitation is therefore largely constant with frequency. However, there are also eddy currents due to the finite size of conductors used in the coils, and these continue to grow with frequency.

Since the energy stored in the air gap can be calculated from HB/2 (or μ0H2/2) times air-gap volume, the force applied across the air gap in the direction perpendicular to the load (viz., the force that directly counteracts gravity) is given by the spatial derivative (= gradient) of that energy. The air-gap volume equals the cross-sectional area multiplied by the width of the air gap, so the width cancels out and we are left with a suspensive force of μ0H2/2 times air-gap cross-sectional area, which means that maximum bearable load varies as the square of the magnetic field density of the magnet, permanent or otherwise and varies directly as the cross-sectional area.

Stability

Static

Unlike configurations of simple permanent magnets, electrodynamic levitation can be made stable. Electrodynamic levitation with metallic conductors exhibits a form of diamagnetism, and relative permeabilities of around 0.7 can be achieved (depending on the frequency and conductor configuration). Given the details of the applicable hysteresis loop, frequency-dependent variability of behavior should be of minimal importance for those magnetic materials that are likely to be deployed.

Dynamic

This form of maglev can cause the levitated object to be subject to a drag-induced oscillation, and this oscillation always occurs at a sufficiently high speed. These oscillations can be quite serious and can cause the suspension to fail.

However, inherent system-level damping can frequently avoid this from occurring, particularly on large-scale systems.

Alternatively, addition of lightweight tuned mass dampers can prevent oscillations from being problematic.

Electronic stabilization can also be employed.