Magnetic levitation


Magnetic levitation or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields. Magnetic force is used to counteract the effects of the gravitational force and any other forces.
The two primary issues involved in magnetic levitation are lifting forces: providing an upward force sufficient to counteract gravity, and stability: ensuring that the system does not spontaneously slide or flip into a configuration where the lift is neutralized.
Magnetic levitation is used for maglev trains, contactless melting, magnetic bearings, and for product display purposes.

Lift

Magnetic materials and systems are able to attract or repel each other with a force dependent on the magnetic field and the area of the magnets. For example, the simplest example of lift would be a simple dipole magnet positioned in the magnetic fields of another dipole magnet, oriented with like poles facing each other, so that the force between magnets repels the two magnets.
Essentially all types of magnets have been used to generate lift for magnetic levitation; permanent magnets, electromagnets, ferromagnetism, diamagnetism, superconducting magnets, and magnetism due to induced currents in conductors.
To calculate the amount of lift, a magnetic pressure can be defined.
For example, the magnetic pressure of a magnetic field on a superconductor can be calculated by:
where is the force per unit area in pascals, is the magnetic field just above the superconductor in teslas, and = 4π N·A−2 is the permeability of the vacuum.

Stability

proves that using only paramagnetic materials it is impossible for a static system to stably levitate against gravity.
For example, the simplest example of lift with two simple dipole magnets repelling is highly unstable, since the top magnet can slide sideways or flip over, and it turns out that no configuration of magnets can produce stability.
However, servomechanisms, the use of diamagnetic materials, superconduction, or systems involving eddy currents allow stability to be achieved.
In some cases the lifting force is provided by magnetic repulsion, but stability is provided by a mechanical support bearing little load. This is termed pseudo-levitation.

Static stability

Static stability means that any small displacement away from a stable equilibrium causes a net force to push it back to the equilibrium point.
Earnshaw's theorem proved conclusively that it is not possible to levitate stably using only static, macroscopic, paramagnetic fields. The forces acting on any paramagnetic object in any combinations of gravitational, electrostatic, and magnetostatic fields will make the object's position, at best, unstable along at least one axis, and it can be in unstable equilibrium along all axes. However, several possibilities exist to make levitation viable, for example, the use of electronic stabilization or diamagnetic materials ; it can be shown that diamagnetic materials are stable along at least one axis, and can be stable along all axes. Conductors can have a relative permeability to alternating magnetic fields of below one, so some configurations using simple AC-driven electromagnets are self stable.

Dynamic stability

When a levitation system uses negative feedback to maintain its equilibrium by damping out any oscillations that may occur, it has achieved dynamic stability.
For the case of a static magnetic field, the magnetic force is a conservative force and therefore can exhibit no built-in damping. In practice many of the levitation schemes are marginally stable and, when non-idealities of physical systems are considered, result in negative damping. This negative damping gives rise to exponentially growing oscillations around the magnetic field's unstable equilibrium point, inevitably causing the levitating object to be ejected from the magnetic field.
Dynamic stability on the other hand, can be achieved by spinning a permanent magnet having poles slightly off the rotation plane in constant speed within a range which can hold another dipole magnet in the air.
For the magnetic levitation scheme to be stable, negative feedback from an external control system can be also used to add damping to the system. This can be accomplished in a number of ways:
For successful levitation and control of all 6 axes a combination of permanent magnets and electromagnets or diamagnets or superconductors as well as attractive and repulsive fields can be used. From Earnshaw's theorem at least one stable axis must be present for the system to levitate successfully, but the other axes can be stabilized using ferromagnetism.
The primary ones used in maglev trains are servo-stabilized electromagnetic suspension, electrodynamic suspension.

Mechanical constraint (pseudo-levitation)

With a small amount of mechanical constraint for stability, achieving pseudo-levitation is a relatively straightforward process.
If two magnets are mechanically constrained along a single axis, for example, and arranged to repel each other strongly, this will act to levitate one of the magnets above the other.
Another geometry is where the magnets are attracted, but prevented from touching by a tensile member, such as a string or cable.
Another example is the Zippe-type centrifuge where a cylinder is suspended under an attractive magnet, and stabilized by a needle bearing from below.
Another configuration consists of an array of permanent magnets installed in a ferromagnetic U-shaped profile and coupled with a ferromagnetic rail. The magnetic flux crosses the rail in a direction transversal to the first axis and creates a closed-loop on the U-shaped profile. This configuration generates a stable equilibrium along the first axis that maintains the rail centered on the flux crossing point and allows to bear a load magnetically. On the other axis, the system is constrained and centered by mechanical means, such as wheels.

Servomechanisms

The attraction from a fixed-strength magnet decreases with increased distance, and increases at closer distances. This is unstable. For a stable system, the opposite is needed: variations from a stable position should push it back to the target position.
Stable magnetic levitation can be achieved by measuring the position and speed of the object being levitated, and using a feedback loop which continuously adjusts one or more electromagnets to correct the object's motion, thus forming a servomechanism.
Many systems use magnetic attraction pulling upward against gravity for these kinds of systems as this gives some inherent lateral stability, but some use a combination of magnetic attraction and magnetic repulsion to push upward.
Either system represents examples of ElectroMagnetic Suspension. For a very simple example, some tabletop levitation demonstrations use this principle, and the object cuts a beam of light or Hall effect sensor method is used to measure the position of the object. The electromagnet is above the object being levitated; the electromagnet is turned off whenever the object gets too close, and turned back on when it falls further away. Such a simple system is not very robust; far more effective control systems exist, but this illustrates the basic idea.
EMS magnetic levitation trains are based on this kind of levitation: The train wraps around the track, and is pulled upward from below. The servo controls keep it safely at a constant distance from the track.

Induced currents

These schemes work due to repulsion due to Lenz's law. When a conductor is presented with a time-varying magnetic field, electrical currents are set up in the conductor which create a magnetic field that causes a repulsive effect.
These kinds of systems typically show an inherent stability, although extra damping is sometimes required.

Relative motion between conductors and magnets

If one moves a base made of a very good electrical conductor such as copper, aluminium, or silver close to a magnet, an current will be induced in the conductor that will oppose the changes in the field and create an opposite field that will repel the magnet. At a sufficiently high rate of movement, a suspended magnet will levitate on the metal, or vice versa with suspended metal. Litz wire made of wire thinner than the skin depth for the frequencies seen by the metal works much more efficiently than solid conductors. Figure-8 coils can be used to keep something aligned.
An especially technologically interesting case of this comes when one uses a Halbach array instead of a single-pole permanent magnet, as this almost doubles the field strength, which in turn almost doubles the strength of the eddy currents. The net effect is to more than triple the lift force. Using two opposed Halbach arrays increases the field even further.
Halbach arrays are also well-suited to magnetic levitation and stabilisation of gyroscopes and spindles of electric motors and generators.

Oscillating electromagnetic fields

A conductor can be levitated above an electromagnet with an alternating current flowing through it. This causes any regular conductor to behave like a diamagnet, due to the eddy currents generated in the conductor. Since the eddy currents create their own fields which oppose the magnetic field, the conductive object is repelled from the electromagnet, and most of the field lines of the magnetic field will no longer penetrate the conductive object.
This effect requires non-ferromagnetic but highly conductive materials like aluminium or copper, as the ferromagnetic ones are also strongly attracted to the electromagnet and tend to have a higher resistivity giving lower eddy currents. Again, litz wire gives the best results.
The effect can be used for stunts such as levitating a telephone book by concealing an aluminium plate within it.
At high frequencies and kilowatt powers small quantities of metals can be levitated and melted using levitation melting without the risk of the metal being contaminated by the crucible.
One source of oscillating magnetic field that is used is the linear induction motor. This can be used to levitate as well as provide propulsion.