Magnetic levitation

Magnetic levitation (maglev) 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 (a) lifting forces – providing an upward force sufficient to counteract gravity, and (b) 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:

P mag = B 2 2 μ 0 {\displaystyle P_{\text{mag}}={\frac {B^{2}}{2\mu _{0}}}}

where P mag {\displaystyle P_{\text{mag}}} is the force per unit area in pascals, B {\displaystyle B} is the magnetic field just above the superconductor in teslas, and μ 0 {\displaystyle \mu _{0}} = 4π×10−7 N·A−2 is the permeability of the vacuum.

Stability Earnshaw's theorem proves that using only paramagnetic materials (such as ferromagnetic iron) 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 (spinning/rotation), 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 (since relative magnetic permeability is less than one); 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 (called tilt) 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:

external mechanical damping (in the support), such as dashpots, air drag, etc. eddy current damping (conductive metal influenced by field) tuned mass dampers in the levitated object electromagnets controlled by electronics

Methods For successful levitation and control of all 6 axes (degrees of freedom; 3 translational and 3 rotational) 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 (EMS), electrodynamic suspension (EDS).

Mechanical constraint (pseudo-levitation)

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