Device Levitation Magnetic

Magnetic levitation , maglev , or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields. Magnetic pressure is used to counteract the effects of the gravitational and any other accelerations.

Earnshaw's theorem proves that using only static ferromagnetism it is impossible to stably levitate against gravity, but servomechanisms, the use of diamagnetic materials, superconduction, or systems involving eddy currents permit this to occur.

In some cases the lifting force is provided by magnetic levitation, but there is a mechanical support bearing little load that provides stability. This is termed pseudo-levitation .

Magnetic levitation is used for maglev trains, magnetic bearings and for product display purposes.

Lift

Magnetic materials and systems are able to attract or press each other apart or together with a force dependent on the magnetic field and the area of the magnets, and a magnetic pressure can then be defined.

The magnetic pressure of a magnetic field can be calculated by:

where P m a g is the force per unit area in pascals, B is the magnetic field in teslas, and μ 0 = 4π×10 −7  N·A −2 is the permeability of the vacuum.

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 combination of gravitational, electrostatic, and magnetostatic fields will make the object's position unstable along at least one axis, and can be unstable 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.

Dynamic stability occurs when the levitation system is able to damp out any vibration-like motion that may occur.

Stability methods

For successful levitation and control of all 6 axes (3 spatial 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 stabilised using ferromagnetism.

The primary ones used in maglev trains are servo-stabilized electromagnetic suspension (EMS), electrodynamic suspension (EDS), and (in the future) Inductrack.

Mechanical constraint (pseudo-levitation)

With a small amount of mechanical constraint for stability, pseudo-levitation is relatively straightforwardly achieved.

If two magnets are mechanically constrained along a single vertical 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 constrained 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 beading from below.

Direct diamagnetic levitation

A substance that is diamagnetic repels a magnetic field. All materials have diamagnetic properties, but the effect is very weak, and is usually overcome by the object's paramagnetic or ferromagnetic properties, which act in the opposite manner. Any material in which the diamagnetic component is strongest will be repelled by a magnet, though this force is not usually very large.

Earnshaw's theorem does not apply to diamagnets. These behave in the opposite manner to normal magnets owing to their relative permeability of μ r  < 1 (i.e. negative magnetic susceptibility).

Diamagnetic levitation can be used to levitate very light pieces of pyrolytic graphite or bismuth above a moderately strong permanent magnet. As water is predominantly diamagnetic, this technique has been used to levitate water droplets and even live animals, such as a grasshopper, frog and a mouse. However, the magnetic fields required for this are very high, typically in the range of 16 teslas, and therefore create significant problems if ferromagnetic materials are nearby.

The minimum criterion for diamagnetic levitation is B \frac{dB}{dz} = \mu_0 \, \rho \, \frac{g}{\chi} , where:

  • χ is the magnetic susceptibility
  • ρ is the density of the material
  • g is the local gravitational acceleration (−9.8 m/s 2 on Earth)
  • μ 0 is the permeability of free space
  • B is the magnetic field
  • \frac{dB}{dz} is the rate of change of the magnetic field along the vertical axis.

Assuming ideal conditions along the z -direction of solenoid magnet:

  • Water levitates at B \frac{dB}{dz} \approx 1400\ \mathrm{T^2/m}
  • Graphite levitates at B \frac{dB}{dz} \approx 375\ \mathrm{T^2/m}.

Superconductors

Superconductors may be considered perfect diamagnets ( μ r  = 0), as well as the property they have of completely expelling magnetic fields due to the Meissner effect when the superconductivity initially forms. The levitation of the magnet is further stabilized due to flux pinning within the superconductor; this tends to stop the superconductor leaving the magnetic field, even if the levitated system is inverted.

These principles are exploited by EDS (Electrodynamic Suspension) magnetic levitation trains, superconducting bearings, flywheels, etc.

In trains where the weight of the large electromagnet is a major design issue (a very strong magnetic field is required to levitate a massive train) superconductors are sometimes proposed for use for the electromagnet, since they can produce a stronger magnetic field for the same weight.

Further information: Superdiamagnetism

Diamagnetically-stabilized levitation

A permanent magnet can be stably suspended by various configurations of strong permanent magnets and strong diamagnets. When using superconducting magnets, the levitation of a permanent magnet can even be stabilized by the small diamagnetism of water in human fingers.

Rotational stabilization

Main article: Spin stabilized magnetic levitation

A magnet can be levitated against gravity when gyroscopically stabilized by spinning it in a toroidal field created by a base ring of magnet(s). However, it will only remain stable until the rate of precession slows below a critical threshold—the region of stability is quite narrow both spatially and in the required rate of precession. The first discovery of this phenomenon was by Roy Harrigan, a Vermont inventor who patented a levitation device in 1983 based upon it. Several devices using rotational stabilization (such as the popular Levitron toy) have been developed citing this patent. Non-commercial devices have been created for university research laboratories, generally using magnets too powerful for safe public interaction.

Servomechanisms

Main article: Electromagnetic suspension

The attraction from a fixed strength magnet decreases with increased distance, and increases at closer distances. This is termed '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 upwards 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 upwards.

This is termed electromagnetic suspension (EMS). For a very simple example, some tabletop levitation demonstrations use this principle, and the object cuts a beam of light 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 il

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