Magnetic levitationFrom Wikipedia, the free encyclopedia

Magnetic levitation, maglev, or magnetic suspension is a method by which an object is suspendedwith no support other than magnetic fields. Magnetic force is used to counteract the effects of thegravitational acceleration and any other accelerations.

The two primary issues involved in magnetic levitation are lifting forces: providing an upward forcesufficient to counteract gravity, and stability: ensuring that the system does not spontaneously slide orflip into a configuration where the lift is neutralized.

Magnetic levitation is used for maglev trains, contactless melting, magnetic bearings and for productdisplay purposes.

Contents

1 Lift

2 Stability

2.1 Static stability

2.2 Dynamic stability

3 Methods

3.1 Mechanical constraint (pseudo­levitation)

3.2 Servomechanisms

3.3 Induced currents

3.3.1 Relative motion between conductors and magnets

3.3.2 Oscillating electromagnetic fields

3.4 Diamagnetically stabilized levitation

3.5 Diamagnetic levitation

3.5.1 Direct diamagnetic levitation

3.6 Superconductors

3.7 Rotational stabilization

3.8 Strong focusing

4 Uses

A superconductor levitating apermanent magnet

4.1 Maglev transportation

4.2 Magnetic bearings

4.3 Levitation melting

5 History

6 See also

7 References

8 External links

Lift

Magnetic materials and systems are able to attract or press eachother apart or together with a force dependent on the magneticfield and the area of the magnets, For example, the simplestexample of lift would be a simple dipole magnet positioned inthe magnetic fields of another dipole magnet, oriented with likepoles facing each other, so that the force between magnets repelsthe two magnets.[1]

Essentially all types of magnets have been used to generate liftfor magnetic levitation; permanent magnets, electromagnets,ferromagnetism, diamagnetism, superconducting magnets andmagnetism due to induced currents in conductors.

To calculate the amount of lift, a magnetic pressure can bedefined.

For example, the magnetic pressure of a magnetic field on asuperconductor can be calculated by:

where is the force per unit area in pascals, is the magnetic field just above the superconductorin teslas, and = 4π×10−7 N·A−2 is the permeability of the vacuum.[2]

Stability

Earnshaw's theorem proves that using only paramagnetic materials (such as ferromagnetic iron) it isimpossible for a static system to stably levitate against gravity.[3]

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 magnetscan produce stability.

However, servomechanisms, the use of diamagnetic materials, superconduction, or systems involvingeddy currents allow stability to be achieved.

In some cases the lifting force is provided by magnetic levitation, but stability is provided by amechanical support bearing little load. This is termed pseudo­levitation.

Static stability

Static stability means that any small displacement away from a stable equilibrium causes a net force topush 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 ofgravitational, electrostatic, and magnetostatic fields will make the object's position, at best, unstablealong at least one axis, and it can be unstable equilibrium along all axes. However, several possibilitiesexist to make levitation viable, for example, the use of electronic stabilization or diamagnetic materials(since relative magnetic permeability is less than one[4]); it can be shown that diamagnetic materials arestable along at least one axis, and can be stable along all axes. Conductors can have a relativepermeability to alternating magnetic fields of below one, so some configurations using simple AC drivenelectromagnets are self stable.

Dynamic stability

Dynamic stability occurs when the levitation system is able to damp out any vibration­like motion thatmay occur.

Magnetic fields are conservative forces and therefore in principle have no built­in damping, and inpractice many of the levitation schemes are under­damped and in some cases negatively damped.[5] Thiscan permit vibration modes to exist that can cause the item to leave the stable region.

Damping of motion is done 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 objectelectromagnets controlled by electronics

Methods

For successful levitation and control of all 6 axes (degrees of freedom; 3 translational and 3 rotational) acombination of permanent magnets and electromagnets or diamagnets or superconductors as well asattractive and repulsive fields can be used. From Earnshaw's theorem at least one stable axis must bepresent for the system to levitate successfully, but the other axes can be stabilized using ferromagnetism.

The primary ones used in maglev trains are servo­stabilized electromagnetic suspension (EMS),electrodynamic suspension (EDS).

Mechanical constraint (in this case thelateral restrictions created by a box)can permit pseudo­levitation ofpermanent magnets

The Transrapid system usesservomechanisms to pull the train upfrom underneath the track andmaintains a constant gap whiletravelling at high speed

Mechanical constraint (pseudo­levitation)

With a small amount of mechanical constraint for stability,achieving pseudo­levitation is a relatively straightforwardprocess.

If two magnets are mechanically constrained along a single axis,for example, and arranged to repel each other strongly, this willact to levitate one of the magnets above the other.

Another geometry is where the magnets are attracted, butconstrained from touching by a tensile member, such as a stringor cable.

Another example is the Zippe­type centrifuge where a cylinder issuspended under an attractive magnet, and stabilized by a needlebearing from below.

Servomechanisms

The attraction from a fixed strength magnet decreases withincreased distance, and increases at closer distances. This isunstable. For a stable system, the opposite is needed, variationsfrom a stable position should push it back to the target position.

Stable magnetic levitation can be achieved by measuring theposition and speed of the object being levitated, and using afeedback loop which continuously adjusts one or moreelectromagnets to correct the object's motion, thus forming aservomechanism.

Many systems use magnetic attraction pulling upwards againstgravity for these kinds of systems as this gives some inherentlateral stability, but some use a combination of magneticattraction and magnetic repulsion to push upwards.

Either system represents examples of ElectroMagneticSuspension (EMS). For a very simple example, some tabletoplevitation demonstrations use this principle, and the object cuts abeam of light to measure the position of the object. Theelectromagnet is above the object being levitated; the electromagnet is turned off whenever the objectgets 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, andis pulled upwards 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 time­varying magnetic field electrical currents in the conductor are set up which create a magnetic field thatcauses a repulsive effect.

These kinds of systems typically show an inherent stability, although extra damping is sometimesrequired.

Relative motion between conductors and magnets

If one moves a base made of a very good electrical conductor such as copper, aluminium or silver closeto a magnet, an (eddy) current will be induced in the conductor that will oppose the changes in the fieldand create an opposite field that will repel the magnet (Lenz's law). At a sufficiently high rate ofmovement, a suspended magnet will levitate on the metal, or vice versa with suspended metal. Litz wiremade of wire thinner than the skin depth for the frequencies seen by the metal works much moreefficiently than solid conductors.

An especially technologically interesting case of this comes when one uses a Halbach array instead of asingle pole permanent magnet, as this almost doubles the field strength, which in turn almost doubles thestrength of the eddy currents. The net effect is to more than triple the lift force. Using two opposedHalbach arrays increases the field even further.[6]

Halbach arrays are also well­suited to magnetic levitation and stabilisation of gyroscopes and electricmotor and generator spindles.

Oscillating electromagnetic fields

A conductor can be levitated above an electromagnet (or vice versa) with an alternating current flowingthrough it. This causes any regular conductor to behave like a diamagnet, due to the eddy currentsgenerated in the conductor.[7][8] Since the eddy currents create their own fields which oppose themagnetic field, the conductive object is repelled from the electromagnet, and most of the field lines ofthe magnetic field will no longer penetrate the conductive object.

This effect requires non­ferromagnetic but highly conductive materials like aluminium or copper, as theferromagnetic ones are also strongly attracted to the electromagnet (although at high frequencies thefield can still be expelled) and tend to have a higher resistivity giving lower eddy currents. Again, litzwire gives the best results.

The effect can be used for stunts such as levitating a telephone book by concealing an aluminium platewithin it.

At high frequencies (a few tens of kilohertz or so) and kilowatt powers small quantities of metals can belevitated and melted using levitation melting without the risk of the metal being contaminated by thecrucible.[9]

One source of oscillating magnetic field that is used is the linear induction motor. This can be used tolevitate as well as provide propulsion.

Diamagnetically stabilized levitation

Earnshaw's theorem does not apply to diamagnets. These behave in the opposite manner to normalmagnets owing to their relative permeability of μr < 1 (i.e. negative magnetic susceptibility).Diamagnetic levitation can be inherently stable.

Diamagnetic levitation of pyrolyticcarbon

A live frog levitates inside a 32 mmdiameter vertical bore of a Bittersolenoid in a magnetic field of about16 teslas

A permanent magnet can be stably suspended by various configurations of strong permanent magnetsand strong diamagnets. When using superconducting magnets, the levitation of a permanent magnet caneven be stabilized by the small diamagnetism of water in human fingers.[10]

Diamagnetic levitation

Diamagnetism is the property of an object which causes it tocreate a magnetic field in opposition to an externally appliedmagnetic field, thus causing the material to be repelled bymagnetic fields. Diamagnetic materials cause lines of magneticflux to curve away from the material. Specifically, an externalmagnetic field alters the orbital velocity of electrons around theirnuclei, thus changing the magnetic dipole moment. According toLenz's law, this opposes the external field. Diamagnets arematerials with a magnetic permeability less than μ0 (a relativepermeability less than 1). Consequently, diamagnetism is a formof magnetism that is only exhibited by a substance in thepresence of an externally applied magnetic field. It is generallyquite a weak effect in most materials, although superconductorsexhibit a strong effect.

Direct diamagnetic levitation

A substance that is diamagnetic repels a magnetic field. Allmaterials have diamagnetic properties, but the effect is veryweak, and is usually overcome by the object's paramagnetic orferromagnetic properties, which act in the opposite manner. Anymaterial in which the diamagnetic component is stronger will berepelled by a magnet.

Diamagnetic levitation can be used to levitate very light pieces ofpyrolytic graphite or bismuth above a moderately strongpermanent magnet. As water is predominantly diamagnetic, thistechnique has been used to levitate water droplets and even liveanimals, such as a grasshopper, frog and a mouse.[11] However,the magnetic fields required for this are very high, typically inthe range of 16 teslas, and therefore create significant problems ifferromagnetic materials are nearby.

The minimum criterion for diamagnetic levitation is

, where:

is the magnetic susceptibility is the density of the material is the local gravitational acceleration (−9.8 m/s2 on Earth) is the permeability of free space is the magnetic field

is the rate of change of the magnetic field along the vertical axis.

The Levitron brand top is an exampleof spin­stabilized magnetic levitation

Assuming ideal conditions along the z­direction of solenoid magnet:

Water levitates at

Graphite levitates at

Superconductors

Superconductors may be considered perfect diamagnets, and completely expel magnetic fields due tothe Meissner effect when the superconductivity initially forms; thus superconducting levitation can beconsidered a particular instance of diamagnetic levitation. In a type­II superconductor, the levitation ofthe magnet is further stabilized due to flux pinning within the superconductor; this tends to stop thesuperconductor from moving with respect to the magnetic field, even if the levitated system is inverted.

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

A very strong magnetic field is required to levitate a train. The JR–Maglev trains have superconductingmagnetic coils, but the JR–Maglev levitation is not due to the Meissner effect.

Rotational stabilization

A magnet or properly assembled array of magnets with a toroidalfield can be stably levitated against gravity when gyroscopicallystabilized by spinning it in a second toroidal field created by abase ring of magnet(s). However, this only works while the rateof precession is between both upper and lower critical thresholds—the region of stability is quite narrow both spatially and in therequired rate of precession. The first discovery of thisphenomenon was by Roy M. Harrigan, a Vermont inventor whopatented a levitation device in 1983 based upon it.[12] Severaldevices using rotational stabilization (such as the popularLevitron branded levitating top toy) have been developed citingthis patent. Non­commercial devices have been created foruniversity research laboratories, generally using magnets toopowerful for safe public interaction.

Strong focusing

Earnshaw's theory strictly only applies to static fields. Alternating magnetic fields, even purelyalternating attractive fields,[13] can induce stability and confine a trajectory through a magnetic field togive a levitation effect.

This is used in particle accelerators to confine and lift charged particles, and has been proposed formaglev trains as well.[13]

Uses

Maglev transportation

Maglev, or magnetic levitation, is a system of transportation that suspends, guides and propels vehicles,predominantly trains, using magnetic levitation from a very large number of magnets for lift andpropulsion. This method has the potential to be faster, quieter and smoother than wheeled mass transitsystems. The technology has the potential to exceed 6,400 km/h (4,000 mi/h) if deployed in anevacuated tunnel.[14] If not deployed in an evacuated tube the power needed for levitation is usually nota particularly large percentage and most of the power needed is used to overcome air drag, as with anyother high speed train.

The highest recorded speed of a maglev train is 603 kilometers per hour (374.69 mph), achieved inJapan on April 21, 2015, 28.2 km/h faster than the conventional TGV speed record.

Magnetic bearings

Magnetic bearingsFlywheelsCentrifugesMagnetic ring spinning

Levitation melting

Electromagnetic levitation (EML), patented by Muck in 1923,[15] is one of the oldest levitationtechniques used for containerless experiments.[16] The technique enables the levitation of an object usingelectromagnets. A typical EML coil has reversed winding of upper and lower sections energized by aradio frequency power supply.

History

1839 Earnshaw's theorem showed electrostatic levitation cannot be stable; later theorem wasextended to magnetostatic levitation by others1912 Emile Bachelet awarded a patent in March 1912 for his “levitating transmitting apparatus”(patent no. 1,020,942) for electromagnetic suspension system1933 Superdiamagnetism Walther Meissner and Robert Ochsenfeld (the Meissner effect)1934 Hermann Kemper “monorail vehicle with no wheels attached.” Reich Patent number 6433161939 Braunbeck’s extension showed that magnetic levitation is possible with diamagneticmaterials1939 Bedford, Peer, and Tonks aluminum plate placed on two concentric cylindrical coils shows6­axis stable levitation.[17]1961 James R. Powell and BNL colleague Gordon Danby electrodynamic levitation usingsuperconducting magnets1970s Spin stabilized magnetic levitation Roy M. Harrigan1974 Magnetic river Eric Laithwaite and others1979 transrapid train carried passengers1984 Low speed maglev shuttle in Birmingham Eric Laithwaite and others1997 Diamagnetically levitated live frog Andre Geim[11]

1999 Inductrack permanent magnet electrodynamic levitation (General Atomics)2000 The first man­loading HTS maglev test vehicle “Century” in the world was successfullydeveloped in China.[18]

2005 homopolar electrodynamic bearing[19]

See also

Acoustic levitationAerodynamic levitationElectrostatic levitationOptical levitationCyclotrons levitate and circulate charged particles in a magnetic fieldInductrack a particular system based on Halbach arrays and inductive track loopsLaunch loopLevitronLinear motorMagnetic bearingMagnetic ring spinningNagahori Tsurumi­ryokuchi LineRapid transits using linear motor propulsionStarTram is an extreme proposal for levitation via superconductors over multiple kilometers ofdistanceZippe­type centrifuge uses magnetic lift and a mechanical needle for stability

References1. calculator (http://www.magnetsales.com/design/calc_filles/pullandpushbetween2discmagnets.asp) for force

between two disc magnets (retrieved April 16, 2014)2. Lecture 19 MIT 8.02 Electricity and Magnetism, Spring 20023. Ignorance = Maglev = Bliss For 150 years scientists believed that stable magnetic levitation was impossible.Then Roy Harrigan came along. By Theodore Gray Posted February 2, 2004(http://www.popsci.com/diy/article/2004­02/ignorance­maglev­bliss)

4. Braunbeck, W. (1939). "Freischwebende Körper im elektrischen und magnetischen Feld". Zeitschrift fürPhysik 112 (11): 753–763. Bibcode:1939ZPhy..112..753B. doi:10.1007/BF01339979.

5. Rote, D.M.; Yigang Cai (2002). "Review of dynamic stability of repulsive­force maglev suspensionsystems". IEEE Transactions on Magnetics 38 (2): 1383. Bibcode:2002ITM....38.1383R.doi:10.1109/20.996030.

6. S&TR | November 2003: Maglev on the Development Track for Urban Transportation(https://www.llnl.gov/str/November03/Post.html). Llnl.gov (2003­11­07). Retrieved on 2013­07­12.

7. Thompson, Marc T. Eddy current magnetic levitation, models and experiments(http://www.classictesla.com/download/ieee_potentials_2000.pdf). (PDF) . Retrieved on 2013­07­12.

8. Levitated Ball­Levitating a 1 cm aluminum sphere (http://sprott.physics.wisc.edu/demobook/chapter5.htm).Sprott.physics.wisc.edu. Retrieved on 2013­07­12.

9. Mestel, A. J. (2006). "Magnetic levitation of liquid metals". Journal of Fluid Mechanics 117: 27.Bibcode:1982JFM...117...27M. doi:10.1017/S0022112082001505.

10. Diamagnetically stabilized magnet levitation (http://netti.nic.fi/~054028/images/LeviTheory.pdf). (PDF) .Retrieved on 2013­07­12.

11. "The Frog That Learned to Fly" (http://www.ru.nl/hfml/research/levitation/diamagnetic/). Radboud UniversityNijmegen. Retrieved 19 October 2010. For Geim's account of diamagnetic levitation, see Geim, Andrey."Everyone's Magnetism (http://www.ru.nl/publish/pages/561854/everyonesmagnetism.pdf) PDF (688 KB).Physics Today. September 1998. pp. 36–39. Retrieved 19 October 2010. For the experiment with Berry, seeBerry, M. V.; Geim, Andre. (1997). "Of flying frogs and levitrons"(http://www.ru.nl/publish/pages/561854/frog­ejp.pdf) PDF (228 KB). European Journal of Physics 18: 307–313. Retrieved 19 October 2010.

12. US patent 4382245 (http://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US4382245), Harrigan,Roy M., "Levitation device", issued 1983­05­03

13. Hull, J.R. (1989). "Attractive levitation for high­speed ground transport with largeguideway clearance andalternating­gradient stabilization". IEEE Transactions on Magnetics 25 (5): 3272.Bibcode:1989ITM....25.3272H. doi:10.1109/20.42275.

14. Trans­Atlantic MagLev | Popular Science (http://www.popsci.com/scitech/article/2004­04/trans­atlantic­maglev). Popsci.com. Retrieved on 2013­07­12.

15. Muck, O. German patent no. 42204 (Oct. 30, 1923)

16. Nordine, Paul C.; Weber, J. K. Richard and Abadie, Johan G. (2000). "Properties of high­temperature meltsusing levitation". Pure and Applied Chemistry 72 (11): 2127–2136. doi:10.1351/pac200072112127.

17. Laithwaite, E.R. (1975). "Linear electric machines—A personal view". Proceedings of the IEEE 63 (2): 250.doi:10.1109/PROC.1975.9734.

18. Wang, Jiasu; Wang Suyu; et al. (2002). "The first man­loading high temperature superconducting maglev testvehicle in the world". Physica C. 378­381: 809–814. Bibcode:2002PhyC..378..809W. doi:10.1016/S0921­4534(02)01548­4.

19. "Design and Analysis of a Novel Low Loss Homopolar Electrodynamic Bearing."(http://www.magnetal.se/Dokument/PhDThesis.pdf) Lembke, Torbjörn. PhD Thesis. Stockholm:Universitetsservice US AB, 2005. Print. ISBN 91­7178­032­7

External links

Maglev Trains (http://www.magnet.fsu.edu/education/community/slideshows/maglev/index.html)Audio slideshow from the National High Magnetic Field Laboratory discusses magnetic levitation,the Meissner Effect, magnetic flux trapping and superconductivityMagnetic Levitation – Science is Fun (http://www.levitationfun.com/index.html)Magnetic (superconducting) levitation experiment (YouTube) (http://www.youtube.com/watch?v=nWTSzBWEsms&feature=related)Superconducting Levitation Demos (http://www.imp.kiev.ua/~kord/levitation)Maglev video gallery (http://users.bigpond.net.au/com/maglevvideogallery/)How can you magnetically levitate objects? (http://my.execpc.com/~rhoadley/maglev.htm)Levitated aluminum ball (oscillating field)(http://sprott.physics.wisc.edu/demobook/chapter5.htm)Instructions to build an optically triggered feedback maglev demonstration(http://www.coilgun.info/levitation/home.htm)Videos of diamagnetically levitated objects, including frogs and grasshoppers(http://www.hfml.sci.kun.nl/levitation­movies.html)Larry Spring's Mendocino Brushless Magnetic Levitation Solar Motor(http://www.larryspring.com/class_motors.html)A Classroom Demonstration of Levitation... (http://arxiv.org/abs/0803.3090)25kg MAGLEV suspension setup (http://www.youtube.com/watch?v=Y_WG4YStMxs&feature=related)25kg MAGLEV suspension control via Classical control strategy(http://www.youtube.com/watch?v=kXodf7WKiFs)25kg MAGLEV suspension via State feedback control strategy (http://www.youtube.com/watch?v=TsgoF13KvYk&feature=related)Frogs levitate in a strong enough magnetic field (http://www.physics.org/facts/frog­really.asp)

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