Eddy current
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Origin of term
The term eddy current comes from analogous currents seen in water in fluid dynamics, causing localised areas of turbulence known as eddies giving rise to persistent vortices. Somewhat analogously, eddy currents can take time to build up and can persist for very long times in conductors due to their inductance.
History
The first person to observe eddy currents was François Arago (1786–1853), the President of the Council of Ministers of the 2nd French Republic during the brief period 10th May to June 24, 1848 (equivalent to the current position of the French Prime Minister), who was also a mathematician, physicist and astronomer. In 1824 he observed what has been called rotatory magnetism, and that most conductive bodies could be magnetized; these discoveries were completed and explained by Michael Faraday (1791–1867).
In 1834, Emil Lenz stated Lenz's law, which says that the direction of induced current flow in an object will be such that its magnetic field will oppose the change of magnetic flux that caused the current flow. Eddy currents produce a secondary field that cancels a part of the external field and causes some of the external flux to avoid the conductor.
French physicist
Explanation
A magnet induces circular electric currents in a metal sheet moving through its magnetic field. See the diagram at right. It shows a metal sheet (C) moving to the right with velocity v under a stationary magnet. The magnetic field (B, green arrows) of the magnet's north pole N passes down through the sheet. Since the metal is moving, the magnetic flux through a given area of the sheet is changing. In the part of the sheet moving under the leading edge of the magnet (left side) the magnetic field through a given point on the sheet is increasing as it gets nearer the magnet, dB/dt > 0. From Faraday's law of induction, this creates a circular electric field in the sheet in a counterclockwise direction around the magnetic field lines. This field induces a counterclockwise flow of electric current (I, red), in the sheet. This is the eddy current. In the part of the sheet under the trailing edge of the magnet (right side) the magnetic field through a given point on the sheet is decreasing as it is moving further away from the magnet, dB/dt < 0, inducing a second eddy current in a clockwise direction in the sheet.
Another equivalent way to understand the current is to see that the free
The magnetic field of the magnet, acting on the electrons moving sideways under the magnet, then exerts a Lorentz force directed to the rear, opposite to the velocity of the metal sheet. The electrons, in collisions with the metal lattice atoms, transfer this force to the sheet, exerting a drag force on the sheet proportional to its velocity. The
Due to
Properties
Eddy currents in conductors of non-zero
Self-induced eddy currents are responsible for the skin effect in conductors.[1] The latter can be used for non-destructive testing of materials for geometry features, like micro-cracks.[2] A similar effect is the proximity effect, which is caused by externally induced eddy currents.[3]
An object or part of an object experiences steady field intensity and direction where there is still relative motion of the field and the object (for example in the center of the field in the diagram), or unsteady fields where the currents cannot circulate due to the geometry of the conductor. In these situations charges collect on or within the object and these charges then produce static electric potentials that oppose any further current. Currents may be initially associated with the creation of static potentials, but these may be transitory and small.
Eddy currents generate resistive losses that transform some forms of energy, such as kinetic energy, into heat. This
The conversion of input energy to heat is not always undesirable, however, as there are some practical applications. One is in the brakes of some trains known as eddy current brakes. During braking, the metal wheels are exposed to a magnetic field from an electromagnet, generating eddy currents in the wheels. This eddy current is formed by the movement of the wheels. So, by Lenz's law, the magnetic field formed by the eddy current will oppose its cause. Thus the wheel will face a force opposing the initial movement of the wheel. The faster the wheels are spinning, the stronger the effect, meaning that as the train slows the braking force is reduced, producing a smooth stopping motion.
Induction heating makes use of eddy currents to provide heating of metal objects.
Power dissipation of eddy currents
Under certain assumptions (uniform material, uniform magnetic field, no skin effect, etc.) the power lost due to eddy currents per unit mass for a thin sheet or wire can be calculated from the following equation:[4]
- P is the power lost per unit mass (W/kg),
- Bp is the peak magnetic field (T),
- d is the thickness of the sheet or diameter of the wire (m),
- f is the frequency (Hz),
- k is a constant equal to 1 for a thin sheet and 2 for a thin wire,
- ρ is the resistivityof the material (Ω m), and
- D is the density of the material (kg/m3).
This equation is valid only under the so-called quasi-static conditions, where the frequency of magnetisation does not result in the skin effect; that is, the electromagnetic wave fully penetrates the material.
Skin effect
In very fast-changing fields, the magnetic field does not penetrate completely into the interior of the material. This skin effect renders the above equation invalid. However, in any case increased frequency of the same value of field will always increase eddy currents, even with non-uniform field penetration.[citation needed]
The penetration depth for a good conductor can be calculated from the following equation:[5]
Diffusion equation
The derivation of a useful equation for modelling the effect of eddy currents in a material starts with the differential, magnetostatic form of
Taking the curl on both sides of this equation and then using a common vector calculus identity for the curl of the curl results in
From Gauss's law for magnetism, ∇ ⋅ H = 0, so
Using Ohm's law, J = σE, which relates current density J to electric field E in terms of a material's conductivity σ, and assuming isotropic homogeneous conductivity, the equation can be written as
Using the differential form of Faraday's law, ∇ × E = −∂B/∂t, this gives
By definition, B = μ0(H + M), where M is the magnetization of the material and μ0 is the vacuum permeability. The diffusion equation therefore is
Applications
Electromagnetic braking
Repulsive effects and levitation
In a varying magnetic field, the induced currents exhibit diamagnetic-like repulsion effects. A conductive object will experience a repulsion force. This can lift objects against gravity, though with continual power input to replace the energy dissipated by the eddy currents. An example application is separation of aluminum cans from other metals in an eddy current separator. Ferrous metals cling to the magnet, and aluminum (and other non-ferrous conductors) are forced away from the magnet; this can separate a waste stream into ferrous and non-ferrous scrap metal.
With a very strong handheld magnet, such as those made from neodymium, one can easily observe a very similar effect by rapidly sweeping the magnet over a coin with only a small separation. Depending on the strength of the magnet, identity of the coin, and separation between the magnet and coin, one may induce the coin to be pushed slightly ahead of the magnet – even if the coin contains no magnetic elements, such as the US penny. Another example involves dropping a strong magnet down a tube of copper[7] – the magnet falls at a dramatically slow pace.
In a perfect conductor with no
Using electromagnets with electronic switching comparable to electronic speed control it is possible to generate electromagnetic fields moving in an arbitrary direction. As described in the section above about eddy current brakes, a non-ferromagnetic conductor surface tends to rest within this moving field. When however this field is moving, a vehicle can be levitated and propelled. This is comparable to a maglev but is not bound to a rail.[8]
Identification of metals
In some coin-operated vending machines, eddy currents are used to detect counterfeit coins, or slugs. The coin rolls past a stationary magnet, and eddy currents slow its speed. The strength of the eddy currents, and thus the retardation, depends on the conductivity of the coin's metal. Slugs are slowed to a different degree than genuine coins, and this is used to send them into the rejection slot.
Vibration and position sensing
Eddy currents are used in certain types of
A Ferraris acceleration sensor, also called a Ferraris sensor, is a contactless sensor that uses eddy currents to measure relative acceleration.[9][10][11]
Structural testing
Eddy current techniques are commonly used for the nondestructive examination (NDE) and condition monitoring of a large variety of metallic structures, including heat exchanger tubes, aircraft fuselage, and aircraft structural components.
Skin effects
Eddy currents are the root cause of the skin effect in conductors carrying alternating current.
Similarly, in magnetic materials of finite conductivity, eddy currents cause the confinement of the majority of the magnetic fields to only a couple
Other applications
- Rock climbing auto belays[12]
- Zip line brakes[13]
- Free fall devices[14]
- Metal detectors
- Conductivity meters for non-magnetic metals[15][16]
- Eddy current adjustable-speed drives
- Eddy-current testing
- Eddy current brake
- Electricity meters (electromechanical induction meters)
- Induction heating
- Cooking (induction stovetops)
- Proximity sensor (displacement sensors)
- Vending machines (detection of coins)
- Coating thickness measurements[17]
- Sheet resistance measurement[18]
- Eddy current separator for metal separation[19]
- Mechanical speedometers
- Safety hazard and defect detection applications
- Magnetic damping
References
- Online citations
- ISBN 978-3-540-43694-2.
- ISBN 978-0-08-094188-2.
- ISBN 978-0-13-084408-8.
- ISBN 0-12-257251-3, page. 31
- ^ Wangsness, Roald. Electromagnetic Fields (2nd ed.). pp. 387–8.
- ^ G. Hysteresis in Magnetism: For Physicists, Materials Scientists, and Engineers, San Diego: Academic Press, 1998.
- ^ Archived at Ghostarchive and the Wayback Machine: "Eddy Current Tubes". YouTube.
- ^ Hendo Hoverboards - World's first REAL hoverboard
- ^ Bernhard Hiller. "Ferraris Acceleration Sensor - Principle and Field of Application in Servo Drives" Archived 27 July 2014 at the Wayback Machine.
- ^ Jian Wang, Paul Vanherck, Jan Swevers, Hendrik Van Brussel. "Speed Observer Based on Sensor Fusion Combining Ferraris Sensor and Linear Position Encoder Signals".
- ^ J. Fassnacht and P. Mutschler. "Benefits and limits of using an acceleration sensor in actively damping high frequent mechanical oscillations". 2001. .
- ^ "TRUBLUE Auto Belay". Head Rush Technologies. Retrieved 8 March 2016.
- ^ "zipSTOP Zip Line Brake System". Head Rush Technologies. Archived from the original on 6 June 2017. Retrieved 8 March 2016.
- ^ "Our Patented Technology". Head Rush Technologies. Archived from the original on 8 March 2016. Retrieved 8 March 2016.
- ^ "Zappi - Eddy Current Conductivity Meter - Products". zappitec.com. Retrieved 8 May 2022.
- ^ "Institut Dr. Foerster: SIGMATEST". www.foerstergroup.de. Retrieved 28 June 2018.
- ^ Coating Thickness Measurement with Electromagnetic Methods
- ^ "Ohm/sq & OD". www.nagy-instruments.de. Archived from the original on 4 March 2016. Retrieved 8 May 2016.
- ^ "Eddy Current Separator for metal separation". www.cogelme.com. Retrieved 8 May 2016.
- General references
- Fitzgerald, A. E.; Kingsley, Charles Jr.; Umans, Stephen D. (1983). Electric Machinery (4th ed.). Mc-Graw-Hill, Inc. p. 20. ISBN 978-0-07-021145-2.
- Sears, Francis Weston; Zemansky, Mark W. (1955). University Physics (2nd ed.). Addison-Wesley. pp. 616–618.
Further reading
- Stoll, R. L. (1974). The Analysis of Eddy Currents. Oxford University Press.
- Reitz, J. R. (1970). Forces on Moving Magnets due to Eddy Currents. Journal of Applied Physics 41, 2067-2071. https://doi.org/10.1063/1.1659166
- Krawczyk, Andrzej; J. A. Tegopoulos. Numerical Modelling of Eddy Currents.
External links
- Eddy Current Separator Cogelme for non-ferrous metals separation – Information and video in Cogelme site