Eddy current

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Eddy currents
)

In

resistivity of the material. When graphed, these circular currents within a piece of metal look vaguely like eddies
or whirlpools in a liquid.

By

laminated magnetic cores or ferrite cores to minimize them. Eddy currents are also used to heat objects in induction heating furnaces and equipment, and to detect cracks and flaws in metal parts using eddy-current testing
instruments.

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

David E. Hughes
used the principles to conduct metallurgical sorting tests.

Explanation

Eddy currents (I, red) induced in a conductive metal plate (C) as it moves to the right under a magnet (N). The magnetic field (B, green) is directed down through the plate. The Lorentz force of the magnetic field on the electrons in the metal induces a sideways current under the magnet. The magnetic field, acting on the sideways moving electrons, creates a Lorentz force opposite to the velocity of the sheet, which acts as a drag force on the sheet. The blue arrows are counter magnetic fields generated by the circular motion of the charges.
right hand rule
this is directed in the +z direction. At e2 this force gives the electron a component of velocity in the sideways direction (v2, black arrow) The magnetic field acting on this sideways velocity, then exerts a Lorentz force on the particle of F2 = −e(v2 × B). From the right hand rule, this is directed in the x direction, opposite to the velocity v of the metal sheet. This force accelerates the electron giving it a component of velocity opposite to the sheet. Collisions of these electrons with the atoms of the sheet exert a drag force on the sheet.
Eddy current brake. The North magnetic pole piece (top) in this drawing is shown further away from the disk than the South; this is just to leave room to show the currents. In an actual eddy current brake the pole pieces are positioned as close to the disk as possible.

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

conventional current
shown.

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

resistance
of the metal, so the metal gets warm under the magnet.

Due to

right hand rule
the counterclockwise current creates a magnetic field pointed up, opposing the magnet's field, causing a repulsive force between the sheet and the leading edge of the magnet. In contrast, at the trailing edge (right side), the clockwise current causes a magnetic field pointed down, in the same direction as the magnet's field, creating an attractive force between the sheet and the trailing edge of the magnet. Both of these forces oppose the motion of the sheet.

Properties

Eddy currents in conductors of non-zero

resistivity generate heat as well as electromagnetic forces. The heat can be used for induction heating. The electromagnetic forces can be used for levitation, creating movement, or to give a strong braking effect. Eddy currents can also have undesirable effects, for instance power loss in transformers. In this application, they are minimized with thin plates, by lamination
of conductors or other details of conductor shape.

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.

laminations
parallel to the field (B, green) with insulation (C) between them reduces the eddy currents. Although the field and currents are shown in one direction, they actually reverse direction with the alternating current in the transformer winding.

Eddy currents generate resistive losses that transform some forms of energy, such as kinetic energy, into heat. This

laminations. Electrons cannot cross the insulating gap between the laminations and so are unable to circulate on wide arcs. Charges gather at the lamination boundaries, in a process analogous to the Hall effect
, producing electric fields that oppose any further accumulation of charge and hence suppressing the eddy currents. The shorter the distance between adjacent laminations (i.e., the greater the number of laminations per unit area, perpendicular to the applied field), the greater the suppression of eddy currents.

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]

where

  • 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
    resistivity
    of 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]

where δ is the penetration depth (m), f is the frequency (Hz), μ is the
electrical conductivity
of the material (S/m).

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

magnetizing field
H surrounding a current density J:

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

Demonstration of Waltenhofen's pendulum, precursor of eddy current brakes. The formation and suppression of eddy currents is here demonstrated by means of this pendulum, a metal plate oscillating between the pole pieces of a strong electromagnet. As soon as a sufficiently strong magnetic field has been switched on, the pendulum is stopped on entering the field.

Electrical resistance
within the plates causes a dragging effect analogous to friction, which dissipates the kinetic energy of the car. The same technique is used in electromagnetic brakes in railroad cars and to quickly stop the blades in power tools such as circular saws. Using electromagnets, as opposed to permanent magnets, the strength of the magnetic field can be adjusted and so the magnitude of braking effect changed.

Repulsive effects and levitation

A cross section through a linear motor placed above a thick aluminium slab. As the linear induction motor's field pattern sweeps to the left, eddy currents are left behind in the metal and this causes the field lines to lean.

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

quantum mechanical phenomenon called the Meissner effect
in which any magnetic field lines present in the material when it becomes superconducting are expelled, thus the magnetic field in a superconductor is always zero.

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

proximity sensors to observe the vibration and position of rotating shafts within their bearings. This technology was originally pioneered in the 1930s by researchers at General Electric using vacuum tube circuitry. In the late 1950s, solid-state versions were developed by Donald E. Bently at Bently Nevada Corporation. These sensors are extremely sensitive to very small displacements making them well suited to observe the minute vibrations (on the order of several thousandths of an inch) in modern turbomachinery. A typical proximity sensor used for vibration monitoring has a scale factor of 200 mV/mil.[clarification needed] Widespread use of such sensors in turbomachinery has led to development of industry standards that prescribe their use and application. Examples of such standards are American Petroleum Institute (API) Standard 670 and ISO
7919.

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.

Lamination of magnetic cores in transformers greatly improves the efficiency by minimising eddy currents

Similarly, in magnetic materials of finite conductivity, eddy currents cause the confinement of the majority of the magnetic fields to only a couple

skin depths of the surface of the material. This effect limits the flux linkage in inductors and transformers having magnetic cores
.

E-I transformer laminations showing flux paths. The effect of the gap where the laminations are butted together can be mitigated by alternating pairs of E laminations with pairs of I laminations, providing a path for the magnetic flux around the gap.

Other applications

References

Online citations
  1. .
  2. .
  3. .
  4. , page. 31
  5. ^ Wangsness, Roald. Electromagnetic Fields (2nd ed.). pp. 387–8.
  6. ^ G. Hysteresis in Magnetism: For Physicists, Materials Scientists, and Engineers, San Diego: Academic Press, 1998.
  7. ^ Archived at Ghostarchive and the Wayback Machine: "Eddy Current Tubes". YouTube.
  8. ^ Hendo Hoverboards - World's first REAL hoverboard
  9. ^ Bernhard Hiller. "Ferraris Acceleration Sensor - Principle and Field of Application in Servo Drives" Archived 27 July 2014 at the Wayback Machine.
  10. ^ Jian Wang, Paul Vanherck, Jan Swevers, Hendrik Van Brussel. "Speed Observer Based on Sensor Fusion Combining Ferraris Sensor and Linear Position Encoder Signals".
  11. ^ J. Fassnacht and P. Mutschler. "Benefits and limits of using an acceleration sensor in actively damping high frequent mechanical oscillations". 2001. .
  12. ^ "TRUBLUE Auto Belay". Head Rush Technologies. Retrieved 8 March 2016.
  13. ^ "zipSTOP Zip Line Brake System". Head Rush Technologies. Archived from the original on 6 June 2017. Retrieved 8 March 2016.
  14. ^ "Our Patented Technology". Head Rush Technologies. Archived from the original on 8 March 2016. Retrieved 8 March 2016.
  15. ^ "Zappi - Eddy Current Conductivity Meter - Products". zappitec.com. Retrieved 8 May 2022.
  16. ^ "Institut Dr. Foerster: SIGMATEST". www.foerstergroup.de. Retrieved 28 June 2018.
  17. ^ Coating Thickness Measurement with Electromagnetic Methods
  18. ^ "Ohm/sq & OD". www.nagy-instruments.de. Archived from the original on 4 March 2016. Retrieved 8 May 2016.
  19. ^ "Eddy Current Separator for metal separation". www.cogelme.com. Retrieved 8 May 2016.
General references

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