Eddy Current Theory and Applications

What is Eddy Current

Eddy currents are circulating currents that form inside a conductor when a changing magnetic field cuts through the bulk. According to Lenz’s law, when a conducting loop is exposed to a changing magnetic field, it generates an emf that induces a current opposing the change. The same process in a solid filament or slab drives current around paths in the material’s cross-sections.

Those circulating currents take the name eddy currents after the small swirling whirlpools seen in lakes and oceans. Those currents heat transformer cores (usually unwanted) and also serve induction heating, metal testing and brakes.

Transformer-core heating is the usual drawback. Industrial uses include induction heating, metallurgy, welding and braking. The rest of the page covers the loss formula, laminations and those uses.

Eddy Current Loss in Transformer

The magnetic field inside a transformer core induces an emf, leading to eddy currents according to faraday law and lenz law. In the core section, the magnetic field B(t) from the winding current i(t) generates eddy currents i_eddy.

The losses due to eddy currents can be written as follows :

Where, k_e = constant depends on the size and inversely proportional to the resistivity of material,
f = frequency of the excitation source,
B_m = peak value of the magnetic field and
τ = thickness of the material.

The above equation shows that the eddy current loss depends on the flux density, frequency and thickness of the material and inversely proportional to the resistivity of the material.

• To reduce eddy current losses in transformer, the core is made of stacked thin plates called laminations. Each plate is insulated to restrict the eddy currents to small cross-sectional areas, minimizing their path and reducing losses.
  The laminated path is shown in the figure below :
  

  

• In order to increase the resistivity of the material cold rolled grain oriented, CRGO grade steel is used as core of transformer.

Properties of Eddy Currents

• Eddy currents form inside conducting materials.
• Cracks, corrosion, edges etc. distort the current paths.
• Eddy currents attenuate with depth with highest intensity present at the surface.

Those properties are why eddy-current probes are used in power, aerospace and petrochemical work to look for metal cracks and other damage.

Application of Eddy Current

Magnetic Levitation: Some maglev systems use electrodynamic (repulsive) levitation. Changing magnetic flux produced by a superconducting magnet placed on the moving train produces eddy currents on the stationary conducting sheet over which train levitates. The eddy currents interact with the magnetic field to produces forces of levitation.

Hyperthermia Cancer Treatment: Local RF heating of tissue has been studied using eddy-current heating of conducting implants. Eddy currents induced in the conducting tubings by proximal wire windings connected to a capacitor to form a tank circuit which is connected to a radio frequency source.

Eddy Current Braking: Kinetic energy converted into heat due to eddy current losses finds numerous applications in industry :

• Braking of trains.
• Braking of a roller coaster.
• Electric saw or drill for its emergency shut-off.

Induction Heating: A high-frequency electromagnet heats a conducting body by inducing eddy currents. Uses include induction cooking, furnaces to melt metals, welding and brazing.
Eddy Current Adjustable Speed Drives: With a feedback controller an eddy current coupled speed drive can be achieved. Uses include metal forming, conveyors, plastic processing etc.

Metal Detectors: A search coil can detect metals inside rocks, soils etc. by eddy current induction in the metal if present.

Data Processing Applications: Eddy current non destructive testing used in investigating composition and hardness of metal structures.

Speedometer and Proximity Sensing Applications