5 Key excerpts on "Eddy Current"

• 

  eBook - ePub

  Inductors and Transformers for Power Electronics

  • Vencislav Cekov Valchev, Alex Van den Bossche(Authors)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  5

   

  Eddy Currents in Conductors

   

     

  5.1  Introduction

  Eddy Current effects in conductors were recognized at an early time. At the end of the nineteenth century, it was known that a conductor of a (telegraphic) coaxial cable has an increased AC resistance for higher frequencies and that the inductance reduces with frequency [1 ]. The method that was applied used mathematical series and the derivative of the current. This approach is different from the methods we use now, but the result was correct.

  Eddy Currents have long been recognized in electrical machines as well. For example, the starting torque in squirrel cage induction motors is improved by a rotor resistance increase and inductance decrease caused by the Eddy Currents. In large machines and transformers, Eddy Currents have a big impact on the process of manufacturing coils because of efforts to avoid them, for example, paralleling wires and Robel bars.

  Although some physical properties were known before, the real breakthrough of ferrites came after 1945 in the Netherlands [2 ]. Using ferrites, the magnetic components could be made much smaller since the main flux path was not going through the conductors and, thus, most of the Eddy Currents could be avoided. In classical electronics, more attention was given to the total core losses and the Q-factor than to a detailed analysis of Eddy Current losses [3 ].

  Current Power Electronics Needs

  Because of improvements in semiconductors and soft switching topologies, much higher switching frequencies are now possible, compared to 20 years ago. As a result, most of the actual designs of magnetic components in power electronics are highly influenced by Eddy Currents.

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  eBook - ePub

  Dictionary of Physics

  • Michael Chapple(Author)
  • 2014(Publication Date)
  • Routledge

    (Publisher)

  E

  Eddy Currents are induced currents in metallic supporting parts of electrical machinery such as motors or transformers. These metal parts either rotate at speed in a magnetic field or stand in a rapidly changing magnetic field. The induced e.m.f.s set up in the conductor drive current loops known as Eddy Currents through the metal. These current loops will, unless they are diminished by good design, represent a serious energy loss. In the case of transformer cores, Eddy Current loss is reduced by constructing the cores from thin steel sheets insulated from one another.

  efficiency (heat engine) is defined as follows:

  where η is the efficiency of the heat engine, Wis the work done by the engine in one complete cycle and Q1 is the heat taken in from the source in one complete cycle. This equation is a definition and true for any heat engine.

  For an engine working with maximum efficiency, one, that is, which neither works against friction nor allows heat to slip across a temperature gradient fruitlessly, the equation can be extended:

  where Q2 is the heat released from the engine to the sink and T1 and T2 are the absolute temperatures of the source and sink respectively. (In fact, this equation defines the absolute thermodynamic temperature scale, but that is another matter.) This equation shows that high efficiency is obtained by ensuring a large temperature difference between source and sink. The efficiency is sometimes given as a percentage instead of as a decimal fraction.

  efficiency (machines): the ratio of the useful work done by a machine (such as a pulley system) on a load (such as a weight) to the work done on the machine by the effort force. It is usually expressed as a percentage.

  This definition can then be shown to be identical to the expression: where

  If a system of levers or a pulley system has an efficiency of 80%, the implication is that about a fifth of any effort applied to the system is expended working against friction. People selling quality pulley systems for boats and other purposes assume an efficiency of about 70% as a rule of thumb when choosing a pulley system.

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  eBook - ePub

  Applied Welding Engineering

  Processes, Codes, and Standards

  • Ramesh Singh(Author)
  • 2011(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  Chapter 7. Eddy Current Testing

  Chapter Outline

  Method305

  In Eddy Current testing, an electric current – either eddy or Foucault current – is induced in the test piece and the changes in that current are measured. The changes occur because of the presence of discontinuities. The test measures the resistivity caused by changes in chemical composition, crystal orientations, heat treatment hardness or discontinuities.

  Keywords Eddy Current testing, electromagnetic testing, discontinuities, resistivity

  The Eddy Current testing process is also called electromagnetic testing. The method is based on the general principle that an electric current will flow in any conductor subjected to a changing magnetic field.

  Depending on the type and thickness of material being tested, the testing frequencies vary from 50Hz to 1MHz. The method is used to check welds in magnetic and non-magnetic material, and is particularly useful in testing bars, billets, welded pipes, and tubes.

  Method

  In Eddy Current testing, an electric current – either an eddy or Foucault current – is induced in the test piece and the changes in that current are measured. The changes occur because of the presence of discontinuities. The test measures the resistivity caused by changes in chemical composition, crystal orientations, heat treatment hardness or discontinuities.

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  eBook - ePub

  Engineering Electrodynamics

  Electric Machine, Transformer, and Power Equipment Design

  • Janusz Turowski, Marek Turowski(Authors)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  Kazmierski in the Power Institute in Lodz, 1969, as well as by computer calculations with BEM—Yang Junyou et al. ICEF’92, China, p. 97; plus several transformer works, and others. 6.5 Transient-Induced Processes 6.5.1 Eddy Currents Let us consider a course and distribution of Eddy Currents induced in an infinitely vast metal sheet with a negligibly small thickness. This induction is caused by a sudden change of the external magnetic field. If A 1 is the magnetic vector potential of the external excitation field, A is the magnetic vector potential of Eddy Currents, which is always parallel to the XY surface of sheet, and J l and σ l are the current density and the sheet’s conductivity, respectively (cf. formula 2.184), then according to Equations 2.3, 2.23, and 2.51, the electric field intensity inside the sheet in point P (Figure 6.11) equals to E = J l σ l = - ∂ (A 1 t + A) d - grad V ⁢ (6.36) and according to Equation 2.50, B = curl A, the flux density inside the sheet (A z = 0) has the form B x = - ∂ A y & ; B y = − ∂ A x ∂ z ⁢ (6.37) Figure 6.11 Induction of instantaneous Eddy Currents in a metal sheet,. by an external field B 1 = curl A 1. (Adapted from Hańka L.: Induced transient phenomena in planar bodies. (in Czech). Elektrotechn., Obzor 8, 1962 (51), 378–382 [ 6.9 ].) If i is the current between point P and edge of the sheet or infinity (Figure 6.11), then from the surface curl (2.193a) and dependence (6.37) we have J x = - 2 H y = - 2 μ ∂ A x ∂ z ; J y = - 2 H x = - 2 μ ∂ A y & ; J l = - 2 μ ∂ A & ⁢ (6.38) After substituting dependences (6.38) into Equation 6.36, we obtain (Hanka. [ 6.9 ]) v ∂ A ∂ z = ∂ (A 1 t + A) d - grad V ⁢ (6.39) where ν = 2/ μ σ

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  eBook - ePub

  Transformer Engineering

  Design, Technology, and Diagnostics, Second Edition

  • S.V. Kulkarni, S.A. Khaparde(Authors)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  Chapter 5 .

  4.1    Field Equations The differential forms of Maxwell’s equations, valid for static as well as time-dependent fields and also for free space as well as material bodies, are

  ∇ × E = − ∂ B ∂ t

  (4.1)

  ∇ × H = J + ∂ D ∂ t

  (4.2)

  ∇ ⋅ B = 0

  (4.3)

  ∇ ⋅ D = ρ

  (4.4)

  where H	= magnetic field strength (A/m)
  E	= electric field strength (V/m)
  B	= flux density (Wb/m2 )
  J	= current density (A/m2 )
  D	= electric flux density (C/m2 )
  ρ	= volume charge density (C/m3 ).

  There are three constitutive relations,

  J = σ   E

  (4.5)

  B = μ   H

  (4.6)

  D = ε   E

  (4.7)

  where μ	= permeability of material (henrys/m)
  ε	= permittivity of material (farads/m)
  σ	= conductivity (mhos/m).

  The ratio of the conduction current density (J) to the displacement current density (∂D/∂t) is given by the ratio σ/(jωε), which is very high even for a poor metallic conductor (where ω is frequency in rad/sec). Since our analysis is for the power frequency, the displacement current density is neglected for the analysis of Eddy Currents in the conducting parts of transformers (copper, aluminum, steel, etc.). Hence, Equation 4.2 is simplified to

  ∇   ×   H   =   J .

  (4.8)

  The principle of conservation of charge gives the point form of the continuity equation,

  ∇ ⋅ J = − ∂ ρ ∂ t .

  (4.9)

  For slow time-varying fields in the present analysis of Eddy Currents in a conductor, displacement currents are neglected:

  ∇ ⋅ J = 0.

  (4.10)

  The first-order differential Equations 4.1 and 4.8 involving both H and E are combined to give a second-order equation in H or E as follows. Taking the curl of both sides of Equation 4.8 and using Equation 4.5

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