Eddy Current Force: Equation & Derivation

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Discussion Overview

The discussion revolves around the force generated by eddy currents, specifically seeking an equation and derivation related to this force. Participants explore the theoretical and practical implications of eddy currents in various contexts, including their role in braking systems and energy losses in materials.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants inquire about the existence of a specific equation for the force generated by eddy currents, noting that they have only found equations related to eddy current density.
  • One participant suggests that knowing the current density and conductivity allows for the calculation of power losses due to eddy currents, implying a relationship to force but not providing a direct equation.
  • Another participant describes the scenario of a plate moving through a magnetic field, explaining how eddy currents are induced and how they interact with the magnetic field, potentially leading to braking forces.
  • There is a discussion about the need for numerical calculations to determine braking force, considering factors like induced eddy current and self-induction.
  • Participants express a desire for resources or problems related to eddy current force, with one mentioning an old book that may not be accessible to others.
  • One participant elaborates on the dynamics of a rotating plate and the effects of eddy currents on magnetic flux, discussing energy density and the tendency of the system to minimize magnetic energy.

Areas of Agreement / Disagreement

Participants generally agree on the complexity of calculating the force related to eddy currents and the need for further exploration of the topic. However, there is no consensus on a specific equation or derivation, and multiple competing views regarding the mechanisms and calculations involved remain present.

Contextual Notes

Participants note limitations in available resources and the complexity of the mathematical derivations required to fully understand the relationship between eddy currents and force. There is an acknowledgment of the need for numerical methods and integration in calculations.

mertcan
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hi, I really wonder ıs there a equation related to force generated by eddy current? And ıs there a derivation of this equation? I am asking because the only thing I can find is the eddy current density equation, no force formula exist on internet.
 
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mertcan said:
I really wonder ıs there a equation related to force generated by eddy current?
mertcan said:
the only thing I can find is the eddy current density equation

Knowing the current density and the conductivity of some material, you can calculate the powerlosses in the material due to eddy currents. ( You will need some integration here. )

Then current losses = supplied energy.
 
Hesch said:
Knowing the current density and the conductivity of some material, you can calculate the powerlosses in the material due to eddy currents. ( You will need some integration here. )

Then current losses = supplied energy.
How can We calculate the force resulted from eddy current ? For instance there are eddy current brakes and generate force, is there a force equation that involves eddy current density ?
 
When a plate passes/rotates by a magnetic field, Eddy currents will be induced in plate due to change of flux through the plate. You may say that the plate around the magnetic field forms a short circuited coil ( 1 turn ). So now you have a magnet outside the plate and an electric magnet inside the plate, and they will attrack each other in a direction perpendicular to the plate, and that will not brake the (rotating) plate. It's the same principle as for an induction motor.

But the coil in the plate has some self induction, thus the growth/decline of the current in the coil will be delayed with respect to passing the outside magnet, and therefore the force between the two magnets will be skew, and the plate will be braked.

I think you will have to calculate the braking force numerically from induced Eddy current and from self induction in the inside coil, passing speed, etc.

At speed ≈ 0, the brake will not work at all, due to Eddy current.
 
Hesch said:
When a plate passes/rotates by a magnetic field, Eddy currents will be induced in plate due to change of flux through the plate. You may say that the plate around the magnetic field forms a short circuited coil ( 1 turn ). So now you have a magnet outside the plate and an electric magnet inside the plate, and they will attrack each other in a direction perpendicular to the plate, and that will not brake the (rotating) plate. It's the same principle as for an induction motor.

But the coil in the plate has some self induction, thus the growth/decline of the current in the coil will be delayed with respect to passing the outside magnet, and therefore the force between the two magnets will be skew, and the plate will be braked.

I think you will have to calculate the braking force numerically from induced Eddy current and from self induction in the inside coil, passing speed, etc.

At speed ≈ 0, the brake will not work at all, due to Eddy current.
ok Hesch thanks for your return, I can understand what you try to say, but also I would like to express that I really lack the sources about this situation, I need to have a look at and get so much involved in some mathematical stuff or derivations about that. I really want to have some practices (questions with solutions) related to eddy current force. So, is there a source you suggest in which I can see some problems and solutions to those problems ?
 
mertcan said:
So, is there a source you suggest in which I can see some problems and solutions to those problems ?
No, I just have an old book (1971), with the subtitle ( in latin ):

Experimenta circa effectum conflictus electrici in acum magneticam.

The content of the book is in danish.

I don't think it's for sale any longer ( and I don't think you can read danish ).
 
Hesch said:
No, I just have an old book (1971), with the subtitle ( in latin ):

Experimenta circa effectum conflictus electrici in acum magneticam.

The content of the book is in danish.

I don't think it's for sale any longer ( and I don't think you can read danish ).
What do you suggest for me then ? I am sure that someone in this forum undoubtedly have a remarkable book or file in the realms of eddy current force...
 
mertcan said:
I am sure that someone in this forum undoubtedly have a remarkable book or file in the realms of eddy current force...
Wait for an english speaking member to guide you.
 
Well, I will try then ( excuse my english ).

Say you have this rotating plate, passing a cylindric magnet close to the plate. Having passed the airgap, the magnetic flux induced by the magnet will pass through the plate. This airgap flux will also become cylindric when the plate and the magnet are close to each other, at least as long as the rotating plate is halted.

When the plate starts spinning, an eddy current will by induced in the plate, that in turn will create an opposite directed flux in the airgap. The sum of these fluxes will not be zero, because there is some resistance ( eddy losses ) in the plate. So now you have a flux space in the airgap, containing reduced magnetic flux, but it is not completely cylindric, due the time delay ( phase shift ) between eddy voltage and eddy current: The eddy current will "see" som self induction in the plate. The center axis in the magnetic "cylindric" flux in the airgap will be stretched/tilted skew. The volume of a skew cylinder ( constant height and cross section area ) will be greater than as for a straight cylinder.

Now, the energy density in a magnetic field: Edens = ½*H*B [ J/m3 ]. Mother nature will try to get rid of magnetic energy, and she knows that if she can bring this cylinder into a straight shape, the volume of flux will be reduced, and so will the magnetic energy = Edens * volume.

That's why the two magnets will attrack each other and will try to bring the plate to a halt.

There is a lot of calculation here, concerning self induction, brake dimensions, flux volumes, amount of flux. That's why I suggested:

Knowing the current density and the conductivity of some material, you can calculate the powerlosses in the material due to eddy currents.

. . . . because I think that you will come up with a more accurate result.
 

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