Eddy Current Force: Equation & Derivation

[mertcan]

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.

 

[Hesch]

I really wonder ıs there a equation related to force generated by eddy current?

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.

 

[mertcan]

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 ?

 

[Hesch]

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.

 

[mertcan]

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 ?

 

[Hesch]

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 ).

 

[mertcan]

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...

 

[Hesch]

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.

 

[Hesch]

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: E_dens = 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 = E_dens * 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.