Re: [femm] Inductance with permanent magnet

[David Meeker <dmeeker@xxxxxxxxxxxxxxxxx>]

vecerkaj@xxxxxxxxx wrote:

> Hello
> First, I would like to thank for the contribution to the discussion
> about ConText and other editors.
> Now, I have met a problem, how to calculate self inductance, if
> magnetic circuit contains permanent magnets (NdFeB-linear
> characteristics) and iron (nonlinear).
> My thinking: Calculation of L directly from the "A.J" integral is
> probably wrong, same as calculation of L from magnetic energy
> (because permanent magnets put additional energy to the magnetic
> circuit).
> My approaches how to solve that:
> 1. To calculate inductance from model with magnet properties set on 0
> (Hc). But the magnetic circuit will not be saturated by magnets and
> result will not be accurate.
> 2.To calculate model without current and with current. To make
> subtraction of energies obtained from the models. To use the result
> for calculation of inductance. I have realized, that this way is
> wrong.
> 3. To calculate model without current and with current. To make
> subtraction of A in every node in mesh (mesh should be the same) out
> of FEMM and to create new .ans file. After that to calculate L
> directly from the "A.J" integral. Till now I think, that this way is
> correct, because this one considers iron saturation. I guess, if
> the "test" current is small then the method is applicable even for
> nonlinear materials.
> I have also a physical model, but the result obtained from FEMM is
> higher than reality I measured on the model ( about 100%). I don't
> understand why, because FEMM doesn't consider leakage inductance in
> winding heads, so the total inductance should be higher then
> calculated value.
> Note all the calculations I did were for 0 Hz (magnetostatic).
> So, I would like to ask anybody, what he thinks about the problem.
> Thank you in advance.
>
> Jiri Vecerka

It sounds like what you want is sort of an incremental inductance of the in
the presence of the magnet. I'd go about this by computing flux linkages.
This is going to be another one of those explanations that's "fun" to do in a
text-based medium. So anyhow, let Ap represent the average A over the (+)
part of your coil, and let Am represent the average A over the (-) part of
your coil. You can get these quantities by integrating A in the
postprocessor and dividing by the coil's cross-section. The total flux
linkage is then:

flux linkage=n*(Ap-Am)

where n is the number of turns in your coil. You'd want to evaluate the flux
linkage in two cases: one with just the magnet, and one with the magnet plus
a small coil current. To get the flux linkage just due to current in the
coil, subtract the two flux linkages:

flux linkage from coil = (flux linkage with coil+magnet) - (flux linkage with
just magnet)

Inductance is then obtained by dividing the flux linkage from the coil by the
current you used to run the (flux linkage with coil+magnet) case:

L = (flux linkage from coil)/(coil current)

Hope this is what you are after.

Dave.


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