Re: [femm] Pole end modeling questions

[David Meeker <dmeeker@xxxxxxxx>]

Tom Hansen wrote:
>   Hi
> David et al,
>
> This is a question about modeling the ends of magnetic poles.
>
> If you have a simple horseshoe magnet with square iron poles and a
> square iron bar near the two ends, the 2D diagram from the side view is
> rather simple to model (see attached file "horseshoe.fem").  However, if
> the horseshoe magnet poles were not a square in cross section, but
> instead were made from round rods of iron, the simple side view would
> only represent a single "slice" of the magnetic field. 
If you have a problem that isn't well-described as a 2D approximation
that is infinitely deep in the "into the page direction" (like your
horseshoe), you'd have to go to a 3d analysis, either accounting for the
3D flux paths via analytical expressions for reluctance à la Roter's Electromagnetic
Devices or 3D finite element, boundary element, etc.
>  It
> would
> therefore be useful to model the ends of the poles as if you were
> looking at the model so you just see the ends of the poles and the iron
> cross bar. A sketch of this is the file "pole ends.fem".  The main issue
> is then how to "material" the ends of the poles so that the magnetic
> field is oriented toward the plane of the screen and away from the plane
> of the screen.  If the "material" chosen is a magnet, the only
> orientation possibilities are currently, as I understand it, in the
> plane of the screen.
>
> Any suggestions on how to achieve this would be appreciated.
>
> Thanks
>
> Tom
>
> P.S. What a great program and group!
Well, there are some case where you might want to do this sort of
analysis, essentially to determine reluctances of parts of a magnetic
circuit that are irritating to write analytical expressions for
reluctance.  In your case, this might be reasonable if your bar were up
in between the pole pieces instead of beneath them.  Anyhow, to do what
you want, you really want a magnetic scalar potential formulation.  If
you had access to such a formulation, you'd specify a constant
magnetomotive force (MMF) on the surface of each pole piece, run the
analysis, and integrate the flux coming out of one of the pole pieces. 
You could then get a reluctance (magnetic circuit analog to resistance)
by dividing the MMF difference between the pole pieces by the total
flux.  You'd then use this result as part of a magnetic circuit model
for the rest of your device (e.g. for the horseshoe, a reluctance and
MMF source in series for the magnet with a leakage path and the flux
path through the pole in parallel for the return path).

The "problem" here is that FEMM uses a vector potential formulation,
where there can be no sources or sinks of flux--unfortunately, this is
exactly what you'd want to model for the reluctance determination
problem.  The "fix" is to mis-use Bela, the sister electrostatics
analysis version of femm, to solve your reluctance problem.  Since Bela
uses a scalar potential formulation, you could interpret the results as
the solution to a magnetic scalar potential problem via a few carefully
chosen conversion factor.  Specifically, if you define the relative
permittivity to be (uo/eo) = 141926 times the desired relative
permeability, you can interpret voltage as MMF in Amp*Turns, Electric
field density, D, as magnetic flux density in units of Tesla, and
Electric field intensity, E, as magnetic field intensity in units of
Amp/meter.

For example, I've attached a marked-up version of your "pole end"
geometry.  The iron sections are not meshed, and their surfaces are
assigned fixed voltages.  This treatment is analogous to an infinitely
permeable magnetic material (a good approximation if there is a big air
gap).  I've just considered one air gap, and I've used a Kelvin
transformation boundary condition to model the problem as if the
solution region is "open".  Anyhow, there is a 1 A*Turn drop across the
gap, the depth is 1" in the "into the page" direction, and I've
assigned the relative permeability of the air region to be 141926, as
described above.  The total charge on the pole piece is 4.69421e-007
Coulombs, which could be interpreted as a 4.69421e-007 Wb flux.  The
reluctance of the air gap is then R = (1 Amp*turn)/(4.69421e-007 Wb) =
2130284 A*turn/Wb.

Dave
-- 
David Meeker
dmeeker@xxxxxxxx
http://femm.berlios.de/dmeeker

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