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# Re: [femm] Pole end modeling questions

- To: femm@yahoogroups.com
- Subject: Re: [femm] Pole end modeling questions
- From: David Meeker <dmeeker@ieee.org>
- Date: Sat, 31 May 2003 22:07:38 -0400
- In-reply-to: <3ED8F37D.5B08C26C@sonic.net>
- References: <F3534F325314A243A60AF220E9A5377BFB6EC4@JAXCP01DATA.cp.ae.ge.com> <3ED6170E.3010204@ieee.org> <3ED8F37D.5B08C26C@sonic.net>
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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@ieee.org
    http://femm.berlios.de/dmeeker

Attachment: `zip00049.zip`
Description: Zip compressed data

- References:
  - RE: [femm] Speed Sensor
    - From: "Earanky, Vijay (GEAE, Unison-JAX)" <Vijay.Earanky@unison.ae.ge.com>
  - Re: [femm] Speed Sensor
    - From: David Meeker <dmeeker@ieee.org>
  - Pole end modeling questions
    - From: Tom Hansen <tomh@sonic.net>

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