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# [femm] PM modeling (Re:Suggestions)

- To: femm@yahoogroups.com
- Subject: [femm] PM modeling (Re:Suggestions)
- From: David Meeker <dmeeker@foster-miller.com>
- Date: Mon, 25 Jun 2001 13:24:06 -0400
- Organization: Foster-Miller, Inc.
- References: <5.0.2.1.2.20010625132623.00b60900@gugu.usal.es>

Victor Javier Raposo Funcia wrote:

> Just two points:

> - What about adding a vector plot of H and B in the postprocessor?
> - When I try to solve a problem consisting on a rectangular magnet (in the
> air) I found the following problem:
> B seems to be correct, but H inside the magnet is in the same direction as
> the magnetization M, and it should be a demagnetizing field (when I solve
> it with the magnetic charges). It seems that H is calculated as H=B/mu
> without considering M.

Well, femm takes the view that permanent magnets are essentially the same as solenoids. The magnet consists of a chunk of low-permeability material (such as air). The "source" of the PM's flux is a current sheet of density Hc*(m cross n) on the edges of the permanet magnet, where Hc is the magnet's coercivity, m is a unit vector in the direction of magnetization, and n is an outward unit normal to the edge of the PM. This is a fairly typical way to model permanent magnets in the context of a finite element formuation (because it is any easy way to include PMs), and it is also equivalent to a magnetic charge-based formulation. An interesting web site that discusses this approach is here, on the Magnequench website. This issue is also discussed in appendix A1 in the femm manual.

In any case, it is possible to back out the demagnetizing H and M that one would obtain in a formulation that represents M explicitly. To do this, we are just mapping back onto the second quadrant of the demagnetization curve. If Hf is the field intensity reported by femm, and Hd is the demagnetizing field intensity, then Hd = Hf - Hc*m, where Hc is the coercivity of the material, and again, m is a unit vector pointing in the magnetization direction. Magnetization is defined by B=muo(Hd+M), so the magnetization corresponding to the operating point on the demagnetization curve is M = B/muo - Hd, where muo is the permeability of free space and B is the flux density. If the magnetic material has a unit relative permeability (nearly true with most SmCo, NdFeB, and some ceramic magnets), M=Hf-Hd.

At least, I don't think I've screwed up this explanation....

Dave Meeker

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- Follow-Ups:
  - Superconductors
    - From: Agnaldo Souza Pereira <agnaldo@if.ufrj.br>
  - Re: [femm] PM modeling (Re:Suggestions)
    - From: "Ivan Reede" <i_reede@amerisys.com>
  - Re: [femm] PM modeling (Re:Suggestions)
    - From: Victor Javier Raposo Funcia <victor@gugu.usal.es>

- References:
  - Re: [femm] Suggestions
    - From: Victor Javier Raposo Funcia <victor@gugu.usal.es>

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