Just two points: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.- 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.
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
begin:vcard n:Meeker;David tel;fax:781-890-3489 tel;work:781-684-4070 x-mozilla-html:TRUE url:http://members.aol.com/_ht_a/dcm3c org:Foster-Miller, Inc.;Electrical and Electronic Systems Group version:2.1 email;internet:dmeeker@xxxxxxxxxxxxxxxxx title:Senior Engineer adr;quoted-printable:;;350 Second Avenue=0D=0A;Waltham;MA;02451-1196;USA fn:David Meeker, Ph.D. end:vcard