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# Re: [FEMM] A DOT J Integral over laminated region

- To: Finite Element Method Magnetics mailing list <femm@list.foster-miller.net>
- Subject: Re: [FEMM] A DOT J Integral over laminated region
- From: David Meeker <dmeeker@foster-miller.com>
- Date: Tue, 21 Oct 2003 09:54:01 -0400
- In-reply-to: <5.1.1.5.2.20031020140818.01b04490@pop.mail.gatech.edu>
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`Thomas Wilson wrote:`

> `I am using the detailed flux field from FEMM to compute lumped parameter coefficients for an external model. The lumped parameter model includes eddy current circuits so I am evaluating the mutual inductance between a coil and the region in which the eddy current flows. The FEMM calculation is axisymmetric and harmonic. The main calculation for the lumped parameter mutual inductance between the coils and eddy currents involve the A dot J block integral. Things work as expected for continuous materials but when I specify "laminated in plane" for the region in which the eddy currents flow then FEMM calculates that the current density and the A dot J integral are zero in that region. Laminations reduce eddy currents but it does not make them zero. So this is not the result that I expect or can use. Any help on how to correct the problem or explanations as to why it correct as is?`

`
The "laminated in plane" case corresponds to a radially laminated configuration for axisymmetric problems. Although this is difficult to construct in practice, I've seen some specialty machines that have been built in this way. With a radial lamination direction, there is no net current in the tangential direction--thus the zero result for the A.J integral. All of the eddy currents are conserved inside each lamination. However, the eddy currents in these laminations do affect the field. The eddy currents make the laminated core appear to have a permeability that is of a lower magnitude than the DC permeability, and they also give a complex component to the permeability. The complex part of the permeability is associated with eddy current (and/or hysteresis) losses.`
`At any rate, a good way to take these effect into account is by their effect on the flux linkage of the coil that drives the eddy currents. The eddy currents (in both laminated and non-laminated regions) make the flux linkage of the driving coil have a frequency dependency. You then assume a lumped-parameter model structure that yields the observed behavior (typically a chain of inductors and resistors like the one that I used in http://femm.berlios.de/dmeeker/pdf/chop2.pdf) and then pick the parameters to be a best fit to the magnitude and phase of the flux linkage as evaulated at a variety of different frequencies.`
`Dave.`
`--
David Meeker
Senior Engineer
Foster-Miller, Inc.
350 Second Avenue
Waltham, MA 02451-1196
781-684-4070
781-890-3489 (fax)
dmeeker@foster-miller.com`
``

- References:
  - [FEMM] A DOT J Integral over laminated region
    - From: Thomas Wilson <gte584m@mail.gatech.edu>

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