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

[David Meeker <dmeeker@xxxxxxxxxxxxxxxxx>]

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@xxxxxxxxxxxxxxxxx