Re: [femm] continuum model of proximity losses (was Re: various induction machine questions)

[David Meeker <dmeeker@xxxxxxxx>]

Muchlis Achmad wrote:

> The example below really helps. I like to ask further questions on the 
> subject:
>
> Is there a good reference paper on getting a closed form solution for 
> apparent resistance and inductance of a coil similar to the example below?
I don't really have a reference for any closed-form solutions to these 
sort of problems.

> Better yet, what if we have an iron-core coil, will FEMM still give an 
> answer which is closed to the exact solution of the eddy current effect?
There's nothing in particular in the derivation that assumes the 
presence or absence of an iron core--in theory, the same approach ought 
to work just fine either way.

So, I tried out a few more examples. For an axisymmetric air-cored coil 
(just the same as the planar one in the example, but run as an 
axisymmetric problem instead), the results are also an excellent match 
to the full discrete-wire model. I also bumped up the frequency to 
100kHz, and the match is still really good for the air-cored coil.

Then, I looked into some iron cored problems. The results were still 
pretty good, but for some cases, there was like a 10% difference between 
the continuum approximation and the full model. In the particular case 
with the worst match, I was analyzing a pot-cored inductor with an air 
gap. What was going on is that most of the prox. losses were occuring in 
only a few turns of the wire that happened to be sitting in the fringing 
field of the gap. One thing that the continuum model assumes is that the 
field "source" field that drives the prox losses can be 
well-approximated as constant across the area of the wire. For these 
turns sitting in the fringing field, there is actually a pretty big 
field gradient over the area of the wire--the assumptions used in 
deriving the continuum model break down a bit in this region. This is 
probably what causes the difference.

> How does FEMM take into account the hysteresis of the iron material?
Currently, FEMM models hysteresis effects through the use of a 
complex-valued magnetic permeability. This is sort of a crude model of 
hysteresis, but it was easy to incorporate into the program... There's a 
nice section on this approach in Stoll's "Analysis of Eddy Currents." 
Much more recently, Hollaus and Biro talk about a generalized version 
for use with a nonlinear BH curve in their paper,

K. Hollaus and O. Biro, “Derivation of a complex permeability from the 
Preisach model,” IEEE Trans. Magnetics,
vol. 38, no. 2, pp. 905–908, 2002.

> Also, what if we have a core that is moving such in motor or solenoid, 
> how do we take into account the back emf effect to the FEMM solution?
The program really only addresses static configurations. In the past, 
people have use FEMM to help identify parameters in circuit models (or 
just flux linkages), which could then be used in combination with motion.

Dave.