Re: [femm] DC vs AC results

[David Meeker <dmeeker@xxxxxxxx>]

Michael Craft wrote:
>  
> Question:
>
> If I apply a very slow AC current (~0.1 Hz) to my
> model (as opposed to a DC excitation) I will get a
> higher flux density (and field intensity) than the
> results for just DC.  Shouldn't these be very similar?
> The descrepency is on the order of 26% increase.  I
> am trying to evaluate the effect of eddy currents vs
> frequency, but I need to know the cause of this large
> difference.
>
> Thanks,
> Michael Craft
I'm guessing that you have saturated iron in your model--that is where
this behavior can arise.  

Anyhow, this is actually what the program is intended to do.  There's a
brief blurb on this in Appendix A.4 of the manual.  Anyhow, remember
that the response of a problem with saturation is nonlinear--you put in
a sine wave of current, but you don't get out a sine wave of flux if
there is saturation--the peak flux densities get clipped.  The idea of
the nonlinear time harmonic solver is to try to determine the amplitude
of the fundamental of the saturated flux density.  To do this,
the program determines an "apparent" B-H curve that is used for AC
problems by assuming that H varies sinusoidally.  This effective B-H
curve is used for any problem where the frequency is not exactly equal
to zero (e.g. 0.1 Hz).  The program then computes the fundamental of
B[H] (essentially by convolving B with H).  Now, the resulting
amplitude of the fundamental can be at a higher flux density than with
the DC curve.  To see why this happens, consider a square wave that
varies between -1 and 1.  In this case, the amplitude of the
fundamental component is 4/Pi, or about 1.27324.  This is about 27%
higher than the peak of the square wave.  You get the same sort of
effect with the B-H curve.

Now, why, one might ask would one go to the trouble of creating an
"effective" B-H curve?  Although it tends to over-report the peak
values of flux density, the whole idea is to get accurate values for
quantities like losses and forces--something which this approach does
pretty well, relative to the amout of effort required to get the
solution.  FEMM also does some fairly subtle things, like including (a
somehwhat rudimentary model of) hysteresis, and deriving effective BH
curves including saturation, eddy currents, and hysteresis for
laminated regions.

If you want to read more, a couple good places to look are:
A. G. Jack and B. C. Mecrow, ”Methods for magnetically nonlinear
problems involving significant hysteresis and eddy currents,” IEEE
Transactions on Magnetics, 26(2):424-429, March 1990.
G. Paoli, O. Biro, and G. Buchgraber, "Complex representation in
nonlinear time harmonic eddy current problems," IEEE Transactions on
Magnetics, 34(5):2625-2628, September 1998

Dave.
-- 
David Meeker
dmeeker@xxxxxxxx
http://femm.berlios.de/dmeeker