Re: hysteresis losses in enclosures

[erik_t_viking@xxxxxxxxxxx]

--- In femm@xxxxxxxxxxx, David Meeker <dmeeker@xxxx> wrote:
> 
> 
> erik_t_viking@xxxx wrote:


...

> > And now my questions, related to FEMM:
> >
> > 1. Why is the electrical conductivity of ALL steels in FEMM set 
to 0?
> > I'm using 9.5 MS/m as a normal value, about 1/3 of the 34.4 MS/m 
of
> > Al.
> 
> I didn't have information on the conductivities of all of the 
materials when
> I made up this library. The point of most of those materials is to 
get a
> B-H curve for magnetostatic analyses. I've recently obtained some
> manufacturer's data sheets on a lot of these materials, so I'll try 
to
> update the library as soon as I can. The value that you used may be
> reasonable for "cheap" iron. The conductivity of steel varies from 
about 2
> MS/m for good silicon steel laminations to about 10 MS/m for rolled 
steel
> that's not particularly intended for EM applications, with 
different types
> of steel falling everywhere within this range.

> 
> > 2. Can I model various phase-shifted currents by setting the real 
and
> > imaginary parts of the current density? I'm using 0.72 MA/m2
> > (resulting in a total peak value of 4000xsrt(2) Amps for the given
> > conductors).
> 
> Yes, that exactly right. However, some sort of subtle things 
happen when
> you do this. The current density that you assign via the material
> properties dialog is really just a _source_ current density--that 
is, the
> current that would be there at 0 Hz. At frequency, eddy currents 
are
> induced that knock down the total current carried in your 
conductor. To
> actually fix the total current in a conductor in a harmonic 
problem, you
> need to get ahold of the femm30 beta version (available at
> http://www.egroups.com/files/femm/). You can then specify total 
currents
> carried by sections of the model via the new "Circuit" properties. 
This is
> what I've done in the attached examples.

I've downloaded the beta version, but since it was accompanied by the 
old manual, I was unaware of this new feature.
Furthermore, FEMM freezes if the frequency is set to 0 Hz in this 
example. Logically, even I couldn't interprete phase shifts at zero 
frequency:-)

> 
> > 3. What boundary conditions to specify for this kind of problems?
> 
> Well, the skin depth of your problem is really small. Skin depth =
> Sqrt[1/(sigma*mu*Pi*freq)] where sigma is the conductivity in MS/m, 
mu is
> the absolute permeability, and freq is the frequency in Hz. The 
result is in
> meters. For the properties you described, the skin depth is about 
0.58 mm.
> This means that the field doesn't get through to the outside part 
of the
> iron, and it is sufficient to specify A=0 on the outside of the 
iron. This
> is what I've done in the attached "viking1.fem" example. Note that 
in this
> problem, I have defined a very thin region about 1 mm width the 
inner
> surface of the iron that is finely meshed in order to capture the 
skin
> effects in the iron in "enough" detail. The result is a mesh with 
a _lot_
> of nodes that takes a long time to solve.

This geometry comes awkwardly close to the one I've used. It must 
have been quite some work and calculation time. 

> 
> An alternative is to specify a "small skin depth" impedance boundary
> condition on the _inside_ of the iron, making that the edge of your 
domain.
> This greatly decreases the size of the problem, since you don't 
have to
> worry about explicitly modeling the skin depth region in the 
enclosure--this
> is taken care of by the boundary condition. The 
attached "viking2.fem"
> takes this approach. There are two down sides to this approach--it 
is more
> difficult to back out the losses in the enclosure. This requires a 
surface
> integral of |A|^2 that the postprocessor doesn't currently perform, 
but
> which you can do by exporting the profile of A along the surface. 
After you
> do this integral, you need to multiply the result by (1/4) * 
(2*Pi*freq)^2
> * sigma * (skin depth) to get total losses. Also, femm currently 
doesn't
> allow you to define a hysteresis lag in the boundary material. 
I'll add
> this in eventually, because it is really a small modification.

this particular behaviour of this boundary condition and the 
inability to calculate the surface integral made me hesitate to use 
it. I even experimented with it on the outside of the conductors, 
with weird results.

> 
> > 4. Along the inner surface of the enclosure, I've specified a 
mesh of
> > 0.02 cm. Is this fine enough given the skin dept of slightly less
> > than 1 mm? More nodes seems to crash this machine :-(
> 
> Yes, this ought to be good enough. See answer to (2)
> 
> > 5. Does anyone know a steel with a relative permeability of around
> > 1600 with 'worse' hysteresis properties as the M-36 steel?
> >
> > 6. If |H| and |B| are known, then how do I estimate the resulting
> > heat losess for this situation. I only have detailed curves for
> > laminated transformer steels for |B| > 1 T, which of course are
> > softer ferrites.
> 
> You can obtain losses directly from the program with block 
integrals.
> Switch to the block integral mode by cliking on the green square on 
the
> femmview toolbar. Then, select the region of interest by clicking 
somewhere
> inside it with the left mouse button. The area selected with light 
up in
> green. When you've selected all the areas of interest, click the 
integral
> sign on the toolbar. Then, choose the "total losses" integral. It 
will add
> up all of the predicted hysteresis and eddy current losses.
> 
> Note--to get hysteresis losses, you have to specify some nonzero 
number for
> the phi_h parmameter in the material property dialog. This 
parameter
> defines a frequency-independent phase lag between B and H in a 
material,
> which is a relatively crude but easy to handle model of hysteresis 
effects.
> To get really good results, you ought to do some tests on a toroid 
made out
> of the material of interests to identify a parameter that makes the 
losses
> matched the observed. Failing that, Stoll's "Analysis of Eddy 
Currents"
> says that the hysteresis lag is "usually less than 20 degrees", so 
for a
> cheap steel not specifically intended for magnetic applications, 20 
degrees
> is probably a reasonable value to assume.

OOOOOPS. This is the main problem for my unearthly results. As a 
matter of fact, I should have this curve somewhere.

> Anyhow, the losses in the attached example of the example problems 
loss
> numbers in the end sections average out to like 760 W/m^2 for the 
surface
> impedance model w/out hysteresis, and more like 960 W/m^2 for the
> brute-force one that also includes hysteresis losses. These losses 
are
> highly dependent on the material parameters that you use. The 
brute-force
> model also shows that the skin region in the enclosure is highly
> saturated--however, the harmonic analyses are all linear, so you 
have to
> take the results with a bit of a grain of salt....

A somewhat accurate prediction of the B-values involved is good 
enough for me. Anyway, this test prototype should be saturated, so 
this calculations make sense.

Thanks and keep up the good work!


Erik Evertz