Re: [femm] Scaling question

[David Meeker <dmeeker@xxxxxxxxxxxxxxxxx>]

rtickle@xxxxxxxx wrote:

> Question for David and group:
>
> I've modelled a simple C core type electromagnet with two sets of
> coils in femm based on a design we are considering building. We are
> looking at building a quarter scale prototype first to make sure we
> can produce the fields the numerical solution tells us we can. I've
> noticed however, that in scaling down the original design by 1/4 and
> recalculating in femm, much smaller fields are produced in the
> airgap. Only by multiplying the original current density by 4 are the
> original fields of the full scale model produced along the centerline
> of the airgap. I had assumed that I would want to keep the current
> density fixed while scaling the model down; the numerics seem to be
> saying this is wrong. Can anyone explain why this is so?

It sounds like you have just scaled all of the dimensions linearly by some
scaling factor. In this case, the amp turns needed to drive a given flux
scales linearly with the scale factor: i.e., if you scale down by with a
scale factor of 1/4, the gap is only 1/4 as long, and you only need 1/4 as
many amp-turns to drive the given level of flux density. However, the total
amp-turns are the product of the current density and the coil area. Coil
area scales with the square of the scaling factor, so if you scale down with
a scaling factor of 1/4, you would only have 1/16 the number of amp-turns
driving the flux if J is held constant. With the scaled system, when the
decreased amp-turns required to get a given flux density in the gap is
combined with the more greatly decreased number of amp-turns, the net result
is only 1/4 of the flux density of the full-scale system. All of this falls
out of considering Ampere's loop law:

Path Length*Field Intensity = Amp-Turns

Dave.


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