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# Re: inductance/flux calculations in 2D/3D

- To: femm@yahoogroups.com
- Subject: Re: inductance/flux calculations in 2D/3D
- From: corneliuspaul@gmx.de
- Date: Wed, 11 Jul 2001 09:24:50 +0200 (MEST)

    k.gregory@lboro.ac.uk wrote

    >Dave is right, it really does depend on whether you have a problem
    >including a high permeability material or not. I've done investigations
    >into this stuff before and always found the same sort of results.
    >
    >If you have a transformer or a machine with a core of permeability
    >significantly greater than 1 then a 2D model works well. The flux linking
    >the winding overhangs (i.e. that bit of the winding not inside the core) is
    >mostly leakage, mostly in air, much smaller (several orders of magnitude)
    >than the main flux component and makes very little difference to the
    >overall result. However, you are right in thinking that ends of the winding
    >make a contribution, they do but it's certainly not "one fourth".
    >
    >The air-cored case though is significantly different. Every part of an
    >air-cored coil contributes to the magnetizing force. But it is a bit
    >simplistic to say that each side contributes a quarter of the total, that
    >would be true only at the coil's centre.
    >
    >I once did some simple experiments to compare inductances calculated from
    >FE models with those determined using the analytic equations in Inductance
    >Calculations - working formulas and tables by Federick W Grover (an old but
    >still good book). For a long pair of parallel wires in a go and return
    >arrangement the comparison was very good, within a few percent if I
    >remember correctly, but for a square coil the differences were quite large,
    >again if my memory serves more that 50% difference for the examples I
    >tried. Circular coils modelled in FEMM axisymmetrically should produce a
    >close agreement.
    >
    >All this means that you have to be very careful how or even if you model
    >what are essentially 3D problems using a 2D solver like FEMM. 2D models can
    >help significantly in understanding a 3D problem but you have to question
    >the absolute accuracy of derived things like inductance.
    >
    >I would add one further point. The derivation of the simple equation you
    >quote for the magnetizing force around a wire really implies that the
    >current returns via some far off and undefined path (otherwise you are
    >accumulating change at a point) so really it's a single turn coil not a
    >wire in isolation.

    Hi Keith,
    thanks for the comments. I am happy I understood it now...
    It really is the difference between flux paths in air and in high mu
    material.
    I have already come across one good example of this in my calculations:

    The transformer I am evaluating is built on a double U core, were both
    (circular) windings are situated concentrically one one leg.
    The primary winding is the inner winding, the secondary is the outer
    winding. When I want to calculate the stray (leakage) inductance
    I drive both coils with the same current (1 ampere), in adjacent
    directions.
    This results in a cancellation of the 2 fields everywhere but in the
    "stray field region" in between the 2 coils. This region lies
    completely in air.
    I then calculate the leakage inductance from the energy E in this
    field L=2E (when current = 1 amp).
    The result is once again in Henries per meter.
    As I am still in the beginner phase I am of course modeling a
    transformer that I have here in reality so I can compare with measurements.
    I only get the correct result when I multiply the Henries/m with half
    the average circumference of the stray field region. (could be called
    "effective path length" or whatever)

    This complies fine with the discussion above, because this time we
    are indeed investigating an area where the whole path is in air,
    therefore every part of the coil(s) is contributing the same amount
    to the B-field.

    Well, isnt it nice to understand what one is doing..? :-)

    BTW, the book by T.W. Preston and A.B.J. Reece arrived today...

    regards,
    Cornelius

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