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# Re: [femm] B.n(avg) vs. B.n^2(avg)

- To: femm@yahoogroups.com
- Subject: Re: [femm] B.n(avg) vs. B.n^2(avg)
- From: David Meeker <dmeeker@foster-miller.com>
- Date: Tue, 15 May 2001 12:51:41 -0400
- Organization: Foster-Miller, Inc.
- References: <NEBBKEEKONJNGCHMJMJNIEPDCBAA.jdgreener@earthlink.net>

    "Jay D. Greener" wrote:

    > I'm having some trouble getting valid force numbers for my
    > axisymmetric pot core solenoid model. I?m not able to define
    > a contour in the very tight air-gaps surrounding the armature.
    >
    > I?ve opted to estimate force using F=(A*B^2)/(2*mu)
    > where A = Armature Area, B=Average Flux Density along
    > Armature Face, mu = permeability of air.
    >
    > My question: Because (B.n.average)^2 doesn?t equal (B.n^2)
    > average. Which should I use? Why? Is this method going to
    > yield accurate results?

    Well, the F=(A*B^2)/(2*mu) is just a simplification of the stress tensor
    integration under the assumptions that:
    1) flux density is constant over the gap;
    2) the iron is infinitely permeable so that the only component of B is
    directed normal to the iron's surface
    In any case, you might as well just do the actual stress tensor
    integration, rather than trying to approximate it. Even if the air gap
    is pretty tight, it's usually not impossible to define a contour through
    it for the stress tensor integration. Sometimes I will even build in
    the contour as lines in the geometry, so that I can force the mesh to be
    fine enough around the contour to work right, even with thin gaps.

    Another way altogether that you might think about computing the force is
    via computation of the coenergy. This is an especially good way to go
    if you are interested in the force over the entire stroke of your device
    (i.e. at a range of points). What you can do is evaluate the coenergy
    at each position of interest, but for the same coil current, building up
    a set of data that defines coenergy versus position. The force is the
    derivative of coenergy with respect to plunger position (for constant
    coil current), so you can fit some sort of curve or splines through the
    coenergy data points and take the derivative of the curve to get force.

    Alternatively, can just evaluate coenergy at two plunger positions and
    evaluate
    Force = (coenergy1-coenergy2)/(position1 - position2)
    where the force result is most valid for the average of position1 and
    position2.

    > Also: is there anyway to show an H density plot around the
    > circuit? I can define a contour around the magnetic circuit then
    > plot H, but this doesn?t give me a feel for the ?high MMF drop?
    > regions as well as an H-density plot would. Any suggestions?
    The program currently only plots density plots of B. I've been thinking
    about augmenting the types of density plots that are possible, but for
    now, the contour plot of H.t is the best you can do.

    Dave.

    begin:vcard
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    tel;fax:781-890-3489
    tel;work:781-684-4070
    x-mozilla-html:TRUE
    url:http://members.aol.com/dcm3c
    org:Foster-Miller, Inc.;Electrical and Electronic Systems Group
    version:2.1
    email;internet:dmeeker@foster-miller.com
    title:Senior Engineer
    adr;quoted-printable:;;350 Second Avenue=0D=0A;Waltham;MA;02451-1196;USA
    fn:David Meeker, Ph.D.
    end:vcard

- References:
  - B.n(avg) vs. B.n^2(avg)
    - From: "Jay D. Greener" <jdgreener@earthlink.net>

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