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# Re: Lua sample of line integral

- To: femm@yahoogroups.com
- Subject: Re: Lua sample of line integral
- From: jim271@hotmail.com
- Date: Fri, 17 Aug 2001 02:35:27 -0000
- In-reply-to: <ff.abff9a6.28ad62e0@aol.com>
- User-agent: eGroups-EW/0.82

    Hello Dave,

    Thank you for explaining that detail about the Lorentz force. I've
    only been using it with a simple coil-plunger combination, so I was
    lucky :-)

    One problem I've had with the stress tensor around a contour is
    having to use a high mesh density in the region where the contour is
    drawn. If I want a very small air gap, this requires a very large
    number of meshes and long execution time.

    I'm wondering if by using the volume integral for coenergy and taking
    the derivative, you actually get more accurate results (compared to
    the stress tensor) with relatively few meshes in the narrow air gap,
    as long as the mesh density is much smaller than the plunger step
    size? That is, since there is no contour in the air gap, is the mesh
    density critical there?

    Also, how do you keep data from one iteration of the lua script to
    pass on to the next iteration so it can calculate the derivative?

    Thanks again.

    -- Jim

    ===================================================================

    --- In femm@y..., dcm3c@a... wrote:
    > In a message dated 8/16/01 11:01:41 AM Eastern Daylight Time,
    > jim271@h... writes:
    >
    >
    > > There is a sample script file that's distributed with FEMM 3.1
    > > showing how to do this very thing using the Lorentz force on the
    > > coil. I've found this to be much easier than drawing a contour to
    use
    > > for the stress tensor. Just highlight the object used for the
    coil
    > > and then calculate the Lorentz force. The force on the coil is
    equal
    > > and opposite (opposite sign) to the force on the plunger.
    > >
    >
    > Well, you have to be a bit careful using Lorentz force with a
    solenoid. It
    > works OK in the coilgun example because there are only 2 objects--
    the coil
    > and a ball bearing. In that case, the force from on the coil must
    equal the
    > force on the ball. However, in the case of a solenoid, there is
    typically an
    > iron core wrapped around the coil. The Lorentz force result here
    would be
    > equal to the net force on the plunger and the stator iron, whereas
    one is
    > probably really interested in just the force on the plunger.
    >
    > However, there is a volume integral way to get force in the case
    where there
    > is an iron core. Instead of integrating Lorentz force over the
    coil,
    > integrate magnetic field coenergy over the entire solution domain
    (i.e.
    > everywhere). Evaluate this result at intervals along the stroke of
    the
    > plunger. The result is a curve of coenergy versus position. You
    then infer
    > what the force is on the plunger by from the coenergy by noting
    that force on
    > the plunger is the derivative of coenergy with respect to position.
    You can
    > approximate the derivative of coenergy with numerical derivatives
    like
    > (Wc[n]-Wc[n-1])/(z[n]-z[n-1]) where Wc[n] is the nth coenergy
    result and z[n]
    > is the nth plunger position. This result is equal to the average
    force over
    > the interval from z[n-1] to z[n]. For this to work right, the mesh
    density
    > in the air around the plunger should be smaller than the size of
    the
    > steps--otherwise, the force results come out noisy.
    >
    > Dave.
    > --
    > David Meeker
    > <A
    HREF="http://members.aol.com/_ht_a/dcm3c";>http://members.aol.com/_ht_a
    /dcm3c</A>

- References:
  - Re: [femm] Re: Lua sample of line integral
    - From: dcm3c@aol.com

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