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# Re: [femm] Force calculation on an axisymmetric model

- To: femm@egroups.com
- Subject: Re: [femm] Force calculation on an axisymmetric model
- From: David Meeker <dmeeker@foster-miller.com>
- Date: Mon, 09 Oct 2000 09:53:38 -0400
- Organization: Foster-Miller, Inc.
- References: <3.0.5.32.20000929182911.00881400@sun.isec.pt> <3.0.5.32.20001006164352.008e5220@sun.isec.pt> <39DE046F.E1F4051D@foster-miller.com> <200010061834.QAA19402@if.ufrj.br>

    Agnaldo Souza Pereira wrote:

    > I have also found some difference in calculating force
    > in axisymetric model: when calculating repulsion forces
    > between two cylindrical blocks, one, a superconductor in
    > mixed state, and the other, a NdFeB magnet, I've found
    > different results using FEMM and student's Quickfield.
    > I don't know how to explain this difference.
    >
    > Agnaldo.

    I think that Quickfield correctly implements the integral for Maxwell's
    stress tensor, but only a rather limited number of node points are allowed
    in the student version (between 250 and 500, depending on which version you
    are using). A lot of elements are generally required to get "good" force
    calculations. Lots of elements are required because you are integrating
    basically B^2 over a contour. Now, flux density B is an order less accurate
    than vector potential A, which is the quantity that's actually obtained in
    the finite element solution--B is basically the derivative (to be exact, the
    curl) of A. In computing force, squaring B exacerbates the problem by
    doubling the error again. The only way to decrease the error is to add more
    elements.

    If anyone is interested, I can post (in the e-group "files" section) the
    files that model an axisymmetric problem two cylindrical magnets acting upon
    one another. If the magnets are relatively far away from one another, there
    is a closed-form expression for force that one can derive by idealizing the
    magnets as simple dipoles. This analytical result can be used as a sanity
    check for numerical results. To test things out, I modeled 2 cylindrical
    magnets that were 0.5" long and 0.5" in diameter, with the faces of the
    magnets separated by 3". I assumed that the magnets had unit relative
    permeability and a Hc of 10^6 A/m. The results for force were:

    Force from analytical expression derived from a dipole approximation:
    0.02486 N
    Force from femm 3.0 using a mesh of about 6000 nodes: 0.02469 N
    Force from Amperes using a 1000 element mesh: 0.025067 N
    Force from Quickfield 3.4a using a 499 node mesh: 0.03883 N

    Now, both the femm and amperes solutions are within 1% of the analytical
    solution, whereas the student quickfield solution comes in about 56% high.
    Again, I'd guess that the difference arises solely from coarser the mesh
    density in the quickfield solution.

    At any rate a good way to get an idea of how many digits you can believe in
    either a femm or quickfield force computation is to integrate the stress on
    different contours around the part that you are interested in. In an exact
    solution, the results should be identical. However, the results from a
    finite element solution, which is only approximate, will be slightly
    different. The differences between contours give you an idea of the order
    of the error in the calculations.

    Dave.

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    tel;fax:781-890-3489
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    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.
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- Follow-Ups:
  - Re: [femm] Force calculation on an axisymmetric model
    - From: Agnaldo Souza Pereira <agnaldo@if.ufrj.br>

- References:
  - Force calculation on an axisymmetric model
    - From: Paulo José Gameiro Pereirinha <ppereiri@sun.isec.pt>
  - Re: [femm] Re: Force calculation on an axisymmetric model
    - From: Paulo José Gameiro Pereirinha <ppereiri@sun.isec.pt>
  - Re: [femm] Re: Force calculation on an axisymmetric model
    - From: David Meeker <dmeeker@foster-miller.com>
  - Re: [femm] Re: Force calculation on an axisymmetric model
    - From: Agnaldo Souza Pereira <agnaldo@if.ufrj.br>

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