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# coenergy vs. stress tensor calculations of magnetic force

- To: "Femm" <femm@yahoogroups.com>
- Subject: coenergy vs. stress tensor calculations of magnetic force
- From: "James Rabchuk" <ja-rabchuk@wiu.edu>
- Date: Thu, 30 Jan 2003 15:02:29 -0600
- Importance: Normal
- Reply-to: <JA-Rabchuk@wiu.edu>

    Hi, I've written before about making a simulation of a levitation device
    with diamagnetic materials in FEMM. I was interested in determing the
    equilibrium position of the levitating magnet by calculating the force for a
    number of positions between the diamagnetic plates.

    Following the advice of the FEMM manual, I used the coenergy method for
    calculating the field energy, and then looking for the force from that. But
    what I found was that the Coenergy displayed no observable trend with height
    of the magnet. On a lark, I tried the same simulation and calculated the
    Force from the stress tensor, using a fixed contour. Surprisingly, I got
    very believable results that showed the stable and unstable equilibrium
    points for the levitating magnet quite nicely. I was content with that, but
    I'm still intrigued why the coenergy method doesn't seem to be working in
    this case. We tried moving the outer boundary to increase the area for the
    problem. I tried increasing the mesh density in the region where the force
    on the magnet is being calculated. But none of those things seems to be able
    to get the coenergy method to provide meaningful results. I might be tempted
    to say that my stress tensor calculations are just misleading, but they
    mirror so nicely the behavior of the actual system that I find that hard to
    believe.

    Would anybody be willing to take a look at the simulation I've put together
    and make some suggestions as to where the coenergy calculation might be
    messing up, or where I could improve the model to get the "right" behavior?

    I've attached the femm file, the associated pre and post lua files, and an
    excel file with the coenergy numbers, and graphs of both the coenergy and
    stress tensor calculations of the force with height (gravity is included
    manually).

    If you look at the Excel file, you can't possibly discern a pattern of
    behavior from the coenergy graph, while the stress tensor graph is pretty
    good, though not as smooth as you might like.

    Any help would be appreciated.

    Thanks,
    Jim

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    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN class=3D833462320-30=
    012003>Hi,=20
    I've written before about making a simulation of a levitation device with=20
    diamagnetic materials in FEMM.&nbsp;I was&nbsp;interested in determing the=
    =20
    equilibrium position of the levitating magnet by calculating the force for =
    a=20
    number of&nbsp;positions between the diamagnetic=20
    plates.&nbsp;</SPAN></FONT></DIV>
    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
    class=3D833462320-30012003></SPAN></FONT>&nbsp;</DIV>
    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
    class=3D833462320-30012003>Following the advice of the FEMM manual,&nbsp;I =
    used=20
    the coenergy method for calculating the field energy, and then looking for =
    the=20
    force from that. But what I found was that the Coenergy displayed no observ=
    able=20
    trend with height of the magnet. On a lark, I tried the same simulation and=
    =20
    calculated the Force from the stress tensor, using a fixed contour.=20
    Surprisingly, I got very believable results that showed the stable and unst=
    able=20
    equilibrium points for the levitating magnet quite nicely. I was content wi=
    th=20
    that,&nbsp;but I'm still intrigued why the coenergy method doesn't seem to =
    be=20
    working in this case. We tried moving the outer boundary to increase the ar=
    ea=20
    for the problem. I tried increasing the mesh density in the region where th=
    e=20
    force on the magnet is being calculated. But none of those things seems to =
    be=20
    able to get the coenergy method to provide meaningful results. I might be=20
    tempted to say that my stress tensor calculations are just misleading, but =
    they=20
    mirror so nicely the behavior of the actual system that I find that hard to=
    =20
    believe. </SPAN></FONT></DIV>
    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
    class=3D833462320-30012003></SPAN></FONT>&nbsp;</DIV>
    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN class=3D833462320-30=
    012003>Would=20
    anybody be willing to take a look at the simulation I've put together and m=
    ake=20
    some suggestions as to where the coenergy calculation might be messing up, =
    or=20
    where I could improve the model to get the "right" behavior?</SPAN></FONT><=
    /DIV>
    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
    class=3D833462320-30012003></SPAN></FONT>&nbsp;</DIV>
    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN class=3D833462320-30=
    012003>I've=20
    attached the femm file, the associated pre and post lua files, and an excel=
    file=20
    with the coenergy numbers, and graphs of both the coenergy and stress tenso=
    r=20
    calculations of the force with height (gravity is included=20
    manually).</SPAN></FONT></DIV>
    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
    class=3D833462320-30012003></SPAN></FONT>&nbsp;</DIV>
    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN class=3D833462320-30=
    012003>If you=20
    look at the Excel file, you can't possibly discern a pattern of behavior fr=
    om=20
    the coenergy graph, while the stress tensor graph is pretty good, though no=
    t as=20
    smooth as you might like. </SPAN></FONT></DIV>
    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
    class=3D833462320-30012003></SPAN></FONT>&nbsp;</DIV>
    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN class=3D833462320-30=
    012003>Any=20
    help would be appreciated.</SPAN></FONT></DIV>
    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
    class=3D833462320-30012003></SPAN></FONT>&nbsp;</DIV>
    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
    class=3D833462320-30012003>Thanks,</SPAN></FONT></DIV>
    <DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN=20
    class=3D833462320-30012003>Jim</SPAN></FONT></DIV></BODY></HTML>

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    - From: David Meeker <dmeeker@ieee.org>
  - Re: [femm] coenergy vs. stress tensor calculations of magnetic force
    - From: "Ahmet Cansiz" <acansiz@atauni.edu.tr>

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