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# Re: Torque calculation

- To: femm@yahoogroups.com
- Subject: Re: Torque calculation
- From: "vecerkaj" <vecerkaj@yahoo.com>
- Date: Thu, 09 May 2002 07:12:56 -0000
- In-reply-to: <3CD7E1B9.5070006@ieee.org>
- User-agent: eGroups-EW/0.82

    >
    > I think that these tiny motors typically have 3 discrete coils with
    the
    > conductors arranged like A+,A-,B+,B-,C+,C- going around the
    > circumference of the stator. The currents would be 120 degrees
    apart,
    > but the force that is produced is highly dependent on orientation
    of the
    > currents relative to the magnet. For the most torque, you want the
    > coils to create a field that is perpendicular to field produced by
    the
    > magnet. (Many of these tiny motors are actively controlled, so you
    can
    > really run them like this.)
    >
    > Anyhow, I've attached a model that does just that. For the instant
    > where the magnet's magnetization is pointed upwards, there should
    be no
    > current in the top coil and equal and opposite currents in the
    bottom
    > coil. The currents in the bottom coils are set to 8.66025 MA/m^2,
    which
    > are the instantaneous values that correspond to a 10 MA/m^2
    amplitude.
    > I just picked this current level off the top of my head--I don't
    know
    > what is the max that you can run in your machines. The maximum is
    > determined by thermal considerations. Due to favorable thermal
    scaling
    > properties, these tiny motors run current densities that would seem
    > astronomical in larger machines.
    >
    > Anyhow, for that particular position, I get a torque of 0.0015 N*m
    per
    > meter of length in the into-the-page direction. This should be the
    max.
    > torque for a 10 MA/m^2 current amplitude. This torque will scale
    > linearly with the stator current amplitude, so it is easy to
    extrapolate
    > to other current levels. In this case, you can use either stress
    tensor
    > or the integral of "Lorentz torque" over the volume of the coils.
    For
    > this situation, the Lorentz torque one might be more accurate.
    >
    > The above analysis neglects eddy currents in the iron. The eddy
    > currents will reduce the torque some, but I'd guess that your iron
    is
    > thin enough that this would be a relatively small effect. But it
    still
    > might be interesting to get a handle on that. This could be done
    by
    > putting AC currents in the windings and replacing the magnetization
    of
    > the magnet with a thin "coil" region on the outside of the magnet.
    > Those "coils" would then carry AC currents. The problem would
    then be
    > analyzed at the speed at which the shaft is turning. The proper
    eddy
    > currents would then be induced in the stator.
    >
    > Dave.

    Hi

    I have just a note. Dave wrote, that torque will scale linearly with
    amplitude of stator current. It's correct, but only upto some value
    of stator current. After that linear torque-current characteristic
    starts to bend. (because of nonlinear material and armature
    interference)
    Practicaly: The characteristic starts to bend from about 1-2
    standstill current for commercial permanent magnet motors rated to
    few Nm. For example the motor needs for torque=3 * standstill torque
    the curent=4 * standstill current. (a motor suplied by converter with
    vector control). (Of course exact value depends on construction of
    the motor).
    I advice you to calculate at least few points of the characteristic
    (diferent current densities) and you will see, whether you should
    consider the bending of characteristic or not.
    Note 2:
    About calculation of torque: if the stator winding is embedded in
    slots (but it is not your case), you can't use Lorentz calculation of
    torque. If you change the geometry to embedded variant, you should
    use torque calculation by stress tensor.

    Jiri Vecerka

- References:
  - Re: [femm] Torque calculation
    - From: David Meeker <dmeeker@ieee.org>

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