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# Re: [femm] Force and torque from stress tensor

- To: femm@yahoogroups.com
- Subject: Re: [femm] Force and torque from stress tensor
- From: David Meeker <dcm3c@earthlink.net>
- Date: Tue, 18 Dec 2001 00:23:34 -0500

    Alberto Perez wrote:

    > As you know I'm simulating an induction motor. Now I'm calculating
    torque and
    > force from stress tensor of two poles motor. I have calculated as
    Meeker says in
    > his manual and I have seen example of horsecore in femm web. To
    calculate Fmax,
    > I'm simulating in magnetostatic and I take 180º of the one pole
    airgap. I get the
    > following values: [...]

    > The forces calculate from femm and from me are similars but torques
    aren´t them.
    > I don?t understand torque from stress tensor, is this torque the
    torque max can I have
    > obtain? Can I calculate the max electromagnetic torque at
    magnetostatic? Or I have to
    > calculate with nominal frequency = 50Hz and starting current?
    >
    > What relations is between force and torque? I have high force but the
    torque is too low.
    >
    > Thank you in advance

    You can't really calculate the torque on an induction motor at DC. At
    DC, there's no torque (except, perhaps, for some cogging torque). What
    you can do instead is perform runs at a range of low frequencies. The
    frequencies correspond to the slip frequency, and the torque that you
    get out of the machine corresponds to what you'd get at synchronous
    speed (e.g. 50 Hz) minus that slip frequency. You'd have to run a
    range of frequencies to find out the max torque for a given current.
    The for a fixed current, the torque rises with increasing slip
    frequency, up to a frequency equal to 1/(rotor time constant). For
    higher slip frequencies, the torque decreases.

    There's not necessarily any correlation between the force result and the
    torque result. The force integral yields the net translational force on
    the rotor--this force doesn't tend to spin the rotor. In contrast, if F
    is the force dictated by the stress tensor at some point on your
    contour, the contribution of that point on the contour to the torque is
    computed by r X F, where r is a vector going from (0,0) to the point of
    interest, and the X represents the cross-product. When this quantity is
    integrated on a contour that runs all the way around the rotor, you get
    the total torque on the rotor. If you think about it, you can imagine
    cases where you can get a net translational force but no torque (e.g. in
    a magnetic bearing), or a torque without any net translational force
    (which is actually what one desires in a rotating machine).

    Dave Meeker

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