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Energy Conversion

  1. May 6, 2017 #1
    1. The problem statement, all variables and given/known data
    7064311f1e.jpg

    2. Relevant equations


    3. The attempt at a solution
    b98bd4d11b.png

    I'm quite new to these chapters and I can't seem to get my head around the theory and especially this question. That's the solution above. Where does the T_max = 1/8... equation come from? I understand that the mechanical work done in this system is the torque. And the derivative of work is power. I'm quite confused
     
  2. jcsd
  3. May 11, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
  4. May 12, 2017 #3

    rude man

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    I got an answer by:
    computing difference in stored magnetic energy as i/2/2 x (Lmax - Lmin))
    and equating it to work done by torque over 90 degrees of rotor angle.
    To compute i I used v = iωL.
    I used the average value of L over the 90 degrees.
    I can't really justify using averaged L, nor why the result should give max. torque rather than averaged. But maybe you can use this as a guide. My answer was 12.5% high.

    (Were you given some kind of formula relating max. torque to Φmax and delta reluctance? You could compute Φmax from v = N dΦ/dt = ωNΦ. Realize that all these formulas are approximations).
     
  5. May 13, 2017 #4

    rude man

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    I think the 1/8 factor is some kind of average number pulled out of the air by your professor.

    It can be fairly accurately computed that
    0π/2 T(θ)dθ = N2Φ2max(1/L1 - 1/L2)
    = Φ2max(R1 - R2)
    where R is reluctance and T is torque;
    but the question is how to apportion T(θ) between θ=0 and θ=π/2. Depending on how you do I imagine the factor 1/8 could be conjured up.
     
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