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Angle of twist

  1. Apr 10, 2016 #1
    1. The problem statement, all variables and given/known data
    Screen Shot 2016-04-11 at 10.06.51 am.png
    What is the angle of twist at gear A relative to the motor? (Round to the closest 6th decimal)
    2. Relevant equations
    I know to find the angle its θ = ∑ (TL/JG)
    but it can also be θ = Lτ/Gr

    3. The attempt at a solution
    So i used both these equations, and I got (-29.18*0.052)/(1.57x10^-8 * 83x10^9) = -1.163833x10^-3 rad, which was the same result for the other one too. However, this was wrong and I'm not sure what I am doing wrong?
     
    Last edited: Apr 10, 2016
  2. jcsd
  3. Apr 10, 2016 #2

    SteamKing

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    G = 83×109 Pa

    You should check your arithmetic. θ seems to be missing a couple of factors of 10.

    When you isolate gear A, you should draw a free body diagram to make sure you have the correct net torque acting at that location. I don't think you can say that the angle of twist is caused only by the torque acting from the left of the gear, and that the torque acting to the right has no effect.
     
  4. Apr 10, 2016 #3
    But the -29.18 is the internal torque between them, so doesn't that account for torque both sides of the gear
     
  5. Apr 10, 2016 #4

    SteamKing

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    If you do a check, that 29 N-m is the torque produced by the 11 kW motor operating at 60 Hz.

    Looking at the rest if the gears on this shaft, there are much greater torque loads being applied than this piddly 29 N-m, and these torques are turning in different directions.
     
  6. Apr 10, 2016 #5
    So would it be more like:
    (-29.18*0.052)/(1.57x10^-8 * 83x10^9) + (1100.82*0.092)/(J * 83x10^9) + (-249.18*0.111)/(J * 83x10^9) + (-779.18*0.138)/(J* 83x10^9)
     
  7. Apr 10, 2016 #6

    SteamKing

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    Something like that.

    You've already calculated J for the 20 mm dia. shaft. You need to calculate J for the 38 mm shaft.
     
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