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Homework Help: Transfer function for a system with lossless gears

  1. Feb 24, 2015 #1
    1. The problem statement, all variables and given/known data

    I am trying to understand the impedance terms for the equivalent system in (b)

    2. Relevant equations
    T1/T2 = N2/N1

    3. The attempt at a solution
    I just don't understand why the impedance before the gears have to be multiplied by (N2/N1)^2 before they can be added to the impedance after the gear.
  2. jcsd
  3. Feb 25, 2015 #2
    What is being done here, is that the load is being referred to the gear's output side. Let's say you had an object of moment of inertia L (load) being rotated through a lossless gear system of ratio N2/N1. If you apply Torque T as input, output torque is scaled by the gear ratio. Now if I ask you to choose a different load which behaves just the way this gear + load combination does, what would the moment of inertia of the simplified load be. Try to analyse what the T vs α would come out as in the case with gears and then try to get the same result out of a simple load without the gears. Follow the same approach for the given (albeit more complex) load in your problem statement.
  4. Mar 2, 2015 #3
    Thanks very much!

    I also have a couple of questions for (b) of the following question
    which has the solution

    1) why isn't an angle defined for the rotation of J2

    2) for the fourth equation of motion (written for the second J=0), I can understand the theta 4 term but I don't understand the other term.
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