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Output power (torque-rotation) equivalent inertia

  1. Jun 23, 2017 #1
    1. The problem statement, all variables and given/known data

    A lot of people are familiar with equivalent inertia problems, where you have a drive train and inertia on different axis and you calculate the equivalent inertia on whichever shaft you want. This time I (try to) bring something new, trying to associate the output power to the equivalent moment of inertia on the input.

    The system and the known information are shown bellow. Let's assume T1 is the driving torque and we want to get an equivalent inertia of the shafts AND the output torque T2
    upload_2017-6-23_9-56-31.png
    2. Relevant equations
    T = I*ω
    EK = (I*ω2)/2
    P=T*ω
    ω2*r1 = ω2*r2

    3. The attempt at a solution
    By means of equivalent kinetic energy, I've come to the following expression:
    Ieq = I1 + I2*r1/r2 + T21/(ω2)2
    I've been trying to eliminate the rotational speed in the last term.
     
  2. jcsd
  3. Jun 23, 2017 #2

    scottdave

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    Gold Member

    Torque = I*alpha {angular accel} not I*ω {angluar velocity}
     
  4. Jun 23, 2017 #3
    Oh! indeed, I am sorry for the mistake. I meant to include a point above.
    Please consider
    Formula: T = I*α
    Attempt at solution: Ieq = I1 + I2*r1/r2 + T21/(α2)2
    Try to cancel the alphas on the last term.
     
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