Output power (torque-rotation) equivalent inertia

[Adriano Marcato]

Homework Statement

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

Homework Equations

T = I*ω
E_K = (I*ω²)/2
P=T*ω
ω₂*r₁ = ω₂*r₂

The Attempt at a Solution

By means of equivalent kinetic energy, I've come to the following expression:
I_eq = I₁ + I₂*r₁/r₂ + T₂*ω₁/(ω₂)²
I've been trying to eliminate the rotational speed in the last term.

 

[scottdave]

Torque = I*alpha {angular accel} not I*ω {angluar velocity}

 

[Adriano Marcato]

Oh! indeed, I am sorry for the mistake. I meant to include a point above.
Please consider
Formula: T = I*α
Attempt at solution: I_eq = I₁ + I₂*r₁/r₂ + T₂*α₁/(α₂)²
Try to cancel the alphas on the last term.