# Coupled gearbox flywheel

1. Nov 23, 2013

### LDC1972

1. The problem statement, all variables and given/known data

Gearbox coupled to a flywheel. The gearbox I 92% efficient and the output shaft rotates at 5 x the speed of the input.
Flywheel mass is 50kg, 0.75 m radius and is to accelerate from 0 to 300 rpm in 60 seconds.

Calculate Input torque and holding torque (value and direction)

2. Relevant equations

rpm x 2∏ / 60 = 31.41592654 rad s
angular acceleration = w2 - w1 / time = w2 / time = 31.41592654 / 60
angular acceleration = 0.5235987756 rad s
I = mk^2 = 0.5mr^2
r = 0.75m
m = 50kg
Moment of inertia (I) ∴ = 0.5 x 50 x .75^2 = 14.0625

3. The attempt at a solution

Torque applied to the flywheel to accelerate = Ta = I x angular acceleration
Ta = 14.0625 x 0.5235987756 = To = 7.363 Nm which is output torque

Ti will be 5 x To as gearbox is stepping up 5 x, so:
Ti = 5 x To = 36.816 Nm

However gearbox is 92% efficient, so add 8% to Ti = 39.761 Nm

I haven't begun the hold down torque yet, but know Ti + Th + To = 0, so this shouldn't be too hard...... Although should I include the 92% efficiency, so ToWo + 0.92TiWi = 0?

Thanks everyone, I know it takes time to help people and I really do appreciate it!

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