How Do You Calculate Torque in a Gearbox-Flywheel System?

[LDC1972]

Homework Statement

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)

Homework 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

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!

 

[KataKoniK]

Thank you for your question. I would like to provide some feedback and suggestions for your solution.

Firstly, your calculation for the output torque (To) is correct. However, I would suggest using the units of rad/s^2 for angular acceleration instead of rad/s, as it is a measure of change in angular velocity over time. This will not change the final answer, but it is important to use the correct units in scientific calculations.

Next, your calculation for the input torque (Ti) is also correct. However, I would suggest not adding 8% to Ti to account for the gearbox efficiency. Instead, you should use the equation Ti = To/Wo, where Wo is the angular velocity of the output shaft. This will give you the correct input torque without having to account for the efficiency separately.

For the holding torque (Th), you are correct in using the equation Ti + Th + To = 0. However, you should also include the gearbox efficiency in this equation, as it will affect the input and output torques. The correct equation would be ToWo + 0.92TiWi + ThWh = 0.

I hope this helps and good luck with your calculations!
Scientist