# Homework Help: Flywheel and Gearbox Coupling Help

Tags:
1. Jan 8, 2016

### Mingsliced

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

I've been working my way through the following question but I am a little bit stuck at this part:

A gearbox and flywheel are as shown in FIGURE 4. The output shaft rotates in the opposite direction to the input shaft at 5 times its speed. The gearbox has an efficiency of 92%.

If the flywheel is solid, has a mass of 50 kg, a diameter of 1.5 m and is to accelerate from rest to 300 revs min–1 in 1 minute:

Calculate the magnitude and direction of the torque required to hold the gearbox stationary (holding torque Th).

2. Relevant equations

Input shaft rotating clockwise.
Output shaft rotating anti-clockwise.

Input Angular Velocity W1 = 0 RAD/s
Final Angular Velocity W2 = (300*2π)/60
Final Angular Velocity W2 = 31.42 RAD/s

Angular Acceleration α = (W2 - W1)/t
Angular Acceleration α = (31.42 - 0)/60
Angular Acceleration α = 0.52 RAD/s

Moment of inertia for solid disc I = 1/2*MR2
Moment of inertia for solid disc I = 0.5*50*0.752
Moment of inertia for solid disc I = 14.06 KG/m2

Torque of output shaft T2 = I*α
Torque of output shaft T2 = 14.06*0.52
Torque of output shaft T2 = 7.3Nm
Regarding gearbox efficiency T2 = (7.3/100)*92
Therefore T2 = 6.716Nm

Torque of input shaft T1 = T2 * 5
Torque of input shaft T1 = 6.716 * 5
Torque of input shaft T1 = 33.58Nm

3. The attempt at a solution

I'm struggling because a lot of the worked examples already have input or output power, which is what I need to calculate the holding torque TH. Could I calculate the output power using T2 * W2? Thus 6.716 * 31.42 = 211Kw and work backwards from there?

Cheers!

2. Jan 8, 2016

### CWatters

I haven't checked your arithmetic but you seem to be doing ok so far.

Take a look at your worked examples again. How do they get from input power to holding torque?

3. Jan 8, 2016

### Mingsliced

By using the angular velocity Wi: input power = Ti * Wi.

I'm guessing to get Wi that you divide the output speed by 5, so 300/5 = 60. Then convert to RAD/s to get 6.283 RAD/s.

Then placing that into input power formula: 33.58 * 6.283 = 210.98 Watts.

Is that correct?

4. Jan 8, 2016

### Mingsliced

Don't worry, I've figured it out. The above post is incorrect anyway. Thanks for the hint :)