Flywheel and Gearbox Coupling Help

[Mingsliced]

Homework Statement

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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).

Homework Equations

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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

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 T_H. Could I calculate the output power using T₂ * W₂? Thus 6.716 * 31.42 = 211Kw and work backwards from there?

Cheers!

 

[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?

 

[Mingsliced]

By using the angular velocity W_i: input power = T_i * W_i.

I'm guessing to get W_i 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?

 

[Mingsliced]

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