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