A single plate clutch is designed to transmit 10 kW power at angular v...
Given data:
- Power transmitted (P) = 10 kW
- Angular velocity (ω) = 200 rad/s
- Mass moment of inertia of input shaft (J
input) = 0.1 kg-m²
- Mass moment of inertia of output shaft (J
output) = 0.4 kg-m²
Calculating torque:
The power transmitted by the clutch can be calculated using the equation:
P = T * ω
Where T is the torque and ω is the angular velocity.
Rearranging the equation, we get:
T = P / ω
Plugging in the values, we have:
T = 10,000 / 200 = 50 Nm
Calculating angular acceleration:
The torque can be related to the angular acceleration (α) using the equation:
T = J * α
Where J is the moment of inertia and α is the angular acceleration.
Rearranging the equation, we get:
α = T / J
For the output shaft, the angular acceleration can be calculated as:
α
output = T / J
output = 50 / 0.4 = 125 rad/s²
Calculating time:
The angular velocity of the output shaft can be related to the angular acceleration and time (t) using the equation:
ω = α * t
Rearranging the equation, we get:
t = ω / α
For the output shaft, the time required to reach the rated speed from rest can be calculated as:
t
output = ω / α
output = 200 / 125 = 1.6 s
Conclusion:
The time required to bring the output shaft to the rated speed from rest is 1.6 seconds.