A new friction clutch is subjected to 20kN axial load during operation, the average speed of shaft is 750 rpm. Central hole diameter is one-fourth of the outer diameter: Assume pressure 0.4 MN/m2 and μ = 0.015The power transmitted is __________ (kW)a) 2b) 3Correct answer is between ' 2, 3'. Can you explain this answer?

Question

Answer

To calculate the power transmitted by the friction clutch, we need to use the formula:

Power (P) = Torque (T) x Angular velocity (ω)

To find the torque, we need to know the force applied and the radius of the clutch. Since the central hole diameter is one-fourth of the outer diameter, the radius of the clutch can be calculated as follows:

Radius (r) = Outer diameter (D) / 2 = 2 x Central hole diameter (d)

Given that the axial load is 20kN, we can convert it to force by multiplying it by the acceleration due to gravity (9.81 m/s^2):

Force (F) = 20kN x 9.81 m/s^2

The angular velocity can be calculated by converting the average speed of the shaft from rpm to rad/s:

Angular velocity (ω) = (750 rpm) x (2π rad/1 min) x (1 min/60 s)

Now, we can calculate the torque:

Torque (T) = Force (F) x Radius (r)

Finally, we can calculate the power transmitted:

Power (P) = Torque (T) x Angular velocity (ω) / 1000 (to convert from Nm/s to kW)

Let's calculate the values step by step.

1. Radius (r):
The central hole diameter is one-fourth of the outer diameter, so the radius can be expressed as:

r = d/4

2. Force (F):
Given that the axial load is 20kN, we can calculate the force as:

F = 20kN x 9.81 m/s^2

3. Angular velocity (ω):
Given that the average speed of the shaft is 750 rpm, we can convert it to rad/s as:

ω = (750 rpm) x (2π rad/1 min) x (1 min/60 s)

4. Torque (T):
The torque can be calculated by multiplying the force and the radius:

T = F x r

5. Power (P):
Finally, we can calculate the power by multiplying the torque and the angular velocity, and then dividing by 1000:

P = T x ω / 1000

Now, let's plug in the values and calculate the power transmitted.

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