Question

A disc clutch is required to transmit 5 kW at 2000 rpm. The disc has a friction lining with the coefficient of friction 0.25. The bore radius of the friction lining is 25 mm. Assume uniform contact pressure of 1 MPa. The value of outside radius of the friction lining in mm is:

1. 59.3
2. 39.4
3. 29.6
4. 49.5

Answer 1

Correct Answer - Option 2 : 39.4

Concept:

Uniform Pressure Theory	Uniform Wear Theory
p = constant	p × ri = constant
\({T_f} = \frac{{2\pi μ p}}{3}\left( {r_o^3 - r_i^3} \right)\)	\({T_f} = \pi μ p{r_i}\left( {r_o^2 - r_i^2} \right)\)

 

 

 

 

Power = ω × T_f

Calculation: 

Given:

Power (P) = 5 kW ⇒ 5 × 10³ W, N = 2000 rpm, μ = 0.25, r_i = 25 mm and p = 1 MPa ⇒ 1 N/mm²

Power = ω × Tf

\(P = \frac{2\pi{N}}{60}× T_f\)

⇒ \(5 × 10^{3}=\frac{2\pi\;×\;{2000}}{60}× T_f\)

∴ T_f = 23.873 × 10³ N-mm.

For Uniform Pressure Theory, the Torque carrying capacity is given by - 

\({T_f} = \frac{{2\pi μ p}}{3}\left( {r_o^3 - r_i^3} \right)\)

⇒ \(23.873\;\times\;10^{3}=\frac{2\pi\;\times\;0.25\;\times\;1}{3}(r_o^{3}\;-\;25^3)\)

∴ r_o = 39.41 mm.