A clutch has to transmit 200 Nm of torque. Assuming uniform pressure theory and the ratio of outer to inner radii is 2.5, what are the radii for a uniform pressure of 2 MPa with the coefficient of friction of the liner material being 0.4?

Concept:

Transmitted torque \(T = \frac{2}{3}\mu W \left( {\frac{{R_o^3 - R_i^3}}{{R_o^2 - R_i^2}}} \right)\)

Pressure, \(P = \frac{W }{{\pi \left( {R_o^2 - R_i^2} \right)}}\)

From the above two expressions,

\(T = 2\mu \pi P\left( {\frac{{R_o^3 - R_i^3}}{3}} \right)\)

Where R_o is the outer radius

R_i is the inner radius

μ is the co-efficient of friction

Calculation:

Given that, T = 200 Nm, P = 2 Mpa, μ = 0.4

\(\frac{{{R_o}}}{{{R_i}}} = 2.5\)

\(T = 2\mu \pi PR_i^3\left( {\frac{{{{\left( {\frac{{{R_o}}}{{{R_i}}}} \right)}^3} - 1}}{3}} \right)\)

\( \Rightarrow 200 = 2\pi \times 0.4 \times 2 \times {10^6} \times R_i^3\left( {\frac{{{{2.5}^3} - 1}}{3}} \right)\)

⇒ R_i = 20.13 mm ≈ 20 mm

⇒ R_o = 2.5 × 20 = 50 mm