Question

A clutch has outer and inner diameters 100 mm and 40 mm respectively. Assuming a uniform pressure of 2 MPa and coefficient of friction of liner material 0.4, the torque carrying capacity of the clutch is
1. 148 Nm
2. 196 Nm
3. 372 Nm
4. 490 Nm

Answer 1

Correct Answer - Option 2 : 196 Nm

Concept:

Total frictional force acting in a clutch:

\(F=2\pi\int_{r_i}^{r_o}pr\ dr\)

Total torque carrying capacityin a clutch:

\(T=2\pi μ\int_{r_i}^{r_o}pr^2\ dr\)

Assuming uniform pressure theory (p = constant)

\(F=\pi p(r_o^2\;-\;r_i^2)\)

\(T=\frac{2}{3}\pi μ p(r_o^3\;-\;r_i^3)\)

Calculation:

Given:

di = 40 mm ⇒ ri = 20 mm, do = 100 mm ⇒ ro = 50 mm, p = 2 MPa ⇒ 2 N/mm2 and μ = 0.4 

Using uniform pressure theory, torque carrying capacity of clutch is given by:

\(T=\frac{2}{3}\pi μ p(r_o^3\;-\;r_i^3)\)

\(T=\frac{2}{3}\pi \times\;0.4\times 2\;\times(50^3\;-\;20^3)\)

∴ T = 196035.381 Nmm ≈ 196 Nm.

Assuming Uniform wear theory (pr = constant)

\(F=2\pi pr_i(r_o\;-\;r_i)\)

\(T=\pi \mu pr_i(r_o^2\;-\;r_i^2)\)