Question

In a disc-type axial clutch, the frictional contact takes place within an annular region with outer and inner diameters 250 mm and 50 mm respectively. An axial force $F_1$ is needed to transmit a torque by a new clutch. However, to transmit the same torque one needs an axial force $F_2$ when the clutch wears out. If contact pressure remains uniform during operation of a new clutch while the wear is assumed to be uniform for an old clutch and the coefficient of friction does not change, then the ratio $\frac{F_1}{F_2}$ is (round off to 2 decimal places)

• A. 0.871

Answer 1

The correct option is A 0.871
$T=\mu W\times R_m$

$T_{new}T=\mu W\times R_m$

$T_{new}=\mu \times W\times R_{new}$

$T_{new}=\mu \times W_{new}\times \frac{2(R_0^3-R_i^3)}{3R_0^2-R_i^2}$

$T_{old}=\mu \times W\times R_{old}$

$T_{new}=T_{old}$

$W_{new}\times \frac{2(R_0^3-R_i^3)}{3R_0^2-R_i^2}=W_{old}\times \frac{(R_0+R_i)}{2}$

$\frac{W_{new}}{W_{old}}=0.871$