If there are n_{1} discs on the driving shaft and n_{2} discs on the driven shaft in a multi-plate clutch, then the number of pairs of contact surface is

This question was previously asked in

UPPSC AE Mechanical 2019 Official Paper I (Held on 13 Dec 2020)

Option 2 : n_{1} + n_{2} - 1

__Explanation:__

**Multiple disc clutch:**

- A multiple-disc clutch, used when a large torque is to be transmitted.
- The inside discs usually made of steel are fastened to the driven shaft to permit axial motion except for the last disc.
- The outside discs usually made of bronze are held by bolts and are fastened to the housing which is keyed to the driving shaft.
- The multiple disc clutches are extensively used in motor cars, machine tools etc.

Number of disks = number of pairs of contacting surface + 1

**∴ Number of pairs of contacting surface = Number of disks - 1 **

**Number of pairs of contact surfaces, n = n _{1} + n_{2} – 1**

where n1 = Number of discs on the driving shaft, n2 = Number of discs on the driven shaft.

__Additional Information__

Total friction torque acting on friction surfaces or on the clutches** T = nμWR**

where, μ = friction coefficient, W = axial force on the clutch

R = Mean radius of friction surfaces** **

For uniform wear criterion** \({\bf{R}} = \frac{{{{\bf{r}}_1} + {{\bf{r}}_{2\;}}}}{2}\)**

For uniform pressure criterion** **\({\bf{R}} = \;\frac{2}{3}\left[ {\frac{{{\bf{r}}_1^3 - {\bf{r}}_2^3}}{{{\bf{r}}_1^2 - {\bf{r}}_2^3}}} \right]\)