Answer to Question #119133 in Mechanical Engineering for Hilal Nasser Nasser

Question

A multi-disc clutch has three discs on the driving shaft and two on the driven shaft. The inner diameter of the contact surface is 120 mm. The maximum pressure between the surface is limited to 0.1 N/mm2. Find the outer diameter for transmitting 25 kW at 1575 rpm. Assume uniform wear condition and coefficient of friction as 0.3.

Answer 1

For uniform wear $p\cdot r=C=const$ . Since

$p\cdot r_2=0.1\cdot120=12N/mm$

Axial force required to engage the clutch

$W=2\pi C(r_1-r_2)$

The torque transmitted

$T=4\cdot\mu W\frac{r_1+r_2}{2}=4\cdot \mu\cdot 2\pi C(r_1-r_2)\cdot\frac{r_1+r_2}{2}=4\cdot\mu\cdot \pi C(r_1-r_2)\cdot (r_1+r_2)$

Power transmitted

$P=T\cdot \omega=4\cdot\mu\cdot \pi C(r_1-r_2)\cdot (r_1+r_2)\cdot 2\pi \nu$ $\to$

$r_1=\sqrt{\frac{P}{8\mu\pi^2C\nu}+r_2^2}=\sqrt{\frac{25000}{8\cdot0.3\cdot3.14^2\cdot12000\cdot26.25}+0.12^2}=0.158m=158mm$ Answer.