A single plate clutch, effective on both sides is required to transmit 25 kW at 3000 rpm. Determine the outer and inner radii of frictional surface if the coefficient of friction is 0.255, the ratio of radii is 1.25 and maximum pressure is not to exceed $0.1 ⅹ106 N/m^2$. Also determine the axial thrust to be provided by strings. Assume uniform wear.

Mumbai University > Mechanical Engineering > Sem 5 > Theory of Machines-II

Marks: 10 Marks

Year: May 2016

$P = 25KW = 25 × 10^3W \\ N = 3000 rpm \\ µ = 0.255 \\ R1/R2 = 1.25 or, R1/1.25 = R2 \\ P_{\max}= 0.1 × 10^6 N/m^2$

To find:

1. R1/R2
2. Axial thrust/Load

$ω_1=\dfrac{2πw}{60}= \dfrac{2 ×π×3000}{60}=314.15 rad/sec \\ P_{\max} = \dfrac{c}{R_2} \\ C = 0.1 × 10^6×R2 \\ C = 0.1 × 10^6× \dfrac{R1}{1.25} \\ C = 80,000R1 \\ P = \dfrac{2πNT}{60}= \dfrac{2×π×2000×T}{60} \\ T =\dfrac{ 25 × 10^3×60}{2 × π ×3000} \\ T = 79.57 N-m \\ T = ½ × nµw(R1+R2) \\ = ½ × 2 × 0.255 × w (R1+0.8R1) \\ = 0.255 × w [1.8R1] \\ W = 2πC(R1 – R2) \\ = 2 × π × 80,000 [R1 – 0.8R1] × R1 \\ W = 100530.96 R12 \\ T = 0.255 × 100530.96 × [1.8 × R1] ×R1^2 \\ T = 46143.7129 R1^3 \\ 79.57 = 46143.7129 × R1^3 \\ 1.724 × 10^{-3}= R1^3 \\ R1 = 0.1199m \\ =119.91mm \\ R1 = 120mm \\ R2 = R1/1.25 = 96mm$