Determine the minimum value for the radius ratio $\dfrac{R_2}{R_1}$ of a single plate clutch at which the capacity of clutch will decrease by not more than 10% during the initial wear period.

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written 7.8 years ago by

teamques10 ★ 64k

modified 2.2 years ago by

pedsangini276 • 4.7k

Mumbai University > MECH > Sem 5 > Theory Of Machines 2

Marks: 5 M

Year: Dec 2014

theory of machines

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written 7.8 years ago by

teamques10 ★ 64k

At uniform pressure:

$Tp = 2/3 μF(R2^3-R1^3)/(R2^2-R1^2)$

At uniform wear:

$Tw = ½ μ F (R1+R2)$

Given: Tw should not decrease more than 10% of Tp. Or Tw should be atleast 90% of Tp

$Tw = 0.9 Tp \\ ½ μ F (R1+R2) = 0.9x2/3 μF(R2^3-R1^3)/(R2^2-R1^2) \\ (R1+R2) = 1.2 (R2^3-R1^3)/(R2^2-R1^2) \\ Let \ \ R2/R1 = k \\ (1 +k) = 1.2 x (k^3 – 1)/(k^2-1) \\ K^2 + k^3 -1 –k = 1.2k^3 -1.2 \\ -K^2 +0.2 k^3 +k -0.2 = 0$

Solving the above equation we get

K = R2/R1 = 3.73

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The ratio of r2 /r1 should be less then "1"by solving on calculator we get ans 3.73 and 0.27 •••••therefore we preferred0.27

7.4 years ago by teamques10 ★ 64k

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