In a disc clutch, the inside and outside radii of the clutch plate are 50 and 100 mm, respectively. If the axial force exerted on the disc is 4 kN, the maximum pressure experienced by the clutch plate in N mm-2 under uniform wear conditions is
GATE AG - 2012,
Answer: C
The maximum pressure is about 0.25 N mm-2.
Under uniform wear the product of pressure and radius is constant, \(p\,r = C\), so the pressure is greatest at the inner radius. The axial force fixes C:
\[ \begin{aligned} F &= 2\pi C (r_{o} - r_{i}) \\ C &= \frac{4000}{2\pi(100 - 50)} = 12.73\ \text{N/mm} \\ p_{max} &= \frac{C}{r_{i}} = \frac{12.73}{50} = 0.255 \end{aligned} \]
0.17 is the uniform pressure answer, \(4000 / [\pi(100^{2} - 50^{2})] = 0.17\), which applies to a new clutch rather than a worn one. 0.13 is the uniform wear pressure at the outer radius (\(12.73/100\)), the minimum, not the maximum.
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