Project ForgeA single-plate clutch has a friction disc with inner and outer radii of 20 mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction μ varies radially as μ=0.01r, where r is in mm. The clutch needs to transmit a friction torque of 18.85 kN·mm. As per uniform pressure theory, the pressure (in MPa) on the disc is __________.
Explanation
For uniform pressure p, torque T = ∫(r1 to r2) μ(r)·p·r·(2πr dr) = 2πp·0.01·∫r³dr from 20 to 40 = 2πp×0.01×[(40⁴−20⁴)/4] = 2πp×0.01×600000 ≈ 37699p (N·mm, p in MPa). Setting T=18850 N·mm: p = 18850/37699 ≈ 0.5 MPa.
Source: GATE ME 2017 Session 2 (ME-2) (2017)
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