GATE 2020 ME (ME1) – Question 47
A disc-type axial clutch has annular contact with outer and inner diameters 250 and 50 mm. A new clutch needs axial force F₁ to transmit a torque; the worn clutch needs F₂ for the same torque. Assume uniform pressure for the new clutch, uniform wear for the old clutch and unchanged coefficient of friction. Find F₁/F₂, to two decimals.
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Correct answer: .85 to .89
Explanation
Torque is μFR. For uniform pressure, $R_p=(2/3)(r_o^3-r_i^3)/(r_o^2-r_i^2)=86.111$ mm. For uniform wear Rw=(125+25)/2=75 mm. Equal torque gives F1/F2=Rw/Rp=0.870968, or **0.87**.