GATE 2019 ME (ME2) – Question 64
Orthogonal cutting with a single-point tool of rake 10° produces uncut and chip thicknesses 0.125 and 0.22 mm. By Merchant’s first solution for minimum cutting force, find chip–tool friction coefficient, to two decimal places.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: .72 to .76
Explanation
Chip ratio is $r=0.125/0.22=0.568182$. From $\tan\phi=r\cos\alpha/(1-r\sin\alpha)$, $\phi\approx31.83^\circ$. Merchant’s relation gives $\beta=90^\circ+\alpha-2\phi\approx36.34^\circ$. Hence $\mu=\tan\beta=0.73554$, or **0.74**.