GATE 2021 ME (ME1) – Question 48
An orthogonal cutting operation is performed using a single point cutting tool with a rake angle of 12° on a lathe. During turning, the cutting force and the friction force are 1000 N and 600 N, respectively. If the chip thickness and the uncut chip thickness during turning are 1.5 mm and 0.75 mm, respectively, then the shear force is _____ N (round off to two decimal places).
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Correct answer: 682.29 to 689.15
Explanation
Chip ratio r=0.5 gives $\tan\phi=r\cos\alpha/(1-r\sin\alpha)$, so φ≈28.626°. Tool-face force relation is $F=F_c\sin\alpha+F_t\cos\alpha$, giving Fₜ≈400.85 N.
Shear force is $F_s=F_c\cos\phi-F_t\sin\phi=\mathbf{685.72}$ N. The supplied 600 N is friction force, not thrust.