GATE 2021 ME (ME2) – Question 50
In a pure orthogonal turning by a zero rake angle single point carbide cutting tool, the shear force has been computed to be 400 N. The cutting velocity, $V_c=100$ m/min, depth of cut, $t=2.0$ mm, feed, $S_o=0.1$ mm/revolution and chip velocity, $V_f=20$ m/min, the shear strength, $\tau$ of the material will be _____ MPa (round off to two decimal places).
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Correct answer: 390.27 to 394.19
Explanation
Continuity gives chip ratio r=Vchip/Vcut=0.2. At zero rake, tanφ=r, so φ=11.3099°. Uncut chip area is A₀=2×0.1=0.2 mm².
Shear-plane area is $A_s=A_0/\sin\phi=1.019804$ mm². Strength is $F_s/A_s=\mathbf{392.23}$ N/mm², equivalent to MPa.