GATE 2018 ME (ME2) – Question 58
In orthogonal turning of a 100 mm diameter rod, rake angle is +15°, uncut chip thickness 0.5 mm and nominal chip thickness after cutting 1.25 mm. Find shear angle (degrees), to two decimal places.
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Correct answer: 22.00 to 24.00
Explanation
Chip ratio is $r=t_1/t_2=0.5/1.25=0.4$. Cutting kinematics gives $\tan\phi=r\cos\alpha/(1-r\sin\alpha)$. Thus $\phi=\tan^{-1}[0.4\cos15^\circ/(1-0.4\sin15^\circ)]=$ **23.32°**.