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GATE 2019 ME (ME1) – Question 45

Machining and Machine Tool Operations · Mechanics of machining · 2 marks · Multiple choice

In orthogonal turning of a cylindrical tube of wall thickness 5 mm, axial and tangential cutting forces are 1259 N and 1601 N. Measured chip thickness is 0.3 mm, rake angle 10°, axial feed 100 mm/min and spindle speed 1000 rpm. Assuming perfectly plastic material and Merchant’s first solution, find the closest shear strength.

  1. 722 MPa
  2. 920 MPa
  3. 200 MPa
  4. 875 MPa

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Correct answer: (A) 722 MPa

Explanation

Uncut thickness is $t_1=100/1000=0.1$ mm, giving chip ratio $r=1/3$. From $\tan\phi=r\cos10^\circ/(1-r\sin10^\circ)$, $\phi\approx19.21^\circ$. Shear force is $F_s=1601\cos\phi-1259\sin\phi\approx1097$ N. Shear area is $5(0.1)/\sin\phi\approx1.52$ mm². Therefore shear strength is approximately **722 MPa, A**.