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Manufacturing Engineering
Machining Processes
GATE 2008
Hard

Orthogonal turning is performed on a cylindrical workpiece with shear strength 250 MPa. Cutting velocity is 180 m/min, feed is 0.20 mm/rev, depth of cut is 3 mm, chip thickness ratio=0.5. The orthogonal rake angle is 7°. Applying Merchant's theory, the shear plane angle (degrees) and the shear force respectively are

  • A52; 320 N
  • B52; 400 N
  • C28; 400 N
  • 28; 320 N

Explanation

tanφ=r·cosα/(1-r·sinα)=0.5cos7°/(1-0.5sin7°)≈0.5285, so φ≈27.8°≈28°. Shear-plane area As=(t1·w)/sinφ=(0.20×3)/sin27.8°≈1.285 mm². Shear force Fs=τs·As=250×1.285≈320 N.

Source: GATE ME 2008 (2008)

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