GATE 2022 ME (ME1) – Question 54
Under orthogonal cutting condition, a turning operation is carried out on a metallic workpiece at a cutting speed of 4 m/s. The orthogonal rake angle of the cutting tool is 5°. The uncut chip thickness and width of cut are 0.2 mm and 3 mm, respectively. In this turning operation, the resulting friction angle and shear angle are 45° and 25°, respectively. If the dynamic yield shear strength of the workpiece material under this cutting condition is 1000 MPa, then the cutting force is ______________ N (round off to one decimal place).
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Correct answer: 2560.53 to 2586.27
Explanation
The shear plane area is $A_s = \frac{wt}{\sin\phi} = \frac{3 \times 0.2}{\sin 25°} = 1.4197$ mm². The shear force is $F_s = \tau_sA_s = 1000 \times 1.4197 = 1419.7$ N. The resultant force is $R = \frac{F_s}{\cos(\phi + \beta - \alpha)} = \frac{1419.7}{\cos 65°} = 3359.3$ N. The cutting force is $F_c = R\cos(\beta - \alpha) = 3359.3 \times \cos 40° = 2573.4$ N.