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).
Explanation
Shear area As=t1·w/sinφ=0.2×3/sin25°≈1.4198mm². Shear force Fs=τs×As≈1419.8N. Merchant's circle: Fc=Fs·cos(β−α)/cos(φ+β−α)=1419.8×cos40°/cos65°≈1419.8×1.8126≈2573.4N.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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