Question

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 45º 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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Answer :

Correct answer is 2573.40

shear strength, τs = 1000 MPa, cutting speed, V = 4 m/s

rake angle α = 5° , uncut chip thickness, t = 0.2 mm

width of cut w = 3 mm, friction angle β = 45°

shear angle ϕ = 25°

F c F s = R c o s ( β α ) R c o s ( ϕ + β α ) , F= τ s w t s i n   ϕ

cutting force Fc = τ s w t s i n   ϕ

Fc = 1000 x  1000 × 3   ×   0.2 sin   25 × cos ( 40 ) cos ( 65 )

Fc = 2573.40 N

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