In an orthogonal cutting operation, the tool has a rake angle = 15°. The chip thickness before the cut = 0.30 mm and the cut yields a deformed chip thickness = 0.65 mm. Calculate (a) the shear plane angle and (b) the shear strain for the operation.

(a) The shear plane angle is: ∅=26. 86°

(b) the shear strain for the operation is: γ = 2.155234

Explanation:

In orthogonal cutting, the wedge-shaped tool used in the cutting edge is perpendicular to the direction of motion.

(a) The shear plane angle is:

shear plane angle is the angle between  shear plane and the cutting velocity in orthogonal cutting.

r= t ÷ t

Where, t= Initial thickness before the cut

            t= deformed thickness

            r = cutting ratio, which signifies the ratio of chip thickness of metal before cutting to the thickness after cutting.

r = 0.30 mm ÷ 0.65 mm

= 0.461538

∅ =  tan∧ ( 0.461538 cos 15  ÷ ( 1 -  0.461538 sin 15) )

= tan∧ (0.506289)

∅=26. 86°

(b) the shear strain for the operation is:

Shear strain is the stress tangent of an angle, that acts parallel to a material cross section.

γ = cot 26.86 + tan (26.86 - 15)

=1.974523 + 0.210004

γ = 2.155234

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