In an orthogonal cutting operation, the tool has a rake angle = 12°. the chip thickness before the cut = 0.32 mm and the cut yields a deformed chip thickness = 0.65 mm. calculate: a-the shear plane angle. b-the shear strain for the operation.

The shear plane angle and shear strain are 28.21° and 2.155 respectively.

Explanation:

(a)

Orthogonal cutting is the cutting process in which cutting direction or cutting velocity is perpendicular to the cutting edge of the part surface.  

Given:  

Rake angle is 12°.  

Chip thickness before cut is 0.32 mm.

Chip thickness is 0.65 mm.  

Calculation:  

Step1  

Chip reduction ratio is calculated as follows:  

r = 0.4923

Step2  

Shear angle is calculated as follows:  

Here, is shear plane angle, r is chip reduction ratio and is rake angle.  

Substitute all the values in the above equation as follows:  

Thus, the shear plane angle is 28.21°.

(b)

Step3

Shears train is calculated as follows:

.

Thus, the shear strain rate is 2.155.