In the metal cutting operation, what will be the shear angle when a cutting tool has positive rake angle α = 20°. The friction angle is 40°. (Use Merchant's shear angle theory)

Concept:

Merchant's Criteria:

For a given workpiece material machining with a given tool under a given condition of machining, the work done during the machining is mainly depends on the shear angle.

The relation between various angles is given by:

2ϕ + β - α = 90°

This is called as optimum shear angle relation for minimum energy or minimum work done or minimum force are also called as Merchant's criteria.

Calculation:

Given:

α = 20°, β = 40° , ϕ =?

Now, we have

2ϕ + β - α = 90°

2ϕ + 40° - 20° = 90°

∴ ϕ = 35° 

Lee and Shaffer Criteria:

The Lee and Shaffer shear angle relation for minimum energy criteria of machining is given by

ϕ + β - α = 45° 

Stabler's Criteria:

Stabler's shear angle relation is given by

ϕ + β - α /2 = 45°