Question

In an orthogonal cutting, rake angle (\( \alpha \)) of the tool is 25° and friction angle (\( \lambda \)) is 27°. Using Merchant's shear angle relationship, the value of shear angle (\( \phi \)) is:

• A. 44°
• B. 61°
• C. 88°
• D. 90°

Hint:

Remember Merchant's shear angle relationship. Ensure you use the correct formula, as there are other variations based on different assumptions. The one used here is based on the minimum energy principle.

Answer 1

The Correct Option is A

Step 1: Recall Merchant's shear angle relationship.
Merchant's circle diagram and force analysis in orthogonal metal cutting led to a relationship between the shear angle (\( \phi \)), the rake angle (\( \alpha \)), and the friction angle (\( \lambda \)). One common form of Merchant's first solution (assuming minimum energy consumption) is given by: \[ \phi = 45^\circ + \frac{\alpha}{2} - \frac{\lambda}{2}. \] Step 2: Identify the given values.
Given:
Rake angle \( \alpha = 25^\circ \)
Friction angle \( \lambda = 27^\circ \)
Step 3: Substitute the given values into Merchant's shear angle relationship.
\[ \phi = 45^\circ + \frac{25^\circ}{2} - \frac{27^\circ}{2} \] Step 4: Calculate the shear angle \( \phi \).
\[ \phi = 45^\circ + 12.5^\circ - 13.5^\circ \] \[ \phi = 57.5^\circ - 13.5^\circ \] \[ \phi = 44^\circ \] The value of the shear angle (\( \phi \)) is 44°. Step 5: Select the correct answer.
The calculated shear angle is 44°, which corresponds to option 1.