Q.2 Prove Merchant's first solution for minimum work done is $2\phi + \beta$
- $\alpha = 90^\circ$ and Merchant's second solution is $2\phi + \beta - \alpha = Cm$
where $\phi$ is shear angle, $\beta$ is friction angle and $\alpha$ is rake angle.
In an orthogonal cutting operation on a material with shear yield
strength of 220 N/mm² the following data is observed:
Length of cut chip obtained from uncut chip length of 100 mm =
50 mm, rake angle of tool = 10, uncut chip thickness = 0.2 mm,
with of cut = 1.5 mm and coefficient of friction = 0.8. Determine
the shear plane angle, resultant force on the tool, cutting force
component of resultant force.
