Question
Download Solution PDFMerchant’s machinability constant is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
The relation between various forces have been worked out by Merchant with a large number of assumptions as follows
- The chip behaves as a free body in stable equilibrium under the action of two equal opposite and collinear resultant forces.
- A continuous chip without a built-up edge is produced.
- The cutting velocity remains constant.
- The cutting tool has a sharp cutting edge and it does not make any flank contact with the workpiece Merchant suggested a compact and easiest way of representing the various forces inside a circle having the vector F as the diameter.
where, γ = Rake angle of the tool, ϕ = Shear angle, β = Friction angle of tool face
According to modified merchant theory relation between rake angle γ, shear angle ϕ, and friction angle β as shown below
- shear will take place in a direction in which energy required for shearing is minimum.
- shear stress is maximum at the shear plane and it remains constant.
we have proved that
Now Fs = fs × A2
where, Fs = Shear stress, A2 = Area of shear plane =
differentiate w.r.t β
In order that ϕ will assume that value which required a minimum force to cut the material.
\(cos\phi \cos \left( {\phi + \beta - \alpha } \right) - sin\phi \sin \left( {\phi + \beta - \alpha } \right) = 0\)
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