Discuss the ernst-merchant theory and lee and shaffer theory of metal cutting.
Answers
Ernst and Merchant developed the first reasonable theory in metal cutting. This assumed that the shear angle would take up a value to make the work done in cutting a minimum.
For given cutting conditions,
The work done is proportional to Fc
An expression has been developed for Fc in terms of the shear angle
Then a value for the shear angle is found for which Fc is a minimum.
by algebra,
2Ф +Τ - =90⁰
where tau is the mean angle of friction between the chip and the tool and
tau = tan- 1 (F/Pn).
Lee and Shaffer found that the above equation could not used where tau = 45⁰ and the rake angle, alpha = 0 as these values give a shear angle, phi = 0.
The formation of a built up edge is formed when conditions of high friction and low rake angle
To meet this, second solution was given where a built up edge is present on the tool face.
On performing experiments, it is fount that no simple unique relationship can go with all experimental results.
The relevant flow stress is not easy to predict, therefore, it becomes difficult to predict forces.
Large shear strains (1 - 5 natural strain) across a narrow zone in a very short period of time mean that strain rates are very high, several 1000 s-1