When metal is cut in a two dimensional cutting operation the total energy will be consumed in the following ways:

1] As shear energy per unit volume Es on the shear plane.

2] As friction energy per unit volume Ef on the tool face.

3] As surface energy per unit volume required for the formation of new surface area.

4] As kinetic energy per unit volume required to accelerate the chip.

5] As chip curl energy Ec per unit volume required to curl the otherwise straight chip.

It is observed that, in a typical cutting operation En and Em almost negligible which Ec is less than 5 percent. Therefore, the total energy per unit volume is assumed to be made up only of Es and Ef.

$\therefore E=$ Total Energy $=E_{s}+E_{f}$

Between the two, Es is about 75 of the total energy. The values of Es and Ef can be calculated from the following relationships.

$E_{s}=\frac{F_{s} \cdot V_{s}}{b . t . V}=\frac{F_{s} \cdot c o s \gamma}{A_{s} \cdot \sin \emptyset . \cos (\emptyset-\gamma)}=\tau . \epsilon$

$E_{f}=\frac{F_{s} \cdot V_{F}}{b \cdot t \cdot V}=\frac{F_{s} \cdot r_{c}}{b \cdot t}$