# Is there quantitative theory of cutting with edge or blade

I wonder if there is some simple theory of what determine efficiency ( speed, energy end force required ) of cutting by edge ( blade , knife, sword )

At least something phenomenological like in case of friction ( which I guess is very much related to cutting ) $F_F = \mu F_\perp$ (where $F_F$ is friction force, $\mu$ is friction coefficient which is tabulated for specific materials, and $F_\perp$ is normal force - the force you push the surfaces into each other )

Particular problems which should be solved by this theory:

• Given a material ( i.e. some coefficients) and total force $F_{tot}$ asserted on the knife, what should be the optimal tilt angle $\alpha$ relative to surface normal to achieve most efficient cutting. $\alpha$ determine decomposition of $F_{tot}$ into components perpendicular $F_\perp = \cos(\alpha) F_{tot}$ and parallel $F_\parallel = \sin(\alpha) F_{tot}$ to the surface.

• How it depends on bevel angle $\theta$ ( or possibly hardness of the tip and cut material )

To have some hint what such theory could be based on - in this video (8:41) is said that the blade actually works like microscopic saw. So, it would be probably quite straightforward to develop such theory having in mind a saw model with considering saw-tooth with particular tooth tip angle $\omega$ or some statistical distribution of such teeth

• $\mu$ can not be tabulated, as it is also a properties of the surface topology, and the sword definition. Furthermore, I think to know from experience the optimal cutting angle also depends on the size of the object to be cut. – Bernhard May 11 '14 at 12:09