2.4 Cutting Theories

Experimentally it has been found that the shear angle and hence the cutting ratio, depend upon the workpiece and tool material and the cutting conditions. Several attempts have been made to establish a theoretical law which predicts the shear angle.

Ernst and Merchant developed the first reasonable theory. 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 F_c, an expression has been developed for F_c in terms of the shear angle and then a value for the shear angle found for which F_c is a minimum.

After some algebra this gives:

where tau is the mean angle of friction between the chip and the tool and

This was later developed and other researchers have developed other expressions.

Lee and Shaffer realised that the above equation could not apply where tau = 45^o and the rake angle, alpha = 0 as these values give a shear angle, phi = 0. They considered that such conditions of high friction and low rake angle are just the conditions that lead to the formation of a built up edge. To meet this a second solution was presented where a built up edge is present on the tool face.

Experimental results show that no simple unique relationship can agree with all experimental results.

It is difficult to predict forces because the relevant flow stress is not easy to predict.

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