The Merchantʹs model of orthogonal cutting revisited: A new insight into the modeling of chip formation

The Merchantʹs model, as the most famous approach of orthogonal cutting, is widely used in introductive courses on machining. However, the shear angle predicted by the Merchantʹs model from the criterion of minimization of the cutting energy, does not generally agree with experimental data and numerical simulations. The aim of this paper is to elucidate the theoretical reason for which the Merchantʹs model fails to predict the correct orientation of the primary shear zone. It is shown that the principle of minimum of the cutting energy must be supplemented by a stability criterion of the chip morphology. A modified Merchantʹs formula is then obtained for the value of the shear angle.