Understanding the unfolding of friction between the tool and the generated chip is of fundamental importance to nanometric machining processes. To this end, this paper investigates the influence of tool geometry, lattice orientation, machining velocity and machined thickness on the resistance encountered by a diamond tool during orthogonal cutting of a copper substrate. A salient result of our molecular dynamics simulations is that the degree of adhesion at the tool-chip interface is a key contributor to friction. Adhesion can be reinforced by varying the tool rake angle and by choosing specific lattice orientations that yield commensurate contact at the interface. On the other hand, we show that increasing the machining velocity reduces frictional forces due to thermal softening. Furthermore, increasing the machined thickness decreases the relative contribution of adhesive forces and thus lowers overall friction.