Slip-line modeling of machining with a rounded-edge tool—Part I: new model and theory

The effect of tool edge roundness attracts growing attention from the international machining research community due to ever accelerating applications of precision, super-precision, micro-, and nano-machining technologies in a wide variety of modern industries. A new slip-line model for machining with a rounded-edge tool and its associated hodograph are proposed in this paper. The model consists of 27 slip-line sub-regions, each sub-region having its own physical meaning. It is demonstrated that the model simultaneously takes into account nine effects, such as the shear-zone effect and the size effect, which commonly occur in machining. Eight groups of machining parameters, such as the ploughing (parasitic or non-cutting) force and the chip up-curl radius, can be simultaneously predicted from the model. Furthermore, the model incorporates eight slip-line models previously developed for machining during the last six decades as special cases. An additional special case that involves a parallel-sided shear zone can also be derived from the new model. A mathematical formulation of the model is established based on Dewhurst and Collins's (1973) matrix technique for numerically solving slip-line problems. A purely analytical equation is proposed to predict the thickness of the primary shear zone. This equation is also employed to predict the shear strain-rate in the primary shear zone.