A generic mathematical model of single point cutting tools in terms of grinding parameters

The paper presents the analytical geometric details of the mathematical modeling of a single point cutting tool with a generic profile. The grinding angles and the ground depths on the tool are allowed to vary along the tool flanks and face, altering the cutting angles from point to point. The surface modeling begins with the creation of a tool blank model. Then unbounded surfaces are considered and transformed to get the cutting tool surfaces. The intersection of these surfaces gives the complete model of the tool. Starting from the basic model where the tool face and flank are planar, the generalization of the geometric design has been done in two steps to give free-form shapes to the tool surfaces, termed as the two generations of the generic profile. Then a forward and inverse mapping has been presented for the basic model and the two generations of the generic tool to relate the grinding angles with the prevalent nomenclatures (ASA, ORS and NRS). The model has been validated and the variation of tool angles with the grinding parameters has been illustrated with an example.