A CAD approach to helical groove machining—I. mathematical model and model solution

Abstract

The problem of helical groove machining in practice is still predominantly approached from an empirical trial and error standpoint. For the analytical resolution of this problem through a CAD approach, a generalized helical groove machining model, utilizing the principles of differential geometry and kinematics, has been formulated. The approach is based on the establishment of the fundamental analytical conditions of engagement between the generating tool surface and generated helical groove surface. The general mathematical relationships established facilitate the determination of the resulting tool or helical groove profile for a given helical groove or cutting tool profile, respectively.