Comparative Analytical Solutions to the Problem of Profiling the End Mill Cutter to Generate Helical Surfaces

Abstract

In this paper, we present, comparatively, two analytical methods for profiling the tools delimited by revolution surfaces, used to generate helical surfaces with constant pitch. The first method lays on a complementary theorem used for tools profiling, namely the Minimum distance theorem. A specific algorithm for applying it has been developed, in order to profile the tools delimited by revolution surfaces, which generates helical surfaces with constant pitch by enwrapping. The methodic is referring, here, to a tool whose symmetry axis is incident and, at the same time, normal to the helical surface axis – the end mill cutter. The other analytical method here applied grounds on Nikolaev classical theorem. We also present an example of application for both methods, in the case of profiling the end mill cutter used to generate a helicoid with circular frontal generatrix. The tool axial sections are determined and compared in a numerical representation.