Analytical and graphical modelling for generation of a non cylindrical helical surface using a pre-formed tool

Abstract

The issue of generating a non-cylindrical helical surface using pre-formed tools — tools bounded by a revolution cylindrical surface or a conical surface, is the main concern for profiling the active blades of centrifugal rotors or the surface called free form surfaces. In this paper is proposed an analytical approach, based on fundamental theorems of surface generating and, also, a graphical development in CATIA design environment. It is developed the analytic support, based on the principle of surface enwrapping (Olivier theorem), for profiling a helical surface with variable pitch (the blade of a centrifugal rotor) belonging to a revolution body
— conical surface with knows generatrix angle. The shape of crossing sections for generated surface is presented for a certain case.