The complementary graphical method used for profiling side mill for generation of helical surface

This paper presents a method developed in CATIA design environment, for profiling tools bounded by revolution peripheral surfaces — side mill tool. The graphical method is based on a complementary theorem of surface enveloping. They are presented specific algorithms and an example for profiling generating tools of helical flutes of compressors rotors with three lobes. The obtained results with graphical method are compared with those obtained by a classical method — the Nikolaev theorem. The graphical method is very intuitive and, at the same time, very rigorous. It is characterized by the simplicity of application and avoids the ambiguity case of solutions, which are frequently met in numerical methods, as profiles overlapping, generating of revolving surfaces or rotating a spatial curve around the tool's axis. Other advantage of using graphical methods is that CNC machines tools, used for generating profiled tools, allows importing the files, which directly result from graphical modeling.