Graphical method for profiling hob mill that generate cycloid worms

The hob mill for generating ordered curls of cycloid surface with non involute profiles may be profiled based on the fundamental theorems of surface enveloping - Olivier - as surface reciprocally enveloping with point like contact. In this paper, is proposed a methodology based on a complementary theorem of the surface enveloping in a graphical expression developed in a graphical design environment - CATIA. The graphical method presented in this paper is developed in two stages: determining of the rack gear model based on the solid model of the surface to be generated, using an original algorithm, following this, based on 3D modelling is determined the solid model of the primary peripheral surface of the hob mill. An application for a cycloid worm is presented - a central screw of helical pumps. In order to prove the quality of method, the analytical and graphical solutions are comparatively presented.