A general mathematical model for gears cut by CNC hobbing machines

Abstract

A hobbing machine's cutting mechanism is a mechanism with multi-degree of freedom during the cutting process. In this paper, we propose a general gear mathematical model simulating the generation process of a 6-axis CNC hobbing machine based on the cutting mechanism of CNC hobbing machine and worm-type hob cutter. The proposed gear mathematical model can be applied to simulate different types of gear cutting. Some examples are included to verify the mathematical model. Also, a novel type of gear named ''Helipoid'' which can be used in crossed axes transmission is proposed. The proposed general gear mathematical model can facilitate a more thorough understanding of generation processes and toward the development of novel types of gears.