Computerized Modeling and Simulation of Spiral Bevel and Hypoid Gears Manufactured by Gleason Face Hobbing Process

The Gleason face hobbing process has been widely applied by the gear industry. But so far, few papers have been found regarding exact modeling and simulation of the tooth surface generations and tooth contact analysis (TCA) of face hobbed spiral bevel and hypoid gear sets. This paper presents the generalized theory of the face hobbing generation method, mathematic models of tooth surface generations, and the simulation of meshing of face hobbed spiral bevel and hypoid gears. The face hobbing indexing motion is described and visualized. A generalized description of the cutting blades is introduced by considering four sections of the blade edge geometry. A kinematical model is developed and analyzed by breaking down the machine tool settings and the relative motions of the machine elemental units and applying coordinate transformations of the elemental motions. The developed face hobbing generation model is directly related to a physical bevel gear generator. A generalized and enhanced TCA algorithm is proposed. The face hobbing process has two categories, non-generated (Formate®) and generated methods, applied to the tooth surface generation of the gear. In both categories, the pinion is always finished with the generated method. The developed tooth surface generation model covers both categories with left-hand and right-hand members. Based upon the developed theory, an advanced tooth surface generation and TCA program is developed and integrated into Gleason $CAGE™$for Windows Software. Two numerical examples are provided to illustrate the implementation of the developed mathematic models.