Geometry of Tooth Profile and Fillet of Face-Hobbed Spiral Bevel Gears

The determination of the geometry for the whole tooth profile, including the meshing profile and the tooth fillet, is important for tooth contact analysis and the mesh generation for FEM analysis of gear pairs. This paper presents a systematic approach for the determination of the complete tooth geometry of face-hobbed hypoid and spiral bevel gears. The detailed mathematical formulation for the generation of gear tooth surface and the equations for the tooth surface coordinates are provided in the paper. The surface coordinates and normal vectors are calculated at grid points selected based on the gear blank dimension. Using the machine tool settings as input, the computer model simulating the gear generation process precisely calculates the tooth geometry parameters on the selected grid. A numerical example is included in the paper to illustrate the presented approach.