Parametric relationship between hypoid gear teeth and accurate face-milling cutter

The cutter systems of hypoid gear cutting machines contain groups of inside and outside blades. In these cutter systems, the side cutting edges of the blades machine the convex and concave gear teeth while rotating about the cutter rotation axis. The side cutting edges lay on the rake face formed through the blade, rake, and relief angles; hence, the normal cross-section of the cutter swept surface forms hyperboloid gear teeth. Using the accurate geometry of the cutter system, a relationship between the pressure and spiral angles of the gear tooth and the parameters of the cutter system is developed for the FORMAT machining of a hypoid gear. A new parameterization of the gear tooth surfaces is introduced to determine these angles for the accurate gear tooth by the accurate cutter system. A numerical example with different cutter systems and blade parameters is presented, demonstrating the effects of rake and relief angles over the pressure and spiral angles on mean point projections and gear tooth surface. Finally, the change in pressure and spiral angles with respect to the rake and relief angles are plotted, and the results are analyzed. Finally, it is concluded that the pressure and spiral angles are changed up to a few seconds of a degree in the operating area of the tooth with the change in the back and side rake angles. The side relief angle exhibited little or no effect over the geometry of the gear tooth.