Mathematical model of face-milling spiral bevel gear with modified radial motion (MRM) correction

Conventional machine setting calculation for the cutting of face-milling spiral bevel and hypoid gears is based on the local synthesis at the mean point. The bias of contact path and motion curve are usually coupled with each other when applying commonly-used tooth flank corrections such as the helical motion, the modify roll method, and the cutter tilt. In this paper, we propose a method to determine the machine settings with modified radial motion (MRM) correction at specified contact point with predetermined motion curve and contact path bias on the pinion tooth surface. Parameters of MRM correction are calculated according to the equations of meshing and relationship between mating curvatures at the specified contact point. As shown by the numerical examples, the bias of contact pattern and the motion curve were controlled separately. The proposed methodology could be used to gain more control on the contact pattern and the motion characteristics.