A vectorization model to closed-form solution for cutting forces prediction during face-hobbing of hypoid gears

Abstract

Cutting forces cause machine tool vibration, deformation and tool wear during machining processes, due to the complexity of the generating kinematic relationship between the head cutter and hypoid gear, great challenges are brought to the prediction of cutting forces. This study focused on a vectorized closed-form solution to cutting force prediction for face-hobbing of hypoid gears. Based on a thorough investigation of the relationships between the series of tooth surface families machined by head cutter during the face-hobbing, a vectorization model for undeformed cutting chip geometry is established. A closed-form solution to cutting forces prediction of face-hobbing of hypoid gears is firstly presented by combining the oblique cutting theory and the established vectorized undeformed chip geometry model. Results shows that the formularized cutting forces prediction model are more accuracy and efficiency than the semi-analytical method. Thus, the proposed model will be suitable for analyzing mechanisms of chatter, and optimization of gear cutting systems.