Linkage model and interpolation analysis of helical non-circular gear hobbing

The design flexibility and transmission stability of the non-circular gears can be improved using the helical tooth scheme. Herein, a linkage model was derived for hobbing the helical non-circular gears based on the influence of the axial feed motion of the hob on the motion of the projecting rack on the gear-blank end face. This axial feed motion produces additional motion effects on the rotary axis of the gear-blank and the moving axis of the hob. Further, the accuracy of the linkage model was verified by kinematic simulations. The global convergence characteristics of the transcendental equation used for obtaining the polar angle of the pitch curve were ascertained to derive the interpolation calculation process for the linkage model-based electronic gearbox. The cause of cumulative error during the multi-turn hobbing process of the gear blank was analyzed. The error accumulation was effectively controlled by optimizing the interpolation algorithm. The hobbing experiments and meshing transmission test were conducted using the self-developed non-circular gear hobbing system to verify the effectiveness of the linkage model and interpolation algorithm. Graphic abstract