High-order tooth flank correction for a helical gear on a six-axis CNC hob machine

•A correction methodology to hob twist-free helical gear on a CNC hobbing machine is proposed.•The hob should be shifted diagonally in hobbing process and with a profile crowned tooth.•Anti-twist longitudinal crowned tooth flank can be hob by modifying the hob tooth thickness and hob tangential feed.•This correction method is flexible by adjusting 2-axis movement formulated as six-degree polynomials.•This methodology is applied to hob gear with double-crown tooth effectively.

The increasing demand for low noise and high strength leads to higher quality requirements in manufacturing modified helical gears. Hobbing is the most widely employed cutting method for producing helical gear owing to its efficiency and economy. In this paper, we propose a general gear mathematical model simulating the generation process of a 6-axis CNC hobbing machine. The universal motion concept has been implemented on the CNC hob machine. Each axis of the hobbing machine is formulated as a high-order polynomial function with two variables, and the sensitivity of the polynomial coefficient is derived based on the topographic normal deviation on the gear tooth flank. The sensitivity of the changes of tooth flank form geometry to the changes of universal motion coefficients is investigated. The corrective universal motion coefficients are determined through an optimization process with the target of minimization of the tooth flank form errors. The hobbed tooth flank can be approximated to the given tooth flank by adjusting the coefficients of the polynomials based on their sensitivity. We demonstrate the validity of this flank correction method numerically using a helical gear made by the six-axis CNC gear profile grinding machine.