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To attain an anti-twist helical gear tooth flank with longitudinal tooth crowning, a novel additional rotation angle is proposed for the work gear during its hobbing process. A congruous nonlinear function with two variables is proposed and supplemented to this additional rotation angle of work gear. Two numeral examples are presented to illustrate the effects of coefficients of the proposed nonlinear function on the twist and evenness of generated helical gear tooth flanks. The twist of the crowned helical tooth flank is reduced significantly by applying the proposed longitudinal crowning gear method.

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In the gear finish hobbing process, to obtain a twist-free tooth flank of helical gears, a novel hobbing method for longitudinal crowning is proposed by applying a new hob’s diagonal feed motion with a dual-lead hob cutter. Wherein the hob’s diagonal feed motion is set as a second order function of hob’s traverse movement and tooth profile of hob cutter is modified in a dual-lead form with pressure angle changed in it’s longitudinal direction. The proposed method is verified by using two computer simulation examples to compare topographies of the crowned work gear surfaces hobbed by the standard and dual-lead rack cutters. The results reveal the superiority of the proposed novel finish hobbing method.