Optimal choice of the shaft angle for involute gear hobbing

With reference to the machining of an involute spur or helical gear by the hobbing process, this paper suggests a new criterion for selecting the position of the hob axis relative to the gear axis. By adhering to the proposed criterion, the hob axis is set at the minimum distance from the gear axis, thus maximizing the depth of the tooth spaces of the gear. The new criterion is operatively implemented by solving a univariate equation, which stems from a new, synthetic analysis of the meshing of crossed-axis, involute gears. A numerical example shows application of the suggested procedure to a case study and compares the optimal hob setting to the customary one.