Theoretical hob length for enveloping gear profile

The analysis and calculation of the cutting edge length of hob is not important for the gear with medium and small modulus, so it covers up the essential problem that hob must have a certain cutting edge length; for some special cases, such as processing a large number of teeth or a large spiral angle gear, the cutting edge length of hob is required to be very long, especially for the large gear with super large displacement. As for the “particularity” of the hobbing of super large modified gears, some literatures have discussed it, but they have not analyzed it from the characteristics and structure of the hobbing process, so the formula of the actual length of the hob blade deduced is also approximate. The following discussion aims to give its accurate calculation formula.

The minimum theoretical length of gear hob should meet two basic requirements: it can completely envelope the tooth profile of gear; the edge tooth of hob should not be overloaded.

Because the meshing process of gear hobbing is essentially the meshing of cross axis helical gears, according to the geometric characteristics of involute helical gears meshing, the length of effective meshing lines on the left and right sides of hob in the direction of hob axis is 2lm, which is calculated as follows:

Where: α t is the end face pressure angle of hob involute basic worm, Tan α t = Tan α n / sin λ 0; Ra0 is the addendum circle radius of hob involute basic worm; β B0 is the base circle helix angle of hob involute basic worm, sin β B0 = cos λ 0cos α n; R0 is the base circle of hob involute basic worm.