About Hob Idle Distance in Gear Hobbing Operation

This study is focused on some features of geometry and kinematics of gear hobbing operation. The principal goal is to determine minimal hob idle distance required for complete generation of the gear teeth. This task is of importance in two aspects: to cut hobbing time and to reduce axial size of a hobbed cluster gear, gear with shoulder etc. The necessity of cutting hobbing time is evident. Reduction of axial size of a hobbed gear cluster leads to reduction of size and weight of the gear cluster itself and of the gear train housing, and therefore its necessity is also evident. Methods of analytical mechanics of gear are applied to determine an exact minimal length of the gear hob idle distance. The resultant formulas obtained have been derived based on graphical solution of the problem under consideration using methods of descriptive geometry. The results reported in the paper are applicable for manufacturing of spur and helical involute gears. Their application allows one to cut hobbing time and to reduce axial size and weight of gear train and gear train housing. Although the consideration below is focused on hobbing of involute gears, slightly modified results obtained are applicable for hobbing of spline, sprockets, ratchets, and other form tooth profiles. The results obtained are of prime importance for application of multi-start hobs of small diameter.