Investigation of the Tooth Geometry of a Hob for Machining of Involute Gears (in the Tool-in-Use Reference System)

This paper is aiming at development of an analytical approach for computation of the geometrical parameters of cutting edges of an involute hob. It is well recognized that the involute hob geometry strongly affects the cutting tool performance, as well as the efficiency of gear hobbing operation. It is proven experimentally and by industrial practice that the optimal value of every geometrical parameter of the tool cutting edge exists and, thus, it can be found out. A method for computation of the cutting edge geometry is necessary for optimization of parameters of a gear hobbing operation. In this paper, an analytical method for the computation of the cutting edge geometry of a gear hob is reported. The method is based on wide application of elements of vector calculus and matrices. The analysis is performed in the tool-in-use reference system. An equation of the penetration curve is derived. The machining zone is partitioned onto several different sectors. The roughing sector and the generating sector are distinguished. Generating of the work-gear tooth profile occurs within the generating sector that is bounded by the penetration curve. The derived equations, as well as the worked-out computer codes are applicable for computation of the cutting edge geometry at any point of the cutting edge of the hob, and at a any instant of time. The equations and the computer codes enable one estimating the impact of (a) the hob diameter, (b) the hob number of starts, (c) the work-gear number of teeth, (d) the hob feed rate, and (e) the hob rotation onto the actual values of the geometrical parameters of the hob cutting edges. Numerical results of the investigation are computed using commercial software MATHCAD-SCIENTIFIC. The results of the computation of the cutting edge geometry of the involute hob enable the user (a) to avoid not-feasible values of any and all geometrical parameters of the cutting edge of the hob teeth, (b) to develop parameters of the hob grinding and reliving operations, which guaranteed the optimal values of any and all geometrical parameters of the hob cutting edges. Ultimately, the application of the hobs with optimal geometry of the cutting edges will result in an increase in the cutting tool performance and in the efficiency of the gear hobbing operation. The latter is of critical importance for high volute production of involute gears for the needs of the automotive industry. The reported research results are ready to be put into practice.