The Numerical Calculus of Hobs Used to Cut W–N Gears

Abstract

AbstractAfter a short introduction showing the evolution of Wildhaber–Novikov (W–N) gears, the evolution of the study of hob geometry is presented, with special focus on the author’s contribution in the field. Then a general method of study of the hob geometry is exposed. The calculus model takes into account the hob with non-zero rake angle, a wide range of re-sharpenings, a generation by relief grinding, which can easily be customized for the type of abrasive tool chosen, to obtain the profile of the abrasive tool and the hob profile for various re-sharpenings. The hob profile deviation is then evaluated in an axial plane. To reduce the cumulated profile error on re-sharpening, the setting parameters on relieving are modified. The algorithm is developed on matrix basis. In the next part of the paper the customizing of the general method is presented, for the case of hobs designed to cut gears with arc-of-circle profile (reference profile with two arcs of circle). This part includes numerical results presented in tables and diagrams, for hobs in the modulus range 4–20, three values of the rake angle (0˚, 3˚, 6˚), three values of the relief for each modulus and three values of the position angle of the generation rack (around the value of the angle of the basic helix) and five values of the re-sharpening angle (0˚, ± 3˚, ± 6˚). The calculi carried out have been the basis for the manufacturing and inspection of four sizes of hobs—for the moduli 4, 10, 14 and 20. Several details of the manufacturing of hobs for W–N gears are presented in the end of the paper.KeywordsW–N gearsHobsHob geometryHob sharpeningGrind relieving of hobs