Ideal Tooth Profiles of Conical-External and -Internal Gears Meshing with Cylindrical-Involute Gears over the Entire Tooth Width.

Abstract

A new method of tooth profile synthesis using vector equations for derivation of the tooth profile of a gear from the given tooth profile of the mating gear is proposed. The ideal tooth profiles of conical-external and-internal gears which engage with the inclined cylindrical-involute gears over the entire tooth width were derived using the proposed method. Moreover, the tooth profiles in a plane perpendicular to the axis of the inclined cylindrical gear were derived from the obtained ideal tooth profiles, and their characteristics were investigated. The following results were obtained: (1) the tooth profiles of the conical-external and-internal gears are almost equal to the involute curves in the plane perpendicular to the axis of the inclined involute gear; (2) the radii of the base circle of the involute curve are given by the equivalent tooth numbers of the conical-external or-internal gear; (3) the profile-shift coefficient is given by the center-to-center distance between the inclined involute gear and the conical-external gear, or between the cylindrical gear and the conical-internal gear; (4) the profile-shift coefficient changes nonlinearly along the axis of the cylindrical-involute gear.