The ideal tooth profiles of conical-external and -internal gears meshing with cylindrical-involute gears over the entire tooth width

A new synthesis method for tooth profiles using vector equations is proposed to precisely derive the curve of tooth profile of conical-external and -internal gears which engage a cylindrical-involute gear over the entire tooth width. As an example, the ideal tooth profiles of conical-external and -internal gears which engage with an inclined cylindrical-involute gear over the entire tooth width have been derived, and their characteristics with repect to a plane perpendicular to the axis of the inclined cylindrical gear have been investigated. The results obtained are as follows. (1)The tooth profiles of conical-external and -internal gears favorably coincide with plane involute curves. (2)The radius of the base circle is given by using the equivalent tooth number 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 of conical-external or -internal gear changes nonlinearly along the axis of the cylindrical-involute gear.