The kinematic synthesis of involute spiral bevel gears and their tooth contact analysis

In this paper, a mathematical model of the spherical involute tooth surface of a spiral bevel gear whose generating curve is an arc of a circle is built. The parameters on the base cone of the gear are derived from those on the pitch cone of the gear. The algorithm derived can be used for designing the spherical involute surface of straight and spiral bevel gears. The curve of action, the paths of contact and the contact patterns of spiral bevel gears are obtained by the tooth contact analysis (TCA). The TCA results show that: 1) the curve of action is on a spherical surface; 2) the paths of contact do not change with the variation of the radii of the generating arcs of circles of the tooth surfaces of the pinion and the gear; 3) the length of the major semi axis of their contact ellipse is determined by the radii of the generating arcs of circles of the tooth surfaces of the pinion and the gear and it does not change during the transmission process. The 3-dimensional (3D) model of the gears is constructed in 3D modeling software based on the proposed method.