Mathematic design and computer analysis of curve-surface conjugated face gear pair

The mathematic model and computer analysis model of curve-surface conjugated face gear pair are developed on the basis of the principle of differential geometry. The meshing performance of face gear pair is discussed in detail, including point contact meshing characteristics, contact trajectory distribution, and sliding coefficient of the tooth surface. The tooth surface contact analysis model of curve-surface conjugated face gear pair is established, and the influences of installation errors on contact trajectory and transmission error are analyzed. The results showed that the face gear and the pinion with normal arc tooth profile mesh at the selected contact trajectory, and the point contact feature can be obtained when the tooth number of the pinion is equal to the shaper. Through the active design of contact trajectory, the curve-surface conjugated face gear pair can realize approximate pure rolling meshing, and the sliding coefficient of tooth surface is very small. Moreover, the curve-surface conjugated face gear pair has the characteristics of long pre-control contact trajectory and insensitive transmission error to installation error.