Aiming at the lack of the theory of transitional surface of face gear, the tooth profile equation of the orthogonal face gear is derived according to the differential geometry and meshing principle; In this paper, a tooth surface structure is proposed, which is a smooth surface of the tooth root transition part. A method of generating transition surface is presented, which takes into account the rounding tooth top of gear shaper cutter; the smooth transition surface equation of face gear tooth root is derived. The 3D solid model of the orthogonal face gear generated by two kinds of structures, the top angle of the gear shaper cutter and the addendum of the gear shaper cutter are established. The curvature analysis shows that the radius of curvature of the orthogonal face gear cut by the rounding tooth top of shaper cutter is larger than the other. The influence of the main parameters on the surface curvature of the face gear transmission is analyzed, the conclusion has reference value for the strength calculation and analysis of the face gear transmission.
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