The tooth surface equation of non-orthogonal arc tooth face-gear was derived according to the principle of face-gear meshing. The undercut phenomenon of this type of face-gear was studied by combining Matlab mathematical model with undercut theory

and the maximum internal diameter of face-gear without undercut was calculated. Catia simulation hobbing was used to verify the accuracy of the calculation. A new type of non-orthogonal face-gear was proposed. The undercut phenomenon of this kind of face-gear was studied through theoretical derivation and simulation. Based on this

the factors affecting the internal diameter of non-orthogonal arc tooth face-gears were explored. Results showed that under the same parameters

when the position parameter increased

the height and inner diameter of the involute section of the tool gradually reduced. When the radius of the tool increased

the inner diameter gradually reduced

and the height of the involute section of the tool gradually increased.