In order to meet the design requirements of face gear transmission in the field of aviation

a type of arc tooth face gear was proposed and its radial effective tooth width characteristics were studied. The involute tooth profile cylindrical gear with arc tooth was used as the generating gear

and the mathematical model of the gear surface was established by envelope forming. Combined with the equation of tooth surface

the tooth surface was visualized in MATLAB

and the parameterized modeling of the gear was realized through the numerical calculation function of the MATLAB software and the complex surface modeling function of the CATIA software. The restrictive conditions of the inner undercut and the outer tip to the radial effective tooth width were established

and the radial effective tooth width of the face gear was calculated. The influences of the arc radius of the tooth line and the position parameters of the coordinate system on the inner radius

the outer radius and the radial effective tooth width were analyzed. Results showed that

when the arc radius of the tooth line was increased

then the inner diameter was decreased

the outer diameter and the radial effective tooth width were increased. When the position parameter of coordinate system was increased

the inner diameter and the outer diameter were increased and the radial effective tooth width was decreased.