Numerical control machining of face gear with arcuate tooth has been proposed

and the meshing characteristics was investigated.Tooth surface equation that was based on the concept of imaginary gear cutter has been derived

flank modification had also been considered;the machining principle in the general multi-axle numerical control machine tool was created by using coordinate transformation

then the polynomial expression of the motion axes can be obtained;tooth contact analysis(TCA)model under different assembly conditions was established.The numerical results reveal that the bearing contacts are not sensitive to the errors of misalignments

and a more favorable type of parabolic function of transmission errors with better symmetry and reduced amplitude may be obtained according to the modification of the face gear.