The speed integration gear is a new type of gear mechanism,which is meshed with cylindrical gears and non-circular face gear and can achieve speed integration transmission. Based on gear mesh theory,the tooth surface equation of non-circular face gear is deduced. Considering the angle error,intersected axis error and axis shift error,the contact model of tooth surface is established. An analysis of distribution characteristics of the contact path is made to obtain the influence of the assembly error on the point contact trace of the teeth. Simulation results indicate that the gradient of the contact path on each tooth of non-circular face gear increases with rate of change of the transmission ratio. The assembly errors cause the shift of the contact path to inner or outer radius,with its movement direction depending on the error direction.