Taking the orthogonal face gear drive system as the research object, a nonlinear dynamic model, in consideration of the tooth surface friction, has been established of the face gear drive system. A numerical simulation has been performed to solve the model by Runge Kutta method with variable step size adaptive 4~5 order based on the combination of bifurcation diagram, time history diagram, and poincare diagram to analyze the influence of the vibration characteristics of gear tooth friction coefficient on the system, followed by a study on the influence of different parameters with period doubling bifurcation on the critical point of friction coefficient. The results show that the response of the system increases positively with the increase of the friction coefficient of the tooth surface, successively making the system response in a state of a single period harmonic response, a period doubling subharmonic response and a chaotic response. The greater the gear tooth width and the driving torque of the cylindrical gear, the greater the critical coefficient of friction coefficient will be, with the system responding to the period doubling bifurcation. With the increase of tooth width and driving torque, the smaller the slope of the critical coefficient of the friction coefficient, the smaller the slope of the driving torque will be to the width of the tooth. The larger the number of face teeth and the greater backlash of the system, the smaller the critical point of the friction coefficient of the system will be when the period doubling bifurcation occurs. The slope of the friction coefficient critical point change curve decreases with the increase of the gear teeth number, with no influence of the tooth side gap on the slope of its change curve.