A dynamic model of offset press gear transmission system made up of gears, cylinders and bearings is proposed in this study. The model based on finite element method (FEM) includes some nonlinearity such as time-varying meshing stiffness, backlash, static transmission error and contact nonlinearity, which lead to complex nonlinear coupling. The Darren Bell principle and Lagrangian approach are applied to derive the motion equations of system, then the Newmark method is used to solve the equations for meshing force, acceleration, shoulder iron and rubber contact force. Eigenvalue solution is used to predict the critical speed, moreover, the influence of the radial and axial stiffness on the first-order critical speed is discussed. Considering the importance of acceleration and meshing force, the RMS value of acceleration and dynamic factor are also studied in this paper. The dynamic orbits of system are observed from the phase diagram, power spectrum, Lyapunov exponent and Poincare map. The figures clearly indicate that there are various forms of periodic and chaotic motions in different conditions. The simulation results show that with the increase of rotating speed, dynamic orbits transfer from periodic motion to chaotic motion in the cylinder discrete state
