Abstract: The spiral bevel gears supported by rotor exhibit emblematical phenomena of nonlinear dynamical system, such as bifurcation, chaos and quasi-periodic response etc, and the nonlinear frequency response characteristics of a spiral bevel gear system are numerically examined. An eight degree freedom dynamic model is developed which includes nonlinearities associated with backlash and time-varying meshing stiffness. The equations of coupled torsional, lateral and longitudinal motion of the spiral bevel gear system are simplified by defining dynamic relative transmission error, and rewritten into state equations by introducing the state variables. With Aoperator method, a numerical algorithm is put forward, and the dynamical responses of the geared system with harmonic internal excitation and parameter excitation are obtained.. Numerical results show that, the system goes through the period doubling route to chaos with change of the meshing frequency, and through Hopf bifurcation to chaos with change of bearing stiffness.Furthermore, the phenomena of jump always occur for different supporting system.

Key words: A-operator method Chaotic vibration, Non-linear vibration Spiral bevel gear