Abstract: By adopting the thought of Adomian's decomposition method, the three-degree-of-freedom non-linear models of the gear system with clearances are transformed into a standard first-order-differential-equations, and then the A-operator method (AOM) for the approximate analytic solution of the system is developed based on the exact solution in form. The symbolic-numeric (S-N) method on the basis of the AOM is proposed for the first time in this paper. By using the AOM, the bifurcation and chaotic behavior of the gear system with clearances is investigated. It shows that under a certain condition the system will become chaotic through the route of period-doubling bifurcation or crisis, which is illustrated by the damping bifurcation diagram and frequency bifurcation diagram. It also follows that the method presented in this paper is of practical significance in nonlinear dynamic analysis of mechanical system.

Key words: A-operator method (AOM) Gear system, Bifurcation, Chaos