CHAOS CONTROL OF 3-DOF GEARED SYSTEM

Based on a three-degree-of-freedom nonlinear geared system with time-varying mesh stiffness and backlash,a multi-step chaos control method is presented to realize the sta- bilization of UPOs(Unstable period orbits)embedded in the chaotic attractor.Firstly,the nonlinear dynamics model of a gear pair system is established.By means of the analysis of the structure of system's UPOs,the existence of complex-conjugate eigenvalues on the unit circle along UPOs and unstable dimen- sion or stable dimension variability of the UPOs indicate the nonhyperbolicity of the gear system.In order to resolv the dif- ficulty that traditional chaos control method is not applicable to nonhyperbolic system,a multi-step method is set up in terms of the unstable and stable direction of UPOs respectively to drive the system state to lie on the local stable manifold of UPOs through continuous parametric perturbations.Numerical simu- lation proves the effectiveness of the control method for the UPOs even with long period in nonhyperbolic and high-dimensional system.