Research On Chaos Control Of Gear System

Chaotic phenomenon only occurs in nonlinear system;the chaotic vibration in gear system can severely affect the performance and operational reliability of the mechanical transmission system. Controlling the chaotic vibration of gear system is of important significance both in theoretic research and engineering application.In this thesis a one-degree freedom nonlinear dynamic model of a gear system has been established considering the backlash, composite error and the time-varying stiffness. The dynamic character of the response of the system exeited by the static transmission error is analyzed. In view of the chaotic motion happening in some parameter space of the system, the OGY chaos control method is used in two ways to stabilize the unstable periodic orbits embedded in the chaotic attractor by making continuous perturbation to the external excitation parameter of the system.Based on the motion equation of the system the Poincare map is defined and the unstable low-period orbits of the system are located by shooting method. The parameter- sensitivity vector and Jacobin matrix at every Poincare surface of the orbits are calculated, through which its unstable eigenvectors and contravariant basis vectors are gained. Then all of the necessary information for estimating the parameterperturbation are obtained.However, in applications, mathematical models of the systems are rarely known. In such situations, the embedding technique is used in this thesis to construct time series of system's stroboscopic section data, from which the unstable periodic orbits and necessary information for estimating the parameter perturbation can be determined.The feasibility of applying the OGY chaos control method to gear system is validated by the two control effects using numerical simulation. The application of embedding technique can control the system without its motion equation, so it has important significance in applying of chaos control theory.