Analysis of bifurcation and nonlinear control for chaos in gear transmission system

Abstract

In order to study the bifurcation characteristics and control chaotic vibration of the gear transmission system. The complex dynamics characters of gear transmission system are studied. The dynamical equation and the state equation of gear transmission system are established according to Newton's rule. The route to chaos of the system is studied by the bifurcation diagram, phase portrait, time course diagram and Poincaré map. A method of controlling chaos by nonlinear feedback controller is developed to guide chaotic motions towards regular motions. Numerical simulation shows that with the increase of meshing stiffness, gear transmission system will be from the periodic motion to chaotic motion by doubling bifurcation, the effectiveness and feasibility of the strategy to get rid of chaos by stabilizing the related unstable periodic orbit. © Maxwell Scientific Organization, 2013.