Bifurcation and chaos control in a gear transmission

The accurate evaluation and experimental investigation of the gear dynamic response have indicated some interesting nonlinear phenomena such as bifurcation and chaotic behavior on some system parameters. The chaotic motion is an unusual and unpredictable behavior and has been considered as an undesirable phenomenon in the nonlinear gear vibration systems. Therefore, in order to design and develop an optimal gear transmission system, it is important to control and eliminate these nonlinear phenomena. This paper presents the design of a gear system in order to control and suppress the chaos. A generalized nonlinear dynamics model of a spur gear pair including the backlash and the static transmission error is formulated. The idea behind the design of this control system is applying an additional control excitation force to the driver gear. The parameter spaces of the control excitation force are obtained analytically by using the Melnikov approach. The numerical simulations including the bifurcation diagram, the phase portrait, and the time history are used to confirm the analytical predictions and show effectiveness of the proposed control system for chaos suppression in nonlinear gear systems.