Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis

• This study deals with the prediction and control of chaos in a nonlinear gear system.
• Melnikov analysis is extended to present a practical gear system to control the chaos.
• The proposed system is effective to eliminate the homoclinic bifurcation and chaos.
• This controller is proposed as a way of implementing the chaos control in gear system.

In this paper, the Melnikov analysis is extended to develop a practical model of gear system to control and eliminate the chaotic behavior. To this end, a nonlinear dynamic model of a spur gear pair with backlash, time-varying stiffness and static transmission error is established. Based on the Melnikov analysis the global homoclinic bifurcation and transition to chaos in this model are predicted. Then non-feedback control method is used to eliminate the chaos by applying an additional control excitation. The regions of the parameter space for the control excitation are obtained analytically. The accuracy of the theoretical predictions and also the performance of the proposed control system are verified by the comparison with the numerical simulations. The simulation results show effectiveness of the proposed control system and present some useful information to analyze and control the gear dynamical systems.