Analysis of Bifurcation and Chaos in Nonlinear Gear System with Backlash, Static Transmission Error and Time Varying Stiffness

In this paper, nonlinear vibrations of gear systems are discussed. A gear model, considering backlash, static transmission error and time varying stiffness, is represented. Nonlinear characteristics of the system such as periodic response, bifurcation and chaos in the model are investigated. In addition, the Incremental Harmonic Balance (IHB) method is extended to analyze the nonlinear dynamics of the gear system. IHB as an analytical method is used to calculate the periodic solutions of the system. The results are verified by comparing them with the results of numerical methods. Also time response, Poincare map and phase plane are presented for comparison and a better understanding of the system’s behavior.