Analyzing Bifurcations of a Three-Degree-of-Freedom Gear Transmission Considering Multi-Piecewise Linear Functions

Abstract Bifurcations of a gear transmission system subjected to forced excitations considering multi-piecewise linear functions are investigated in this work by using the incremental harmonic balance (IHB) method. The nonlinear motion ordinary differential equations of the gear transmission system are formulated by employing the Newton’s second law. Analytical results reveal abundant bifurcation phenomena, including period-doubling bifurcations, saddle-node bifurcations, and Hopf bifurcations, which have not been exhibited in existing investigations on nonlinear behaviors of the gear transmission system. The bifurcation types are determined with the ways leaving the unit circle of Floquet multipliers.