Nonlinear characteristics and stability research on planetary gear system with self-adaptive backlash control module

Abstract This paper proposes a new transverse-torsional coupled planetary gear transmission model with a self-adjustment backlash control model, which offers an effective approach to reducing vibration and controlling system stability. The nonlinear governing equation is derived, and the system dynamics behaviors and double-parameter stability region are explored. Several valuable conclusions can be drawn. First, bifurcation diagrams under different parameters are obtained. Colorful bifurcation characteristics are observed, and different parameters cause remarkable differences in the system dynamic response. Second, different initial values can lead to dramatically different motion states, and the change in system input parameters can significantly affect the attractor’s structure. Third, solution domain structures under different parameter combinations are obtained and comprehensively analyzed. A flame-shaped structure is observed and evolves with the change of parameters. Fourth, double-parameter stable regions are presented and carefully analyzed, providing an effective visual tool to study system stability and the variation trend caused by parameter changes. The research on bifurcation characteristics, initial attractor, solution domain structure, and double-parameter stability significantly reveals the colorful nonlinear behaviors of the planetary gear system. The study in this paper could be utilized as the optimization method for the design of gear transmission system and a guide for field problems.