Study on Bifurcation, Attractor and Stability of Backlash Adjustable Single Pair Gear System

This paper proposed a single-pair gear system model with transverse-torsional coupling and backlash adjustment mechanism. This model can provide a brand-new way to control the system’s motion state and improve its stability. Systematically, the system’s nonlinear dynamics, initial attractors, solution domain structure, and stability region analysis under different parameters were obtained and investigated. Based on this model and related analysis, several conclusions can be summarized. First, the bifurcation diagrams were obtained, and the critical switching points and the routes from 1[Formula: see text]-periodic motion to chaos motion were systematically analyzed. This is valuable for static system parameter control. Second, the initial motion attractors under different parameters were investigated. This reveals the nonlinear behaviors and dynamic distribution of solutions during field adjustment. Furthermore, the solution domain structures under different parameter combinations were studied. This offers a visualized method to assist in the gear system’s design and an effective tool to ensure motion stability. Finally, a double-parameter stability analysis was conducted based on different parameter combinations. Once unstable motion is generated, this can be used to provide the nearest or fastest route to 1[Formula: see text]-periodic motion. The study of nonlinear behaviors and stability has significantly expanded the understanding of the gear system and can be used as guidance for parameter control in practical applications.