Numerical Characterization of Evolution Behaviors of Attractor in Gear Transmission with Multiple Excitations

Investigating the global evolution of attractors in gear systems is crucial for understanding potential vibration behaviors. This article establishes a rotational vibration model for a power combined gear system with three spur gears. We use the global cell mapping method to study and characterize the transition processes of attractors in the state space. By computing parametric dynamic solutions from two different excitations, we detected unstable periodic cells within chaotic basins of attraction. The results show that mesh vibration undergoes period-doubling bifurcations as it transitions into chaos. A series of chaotic Poincaré maps exhibit significant changes, such as isolation and branching, indicating attractor distortion. As the damping ratio decreases further, chaotic attractors expand and show fractal structures. Using the G-P algorithm, the quantitative features of periodic attractors present a one-dimensional structure. While, the topological characteristics of chaotic attractors present a correlation dimension of about 1.5. The period-1 (P1) basins of attraction evolve and stabilize subject to changes of transmission error. Other periodic basins are gradually replaced by chaotic basins of attraction. This study describes the dynamic behavior of gear transmission systems through global analysis and numerical characterization of attractors. The conclusions can provide a basis for selecting dynamical parameters in the theoretical design process of gear transmission systems, helping to reduce vibration impacts during actual operation.