Nonlinear vibrations of marine gear transmission systems considering shafting coupling: mechanism analysis and control method

Parallel transmission mechanisms are pivotal to high-performance propulsion systems in marine and aerospace engineering. However, such systems are highly susceptible to nonlinear instabilities driven by power distribution imbalances and intrinsic excitations, including time-varying meshing stiffness (TVMS), composite transmission errors, and backlash. This study establishes a high-dimensional coupled bending–torsional–longitudinal nonlinear dynamic model incorporating gyroscopic effects. Through bifurcation analysis and time–frequency spectra, the investigation quantitatively identifies transmission error as the dominant instability source, while demonstrating that increased load or load ratio significantly enhance stability margins. Critical thresholds for chaos transition are identified under various operational parameters. While gyroscopic effects are essential for predicting high-speed resonance regions, their impact on bifurcation thresholds governing chaotic evolution is limited. Furthermore, a semi-active vibration control strategy employing a magnetorheological fluid (MRF) damper​ with PI feedback is proposed. Numerical results indicate that optimal placement of the damper near the flywheel reduces gear meshing vibration by over 40% and effectively suppresses broadband stochastic components. The damper exhibits strong adaptive suppression, with peak reduction rates exceeding 75% in high-sensitivity unstable regions and maintaining 25% in high-load stable regimes. This research provides a robust framework for the stability analysis and adaptive vibration control of high-performance propulsion systems.