Abstract
This study explores the nonlinear dynamics of a gear meshing system equipped with Hybrid Squeeze Film Dampers (HSFDs), focusing on the impact of operational parameters, including the rotational speed ratio s, the unbalanced parameter β, and the dimensionless damping ratio ξ. The analysis demonstrates that when β is low, the system exhibits periodic motion; however, as β increases, the system transitions to quasi-periodic and chaotic behaviors. Phase diagrams reveal complex dynamic patterns that suggest a shift toward chaotic motion, while power spectra highlight a broad spectrum of excitation frequencies, influenced by multiple harmonics. The confirmation of chaotic dynamics is supported by a positive Lyapunov exponent, indicating exponential divergence of nearby trajectories, and fractal dimensions of 1.26 for β = 0.34, underscoring the system’s complex behavior and fractal-like geometry. Moreover, the study underscores the significant role of damping in stabilizing the system, where higher damping ratios facilitate a transition from non-periodic to periodic motion, enhancing system stability. The analysis also considers the effects of temperature-dependent viscosity, which alters the damping characteristics and overall dynamic response of the system. These findings contribute to a deeper understanding of dynamic behaviors in gear systems and provide valuable insights for optimizing operational parameters to improve system performance and stability. Future research could explore the combined effects of temperature variations and meshing errors, offering further insights into the chaotic dynamics of mechanical systems.
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