Nonlinear Dynamic Behavior and Rubbing-Induced Instability of Flexible Shaft Systems With an Amplitude-Limiting Dry Friction Damper

As a passive vibration suppression system, amplitude-limiting dry friction dampers can effectively mitigate abnormal vibrations in flexible shaft systems during critical speed transitions. However, they can also induce reverse whirling instability due to rubbing interactions. To address this issue, this study establishes a dynamic model of the shaft system incorporating coupled rubbing and dry friction effects, using lumped mass and finite element methods. The accuracy of the proposed model is experimentally validated. Further, numerical analysis is employed to reveal the mechanisms driving instability evolution as well as the influence of key parameters. The results demonstrate that the rubbing-friction coupling effect induces stiffness hardening of the shaft, increasing the natural frequency from 4[Formula: see text]000[Formula: see text]r/min to 4[Formula: see text]325[Formula: see text]r/min while reducing the resonance amplitude by 57.5%. The system undergoes a complete dynamic evolution through the following states: periodic-1, quasi-periodic, chaotic, quasi-periodic, and then returning to the periodic-1 state, with chaotic motion emerging near resonance due to torus breakdown. Under small shaft eccentricity, rubbing remains localized and controlled, whereas large eccentricity causes persistent rubbing and secondary impacts, maintaining prolonged chaotic behavior. A critical threshold for the coefficient of friction is identified: insufficient friction results in inadequate damping, while excessive friction triggers reverse whirling instability through a sudden transition to chaos. Furthermore, increasing the rubbing gap raises the critical speed for reverse whirling and amplifies instability amplitude. Although reducing preload lowers the threshold speed for instability, it increases vibration amplitude, with diminishing effects beyond a certain preload level. Overall, this research provides valuable theoretical insights into stability-oriented design of amplitude-limiting dry friction dampers in supercritical shaft systems.