Multilevel Modeling and Validation of Thermo-Mechanical Nonlinear Dynamics in Flexible Supports

Prediction accuracy for complex flexible support systems is often limited by insufficiently characterized thermo-mechanical couplings and nonlinearities. To address this, we propose a multilevel hybrid parallel–serial model that integrates the thermo-viscous effects of a Squeeze Film Damper (SFD) via a coupled Reynolds–Walther equation, the structural flexibility of a squirrel-cage support using Finite Element analysis, and the load-dependent stiffness of a four-point contact ball bearing based on Hertzian theory. The resulting state-dependent system is solved using a force-controlled iterative numerical algorithm. For validation, a dedicated bidirectional excitation test rig was constructed to decouple and characterize the support’s dynamics via frequency-domain impedance identification. Experimental results indicate that equivalent damping is temperature-sensitive, decreasing by approximately 50% as the lubricant temperature rises from 30 °C to 100 °C. In contrast, the system exhibits pronounced stiffness hardening under increasing loads. Theoretical analysis attributes this nonlinearity primarily to the bearing’s Hertzian contact mechanics, which accounts for a stiffness increase of nearly 240%. This coupled model offers a distinct advancement over traditional linear approaches, providing a validated framework for the design and vibration control of aero-engine flexible supports.