Shaft-flexibility-induced hydrodynamic support redistribution and modal response in a multi-support bearing-rotor system

Shaft flexibility in a multi-support bearing-rotor system simultaneously alters the journal attitudes at multiple supports, thereby redistributing the hydrodynamic support conditions along the shaft. This study investigates this system-level transmission in a three-disk, four-support bearing-rotor system subjected to end loading. The eccentricity and inclination states of all four journals are determined simultaneously through a coupled equilibrium solution of a Timoshenko beam structural model and a finite-length Reynolds lubrication model, and the resulting load- and speed-dependent oil-film coefficients are introduced into a finite-element rotordynamic model. End loading produces a strongly nonuniform support response: at 3000 rpm, the stiffness and damping traces of the loaded-end support J 4 increase by 4298.0 % and 293.6 %, respectively, and at 2884 rpm its direct-stiffness trace reaches approximately 47 times the initial value. Continuous modal-branch tracking shows, however, that the neighboring low-order FW and BW synchronous branches change by only −0.00037 % and +0.00039 %, whereas the higher-order H1 and H2 branches change by +0.0140 % and +0.1477 %, respectively. The contrast is explained by the markedly different generalized participation of the bearing locations in the corresponding modal branches. These results show that the global dynamic consequence of local oil-film strengthening is governed by hydrodynamic support redistribution and modal participation at the support locations rather than by the magnitude of the local bearing-stiffness change alone.