Coupled bearing-rotor modeling of four-point contact ball bearing misalignment and its effects on high-speed flexible rotor vibration

Four-point contact ball bearings (FPCBBs) can show multi-point ball-raceway contact at high speed. Their contact states may also switch during operation. These features make misalignment effects more complex than in conventional rolling bearings. However, the way in which FPCBB misalignment modifies internal contact states and transfers nonlinear excitation to a flexible rotor remains unclear. This study develops an FPCBB misalignment model based on the assembly adjustment process. The model is then coupled with a high-speed flexible rotor model. The nonlinear bearing reaction force is obtained from the instantaneous ball-raceway contact state and fed back into the rotor equations. The model is verified using critical-speed tests and constant-speed vibration measurements. The results show that static tilt misalignment and shaft-rotating misalignment both reduce the first critical speed, but produce different trends in the second critical speed. More importantly, the two misalignment types induce different nonlinear vibration routes. Static tilt misalignment generates period-doubling motion and high-speed complex nonlinear responses, whereas shaft-rotating misalignment mainly produces lower-speed period-doubling vibration. Analysis of the bearing contact states identifies two related mechanisms. Changes in the number of loaded balls, contact angle distribution, and inner-raceway contact state modify the equivalent radial stiffness. The transition of the contact load distribution from single-period to multi-period behavior is associated with subharmonic excitation. The study clarifies the contact-state mechanism by which FPCBB misalignment affects high-speed flexible rotor vibration.