An improved dynamic model for defective Inter-Shaft bearing incorporating rolling element dimensions and Multi-Impact vibration behavior analysis

Aero-engine inter-shaft bearings in dual-rotor systems are subjected to dual rotational speeds, leading to highly complex defect-induced vibration behavior. Existing dynamic models for defective inter-shaft bearings are predominantly based on lumped-mass formulations and simplified displacement-based defect models. As a result, they neglect the finite geometry and centrifugal effects of rolling elements (REs) and fail to capture multi-stage contact transitions and the resulting multi-impact vibration mechanisms. To address these limitations, this study develops an improved dynamic model for defective inter-shaft bearings, in which the finite geometry of REs, the geometric interaction between REs and defects, and the centrifugal effects of REs are explicitly incorporated. Based on the geometric relationship between REs and defect size, a classification criterion is proposed to distinguish two defect types: line-spall defects and extended-spall defects. The results reveal that extended-spall defects induce pronounced multi-impact vibration behavior. The underlying physical mechanism is clarified by analyzing the distinct contact states between REs and the defect leading edge, defect bottom, and trailing edge. Specifically, interactions with the defect leading edge produce a low-frequency step response associated with a de-stressing state, whereas interactions with the defect bottom and trailing edge generate multiple high-frequency impulsive responses corresponding to successive re-stressing states. Compared with conventional displacement-based models, the proposed model captures the full sequence of contact transitions and provides a physically consistent description of multi-impact excitation mechanisms. The transmission of impact vibrations from the inter-shaft bearing to the rotor structure is further investigated, showing that the impulsive characteristics are preserved despite significant amplitude attenuation. Quantitative validation through simulations and experiments demonstrates strong agreement in impact timing, characteristic frequencies, and energy distribution across time, frequency, time–frequency, and envelope domains. These results confirm the capability of the proposed model in accurately characterizing defect-induced multi-impact vibration behavior and provide a reliable basis for defect severity assessment in inter-shaft bearings.