Unveiling the masking effect of unbalance force on incipient bearing cracks in flexible rotor systems: dynamic modeling and physics-guided VMD-TEO diagnosis

While localized bearing defects have been extensively modeled in isolation, their dynamic interaction with flexible rotors under heavy unbalance—and the resulting signal masking—remains underexplored. This paper investigates the nonlinear dynamic evolution and signal detectability of inclined raceway cracks in a coupled rotor-bearing system. A refined dynamic model is established, incorporating time-varying stiffness (TVS) and displacement (TVD) excitations within a Timoshenko beam finite element framework. A critical “masking effect” is revealed: under large eccentricity, the massive centrifugal load pins the journal and linearizes the system stiffness, completely submerging the crack-induced nonlinear signatures. To overcome this detectability challenge, a Physics-Guided Variational Mode Decomposition and Teager Energy Operator (PG-VMD-TEO) strategy is proposed. Unlike purely data-driven methods that easily trap into unbalance-dominated local optima, this strategy utilizes high-fidelity simulation priors to pinpoint sensitive frequency bands. Experimental validations confirm that the proposed method accurately decouples weak fault features from severe synchronous interference. This study provides a rigorous theoretical basis for compound fault diagnosis and offers robust engineering guidelines for heavy rotating machinery.