Resonances analysis of a parametrically excited imbalanced asymmetrical rotor with an imbalanced disk exposed to lubricated and electromagnetic loads

This study investigates the nonlinear dynamics of a parametrically excited, imbalanced asymmetrical rotor-disk system subjected to combined electromagnetic, journal bearing, and eccentricities. The equations of motion are derived using a variational approach and solved with the method of multiple scales to analyze primary, parametric, and combination resonances. The findings reveal that in the absence of electromagnetic excitation, the symmetrical and asymmetrical systems exhibit hardening nonlinearities with negligible backward mode amplitudes. As the electromagnetic parameter increases, softening nonlinearities dominate, activating both forward and backward modes and introducing new solution branches. The importance of defining multiple detuning parameters is underscored, as this enables the capture of forward and backward amplitudes and new solution branches, which are otherwise unattainable. The study further reveals that shaft and disk eccentricities significantly influence system behavior. In the absence of shaft eccentricity, symmetrical systems exhibit simpler dynamics without backward amplitudes, while asymmetrical systems retain their dynamic richness, including stable and unstable solutions, jump phenomena, and new branches rooted in backward modes. The findings highlight that symmetrical systems are more sensitive to shaft eccentricity, while asymmetrical systems, driven by parametric excitations from shaft asymmetry, exhibit resilience to such changes. Additionally, the electromagnetic field's phase plays a crucial role in shaping higher stable solutions, with minimal impact on lower amplitudes. As the electromagnetic parameter increases, the system transitions from harmonic responses to multi-harmonic, quasi-periodic, and chaotic behaviors. These insights provide a comprehensive understanding of rotor dynamics under combined excitations.