Fractional-order mathematical model of single-mass rotor dynamics and stability

Ensuring the vibration reliability of rotary machines is based on the reliable mathematical model of rotor movement. Considering the critical factors leading to a stability loss is an important problem in up-to-date machinery. However, the presence of fractional-order hydrodynamic features of gap seals and the effect of anomalous energy dissipation lead to a need to clarify existing rotordynamic models by considering the fractional-order terms. Therefore, this article deals with the comprehensive modeling approach to study forced oscillations of a single-mass rotor and check its dynamic stability considering the fractional-order origin of the damping force. Moreover, the impact of fractional order on the damping factor and dynamic stability of whirl movement considering the circulation force in gap seals, is still not fully explored. This problem adds particular importance to the presented research. As a result, a single-mass flexible rotor model was extended by considering the fractional-order damping force. Moreover, based on the discovered asymptotic property of the Mittag-Leffler function, the impact of fractional order on the amplitude-frequency response was also determined. Finally, boundaries for dynamic stability loss were identified considering the fractional-order damping force. Overall, the study allowed the development and substantiation of a more generalized scientific and methodological approach to ensuring the vibration reliability of rotary machines.