Eigen and temporal characteristics of multi-frequency parametrically-excited rotor-oscillator systems

Traditional investigation on the dynamics of rotating systems assumes the axis of the rotor to be fixed. This assumption is valid as long as the stator is significantly heavier than the rotor, or is otherwise constrained to have negligible motion. However, in certain engineering applications where the rotor and the stator have comparable inertia and compliances, the stator's motion is not only significant but also coupled with that of the rotors'. This paper examines the complicated temporal and eigen behaviors of such a generic multi-rotor system in which the (non-static) `stator' and the rotors have comparable inertia and compliances. The multi-frequency parametrically-excited equations governing the dynamics of a representative dual-rotor case were numerically-integrated to obtain the responses. The effects of system parameters on the responses were analyzed using the two time-scale perturbation method. It was found that the frequency spectra comprised side-bands centered around the unforced natural frequencies. The genesis of the complicated frequency spectra was traced to the cyclically time-varying eigen-structure. Further, the underlying eigen-structure was noted to be periodic at a frequency related to that of the individual rotor speeds. Frequency components of the obtained responses were validated against measurements performed on an analogous experimental system. These results suggest that even a seemingly simple multi-frequency parametrically excited rotating system that considers the coupling between the rotor and the stator exhibits complicated eigen as well as temporal characteristics. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

The paper investigates the dynamics of a generic multi-rotor system where the rotor and stator have comparable inertia and compliances. Numerical integration of parametrically-excited equations for a representative dual-rotor case reveals complex frequency spectra and cyclically time-varying eigen-structure. The results suggest that even seemingly simple multi-frequency parametrically excited rotating systems exhibit complicated eigen and temporal characteristics.