Exploiting modal interaction during run-up of a magnetically supported Jeffcott rotor

Abstract

Introducing a parametric anti-resonance in a vibrating system couples two of the many vibration modes and enables an energy exchange between those two. This feature is employed during the run-up of a JEFFCOTT rotor supported by two active magnetic bearings. The vibration performance at bearing stiffness modulation is compared to the well-known performance at nominal bearing characteristics for a simple run-up at a constant acceleration. It is shown that by introducing a specific periodic change of the bearing stiffness coefficients, a mode coupling between two selected modes is activated. This coupling impacts the maximum amplitude developed during passage through resonance. At each critical speed transient vibrations of the corresponding mode are excited. Due to the modal coupling, if one mode is excited at a critical speed then energy is exchanged with the coupled mode. On one hand, the maximum amplitude at the first critical speed is decreased by modulation since some vibration energy is transferred to the highly damped second mode where it is partly dissipated. On the other hand, the maximum amplitude at the second critical speed is increased by modulation since some vibration energy is transferred to the lightly damped first mode. The concept is outlined in detail based on numerical studies.