Balancing fast flexible gyroscopic systems at low speed using parametric excitation

Presented is a method to identify the projection of imbalance forces on high speed related modes of vibration, using data measured rotating at low rotating speeds. The method employs two actuators and several sensors to generate information not available otherwise in rotating structures. The challenges this method aims to solve are: (i) Overcome the inability to detect the small response at low speed due to imbalance which is often below noise level; (ii) Isolate the contribution of individual modes although the measured response, far from critical speeds, combines the effect of many modes; (iii) Lack of suitable formulation for the dynamics of fast rotating structures exhibiting gyroscopic and imbalance forces, parametric excitation and nonlinear stiffness. To overcome these obstacles, a new formulation for parametrically excited gyroscopic systems is developed and an amplification scheme projecting the imbalance forces on any mode of vibration is developed. The paper outlines the mathematical background and verifies the results using finite element simulations incorporating parametric excitation and nonlinear feedback computed in real time by a digital processor and imposed by electromechanics actuators.