Abstract

The methods described allow one to directly measure the individual branches of the Campbell Diagram of a physical gyroscopic system at any rotation speed. Typically, such data is acquired by exciting the vibration modes through naturally occurring imbalance forces. During run-up, these forces expose some of the Campbell Diagram, but mainly the forward whirling branches, leaving the backward whirling branches mostly hidden. Furthermore, good modal frequency data is only acquired at the critical speeds. The methods proposed here allow one to excite either a forward or backward whirling mode at any rotation speed in a precisely controlled manner, greatly improving the quality of an acquired Campbell Diagram. The technique employs an external excitation device that automatically produces oscillating forces at a chosen modal frequency. Control is based on the autoresonance algorithm, which can excite a mechanical system at resonance effectively. It will also be shown that with two actuators and two sensors, one can choose which bending mode to excite at resonance in either the forward or backward whirling direction. As the rotation speed is then gradually increased, one can measure the speed dependence of the resonant frequency. Furthermore, when combining autoresonance with a phase locked loop, one can acquire very clean measurements by removing most of the noise generated by the imbalance and other sources. The technique is demonstrated analytically, numerically, and experimentally.

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