Balancing rotating structures using slow-speed data via optimized parametric excitation and nonlinear feedback

The paper presents an improved mass balancing procedure for fast rotating machinery, while it is being rotated at speeds considerably slower than the "critical speeds", where dangerously high vibration amplitudes may arise. By utilizing tuned dual frequency parametric excitation along with optimized nonlinear feedback terms, the slow imbalance forces are projected onto a chosen mode of vibration. This allows to identify the imbalance projection on that specific mode, and to cancel these forces by adding or reducing mass. The scheme benefits from two kinds of parametric excitation yielding combination and principal parametric resonances. The former is used to project the imbalance forces onto a selected vibration mode, and the latter significantly amplifies the response. By tuning the parametric excitation and the nonlinear terms in an optimal manner, a pseudo-linear behavior is formed. This behavior enables to increase both amplification and sensitivity to the imbalance forces without having to compromise between the two.