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Shock and Vibration
Volume 2016, Article ID 4197203, 11 pages
Research Article

Nonlinear Dynamic Behaviors of Rotated Blades with Small Breathing Cracks Based on Vibration Power Flow Analysis

1Science and Technology on Integrated Logistics Support Laboratory, National University of Defense Technology, Changsha 410073, China
2Faculty of Engineering and the Environment, University of Southampton, Southampton SO16 7QF, UK

Received 12 April 2016; Accepted 29 June 2016

Academic Editor: Athanasios Chasalevris

Copyright © 2016 Hailong Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Rotated blades are key mechanical components in turbomachinery and high cycle fatigues often induce blade cracks. Accurate detection of small cracks in rotated blades is very significant for safety, reliability, and availability. In nature, a breathing crack model is fit for a small crack in a rotated blade rather than other models. However, traditional vibration displacements-based methods are less sensitive to nonlinear characteristics due to small breathing cracks. In order to solve this problem, vibration power flow analysis (VPFA) is proposed to analyze nonlinear dynamic behaviors of rotated blades with small breathing cracks in this paper. Firstly, local flexibility due to a crack is derived and then time-varying dynamic model of the rotated blade with a small breathing crack is built. Based on it, the corresponding vibration power flow model is presented. Finally, VPFA-based numerical simulations are done to validate nonlinear behaviors of the cracked blade. The results demonstrate that nonlinear behaviors of a crack can be enhanced by power flow analysis and VPFA is more sensitive to a small breathing crack than displacements-based vibration analysis. Bifurcations will occur due to breathing cracks and subharmonic resonance factors can be defined to identify breathing cracks. Thus the proposed method can provide a promising way for detecting and predicting small breathing cracks in rotated blades.