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

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.

[1]  Yeping Xiong,et al.  Power flow behaviour and dynamic performance of a nonlinear vibration absorber coupled to a nonlinear oscillator , 2015 .

[2]  Alessandro De Stefano,et al.  A novel approach to detecting breathing-fatigue cracks based on dynamic characteristics , 2013 .

[3]  C. W. Smith,et al.  A photoelastic evaluation of the influence of closure and other effects upon the local bending stresses in cracked plates , 1970 .

[4]  Yuan-Di Zhao,et al.  Structural power flow analysis of Timoshenko beam with an open crack , 2006 .

[5]  Zheng Hu,et al.  Non-contact crack detection of high-speed blades based on principal component analysis and Euclidian angles using optical-fiber sensors , 2013 .

[6]  Joseph C. Slater,et al.  Investigation of Candidate Features For Crack Detection in Fan and Turbine Blades and Disks , 2009 .

[7]  A. Dimarogonas.  Vibration for engineers , 1992 .

[8]  Mousa Rezaee,et al.  Free Vibration Analysis of Simply Supported Beam with Breathing Crack using Perturbation Method , 2010 .

[9]  Athanasios Chasalevris,et al.  Identification of multiple cracks in beams under bending , 2006 .

[10]  Giancarlo Genta,et al.  Dynamics of Rotating Systems , 2005 .

[11]  D. J. Ewins,et al.  Analysis of the Worst Mistuning Patterns in Bladed Disk Assemblies , 2003 .

[12]  Christophe Pierre,et al.  Vibration and Power Flow Analysis of a Vehicle Structure Using Characteristic Constraint Modes , 2003 .

[13]  A. Barr,et al.  Torsional vibration of cracked beams of non-circular cross-section , 1986 .

[14]  Ugo Andreaus,et al.  Cracked beam identification by numerically analysing the nonlinear behaviour of the harmonically forced response , 2011 .

[15]  M. Rezaee,et al.  A new approach to free vibration analysis of a beam with a breathing crack based on mechanical energy balance method , 2011 .

[16]  Samer Masoud Al-Said,et al.  A New Algorithm for Crack Localization in a Rotating Timoshenko Beam , 2009 .

[17]  Dongxiang Jiang,et al.  Crack modeling of rotating blades with cracked hexahedral finite element method , 2014 .

[18]  T. Chondros,et al.  VIBRATION OF A BEAM WITH A BREATHING CRACK , 2001 .

[19]  R. G. White,et al.  Vibrational power flow from machines into built-up structures, part I: Introduction and approximate analyses of beam and plate-like foundations , 1980 .

[20]  S. M. Al-Said,et al.  Flexural Vibration of Rotating Cracked Timoshenko Beam , 2006 .

[21]  J. A. Loyaa,et al.  Natural frequencies for bending vibrations of Timoshenko cracked beams , 2005 .

[22]  Vadim V. Silberschmidt,et al.  Effect of crack induced nonlinearity on dynamics of structures: application to structural health monitoring , 2013 .

[23]  T. Chondros,et al.  Identification of cracks in welded joints of complex structures , 1980 .

[24]  S. Masoud,et al.  EFFECT OF CRACK DEPTH ON THE NATURAL FREQUENCY OF A PRESTRESSED FIXED–FIXED BEAM , 1998 .

[25]  Andrew D. Dimarogonas,et al.  A CONTINUOUS CRACKED BEAM VIBRATION THEORY , 1998 .

[26]  P. Casini,et al.  Non-linear dynamics of a cracked cantilever beam under harmonic excitation , 2007 .

[27]  Jao-Hwa Kuang,et al.  The effect of blade crack on mode localization in rotating bladed disks , 1999 .

[28]  Fabrice Thouverez,et al.  DYNAMIC NON-LINEAR ANALYSIS OF A CRACKED BLADE , 2008 .

[29]  D. J. Ewins,et al.  Management of the variability of vibration response levels in mistuned bladed discs using robust design concepts, Part 1: Parameter design , 2010 .

[30]  Leontios J. Hadjileontiadis,et al.  Time–frequency analysis of the free vibration response of a beam with a breathing crack , 2005 .

[31]  Animesh Chatterjee,et al.  Nonlinear Dynamics and Damage Assessment of a Cantilever Beam With Breathing Edge Crack , 2011 .

[32]  MirosBaw WitoV,et al.  High Sensitive Methods for Health Monitoring of Compressor Blades and Fatigue Detection , 2015 .

[33]  S. Cheng,et al.  VIBRATIONAL RESPONSE OF A BEAM WITH A BREATHING CRACK , 1999 .

[34]  K. Alnefaie,et al.  Effect of unbalanced rotor whirl on blade vibrations , 2011 .