A Floquet-based damage detection methodology for cracked rotor systems is developed and demonstrated on a shaft-disk system. This approach utilizes measured changes in the system natural frequencies to estimate the severity and location of shaft structural cracks during operation. The damage detection algorithms are developed with the initial guess solved by least square method and iterative damage parameter vector by updating the eigenvector updating. Active Magnetic Bearing is introduced to break the symmetric structure of rotor system and the tuning range of proper stiffness/virtual mass gains is studied. The system model is built based on energy method and the equations of motion are derived by applying assumed modes method and Lagrange Principle. In addition, the crack model is based on the Strain Energy Release Rate (SERR) concept in fracture mechanics. Finally, the method is synthesized via harmonic balance and numerical examples for a shaft/disk system demonstrate the effectiveness in detecting both location and severity of the structural damage.
A novel vibration-based damage identification methodology for the truss system with mass and stiffness uncertainties is proposed and demonstrated. This approach utilizes the damaged-induced changes of frequency response functions (FRF) to assess the severity and location of the structural damage in the system. The damage identification algorithm is developed basing on the least square and Newton-Raphson methods. The dynamical model of system is built using finite element method and Lagrange principle while the crack model is based on fracture mechanics. The method is synthesized via numerical examples for a truss system to demonstrate the effectiveness in detecting both stiffness and mass uncertainty existed in the system.
Jeffcott rotor is employed to study the nonlinear vibration characteristics of breathing cracked rotor system and explore the possibility of further damage identification. This paper is an extension work of prior study based on 4 degree-of-freedom Jeffcott rotor system. With consideration of disk tilting and gyroscopic effect, 6-dof EOM is derived and the crack model is established using SERR (strain energy release rate) in facture mechanics. Same as the prior work, the damaged stiffness matrix is updated by computing the instant crack closure line through Zero Stress Intensity Factor method. The breathing crack area is taken as a variable to analyze the breathing behavior in terms of eccentricity phase and shaft speed. Furthermore, the coupled vibration among lateral, torsional and longitudinal d.o.f is studied under torsional/axial excitation. The final part demonstrates the possibility of using vibration signal of damaged system for the crack diagnosis and health monitoring.
In this paper, finite element model of a shaft-disk system is developed to investigate the nonlinear breathing behavior of transverse cracks in terms of crack location and rotation speed. The crack model is built using the released strain energy concept in fracture mechanics. Zero Stress Intensity Factor (SIF) method is employed to determine the crack closure line at each time step by calculating the stress intensity factor of opening mode for prescribed resolutions in crack area. The stiffness matrix is updated every time step by integrating compliant coefficients over instantly calculated crack open area. With the finite element model of rotor system, the breathing behavior of cracks is explored as a function of eccentricity phase under different rotation speeds. The coupling of lateral, longitudinal and torsional vibration is studied in time and frequency domain, which may indicate the existence of damage.
This paper develops a new vibration based damage detection method to identify the location and severity of
structural damage of periodically time-varying systems. The frequency response function (FRF) shifts induced by cracks are utilized to detect the location, depth and orientation angle of open transverse cracks on a shaft-disk system. The dynamical model of system is built based on the Lagrange principle and the assumed mode method while the crack model for periodically time-varying systems is based on the fracture mechanics. This method provides the advantages of arbitrary interrogation frequency and multiple inputs/outputs which greatly enriches the dataset for damage identification. The method is synthesized via harmonic balance and numerical examples for a shaft/disk system to demonstrate the effectiveness in detecting both location and severity of the structural damage.
The breathing cracks in truss system are detected by Frequency Response Function (FRF) based damage identification method. This method utilizes damage-induced changes of frequency response functions to estimate the severity and location of structural damage. This approach enables the possibility of arbitrary interrogation frequency and multiple inputs/outputs which greatly enrich the dataset for damage identification. The dynamical model of truss system is built using the finite element method and the crack model is based on fracture mechanics. Since the crack is driven by tensional and compressive forces of truss member, only one damage parameter is needed to represent the stiffness reduction of each truss member. Assuming that the crack constantly breathes with the exciting frequency, the linear damage detection algorithm is developed in frequency/time domain using Least Square and Newton Raphson methods. Then, the dynamic response of the truss system with breathing cracks is simulated in the time domain and meanwhile the crack breathing status for each member is determined by the feedback from real-time displacements of member’s nodes. Harmonic Fourier Coefficients (HFCs) of dynamical response are computed by processing the data through convolution and moving average filters. Finally, the results show the effectiveness of linear damage detection algorithm in identifying the nonlinear breathing cracks using different combinations of HFCs and sensors.
Frequency Response Function (FRF) based damage detection method is utilized in this paper to
identify the breathing cracks on a rotordynamic system in both frequency and time domain. The cracks
are considered to be breathing during rotation due to the effect of gravity or imbalance mass. Zero-SIF
(Stress Intensity Factor) method is employed to determine the crack closure line of open crack area. It
is found that the stiffness reduction induced by a breathing crack is a function of both crack phase and
rotation angle. The dynamical model of system is built based on the Lagrange principle and the
assumed mode method while the crack model for periodically time-varying systems is based on the
fracture mechanics. The steady-state equation of system is constructed via harmonic balance with a
laser scanner as output sensor. The laser scanner enables the sufficient outputs from a single sensor by
varying the scanning frequency or scanning function. Assuming a cosine function to approximate the
nonlinear breathing behavior of cracks, the linear damage identification algorithms are established via
Least Square and Newton Raphson methods. Finally, the dynamic response of a rotor system with
nonlinear breathing cracks is simulated in time domain and the breathing cracks are successfully
identified by developed damage detection algorithm.