Nonlinear Breathing Behavior Study of Transverse Crack on a Jeffcott Rotor Under Torsional Excitation

2014 ◽  
Author(s):  
J. Zhao ◽  
H. A. DeSmidt ◽  
W. Yao
Keyword(s):  
Damage Detection ◽  
Stiffness Matrix ◽  
Strain Energy Release ◽  
Vibration Response ◽  
Crack Model ◽  
Open Area ◽  
Lagrange Principle ◽  
Time Step ◽  
Crack Open ◽  
Jeffcott Rotor

In this paper, Jeffcott rotor model is employed to explore the vibration response of breathing cracked system with unbalance mass. Based on the energy method and Lagrange principle, 6 degree-of-freedom equation of motion is derived in fixed coordinate system. The crack model is established using strain energy release theory of facture mechanics. The stiffness matrix induced by the crack is changing with the variation of crack open area. Zero stress intensity factor (SIF) method is used to determine the crack closure line by computing the SIF for opening mode. By integrating compliant coefficients over newly determined crack open area, the stiffness matrix is updated and vibration response is solved for every time step by Gear’s method. In addition, the breathing behavior of the crack is studied for multiple eccentricity phases and rotation speeds in order to provide effective guidance for damage detection. The paper explores the effect of external torsional loading on the crack breathing behavior. Finally, the coupling of lateral and torsional vibration is investigated to be used as an indicator of damage detection and health monitoring.

Nonlinear Dynamics of Breathing Cracked Jeffcott Rotor Under Axial Excitation

2014 ◽  
Author(s):  
J. Zhao ◽  
H. A. DeSmidt ◽  
W. Yao
Keyword(s):  
Damage Detection ◽  
Coupling Effect ◽  
Longitudinal Vibration ◽  
Axial Loading ◽  
Crack Model ◽  
Open Area ◽  
Time Step ◽  
Crack Open ◽  
Axial Excitation ◽  
Jeffcott Rotor

The rotor may operate at various working conditions in practice and the crack breathing behavior at different rotating speeds is essential for damage detection and health monitoring of rotor system. In this paper, the coupling of lateral and longitudinal vibration is investigated by building a Jeffcott rotor model with imbalance. By using D’Alambert Principle, four degree-of-freedom equation of motion is derived in fixed coordinate system and the crack model is built based on the fracture mechanics. Zero SIF method is used to determine the crack open area by computing the SIF of opening mode for every point in crack area. The stiffness matrix is updated every time step by integrating compliant coefficients over instantly calculated crack open area. In addition, the breathing behavior of the crack under axial excitation is studied in terms of several eccentricity phases and rotation speeds, which provide effective guidance for damage detection in such scenarios. The paper also explores the coupling effect of external axial loading on the vibration response and its effectiveness for damage detection.

scholarly journals Harmonic Transfer Function Based Damage Identification of Breathing Cracked Jeffcott Rotor

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Jie Zhao ◽  
Hans DeSmidt ◽  
Meng Peng
Keyword(s):  
Transfer Function ◽  
Damage Identification ◽  
Strain Energy Release ◽  
Damage Parameter ◽  
Rotor System ◽  
Crack Model ◽  
Identification Algorithm ◽  
Lagrange Principle ◽  
Jeffcott Rotor ◽  
Vibration Responses

This paper proposes a vibration-based damage identification method based on 6-dof Jeffcott rotor system, which is based on harmonic balance and Newton-Raphson methods. First, the equations of motion are derived by using energy method and Lagrange principle. The crack model is based on strain energy release rate (SERR) in fracture mechanics and modified to accommodate 6-dof Jeffcott rotor model. Then, Gear’s method is used to solve the vibration responses of nominal and damaged rotor systems. By processing vibration responses, the transfer function shifts between nominal and damaged systems are taken as the input of damage identification algorithm. Finally, damage severity can be correlated with the damage parameter estimated via developed damage identification model. Numerical examples are shown to demonstrate the effectiveness in identifying the breathing crack in the rotor system.

Roll-Yaw Coupling Effect of Jeffcott Rotor With Breathing Crack

2015 ◽  
Author(s):  
J. Zhao ◽  
H. A. DeSmidt ◽  
M. Peng ◽  
W. Yao
Keyword(s):  
Coupling Effect ◽  
Rotor System ◽  
Crack Model ◽  
Breathing Crack ◽  
Cracked Rotor ◽  
Lagrange Principle ◽  
Jeffcott Rotor ◽  
Vibration Responses ◽  
Cracked Rotor System ◽  
Rotor Model

A new rotor model is developed in this paper to explore the dynamic coupling effect of roll-yaw motion. The rotor model employs a 6 degree-of-freedom Jeffcott rotor with a breathing crack. Based on the energy method and Lagrange principle, equation of motion is derived in yawing coordinate system with consideration of unbalance mass. The breathing crack model is established by Zero Stress Intensity Factor (SIF) method based on the crack released strain energy concept in fracture mechanics. SIF method is used to determine the crack closure line by computing SIF for opening mode. The vibration responses of the cracked rotor system are solved by Gear’s method. The coupling effect of yawing and rolling motion is studied in this paper to investigate vibration response of cracked rotor system. With the yawing motion, the dynamics of the rotor-bearing system is changed by additional stiffness and force terms. The parametric study is conducted to analyze the effect of yawing rate and acceleration on the crack breathing behavior. Finally, the vibration responses of the nominal and damaged rotor systems are analyzed to find out the indication for the damage detection and health monitoring.

Parametric Study on Dynamics of Breathing Cracked Rotor via Laser Scanner

2015 ◽  
Author(s):  
J. Zhao ◽  
H. A. DeSmidt ◽  
M. Peng ◽  
W. Yao
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Parametric Study ◽  
Laser Scanner ◽  
Crack Model ◽  
Transverse Cracks ◽  
Time Step ◽  
Crack Open ◽  
Opening Mode

The study is based on the finite element model which was 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 crack is considered open at the points where the stress intensity factor for opening mode is larger than zero. The stiffness matrix is updated at every time step by integrating compliant coefficients over instantly calculated crack open area. With the updated stiffness and force matrices, the vibration response at next time step is solved by Newmark integration method. To investigate the effectiveness of laser scanner, parametric study is conducted to analyze the vibration responses collected by the laser scanner with different scanning functions and frequencies. With this model, the displacement or velocity along the shaft can be extracted to form time based data sets for different scanning function or scanning frequency to explore its usefulness for damage identification.

A Study on Structural System Identification and Damage Detection for Free Vibration Response Using the Wavelet Transform

2015 ◽  
Vol 752-753 ◽  
pp. 1029-1034
Author(s):  
Asnizah Sahekhaini ◽  
Pauziah Muhamad ◽  
Masayuki Kohiyama ◽  
Aminuddin Abu ◽  
Lee Kee Quen ◽  
...  
Keyword(s):  
Free Vibration ◽  
Damage Detection ◽  
Vibration Response ◽  
Structural System ◽  
Modal Parameter ◽  
Modal Parameter Identification ◽  
Complex Morlet Wavelet ◽  
Structural System Identification ◽  
Free Vibration Response ◽  
Energy Components

This paper presents a wavelet-based method of identification modal parameter and damage detection in a free vibration response. An algorithm for modal parameter identification and damage detection is purposed and complex Morlet wavelet is chosen as an analysis wavelet function. This paper only focuses on identification of natural frequencies of the structural system. The method utilizes both undamaged and damage experiment data of free vibration response of the truss structure system. Wavelet scalogram is utilizes for damage detection. The change of energy components for undamaged and damage structure is investigated from the plot of wavelet scalogram which corresponded to the detection of damage.

Contribution to Bridge Damage Analysis

2014 ◽  
Vol 704 ◽  
pp. 435-441 ◽  
Author(s):  
Mohammed Lamine Moussaoui ◽  
Abderrahmane Kibboua ◽  
Mohamed Chabaat
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Damage Detection ◽  
Sparse Matrix ◽  
System Of Equations ◽  
Shape Functions ◽  
Time Step ◽  
Analytical Geometry ◽  
Matrix Algorithms ◽  
Bridge Damage

Structural damage detection has become an important research area since several works [2] were focused on the crack zones detection in order to foresee the appropriate solutions. The present research aims to carry out the reinforced concrete bridge damage detection with the finite element mathematical model updating method (MMUM). Unknown degrees of freedom dof are expanded from measured ones. The partitioned system of equations has provided a large sub-system of equations which can be solved efficiently by handling sparse matrix algorithms at each time step of the finite time centered space FTCS discretization. A new and efficient method for the calculation of the constant strain tetrahedron shape functions has been developed [1,3,4,5,6]. The topological and analytical geometry of the tetrahedron and its useful formulae enabled us to develop its shape functions and its corresponding finite element matrices. The global finite element matrices and sparse matrix computations have been achieved with a calculus source code. The reinforced concrete mixture has been modeled with the mixture laws [16] which led to its material properties matrix as an orthotropic case with 9 constants and 2 planes of symmetry from the generalizedHooke’slaw [1]. It is noticed that the material is made of steel, cement, gravels, sand and impurities. The data computations have been implemented with optimized cpu time and data storage using vectorial programming of efficient algorithms [11,12]. The sparse matrix algorithms used in this study are: solution of symmetric systems of equations UTDUd=R, multiplication, addition, transposition, permutation of rows and columns, and ordering of the matrices representations. All the sparse matrices are given in row-wise sparse format.

Vibration Response Analysis of a Stepped Beam with Crack Using Composite Element Method

2011 ◽  
Vol 199-200 ◽  
pp. 835-838
Author(s):  
Xu Bin Lu ◽  
Zhong Rong Lv ◽  
Ji Ke Liu
Keyword(s):  
Forced Vibration ◽  
Vibration Response ◽  
Dynamic Responses ◽  
Response Analysis ◽  
Crack Model ◽  
Composite Element ◽  
Stiffness Reduction ◽  
Stepped Beam ◽  
Composite Element Method ◽  
Element Method

The composite element method is utilized to discretise a stepped Euler-Bernoulli beam with a crack. The local stiffness reduction due to the crack is introduced by using a simplified crack model. The finite element equation for the forced vibration analysis is obtained using the composite element method (CEM). The forced vibration response of the cracked stepped beam is numerically calculated using Newmark integration method. Numerical results indicate that the position and depth of a crack affects the low and high natural frequencies and modes of a cantilever beam, respectively. And the position of the crack has significant effects on the dynamic responses of the beam.

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