On the Modeling of Open and Breathing Cracks of a Cracked Rotor System

2010 ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Eric A. Butcher
Keyword(s):  
Finite Element ◽  
Crack Detection ◽  
Linear Time ◽  
Harmonic Balance Method ◽  
Rotor System ◽  
Crack Model ◽  
Open Crack ◽  
Cracked Rotor ◽  
Critical Rotational Speed ◽  
Cracked Rotor System

The modeling of a cracked rotor system with an open or breathing transverse crack is addressed here. The cracked rotor with an open crack model behaves as an asymmetric shaft. Hence, the time-varying area moments of inertia of the cracked section are employed in formulating the periodic finite element stiffness matrix for both crack models which yields a linear time-periodic system. The harmonic balance method (HB) is used in solving the finite element (FE) equations of motions for studying the dynamic behavior of the cracked rotor system. The unique behavior of the whirl orbits during the passage through the subcritical rotational speeds and the sensitivity of these orbits to the unbalance force direction can be used for early crack detection of the cracked rotor for both crack models. These whirl orbits were verified experimentally for the open crack model in the neighborhood of 1/2 of the first critical rotational speed where a good match with the theoretical whirl orbits was observed.

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.

Dynamics of Slant Cracked Rotor for a Steam Turbine Generator System

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Chao Liu ◽  
Dongxiang Jiang
Keyword(s):  
Steam Turbine ◽  
Turbine Unit ◽  
Crack Detection ◽  
Rotor System ◽  
Fault Detection And Isolation ◽  
Cracked Rotor ◽  
Generator System ◽  
Vibration Data ◽  
Torsional Excitation ◽  
Cracked Rotor System

Root causes of several recent crack failures in turbine units are attributed to oscillation and interaction between generator of turbine unit and devices on the grid, where torsional vibration of the rotor bearing system is observed and identified as an important cause. Exploring vibrational (lateral, torsional, and axial) features in the cracked rotor system with torsional excitation (TE) present can provide a novel view in crack detection and isolation. This work presents dynamic analysis of a cracked rotor system in a steam turbine unit (a typical rotor system with multiple rotors, multiple supports, and oscillating loads), and the vibrational features of the cracked rotor system with comparisons to typical features in monitored vibration data. The results show that coupled vibration in both lateral and torsional components is an effective indicator for cracks in the presence of torsional excitation. Also, vibration characteristics evaluated in different locations of the rotor system are beneficial for fault detection and isolation.

Nonlinear Dynamic Analysis of a Cracked Rotor-Bearing System With Fractional Order Damping

2011 ◽  
Author(s):  
Shiming Xue ◽  
Junyi Cao ◽  
Yangquan Chen
Keyword(s):  
Fractional Order ◽  
Crack Depth ◽  
Nonlinear Dynamic Analysis ◽  
Orientation Angle ◽  
Rotor System ◽  
Speed Ratio ◽  
Crack Model ◽  
Cracked Rotor ◽  
Mass Eccentricity ◽  
Cracked Rotor System

Fatigue cracking of the rotor shaft is an important fault observed in rotating machinery of key industry, which can lead to catastrophic failure. Nonlinear dynamics of a cracked rotor system with fractional order damping is investigated by using a response-dependent breathing crack model. The four-th order Runge-Kutta method and ten-th order CFE-Euler (Continued Fraction Expansion-Euler) method are introduced to simulate the proposed system equation of fractional order cracked rotors. The effects of derivative order of damping, rotating speed ratio, crack depth, orientation angle of imbalance relative to the crack direction and mass eccentricity on the system dynamics are demonstrated by using bifurcation diagram, Poincare map and rotor trajectory diagram. The results show that the rotor system displays chaotic, quasi-periodic and periodic motions as the fractional order increases. It is also found that the imbalance eccentricity level, crack depth, rotational speed, fractional damping and crack angle all have considerable influence on the nonlinear behavior of the cracked rotor system.

Nonlinear Dynamic Analysis of a Cracked Rotor-Bearing System With Fractional Order Damping

2012 ◽  
Vol 8 (3) ◽  
Author(s):  
Junyi Cao ◽  
Shiming Xue ◽  
Jing Lin ◽  
Yangquan Chen
Keyword(s):  
Fractional Order ◽  
Crack Depth ◽  
Nonlinear Dynamic Analysis ◽  
Orientation Angle ◽  
Rotor System ◽  
Speed Ratio ◽  
Crack Model ◽  
Cracked Rotor ◽  
Mass Eccentricity ◽  
Cracked Rotor System

Fatigue cracking of the rotor shaft is an important fault observed in the rotating machinery of key industries, which can lead to catastrophic failure. Nonlinear dynamics of a cracked rotor system with fractional order damping is investigated by using a response-dependent breathing crack model. The fourth-order Runge–Kutta method and tenth-order continued fraction expansion-Euler (CFE-Euler) method are introduced to simulate the proposed system equation of fractional order cracked rotors. The effects of the derivative order of damping, rotating speed ratio, crack depth, orientation angle of imbalance relative to the crack direction, and mass eccentricity on the system dynamics are demonstrated by using a bifurcation diagram, Poincaré map, and rotor trajectory diagram. The simulation results show that the rotor system displays chaotic, quasi-periodic, and periodic motions as the fractional order increases. It is also observed that the imbalance eccentricity level, crack depth, rotational speed, fractional damping, and crack angle all have considerable influence on the nonlinear behavior of the cracked rotor system. Finally, the experimental results verify the effectiveness of the theoretical analysis.

scholarly journals Application of Non-Symmetric Bending Principles on Modelling Fatigue Crack Behaviour and Vibration of a Cracked Rotor

2020 ◽  
Vol 10 (2) ◽  
pp. 717 ◽  
Author(s):  
Joseph Spagnol ◽  
Helen Wu ◽  
Chunhui Yang
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Harmonic Balance Method ◽  
Element Model ◽  
Neutral Axis ◽  
Crack Model ◽  
Cracked Rotor ◽  
Proposed Model ◽  
Dimensional Finite Element ◽  
Breathing Model

Many studies on cracked rotors developed crack breathing models that assume that the neutral axis of bending always remains horizontal for simplification. These models may generate significant discrepancies and thus there is a need to develop more sophisticated models to look into the shifting of the neutral axis for a cracked rotor. Herein, a case study on the shifting of the neutral axis for a cracked rotor is firstly performed by using a three-dimensional finite element model to confirm that the neutral axis becomes inclined as the cracked rotor rotates. In response to this finding, non-symmetric bending principles are used to develop a new crack breathing model which has the advantage of being able to numerically calculate the inclination angle of the neutral axis. When compared to an existing crack model in the literature that assumes that the neutral axis remains horizontal (HNA model), the proposed model is relatively less stiff in bending as a result of an overall lower area moment of inertia. Using the harmonic balance method, a two-dimensional finite element vibration model of a cracked rotor was devised by employing the proposed crack breathing model and the HNA model for validation. It can be found that the vibration amplitudes of the first three frequency components are similar between the two models for shallow cracks and significantly differed for deep cracks. This result highlights the potential of the proposed model for modelling and detecting mid-to-late-stage cracks in rotors.

scholarly journals Stability Analysis of a Breathing Cracked Rotor with Imposed Mass Eccentricity

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Huichun Peng ◽  
Qing He ◽  
Yaxin Zhen
Keyword(s):  
Crack Detection ◽  
Rotation Speed ◽  
Rotor System ◽  
Critical Ratio ◽  
Cracked Rotor ◽  
Stability Diagrams ◽  
Mass Eccentricity ◽  
Stability And Bifurcations ◽  
The Stability ◽  
Cracked Rotor System

The investigation of the effects of mass eccentricity on stability of a gravity dominated cracked Jeffcott rotor would generally provide practical applicability to crack detection and instability control of the heavy loading turbo-machinery system. Based upon the numerical Floquet method, the stability and bifurcations of the periodic time-dependent rotor with a transverse breathing crack are studied with respect to the varied mass eccentricity at different rotation speed, and the stability diagrams in the parameter plane are obtained which the previous studies have not covered. The numerical response of the cracked rotor system is also analyzed by the frequency spectrum to present the vibration characters while the rotation speed approaches the critical ratio. The detailed numerical eigenvalues of the transition matrix are applied to analyze the types of the bifurcations of the cracked rotor system. Three types of bifurcations are found and responses of the cracked rotor system at these bifurcations are presented for the visualized comparisons.

Approach for Stability Analysis of a Cracked Rotor With Time-Varying Stiffness

2013 ◽  
Author(s):  
Mohammad A. Al-Shudeifat
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Dynamic Stability ◽  
Coefficient Matrix ◽  
Rotor System ◽  
Time Varying ◽  
Cracked Rotor ◽  
Parametrically Excited ◽  
Time Periodic ◽  
Cracked Rotor System

An approach for dynamic stability analysis of a cracked rotor system with transverse crack is addressed here. The time-varying area moments of inertia of the cracked section are employed in formulating the time-periodic finite element stiffness matrix which yields a linear time-periodic system. The harmonic balance method (HB) is used in solving the finite element (FE) equations of motion for studying the dynamic stability of the system. The sign of the determinant of the scaled coefficient matrix resulting from applying the HB solution to the cracked rotor system is found to be a reliable approach for identifying the major unstable regions of the system in the parameter plane obtained by plotting the shaft speeds of rotation vs. the crack depths. Specifically, the negative values of the determinant of this scaled coefficient matrix identify the unstable regions of the cracked system. This approach is applied here to the parametrically excited Mathieu’s equation, two degree-of-freedom gyroscopic system, and then to the FE model of the cracked rotor system. The results of applying this approach are verified using the Floquet’s theory. Compared with the theory, the sign of the determinant of the scaled coefficient matrix is found here to be an efficient tool for identifying the unstable regions of linear parametrically excited systems, especially the large scale dynamic systems where this approach requires considerably less computational time than the Floquet’s theory.

Sign in / Sign up

Export Citation Format

Share Document