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.

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.

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.

Nonlinear Response Characteristics of a Cracked Rotor in Maneuvering Aircraft

2003 ◽  
Author(s):  
Fu-Sheng Lin ◽  
Guang Meng ◽  
Eric Hahn
Keyword(s):  
Fault Diagnosis ◽  
Constant Velocity ◽  
Nonlinear Response ◽  
Nonlinear Behavior ◽  
Rotor System ◽  
Parameter Range ◽  
Cracked Rotor ◽  
Periodic Response ◽  
Response Characteristics ◽  
Cracked Rotor System

This paper investigates numerically the nonlinear response of a simple cracked rotor in moving supports, as may occur in aircraft rotors when the aircraft is maneuvering with constant velocity or acceleration. Of particular interest is the influence of the aircraft climb angle. Results show that the climb angle can markedly affect the parameter range for which the system is stable; and over which there results bifurcation, quasi-periodic response or chaotic response. It is shown that aircraft acceleration can also significantly affect the nonlinear behavior of the cracked rotor system, illustrating the possibility for online rotor crack fault diagnosis.

Dynamics of a cracked rotor system with oil-film force in parameter space

2017 ◽  
Vol 88 (4) ◽  
pp. 2347-2357 ◽  
Author(s):  
Xiao-Bo Rao ◽  
Yan-Dong Chu ◽  
Ying-Xiang Chang ◽  
Jian-Gang Zhang ◽  
Ya-Ping Tian
Keyword(s):  
Parameter Space ◽  
Rotor System ◽  
Cracked Rotor ◽  
Oil Film ◽  
Cracked Rotor System

Vibration Analysis and Detection of Rotor Crack in a Multi-Disk Rotor System by Periodic Excitation Using AMB

2007 ◽  
Author(s):  
Tsuyoshi Inoue ◽  
Toshihiro Yamamichi ◽  
Masato Kato ◽  
Yukio Ishida
Keyword(s):  
Rotating Machinery ◽  
Rotor System ◽  
Dynamic Responses ◽  
Periodic Excitation ◽  
Cracked Rotor ◽  
Risk Condition ◽  
Cracked Rotor System ◽  
Two Degree Of Freedom ◽  
Crack Element ◽  
Rotor Model

Operating of rotating machinery with a rotor crack is a risk condition, since the rotor crack grows gradually and may fail causing a catastrophic accident. Therefore, it is very important to detect the occurrence of a crack on rotating machinery in early stages. The authors have used the simple two-degree-of-freedom cracked rotor model, and investigated the usage of periodic excitation for the detection of the rotor crack. This paper constructs a finite element rotor model with breathing crack element, and performs the numerical investigation. The dynamic responses of a cracked rotor system under applied periodical external excitation are investigated. The occurrences of various kinds of nonlinear sub-resonances are observed numerically, and the dynamical characteristics of these sub-resonances are clarified. The influences of the position and depth of the crack are clarified. Furthermore, these sub-resonances due to crack are observed in the experiment. This result made us enable to detect the occurrence of a rotor crack.

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