Application of the POD Method for Cracked Rotors

2017 ◽  
Author(s):  
Ayesha Al Mehairi ◽  
Mohammad A. AL-Shudeifat ◽  
Shadi Balawi ◽  
Adnan S. Saeed
Keyword(s):  
Covariance Matrices ◽  
Cracked Rotor ◽  
Force Vector ◽  
Highly Sensitive ◽  
Jeffcott Rotor ◽  
Unbalance Force ◽  
Proper Orthogonal ◽  
Integration Response ◽  
Cracked Rotor System ◽  
Rotor Model

The application of the proper orthogonal decomposition (POD) method to the vibration response of a cracked Jeffcott rotor model is investigated here. The covariance matrices of horizontal and vertical whirl amplitudes are formulated based on the numerical integration response and the experimental whirl response, respectively, for the considered cracked rotor system. Accordingly, the POD is directly applied to the obtained covariance matrices of the numerical and experimental whirl amplitudes where the proper orthogonal values (POVs) and the proper orthogonal modes (POMs) are obtained for various crack depths, unbalance force vector angles and rotational speeds. It is observed that both POVs and their corresponding POMs are highly sensitive to the appearance of the crack and the unbalance angle changes at the neighborhoods of the critical. The sensitivity zones of the POVs and POMs to the crack propagation coincide with the unstable zones of the cracked system obtained by Floquets theory.

Application of the Proper Orthogonal Decomposition Method for Cracked Rotors

2018 ◽  
Vol 13 (11) ◽  
Author(s):  
Mohammad A. Al-Shudeifat ◽  
Ayesha Al Mehairi ◽  
Adnan S. Saeed ◽  
Shadi Balawi
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Covariance Matrices ◽  
Rotor System ◽  
Orthogonal Decomposition ◽  
Cracked Rotor ◽  
Response Data ◽  
Highly Sensitive ◽  
Unbalance Force ◽  
Proper Orthogonal ◽  
Cracked Rotor System

The application of the proper orthogonal decomposition (POD) method to the vibration response of a cracked rotor system is investigated. The covariance matrices of the horizontal and vertical whirl amplitudes are formulated based on the numerical and experimental whirl response data for the considered cracked rotor system. Accordingly, the POD is directly applied to the obtained covariance matrices where the proper orthogonal values (POVs), and the proper orthogonal modes (POMs) are obtained for various crack depths, unbalance force vector angles, and rotational speeds. It is observed that both POVs and their corresponding POMs are highly sensitive to the appearance of the crack and the unbalance force angle direction in the neighborhoods of the critical rotational speeds. The sensitivity zones of the POVs and POMs to the crack propagation are found to be coinciding with the unstable zones found by the Floquet's theory of the considered cracked system.

Negative Effective Stiffness Content in Cracked Rotors

2018 ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Fatima K. Alhammadi
Keyword(s):  
Equations Of Motion ◽  
Rotor System ◽  
Effective Stiffness ◽  
Cracked Rotor ◽  
Force Vector ◽  
Rotor Systems ◽  
Wide Range ◽  
Unbalance Force ◽  
Time Periodic ◽  
Cracked Rotor System

The appearance of cracks in rotor systems affects the whirl response in the neighborhood of the critical whirl rotational speeds. The combined effect of the crack depth and the unbalance force vector angle orientation with respect to the crack opening direction on the effective stiffness content of the cracked rotor system in the neighborhood of the critical rotational speed is addressed here. The effective stiffness expression of the cracked system can be obtained from the direct integration of the equations of motion of the cracked rotor system. The cracked rotor equations of motion can be expressed by the Jeffcott rotor or the finite element models. The appearance of cracks in rotor systems converts them into parametrically excited dynamical systems with time-periodic stiffness components. The interaction between the time-periodic stiffness and the external periodic forcing function of the unbalance force significantly alters the effective stiffness content in the system at both transient and steady state operations. For wide range of crack depths and unbalance force vector angles, the effective stiffness has been found to be of negative values. This means that the cracked rotor system tends to have more resistance to deflect towards the center of its whirl orbit and less resistance to deflect away under the unbalance force excitation effect. Consequently, in the negative stiffness content zone of the unbalance force vector angles, the cracked rotor system tends to exhibit a sharp growth in the vibration whirl amplitudes. However, for positive effective stiffness values, the shaft has more resistance to deflect away from its whirl orbit center. Therefore, the cracked rotor system is at higher risk of failure in the negative effective stiffness zone of unbalance force vector angles than the positive effective stiffness zone of these angles.

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.

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.

Effect of Unbalance Force Direction on a Cracked Rotor Whirl Response

2017 ◽  
Author(s):  
Hanan Al Hosani ◽  
Mohammad A. AL-Shudeifat ◽  
Adnan S. Saeed ◽  
Shadi Balawi
Keyword(s):  
Numerical Simulation ◽  
Crack Opening ◽  
Crack Model ◽  
Open Crack ◽  
Cracked Rotor ◽  
Force Vector ◽  
Critical Speeds ◽  
Unbalance Force ◽  
Vector Angle ◽  
Time Periodic

The combined effect of the crack and the unbalance force vector angle on the values and locations of the whirl amplitudes at the critical whirl speeds for a cracked rotor-bearing-disk system is numerically and experimentally investigated here. The strongly nonlinear time-periodic equations of motion, which are analogous to Mathieus equation, of the cracked system with an open crack model are formulated according to the finite element time-periodic stiffness matrix. The whirl response during the passage through the critical speeds is obtained via numerical simulation for different unbalance vector angles with respect to the crack opening direction. It is found that the variation in the unbalance force vector angle with respect to the crack opening direction significantly alters the peaks of the critical whirl amplitudes and their corresponding critical whirl speeds. Consequently, the critical speeds of the cracked rotor are either shifted to higher or lower values according to the unbalance force vector angle value. These significant numerical simulation observations are also verified via robust experimental results.

Effect of Unbalance Force Vector Orientation on the Whirl Response of Cracked Rotors

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Hanan Al Hosani ◽  
Adnan S. Saeed ◽  
Shadi Balawi
Keyword(s):  
Crack Opening ◽  
Equations Of Motion ◽  
Cracked Rotor ◽  
Force Vector ◽  
Rotor Systems ◽  
Free Case ◽  
Unbalance Force ◽  
Whirl Speed ◽  
Vector Orientation ◽  
Time Periodic

The combined effect of a crack with unbalanced force vector orientation in cracked rotor-bearing-disk systems on the values and locations of critical whirl amplitudes is numerically and experimentally investigated here for starting up operations. The time-periodic equations of motion of the cracked system are formulated according to the finite element (FE) time-varying stiffness matrix. The whirl response during the passage through the critical whirl speed zone is obtained via numerical simulation for different angles of the unbalance force vector. It is found that the variations in the angle of unbalance force vector with respect to the crack opening direction significantly alters the peak values of the critical whirl amplitudes and their corresponding critical whirl speeds. Consequently, the critical speeds of the cracked rotor are found to be either shifted to higher or lower values depending on the unbalance force vector orientation. In addition, the peak whirl amplitudes are found to exhibit significant elevation in some zones of unbalance force angles whereas significant reduction is observed in the remaining zones compared with the crack-free case. One of the important findings is that there exists a specific value of the unbalance force angle at which the critical whirl vibration is nearly eliminated in the cracked system compared with the crack-free case. These all significant numerical and experimental observations can be employed for crack damage detection in rotor systems.

scholarly journals Negative potential energy content analysis in cracked rotors whirl response

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Fatima K. Alhammadi
Keyword(s):  
Steady State ◽  
Crack Detection ◽  
Energy Content ◽  
Negative Potential ◽  
Effective Stiffness ◽  
Cracked Rotor ◽  
Force Vector ◽  
Rotor Systems ◽  
Unbalance Force ◽  
Vector Orientation

AbstractAppearance of transverse cracks in rotor systems mainly affects their stiffness content. The stability of such systems at steady-state running is usually analyzed by using the Floquet’s theory. Accordingly, the instability zones of rotational speeds are dominated by negative stiffness content in the whirl response in the vicinity of critical rotational speeds. Consequently, an effective stiffness measure is introduced here to analyze the effect of the crack and the unbalance force vector orientation on the intensity of negative potential and stiffness content in the whirl response. The effective stiffness expression is obtained from the direct integration of the equations of motion of the considered cracked rotor system. The proposed effective stiffness measure is applied for steady-state and transient operations using the Jeffcott rotor model with open and breathing crack models. The intensity of negative potential and stiffness content in the numerical and experimental whirl responses is found to be critically depending on the propagation level of the crack and the unbalance force vector orientation. Therefore, this can be proposed as a crack detection tool in cracked rotor systems that either exhibit recurrent passage through the critical rotational speeds or steady-state running.

scholarly journals Negative Potential Energy Content Analysis in Cracked Rotors Whirl Response

2021 ◽  
Author(s):  
Mohammad AL-Shudeifat ◽  
Fatima Alhammadi
Keyword(s):  
Steady State ◽  
Crack Detection ◽  
Fatigue Cracks ◽  
Negative Potential ◽  
Effective Stiffness ◽  
Cracked Rotor ◽  
Force Vector ◽  
Rotor Systems ◽  
Unbalance Force ◽  
Vector Orientation

Abstract Appearance of fatigue cracks in rotor systems mainly affects their stiffness content. The stability of such systems at steady-state running is usually analyzed by using the Floquet’s theory. Accordingly, the instability zones of rotational speeds are dominated by negative stiffness content in the whirl response in the vicinity of critical rotational speeds. Consequently, an effective stiffness measure is introduced here to analyze the effect of the crack and the unbalance force vector orientation on the intensity of negative potential and stiffness content in the whirl response. The effective stiffness expression is obtained from the direct integration of the equations of motion of the considered cracked rotor system. The proposed effective stiffness measure is applied for steady-state and transient operations using the Jeffcott rotor model with open and breathing crack models. The intensity of negative potential and stiffness content in the numerical and experimental whirl responses is found to be critically depending on the propagation level of the crack and the unbalance force vector orientation. Therefore, this can be proposed as a crack detection tool in cracked rotor systems that either exhibit recurrent passage through the critical rotational speeds or steady-state running.

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.

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