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.

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.

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.

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.

Study on the transient response and wavelet time—frequency feature of a cracked rotor passage through a subcritical speed

2003 ◽  
Vol 38 (3) ◽  
pp. 269-276 ◽  
Author(s):  
J Zou ◽  
J Chen ◽  
J. C Niu ◽  
Z. M Geng
Keyword(s):  
Numerical Simulation ◽  
Transient Response ◽  
Crack Model ◽  
Cracked Rotor ◽  
Time Frequency ◽  
Stiffness Variation ◽  
The Difference ◽  
Frequency Features ◽  
Cracked Rotor System ◽  
Subcritical Speed

The dynamic model in dimensionless form of the transient response of a cracked rotor system is derived, which is based on the simple hinge crack model. By numerical simulation, the transient responses of the uncracked rotor and the cracked rotor are obtained and the subharmonic resonance of the cracked rotor is analysed. The influence of the unbalance, the inhabiting angle and the stiffness variation on the transient response is investigated. The wavelet time-frequency features of the cracked rotor and the uncracked rotor are studied, and the difference between them is discussed. The numerical simulation demonstrates that the wavelet analysis algorithm is valid for the identification of cracked rotor.

On the wavelet time-frequency analysis algorithm in identification of a cracked rotor

2002 ◽  
Vol 37 (3) ◽  
pp. 239-246 ◽  
Author(s):  
J Zou ◽  
J Chen ◽  
Y P Pu ◽  
P Zhong
Keyword(s):  
Numerical Simulation ◽  
Detection Algorithm ◽  
Sampling Frequency ◽  
Crack Model ◽  
Cracked Rotor ◽  
Simulation Research ◽  
Time Frequency ◽  
Local Flexibility ◽  
The Difference ◽  
Frequency Properties

Based on the hinge crack model and the local flexibility theorem, the local flexibility of a cracked rotor due to the crack and the modified function of the opening and closing of the crack are given; the corresponding dynamic equation of the cracked rotor is modelled; the numerical simulation solutions of the cracked rotor and the uncracked rotor are obtained. By the continuous wavelet time—frequency transform, the wavelet time-frequency properties of the uncracked rotor and the cracked rotor are discussed; the difference between the wavelet time-frequency properties of the cracked rotor and those of the uncracked rotor is presented. A new detection algorithm that uses the wavelet time-frequency transform to identify the crack is proposed. The influence of the sampling frequency on the accuracy and validity of the wavelet time-frequency transform is analysed by numerical simulation research; the preferred sampling frequency is suggested. The experiments on the cracked rotor and the uncracked rotor demonstrate the validity and availability of the algorithm in the identification of the cracked rotor in engineering practices.

Application of the Wigner-Ville distribution to identification of a cracked rotor

2003 ◽  
Vol 217 (5) ◽  
pp. 551-556 ◽  
Author(s):  
J Zou ◽  
J Chen ◽  
J C Niu ◽  
Z M Geng
Keyword(s):  
Numerical Simulation ◽  
Transient Response ◽  
Crack Model ◽  
Cracked Rotor ◽  
Simulation Research ◽  
Time Frequency ◽  
Stiffness Variation ◽  
Engineering Practices ◽  
Frequency Features ◽  
Frequency Feature

The dynamic equation of transient response in a cracked rotor is modelled, and is based on the simple hinge crack model. The numerical simulation solutions of the uncracked rotor and the cracked rotor are obtained from the model. Using the Wigner-Ville distribution, the time-frequency features of the cracked rotor and the uncracked rotor are compared, and a new algorithm using the Wigner-Ville distribution to identify the cracked rotor is proposed. By simulation research, the sensitivity of the Wigner-Ville distribution to the stiffness variation is investigated, and the influence of the unbalance and the inhabiting angle on the time-frequency feature is discussed. The Wigner-Ville time-frequency feature is unique, and can be used as the criterion for identification of a cracked rotor in engineering practices.

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.

Feature investigation of a cracked rotor with initial deflection

2003 ◽  
Vol 217 (7) ◽  
pp. 787-796 ◽  
Author(s):  
J Zou ◽  
J Chen ◽  
G M Dong
Keyword(s):  
Numerical Simulation ◽  
Dynamic Equation ◽  
Subharmonic Resonance ◽  
Initial Deflection ◽  
Crack Model ◽  
Cracked Rotor ◽  
Simulation Research ◽  
Vibrational Characteristics ◽  
Frequency Components ◽  
Stiffness Variation

The dynamic equation of a cracked rotor with initial deflection is modelled, which is based on the simple hinge crack model; the numerical simulation solutions are obtained from the model. The subharmonic resonance of the cracked rotor is analysed and the frequency components of the cracked rotor with initial deflection and without initial deflection are investigated. By simulation research, the influence of the stiffness variation, the initial deflection, the unbalance, the unbalance angle and the orientation of the initial deflection on the vibrational characteristics is studied, which can be used as the criterion for identification of a cracked rotor.

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.

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