Rotordynamic Crack Diagnosis: Distinguishing Crack Depth and Location

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Philip Varney ◽  
Itzhak Green
Keyword(s):  
Condition Monitoring ◽  
Crack Detection ◽  
Fatigue Cracks ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Forced Response ◽  
Contour Plot ◽  
Crack Model ◽  
Finite Width ◽  
Shaft Speed

The goal of this work is to establish simple condition monitoring principles for diagnosing the depth and location of transverse fatigue cracks in a rotordynamic system. The success of an on-line crack diagnosis regimen hinges on the accuracy of the crack model, which should account for the crack's depth and location. Two gaping crack models are presented; the first emulates a finite-width notch typically manufactured for experimental purposes, while the second models a gaping fatigue crack. The rotordynamic model used herein is based upon an available overhung rotordynamic test rig that was originally constructed to monitor the dynamics of a mechanical face seal. Four degree-of-freedom, linear equations of motion for both crack models are presented and discussed. Free and forced response analyses are presented, emphasizing results applicable to condition monitoring and, particularly, to diagnosing the crack parameters. The results demonstrate that two identifiers are required to diagnose the crack parameters: the 2X resonance shaft speed and the magnitude of the angular 2X subharmonic resonance. First, a contour plot of the 2X resonance shaft speed versus crack depth and location is generated. The magnitude of the 2X resonance along the desired 2X frequency contour is then obtained, narrowing the possible pairs of crack location and depth to either one or two possibilities. Practical aspects of the suggested diagnostic procedure are discussed, as well as qualitative observations concerning crack detection.

Rotordynamic Crack Diagnosis: Distinguishing Crack Depth and Location

2013 ◽  
Author(s):  
Philip Varney ◽  
Itzhak Green
Keyword(s):  
Fatigue Crack ◽  
Condition Monitoring ◽  
Crack Depth ◽  
Forced Response ◽  
System Response ◽  
Contour Plot ◽  
Crack Model ◽  
Finite Width ◽  
Angular Response ◽  
Crack Location

The goal of this work is to establish a condition monitoring regimen capable of diagnosing the depth and location of a transverse fatigue crack in a rotordynamic system. The success of an on-line crack diagnosis regimen hinges on the accuracy of the crack model used. The model should account for the depth of the crack and the localization of the crack along the shaft. Negating the influence of crack location on system response ignores a crucial component of real cracks. Two gaping crack models are presented; the first simulates a finite-width manufactured notch, while the second models an open fatigue crack. An overhung rotordynamic system is modeled, imitating an available rotordynamic test rig. Four degree-of-freedom equations of motion for both crack models are presented and discussed, along with corresponding transfer matrix techniques. Free and forced response analyses are performed, with emphasis placed on results applicable to condition monitoring. It is demonstrated that two identifiers are necessary to diagnose the crack parameters: the 2X resonance frequency and the magnitude of the 2X component of the rotor angular response at resonance. First, a contour plot of the 2X resonant shaft speed versus crack depth and location is generated. The magnitude of the 2X component of the rotor’s angular response along the desired contour is obtained, narrowing the possible pairs of crack location/depth to either one or two possibilities. Practical aspects of the diagnosis procedure are then discussed.

Vibration Analysis of Rotor for Crack Identification

2002 ◽  
Vol 8 (1) ◽  
pp. 51-67 ◽  
Author(s):  
P. N. Saavedra ◽  
L. A. Cuitiño
Keyword(s):  
Crack Detection ◽  
Equations Of Motion ◽  
Fem Analysis ◽  
Computational Effort ◽  
Crack Identification ◽  
Crack Model ◽  
Excited System ◽  
Closing Crack ◽  
Stationary Vibration ◽  
Rotating Shafts

A theoretical and experimental dynamic analysis of a rotor-bearing system with a transversely cracked shaft is presented. To model the system for FEM analysis, a finite element for a cracked cylindrical shaft is developed. The additional flexibility due to the crack is evaluated from the linear fracture mechanics, using a breathing crack model derived in a rigorous way. A simplified opening/closing crack model is proposed to reduce the computational effort. The resulting parametrically excited system is nonlinear, and the equations of motion are solved using Hilbert, Hughes, and Taylor integration method (HHT) implemented in Matlab platform, where the stationary vibration caused by gravity and unbalance is analyzed. The results show that for half the first critical speed, the super-harmonic 2 ×Ω and the typical orbit provide good indices for crack detection in rotating shafts.

Modal Analysis and Dynamic Responses of a Hysteretically Damped Axle Shaft With a Transverse Crack

2019 ◽  
Author(s):  
C. Shravankumar ◽  
Yash K. Sarda ◽  
V. Thamarai Selvan
Keyword(s):  
Modal Analysis ◽  
Condition Monitoring ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Fatigue Cracks ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Fast Fourier Transformation ◽  
Transverse Loads ◽  
Eigen Value

Abstract An axle shaft supports rotating elements, and is fitted to the housing by means of bearings. It mostly does not transmit torque, with exceptions such as in train axles. Non-rotating axles are subjected to bending moments due to dynamic transverse loads. Axles such as in automobiles are marked with occasional failures due to fatigue cracks, which can prove serious, if the cracks are not detected early. Vibration based condition monitoring is the field concerned with crack detection based on the dynamic responses of the system. In this light, the present paper discusses the vibration analysis of a cracked axle. The cracked shaft is modelled using finite element method, for transverse vibration conditions. The shaft is modelled based on Euler-Bernoulli theory for bending, while the crack is modelled based on fracture mechanics approach. After modelling, modal analysis of the system is carried out, with the consideration of proportional hysteretic damping. The Eigen value problem provides the natural frequencies and mode shapes. The Frequency Response Functions (FRF’s) magnitude and phase plots are obtained, from which the natural frequencies and structural damping loss factors can be calculated. Further, the free vibration and forced vibration system time responses are obtained, using numerical integration methods. The corresponding responses in frequency domain are obtained using Fast Fourier Transformation (FFT). The FRF’s and dynamic responses of the shaft without and with crack are comparatively studied. The study provides the platform for condition monitoring of shaft cracks.

Development of a Novel Algorithm for a Crack Detection, Localization, and Sizing in a Beam Based on Forced Response Measurements

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
M. Karthikeyan ◽  
R. Tiwari ◽  
S. Talukdar
Keyword(s):  
Natural Frequency ◽  
Crack Detection ◽  
Beam Theory ◽  
Crack Size ◽  
Forced Response ◽  
Crack Model ◽  
Beam Model ◽  
Crack Location ◽  
Forced Responses ◽  
Crack Element

The present work aims at the development of a method for the crack detection, localization and sizing in a beam based on the transverse force and response signals. The Timoshenko beam theory is applied for transverse vibrations of the beam model. The finite element method is used for the cracked beam forced vibration analysis. An open transverse surface crack is considered for the crack model, which contains standard five flexibility coefficients. The effect of the proportionate damping is also included. A harmonic force of known amplitude with sine-sweep frequency is used to dynamically excite the beam, up to few flexible modes, which could be provided with the help of an exciter. In practice, linear degrees of freedom (DOFs) can be measured quite accurately; however, rotational DOFs are difficult to measure accurately. All rotational DOFs, except at crack element, are eliminated by a dynamic condensation scheme; for elimination of rotational DOFs at the crack element, a new condensation scheme is implemented. The algorithm is iterative in nature and starts with a presumption that a crack is present in the beam. For an assumed crack location, flexibility coefficients are estimated with the help of forced responses. The Tikhonov regularization technique is applied in the estimation of bounded crack flexibility coefficients. These crack flexibility coefficients are used to obtain the crack size by minimizing an objective function. With the help of the estimated crack size and measured natural frequency, the crack location is updated. The procedure iterates till the crack size and location get stabilized up to the desired level of accuracy. The algorithm has a potential to detect no crack condition also. The crack flexibility and damping coefficients are estimated as a by-product. Numerical examples, with the simply supported and cantilevered beams, are given to justify the applicability and versatility of the algorithm in practice. With the numerically simulated forced responses, which have the noise contamination and the error in the natural frequency measurements, the estimated crack parameters (i.e., the crack location and size) are in good agreement.

scholarly journals Mechanical structural health prognosis with nonlinear mixed frequency ultrasonic signal analysis

2021 ◽  
Vol 268 ◽  
pp. 01075
Author(s):  
Hanxin Chen ◽  
Mingming Liu ◽  
Zhenyu Hu ◽  
Menglong Li ◽  
Sen Li
Keyword(s):  
Crack Detection ◽  
Prediction Models ◽  
Fatigue Cracks ◽  
Crack Depth ◽  
Research Work ◽  
Nonlinear Coefficient ◽  
Difference Frequency ◽  
Average Error ◽  
Sum Frequency ◽  
The Difference

In order to detect the early fatigue crack of mechanical components simply, this paper puts forward the ultrasonic testing technology of different side collinear mixing. Firstly, based on the nonlinear ultrasonic theory, the method of calculating the difference frequency and sum frequency nonlinear coefficients of mixing ultrasonic is deduced. Then, the ram-5000 SINAP ultrasonic system is used to detect the aluminum alloy specimens with five different depth fatigue cracks, and the corresponding spectrum diagram is drawn. From the experimental results, we get that the crack depth is positively correlated with the nonlinear coefficients of difference frequency and sum frequency within a certain crack depth. Finally, by analyzing and fitting the experimental data, the prediction models of the difference frequency and sum frequency nonlinear coefficients on the crack depth are established. Through the analysis and combination of the above two prediction models, the prediction model of the mixing relative nonlinear coefficient is established, and the average error of the three prediction models is compared. The results show that the mixing relative nonlinear model has better results. The research work in this paper makes a useful exploration for crack detection and crack depth prediction.

Coupled Lateral and Torsional Vibrations of a Cracked Rotor

2004 ◽  
Author(s):  
Jerzy T. Sawicki ◽  
George Y. Baaklini ◽  
Andrew L. Gyekenyesi
Keyword(s):  
Crack Detection ◽  
Vibration Spectrum ◽  
Equations Of Motion ◽  
Structural Response ◽  
Crack Model ◽  
Cracked Rotor ◽  
Lateral Vibrations ◽  
Crack Problems ◽  
Torsional Excitation ◽  
Cracked Shaft

Rotor crack problems present a significant safety and loss hazard in nearly every application of modern turbomachinery, particularly in the power generation industry. However, early crack detection is not easily achieved during the operation of machinery. The difficulty is based on the fact that a crack produces an undetectable change in the overall structural response. This paper analyzes the coupling of torsional and lateral vibrations for an unbalanced cracked rotor. The rotor equations of motion for a system with cracked shaft, obtained using Lagrangian dynamics, show coupling and nonlinear interaction between the torsional and lateral vibrations. To investigate the effect of a transverse surface crack on the dynamic rotor response the breathing crack model was employed. By applying an external torsional excitation together with the excitation due to unbalance, signature responses were observed in the rotor vibration spectrum at sum and difference frequencies. These signature responses were due to the nonlinear effect of the crack. The observed phenomena, analytically defined here, offers a new methodology concerning crack detection and prognosis in rotors.

scholarly journals On the probability of an undetected surface-breaking crack

2008 ◽  
Vol 35 (1-3) ◽  
pp. 1-10
Author(s):  
J.D. Achenbach ◽  
S.S. Kulkarni
Keyword(s):  
Crack Detection ◽  
Fatigue Cracks ◽  
Crack Depth ◽  
Critical Value ◽  
Stress Fields ◽  
Cyclic Loads ◽  
Paris Law ◽  
Number Of Cycles ◽  
Damage Tolerant ◽  
Surface Breaking Crack

Surface-breaking fatigue cracks are common defects in metal components subjected to cyclic loads. Such cracks tend to propagate in stress fields that are below the critical stress level for static loading. An important part of a damage tolerant design philosophy is the requirement that surface-breaking cracks should be detectable before they reach a critical depth. In this paper, we consider a surface-breaking crack in a two-dimensional geometry, whose original depth is defined by a probability density function. The increase of the crack depth with number of cycles is governed by Paris law, and the detectability depends on a probability of crack detection (POD). Based on this information we determine the probability that the crack depth will have exceeded a prescribed critical value at a specified number of cycles.

Dynamics of Large Power Rotating Machine with Cracked Shaft

2005 ◽  
Vol 293-294 ◽  
pp. 337-346
Author(s):  
Slawomir Banaszek
Keyword(s):  
Crack Detection ◽  
Crack Depth ◽  
Computer Code ◽  
Crack Model ◽  
Simulation Research ◽  
Large Power ◽  
Crack Location ◽  
Rotating Machine ◽  
Diagnostic Indicator ◽  
Cracked Shaft

The paper presents the course and results of crack propagation simulation research. The object taken into account is a large power turbo-set rotor. The computer code system NLDW is presented. It uses a non-linear model of journal bearings, and well known crack model. Crack depth is marked by a crack coefficient. It is shown the crack generates a coupled forms of lateral, axial and torsional vibrations in multi-support rotor. Their intensity depends on the axial and circumferential crack location on the shaft. The attempt at pointing a proper diagnostic indicator for crack detection in large rotating machine is made according to obtained results.

Nonlinear Dynamics and Damage Assessment of a Cantilever Beam With Breathing Edge Crack

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Animesh Chatterjee
Keyword(s):  
Cantilever Beam ◽  
Crack Detection ◽  
Volterra Series ◽  
Fatigue Cracks ◽  
Harmonic Excitation ◽  
Crack Model ◽  
Open Crack ◽  
Breathing Crack ◽  
Vibration Testing ◽  
Polynomial Series

Failures in structures and machine elements can be prevented through early detection of fatigue cracks using various nondestructive testing methods. Vibration testing forms one of the most effective and recent one among these methods. There are mainly two approaches to crack detection through vibration testing: open crack model and breathing crack model. The present study is based on breathing crack model, in which the nonlinear vibration response under harmonic excitation is formulated through Volterra series and higher order frequency response functions. Bilinear stiffness characteristic of a cracked cantilever beam is approximated by a truncated polynomial series and response amplitudes of various harmonics are investigated for both qualitative and quantitative characterization. A new procedure is suggested whereby the presence of a breathing crack in a structure can be first identified and then the severity of the damage can be estimated through harmonic probing.

Fatigue crack detection method using analysis of vibration signal

2017 ◽  
Vol 1 (20) ◽  
pp. 63-74 ◽  
Author(s):  
Arkadiusz Rychlik ◽  
Krzysztof Ligier
Keyword(s):  
Crack Detection ◽  
Fatigue Cracks ◽  
Fatigue Cracking ◽  
Vibration Signal ◽  
Technical Condition ◽  
Visual Methods ◽  
Signal Characteristics ◽  
Fatigue Crack Detection ◽  
Sample Structure ◽  
Change Identification

This paper discusses the method used to identify the process involving fatigue cracking of samples on the basis of selected vibration signal characteristics. Acceleration of vibrations has been chosen as a diagnostic signal in the analysis of sample cross section. Signal characteristics in form of change in vibration amplitudes and corresponding changes in FFT spectrum have been indicated for the acceleration. The tests were performed on a designed setup, where destruction process was caused by the force of inertia of the sample. Based on the conducted tests, it was found that the demonstrated sample structure change identification method may be applied to identify the technical condition of the structure in the aspect of loss of its continuity and its properties (e.g.: mechanical and fatigue cracks). The vibration analysis results have been verified by penetration and visual methods, using a scanning electron microscope.

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