Dynamic Behavior Analysis of a Rotating Shaft with an Elliptical Breathing Surface Crack

Open access via the Springer Compact Acknowledgements The authors would like to thank the anonymous reviewers for their valuable suggestions that helped in improving the manuscript.Peer reviewedPublisher PD

Vibration Analysis of a Shaft-Disc System for On-line Crack Detection

This dissertation research concerns detection of cracks in rotating shaft-disc systems using the vibration-based methods. Turbines, pumps and jet engines are some examples of the shaft-disc systems, where crack failures may cause catastrophic effects. Detection of cracks at the early stages of growth is thus vital for prevention of failures, and has been the subject of many studies. Various crack detection methods such as ultrasonic, x-ray and vibration-based methods have been widely developed. Among these, the vibration-based methods are better suited for on-line crack detection. The reliability of such methods, however, relies upon the acquisition of an adequate vibration signature and its correlation with the crack, particularly for small size cracks. The reported studies have employed varying signal processing and crack modeling methods, although the models generally lack of consideration of effects of crack location and other possible faults. An analytical model of a flexible shaft with two transverse fatigue cracks and two discs mounted on rigid/ resilient supports is formulated, and the corresponding boundary and continuity conditions are developed. A modified harmonic balance method is subsequently proposed for solutions of the governing equations of the analytical model to investigate changes in the selected vibrational properties such as shaft critical speeds, shaft center orbits and super-harmonic components of the steady-state lateral response to an unbalance excitation. The effects of single crack properties such as depth and location on the responses are investigated considering short/long and rigid/flexible bearing supports. The crack is considered as a breathing crack, and is characterized by an exponential function, which facilitated its integration in the modified harmonic balance method. Furthermore, the effects of two cracks’ characteristics such as depth, location and relative angular position on selected vibrational properties are studied. Each crack is initially described by a breathing function proposed by Mayes and Davies, which is subsequently modified as a softly-clipped cosine function to accurately describe saturation in breathing phenomenon. The response characteristics of the cracked shaft are also compared with those of the system with an intact shaft in order to identify potential measures for detecting cracks. The validity of the proposed analytical model and the solution strategy is illustrated through comparisons of the model results with those obtained from a finite element model and limited experiments. The crack-induced changes in transient lateral responses of the shaft-disc system are also considered for transverse crack detection. The shaft-disc system is simply modeled as a Jeffcott rotor to compute its start-up responses in the lateral direction. The breathing behavior of the crack is characterized with respect to stress intensity factor at different points on the crack edge at each shaft angle. A positive stress intensity factor corresponds to the open part of the crack, while the closed part shows a negative stress intensity factor. The breathing crack excites super-harmonic components of the transient as well as the steady-state lateral responses. Time-frequency representation of the transient lateral response obtained from Hilbert-Huang transform based on an improved empirical mode decomposition is used for crack detection. The results show that observed changes in the transient and steady-state lateral vibration responses could lead to effective detection of relatively small size cracks

On the characteristics of fault-induced rotor-dynamic bifurcations and nonlinear responses

Rotor-dynamic stability is a very important subject impacting the design, control, maintenance, and operating safety and reliability of rotary mechanical systems. As rotor-dynamic nonlinearities are significantly more prominent at higher rotary speeds, the demand for better and improved performance achievable through higher speeds has rendered the use of a linear approach for rotor-dynamic analysis both inadequate and ineffective. To establish the fundamental knowledge base necessary for addressing the need, it is essential that nonlinear rotor-dynamic responses indicative of the causes of nonlinearity, along with the bifurcated dynamic states of instability, be fully characterized. The objectives of the research are to study the various rotor-dynamic instabilities induced by crack breathing and bearing fluid film forces using a model rotor-bearing system and to investigate the applicability of the fundamental concept of instantaneous frequency for characterizing rotor-dynamic nonlinear responses. A comprehensive finite element model incorporating translational and rotational inertia, bending stiffness and gyroscopic moment is developed. The intrinsic modes extracted using the Empirical Mode Decomposition along with their instantaneous frequencies resolved using the Hilbert transform are applied to characterize the inception and progression of bifurcations suggestive of the changing rotor-dynamic state and impending instability. The dissertation presents and demonstrates an effective approach that integrates nonlinear rotor-dynamics, instantaneous time-frequency analysis, advanced notions of dynamic system diagnostics and numerical modeling applied to the detection and identification of sensitive variations indicative of a bifurcated dynamic state. All presented studies on rotor response subjected to various system configurations and ranges of parameters show good agreements with published results. Under the influence of crack opening, the rotor-bearing model system displays transitional behaviors typical of a nonlinear dynamic system, going from periodic to period-doubling, chaotic to eventual failure. When film forces are also considered, the model system demonstrates very different behaviors and failures from different settings and ranges of control parameters. As a result, a dynamic failure curve differentiating zones of stability and bifurcated instability from zones of dynamic failure is constructed and proposed as an alternative to the traditional stability chart. Observations and results such as these have important practical implications on the design and safe operation of high performance rotary machinery

Experimental Investigation of Damage Detection in Beam Using Dynamic Excitation System

Most structural failures are due to break in consisting materials. These breaks begin with a crack, the extension of which is a serious threat to the behaviour of structure. Thus the methods of distinguishing and showing cracks are the most important subjects being investigated. In this article, a new smart portable mechanical system to detect damage in beam structures via using fuzzy-genetic algorithm is introduced. Acceleration-time history of the three points of beam is obtained. The signals are then decomposed into smaller components using new EMD (Empirical Mode Decomposition) method with every IMF containing a specific range of frequency. The dominant frequencies of the structure are obtained from these IMFs using Short-term Fourier transform. Subsequently, a new method of damage detection in simply supported beams is introduced based on fuzzy-genetic algorithm. The new method is capable of identifying the location and intensity of the damage. This algorithm is developed to detect the location and intensity of the damage along the beam, which can detect the damage location and intensity based on the pattern of beam frequency variations between undamaged and damaged states

Blade fault diagnosis using artificial intelligence technique

Blade fault diagnosis is conventionally based on interpretation of vibration spectrum and wavelet map. These methods are however found to be difficult and subjective as it requires visual interpretation of chart and wavelet color map. To overcome this problem, important features for blade fault diagnosis in a multi row of rotor blade system was selected to develop a novel blade fault diagnosis method based on artificial intelligence techniques to reduce subjective interpretation. Three artificial neural network models were developed to detect blade fault, classify the type of blade fault, and locate the blade fault location. An experimental study was conducted to simulate different types of blade faults involving blade rubbing, loss of blade part, and twisted blade. Vibration signals for all blade fault conditions were measured with a sampling rate of 5 kHz under steady-state conditions at a constant rotating speed. Continuous wavelet transform was used to analyse the vibration signals and its results were used subsequently for feature extraction. Statistical features were extracted from the continuous wavelet coefficients of the rotor operating frequency and its corresponding blade passing frequencies. The extracted statistical features were grouped into three different feature sets. In addition, two new feature sets were proposed: blade statistical curve area and blade statistical summation. The effectiveness of the five different feature sets for blade fault detection, classification, and localisation was investigated. Classification results showed that the statistical features extracted from the operating frequency to be more effective for blade fault detection, classification, and localisation than the statistical features from blade passing frequencies. Feature sets of blade statistical curve area was found to be more effective for blade fault classification, while feature sets of blade statistical summation were more effective for blade fault localisation. The application of feature selection using genetic algorithm showed good accuracy performance with fewer features achieved. The neural network developed for blade fault detection, classification, and localisation achieved accuracy of 100%, 98.15% and 83.47% respectively. With the developed blade fault diagnosis methods, manual interpretation solely dependent on knowledge and the experience of individuals can be reduced. The novel methods can therefore be used as an alternative method for blade fault diagnosis

An Investigation into Vibration Based Techniques for Wind Turbine Blades Condition Monitoring

The rapid expansion of wind power has been accompanied by reported reliability problems and the aim is to provide a means of increasing wind turbine reliability, prevent break downs, increase availability and reduce maintenance costs and power outages. This research work reports the development of condition monitoring (CM) for early fault detection in wind turbine blades based on vibration measurements. The research started with a background and a survey of methods used for monitoring wind turbines. Then, finite element modelling (FEM) of three bladed horizontal axis wind turbine (HAWT) was developed to understand the nature and mechanism of the induced vibration. A HAWT test rig was constructed and equipped with computerised vibration measuring system for model verification. Statistical and spectral processing parameters then were used to analyse vibration signals that collected in healthy and faulty cases. Results obtained using time and frequency based techniques are not suitable for extracting blades condition related information. Consequently, empirical mode decomposition method (EMD), principal component analysis method (PCA) and continuous wavelet transform (CWT) are applied for extraction blade condition related features from the measured vibration. The result showed that although these methods generally proved their success in other fields, they have failed to detect small faults or changes in blade structure. Therefore, new techniques were developed using the above mentioned methods combined with feature intensity level (FIL) and crest factor. Namely, those are EDFIL, RMPCA and wavelet based FIL. The new techniques are found to be reliable, robust and sensitive to the severity of faults. Those analysis techniques are suitable to be the detection tool for an integrated wind turbine condition monitoring system. Directions for future work are also given at the end of the thesis

Mathematical Validation of Experimentally Optimised Parameters Used in a Vibration-Based Machine-Learning Model for Fault Diagnosis in Rotating Machines

Mathematical models have been widely used in the study of rotating machines. Their application in dynamics has eased further research since they can avoid time-consuming and exorbitant experimental processes to simulate different faults. The earlier vibration-based machine-learning (VML) model for fault diagnosis in rotating machines was developed by optimising the vibration-based parameters from experimental data on a rig. Therefore, a mathematical model based on the finite-element (FE) method is created for the experimental rig, to simulate several rotor-related faults. The generated vibration responses in the FE model are then used to validate the earlier developed fault diagnosis model and the optimised parameters. The obtained results suggest the correctness of the selected parameters to characterise the dynamics of the machine to identify faults. These promising results provide the possibility of implementing the VML model in real industrial systems

Crack breathing mechanism in a cracked shaft subject to nontrivial mass unbalance

Rotating machinery is widely used in many industrial fields and is often damaged owing to the breathing of the fatigue crack. The fatigue crack opens and closes once per revolution during shaft rotation. The breathing of the fatigue crack reduces the stiffness of the shaft and hence alters its dynamic response. It changes the vibration characteristics of the shaft. Fatigue cracks are a common occurrence in large rotor systems and can cause catastrophic failure. Detecting faults in rotating machinery before failure is the best way to avoid damage. However, a generalised method of positively identifying a fatigue crack as the cause of anomalous vibrations is not yet available. Vibration diagnostics deliver insights into the mechanical ‘health’ of rotating machinery in real-time when the machine is running. However, studying the vibrations of naturally occurring fatigue cracks is difficult because shafts will often either fail before, or be taken out of service once, the crack is identified. Artificially introduced cracks do not exhibit behaviour identical to that of natural ones owing to the difficulty in cutting into a shaft and leaving a slot with close to zero radius at the crack tip. Therefore, considerable efforts have been devoted to numerically modelling cracked rotors and simulating their operating conditions so that the vibrations can be studied. Numerical modelling techniques are many and varied. In the present thesis, the literature on cracked rotor dynamics is reviewed. Of the crack modelling techniques reviewed, the second area moment method is identified as having potential for improvement. The second area moment method accounts for reduction in bending stiffness of a cracked rotor. Breathing of the fatigue crack is directly related to the second area moment at the crack location. It leads to changes in one of the shaft mechanical properties, stiffness. In a shaft with a crack, the shaft stiffness will change periodically at different rotational angles. Modelling the breathing of the fatigue crack is the key step to analyse the vibration response of a cracked shaft. This breathing phenomenon must be modelled accurately to detect the crack in a rotor. However, it is not yet fully understood how partial crack closure interacts with changes in shaft stiffness, and further, with key variables of the crack detection problem. Unfortunately, almost all existing models are not applicable near the shaft critical speed, because equations of motion developed under the assumption of rotor weight dominance are no longer suitable for analysis near the critical speed. Moreover, localised reduction in stiffness is directly related to crack depth, whereas global reduction in stiffness is directly related to the crack depth and crack location along the shaft. However, researchers opt to either ignore crack location or mitigate its effects. From the literature review, it is evident that accurate modelling, which considers the influence of the crack location and the effect of the unbalance force on the crack breathing behaviour of the fatigue crack to calculate the second area moment of inertia of a cracked shaft to form the stiffness matrix, is still absent. The first topic in this research work is developing a new unbalance model—effectual bending angle—to evaluate the crack breathing response and calculate the second area moment of inertia at any crack location along the shaft length. It is developed considering the effects of unbalance force, rotor weight, rotor physical and dimensional properties and a more realistic fixed-end boundary condition. It governs the opening and closing of a shaft crack that describes the proximity of the shaft bending direction (or shaft deformation direction) relative to the crack direction. The crack breathing behaviours have been studied for every possible crack location and shaft rotation angle. The presented model identifies unique crack breathing behaviours under the influence of unbalance force and rotor physical and dimensional properties, showing the strong dependence of the breathing mechanism on the crack location. Further, the newly developed model is used to obtain the second area moment of inertia of crack cross-section closed area at any crack location along the shaft length under the unbalance force effect about the centroid. The newly developed unbalance model results are validated through 3D FEM results. This thesis finds that this analytical unbalance model captures the main features of crack breathing and is in good agreement with the 3D FEM. However, the approach adopted in this study of using the existing balance model to identify the crack breathing behaviour and the second area moment of inertia needs to be improved. In this research work, a new method is developed to determine crack breathing, which is an improvement in terms of accuracy on adopted methods. The improvement is owing to the removal of two simplifying assumptions used by previous authors, namely, that the cracked shafts will only experience symmetrical bending and the neutral axis would lie perpendicular to the bending direction, that is, always be horizontal. Both assumptions are shown to be invalid on comparison with results from a three-dimensional finite element model. The newly developed method is then used to evaluate nonlinear crack breathing behaviour under different weight–unbalance force ratios at different crack locations by examining the percentage of opening of a crack. The breathing response predicted by the developed method is validated using the three-dimensional finite element model. The results of the algorithm show a significant improvement in accuracy when compared with data from the three-dimensional finite element model of cracked rotors. The mathematical modelling of calculating the cross-section properties, namely, the second area moment and centroid location, is also improved in this research work by considering neutral axis inclination, removing the assumption of collinearity between the bending moment and neutral axis at the crack location. The newly developed equations are used to evaluate the second area moment of inertia as a function of the crack locations and shaft’s angle of rotation about centroid axes. It is found to be highly dependent on crack location, similar to crack breathing behaviours. The work presented in this thesis demonstrates that a common assumption in the literature—that the effects of axial position of a crack can be neglected—is incorrect. The second topic of this research work is analysis of the crack breathing behaviour of an unbalance shaft with a more realistic transverse slant crack and elliptical crack at different crack locations along the shaft length. A three-dimensional finite element model consisting of a two-disk rotor with a crack is simulated with unbalance mass. The finite element model is simulated using Abaqus/standard. It is simulated considering the effects of unbalance force, rotor weight, rotor physical and dimensional properties and a more realistic fixed-end boundary condition. Crack breathing behaviours are visualised by the variation of the crack closed area and represented quantitatively by the percentage of the closing of the crack. Crack breathing behaviour is found to strongly depend on its axial position, angular position and depth ratios as well as unbalance force ratios and angular position of unbalance force. Compared with the balance shaft crack breathing behaviour, two different crack breathing regions along the shaft length are identified, where shaft stiffness is larger or smaller, depending on the unbalance force orientation, magnitude and crack location. However, four specific crack locations along the shaft length are identified where the crack remains fully closed or open or the same as in balance shaft crack breathing during shaft rotation under different loading conditions. The presented research results suggest that a more accurate prediction of the dynamic response of cracked rotors can be expected on considering the effects of unbalance force and individual rotor physical properties on crack breathing. The presented method and results of this research can be used to obtain the stiffness matrix of a cracked shaft element and then to study the vibration response of a cracked rotor where the rotor-weight-dominant assumption on crack breathing no longer holds

Non-probabilistic analysis of a double-disk rotor system with uncertain parameters

Vibration is a major issue in rotor systems. Due to the presence of material property dispersions, manufacture or assembling errors and time-varying working status, rotor systems are always subject to uncertainties. The uncertainties should be taken into consideration to understand the dynamic characteristics of rotors more thoroughly. In this study, interval analysis is carried out to investigate the non-probabilistic characteristics of a double-disk rotor with uncertain parameters. The uncertainties are modeled as uncertain-but-bounded variables due to insufficient essential information to define their precise probabilistic distributions. The deterministic analysis model is derived by the finite element method (FEM). The accuracy and effectiveness of the proposed method in solving uncertain rotor problems are validated by comparative study with the Monte Carlo simulation (MCS). Several cases where different physical parameters are regarded as uncertain are investigated and the dynamic response bounds are obtained. Simulations suggest that uncertainties have significant influence on the dynamic characteristics of the rotor system. Multi-source uncertainties propagation can cause heavy vibrations in mechanical systems