Breathing Crack Research Articles

Damage Detection in a Rotor Dynamic System by Monitoring Nonlinear Vibrations and Antiresonances of Higher Orders

Since rotor systems are very sensitive and vulnerable to transverse crack, early detection of damage is of paramount importance and essential for rotating machinery. Therefore, one of the main issues is to identify robust characteristics of the rotor vibration response that can be directly attributed to the presence of a transverse crack in a rotating shaft, preferably when the crack is small enough, in order to avoid catastrophic failures of rotating machines. This study investigates the potential links between the nonlinear vibrations and the locations of higher-order antiresonances and structural modifications due to the presence of a breathing crack in rotor systems. Using the proposed numerical results on the evolution of the nonlinear responses of a cracked rotor system, it was observed that a robust diagnostic of the presence of slight damage can be conducted by tracking nonlinear vibrational measurements, with particular attention to the antiresonance behavior of higher orders. These observations can easily serve as target observations for the monitoring system and for identifying the positions of damage at an early stage.

Determining the position of two cracks in a cantilever beam using artificial neural networks

During functioning time, structures such as beams are subjected to a variety of loads caused by the working conditions and environment, which can lead to the development of cracks. The current research is concerned with detecting the presence and location of two transverse breathing cracks, in cantilever beams. Starting from the known fact that damages produce a stiffness degradation in structures altering their dynamic parameters, we performed modal simulations of damaged beams to determine their natural frequencies. By using the simulation data, we trained an artificial neural network (ANN), using the feedforward backpropagation algorithm, that is capable to detect the presence of the cracks, their position and for the case when the damages are in proximity, the model can determine if the cracks occur on the same face or opposite faces.

A Feature of Mechanics-Driven Statistical Moments of Wavelet Transform-Processed Dynamic Responses for Damage Detection in Beam-Type Structures

Multiple damage detection using structural responses only is a problem unresolved that is in the field of structural health monitoring. To address this problem, a novel feature of mechanics-driven statistical moments of wavelet transform-processed dynamic responses is proposed for multi-damage identification in beam-type structures. This feature is referred to as a continuous wavelet transform (CWT)-second-order strain statistical moment (SSSM), with CWT-SSSM in the abbreviation. The mechanical connotation of CWT-SSSM lies in that the SSSM of each order principal vibration contains strain mode shapes, inducing greater sensitivity to local damage. With this method, the CWT is used to extract and amplify the singularities caused by damage in each order SSSM curve, following which the data fusion technology and three-sigma rule in statistics are adopted to construct the damage index. The presence of damage is characterized by the abrupt change in the damage index. The soundness and characteristics of the CWT-SSSM feature are verified by identifying multiple damages in a cantilever beam bearing two breathing cracks. The results show that the proposed feature can accurately designate multiple cracks free of baseline information on the intact counterpart; moreover, it has robustness against noise and applicability under excitations of approximately uniform spectra.

Dynamic modeling of rotary blade crack with regard to three-dimensional tip clearance

To investigate the dynamic characteristics of the three-dimensional blade tip clearance (3D-BTC) of rotary blade cracks, a novel dynamic model of the rotary blade crack with regard to the 3D-BTC is derived based on the Timoshenko beam theory. In this model, the modal shape functions of the blade are derived based on the transfer matrix method, and the axial and circumferential aerodynamic loads are introduced to better obtain the dynamic responses of the blade vibration. Then, a breathing crack model of the blade trailing edge crack is established by considering the coupling effects of the centrifugal stress, axial bending stress, and circumferential bending stress. The crack opening width is introduced into the breathing crack model to comprehensively depict the crack together with the crack depth and crack location. Moreover, a numerical calculation method for the 3D-BTC is proposed for the rotary blade with cracks. The dynamic model is validated by comparing it with the finite element model and the experiment. Finally, the effects of the blade trailing edge crack on the 3D-BTC are analyzed. The results show that the cracked blade's first-order natural frequency decreases with the crack depth increase, and it increases first and then decreases slightly when the crack location moves away from the blade root. The effects of crack opening width on the first-order natural frequency are relatively small due to its small size. In the meantime, the nonlinear damage indicators (NDIs) of the 3D-BTC are calculated. The results show that the NDIs can reflect the severity of the blade crack, and the proposed model can comprehensively analyze the effects of rotary blade crack on the 3D-BTC, which is beneficial for the diagnosis method for blade cracks based on the 3D-BTC.

Nonlinear vibration analysis of beam-like bridges with multiple breathing cracks under moving vehicle load

The beam-like bridges with small and medium spans are designed to mainly sustain the moving vehicle. Hence, the dynamic behavior of bridges under vehicular loading can provide important information for the bridge design, assessment, and maintenance. Cracks, as one of the most common damage in the bridge structures, alter the bridge dynamic characteristics and therefore responses to the moving vehicle. This paper proposes a novel semi-analytical approach for nonlinear vibration analysis of the beam-like bridges with breathing cracks subjected to vehicular loading, taking into account the dynamic interactions between the vehicle and cracked bridge. The Dirac’s delta function is utilized to represent the local stiffness change at the crack location, leading to closed-form solutions of mode shapes of the cracked beam. The breathing process of the crack, causing eigenproperties of the beam to change over time, is characterized by the time-varying curvature of the bridge. Subsequently, the nonlinear dynamic equation of the vehicle-cracked bridge interaction system is established, which is solved through a formulated double-iterative numerical scheme. Eigenvalues and dynamic responses of the bridge with open crack presented in the literature are compared with those obtained from the proposed approach for purposes of validation. The effects of various crack parameters, vehicle speed, and bridge surface irregularity are investigated through a parametric study. In addition, the detection of breathing cracks is also discussed. The results show that the proposed approach can be used to effectively obtain the nonlinear vibration characteristics and dynamic responses of the beam-like bridge with general boundary conditions and different crack numbers, locations, depths, and initial status under moving vehicle. Moreover, the approach has the potential to be incorporated into the vibration-based bridge damage detection.

Quantification of the effect of pump wave amplitude on crack breathing for the Nonlinear Coda Wave Interferometry

In civil engineering, an emerging ultrasonic approach based on Code Wave Interferometry (CWI), called Nonlinear Coda Wave Interferometry (NCWI) has been developed to detect microcracks in cementitious materials that cannot be detectedby conventional ultrasonic methods. NCWI uses a high amplitude low frequency (LF) nonlinear pump wave to generate a nonlinear clapping effect at microcracks that can be detected by a high frequency (HF) probe wave. The imaging of cracks inside heterougeneous materials using NCWI requires the inversion technique, which is constitued by model space and data space, in which conatains model parameters and data parameters respectively. In the frame of inversion with NCWI, the model parameter used is the scatetring cross section of a crack sigmaD, and the experimental parameter is the decorrelation coefficient Kd. Knowing that sigmaD depends on the pump wave amplitude. Therefore, in order to introduce NCWI in inversion, the relationship between the pump wave and sigmaD is needed, which is the goal of this study. The dynamic pump wave generates clapping effect at crack tips, the probe wave frequencies are higher than the pump waves’ by an order of magnitude, hence the effect of pump wave on the coda wave is rather averaged. Previous study showed that this clapping effect is equivalent to a single crack length change dL, dL can be related to an equivalent static stress sigma0 which produces the same dL in quasi-static regime, which is equivalent to the dynamic pump wave. Therefore, a relation can be established between sigma0 and sigmaD. This introduces NCWI into the inverison. Then, the theoretical estimation of Kd can be achieved by the simulation of NCWI using 2D Spectral Element Method (SEM2D), combining with the relationship between sigma0 and sigmaD, which can be used later on in the inversion for the crack imaging.

The dual Fourier transform spectra (DFTS): a new nonlinear damage indicator for identification of breathing cracks in beam-like structures

The dual Fourier transform spectra (DFTS): a new nonlinear damage indicator for identification of breathing cracks in beam-like structures

Axial-bending coupling vibration characteristics of a rotating blade with breathing crack

Blade crack is one of the most common blade failures of rotating machines which may lead to catastrophic accidents. Although many nonlinear vibrations of breathing crack have been investigated, there are few reports on the axial-bending coupling vibration caused by crack. With the aim of providing physical insight into the mechanisms of axis-bending coupling due to crack, a novel axial-bending coupled breathing crack model (ABCBCM) for the rotating blade is proposed in this study. The proposed ABCBCM is analytically formulated based on the Timoshenko beam theory and Castigliano’s principle, and validated by comparing the natural and dynamic characteristics with the finite element model (FEM) and experimental tests. In addition, the effects of boundary conditions (rotational speed), crack parameters (crack depth and crack location) and loading conditions (excitation load) on the vibration characteristics of the cracked blade are investigated. The results indicate that the blade axial response is more sensitive to the nonlinearity caused by the breathing crack than the bending response; the axial-bending coupling caused by the crack changes the equilibrium position of the axial and bending displacement; the phase portrait of axial response and the orbit of axial-bending displacement are effective methods to detect breathing crack; and the axial displacement amplitude ratio and the axial acceleration amplitude ratio also are valuable indicators to estimate the severity of the blade crack. The proposed model can provide valuable insights for fault diagnosis and safety monitoring of cracked blade.

Localization of breathing cracks in engineering structures with transmissibility function-based features

Structures such as fuselage, blade and wing in aeronautical and astronautical engineering are often subjected to cyclic loads in their service life, which in turn causes breathing cracks in these structures. To provide much more precise position of breathing cracks in structures and avoid structure failure, a local vibration-based approach using transmissibility function-based features is proposed and verified in this study. In the new method, nonlinear dynamic behaviour of cracked structures is simulated by a chain-type multiple-degree-of-freedom (MDOF) model, in which breathing cracks are represented as related nonlinear connections between masses. By modifying local structural physical parameters (mass, stiffness or damping coefficient), transmissibility function-based features are derived from cracked structures only and corresponding damage indicator is calculated for fault localization. Based on results of simulations on the chain-type model with breathing cracks, the effectiveness and practicability of damage indicator and method are verified and demonstrated. Moreover, merits, drawbacks and further development of this method are summarized and discussed.

Vertical Transient Response Analysis of a Cracked Jeffcott Rotor Based on Improved Empirical Mode Decomposition

The crack-induced changes in the vertical transient response of a rotating shaft–disc system, Jeffcott rotor, are investigated for transverse crack detection. The crack is considered as a breathing crack. A novel breathing function is proposed, in which the partially open–closed crack breathing behavior is interpolated between the fully open and closed crack behaviors. The breathing crack excites superharmonic response components of the transient as well as the subharmonic components. A Hilbert–Huang transform based on an improved empirical mode decomposition algorithm is subsequently formulated to evaluate the time–frequency representation of the vertical transient response of the rotor to detect the crack. The results show that the proposed breathing function can effectively reduce the computational effort without sacrificing the accuracy of the crack breathing behavior in the presence of small cracks. It is shown that time–frequency representations based on an improved empirical mode decomposition algorithm can lead to the detection of smaller cracks compared with those based on the empirical mode decomposition algorithm.

Dynamic Analysis of a Rotating Cardan Shaft under the Influence of a Breathing Crack and Dense Fluid Force

To extract any information from a complex data vibration, the time-frequency technique represents a suitable tool and a better indicator of the overall asset health of a rotating machine. Fluid influences on a cracked driveshaft and dynamic analysis of a rotating Cardan shaft are discussed in this paper. The study of the forced vibration signals of the rotating Cardan shaft focused uniquely on the impact of the hydrodynamic forces near the cracked driveshaft and its transmission of power to a driven shaft. By merging each subsystem consisting of the breathing crack mechanism in a rotating shaft, the perturbation function between misaligned shafts and transient hydrodynamic forces results in a strongly nonlinear system of partial differential equations, which becomes complicated when analyzing the dynamic response of the Cardan system. In view of the complexity of the Cardan system, the instantaneous frequency identification based on synchrosqueezing wavelet transform filters is numerically used to provide a reliable indication of the rotating system equipment’s health. A conclusive dynamic analysis through the wavelet synchrosqueezing demonstrated that the Cardan joint and the hydrodynamic resistance forces have a high impact on the system’s vibration characteristics and significantly influence the transmission motion with a continuous increase of the driven shaft vibration amplitudes.

Structural fatigue crack localisation based on spatially distributed entropy and wavelet transform

Fatigue cracks are inevitable in the service life of engineering structures and can cause unexpected severe structural failures if left unattended. During structural vibrations, fatigue cracks, specifically at the initial stage, exhibit a repetitive open-close breathing-like phenomenon. Breathing cracks cause irregularities, bi-linearity, or perturbations in the vibration responses at different locations in engineering structures. Entropy can be used to quantify the different irregularities or bi-linearity induced by breathing phenomenon. This paper presents a new breathing crack localisation method based on a spatially distributed wavelet entropy approach. A numerical analysis was conducted to validate the proposed method and illustrate the fundamentals of the proposed methodology by analysing the localisation of breathing cracks at different locations in a beam structure. Furthermore, the vibration responses of the beam with predefined breathing cracks were analysed using spatial wavelet entropy in a laboratory setup to further prove the feasibility of the proposed method. It was concluded that the proposed spatial wavelet entropy approach can be effectively used for breathing crack localisation in engineering structures.

Analytical bending stiffness model of composite shaft with breathing fatigue crack

In this paper, an improved stiffness model of the breathing crack of the composite shaft tube was established based on the Layer-wise theory, which considered the influence of orientation angle and stacking sequence of the cracked layers. Then, the model was compared with the horizontal neutral axis model, Mayes' model and analytical model. The results showed that the improved model can more effectively reflect the influence of the laminate parameters on the stiffness. Based on the model, the bending stiffness characteristics of the cracked composite shaft were studied, and the effects of laminate parameters on the stiffness were obtained.

Evaluation of the residual carrying capacity of a large-scale model bridge through frequency shifts

Structural systems are often subjected to degradation processes due to different kinds of phenomena like unexpected loadings, ageing of the materials, and fatigue cycles. This is true, especially for bridges, in which their safety evaluation is crucial for planning maintenance activities. This paper discusses the experimental evaluation of the residual carrying capacity from frequency changes due to distributed damage scenarios. For this purpose, in the laboratory of the University of Bologna, an experimental reinforced concrete model bridge was built and loaded. The applied forces produced bending moments causing up to three increasing levels of damage severity, namely early and diffused concrete cracking, and finally rebar yielding. By processing the acceleration signals recorded during the dynamic tests on the model bridge, the main natural frequencies of the bridge were obtained and the remaining bearing capacity was estimated based on the damage state. The opening and closure of cracks during a dynamic excitation produced a biased estimation of natural frequencies related to each damaged condition. The frequency decay predicted by the theory of breathing cracks applied to the performed experiments properly estimated the losses in the carrying capacity.

Vibration characteristics of cracked compressor blades with different materials

Aiming at the influence of different material properties on the vibration characteristics of cracked gas turbine compressor blades, the vibration characteristics of cracked compressor blades with three different materials were studied by numerical calculation. The first order bending vibration of a cracked cantilever beam was simplified to a single degree of freedom system. The breathing crack stiffness model was introduced to change the elastic modulus and other parameters of the material. The fourth-order Runge-Kutta method and fast Fourier transform were used to obtain the cantilever beam vibration characteristic diagram, and the relationship between the material properties and the structural vibration was analyzed. The results show that the elastic modulus of the material is proportional to the stiffness, and the stiffness of the material affects the vibration displacement response of the cantilever beam, and the larger the stiffness is, the smaller the vibration displacement is.

Effective Identification and Localization of Single and Multiple Breathing Cracks in Beams under Gaussian Excitation Using Time-Domain Analysis

The output response of any intact oscillatory system subjected to a Gaussian excitation is also Gaussian in nature. On the contrary, when the system contains any type of underlying nonlinearity, the output signal is definitely non-Gaussian. In beam structures, the presence of fatigue-breathing cracks significantly influences the dynamic response characteristics under Gaussian excitation. The presence of such cracks alters the response to be nonlinear, and the non-Gaussianity of the system will arise. In order to examine the non-Gaussianity features and ability for the detection and localization of fatigue cracks, several breathing crack identification scenarios in beam-like structures are presented in this paper. The effects of single and multiple breathing cracks corresponding to different boundary conditions on the responses of beams are studied. The results are analyzed based on the higher-order time-domain transformations. Higher-order transformations, namely the skewness and kurtosis coefficients in addition to the Shannon entropy, are exploited to provide dynamic details about the response, which the conventional second-order statistics cannot show. The results exhibit that the proposed methods are robust and immune to noise and can detect and localize breathing cracks with different sensitivities.

Post-resonance backward whirl analysis in cracked overhung rotors

Overhung rotors usually exhibit recurrent transitions through critical whirl rotational speeds during startup and coast down operations, which significantly differ from their steady-state whirl responses. The presence of angular acceleration results in a linear-time-varying (LTV) system, which, although technically linear, still presents complexities often evinced by a nonlinear system. In general, backward whirl zones can either precede the critical forward whirl speed (termed as pre-resonance backward whirl, Pr-BW), or immediately follow the critical forward whirl speed (termed as post-resonance backward whirl, Po-BW). The Po-BW in the whirl response of a cracked overhung rotor with a breathing crack is studied here as distinct from that of geometrically symmetric configurations of other rotor systems. The equations of motion from the finite element (FE) model of an overhung rotor system with a breathing crack are numerically integrated to obtain the whirl response. The transient whirl responses with different bearing conditions are thoroughly investigated for excitation of Po-BW. The Po-BW zones of rotational speeds are determined via the wavelet transform method and full spectrum analysis (FSA) and applied to signals with added noise. The results of this work confirm the excitation of the Po-BW in cracked overhung rotors and confirm the robustness of the employed methods.

Nonlinear damage identification method of transmission tower structure based on general expression for linear and nonlinear autoregressive model and Itakura distance

Fatigue cracks and bolt looseness are two kinds of common nonlinear damage in a transmission tower structure. However, due to the complexity of the transmission tower structure, it is difficult to identify the nonlinear damage accurately by using traditional damage identification methods. To solve this problem effectively, a time domain damage identification method based on general expression for linear and nonlinear autoregressive model (GNAR model) and Itakura distance is proposed. To describe the stochastic characteristics of time series more concisely and accurately, the optimized structure of GNAR model was selected by the stochastic pruning algorithm based on greedy strategy. And Itakura distance was used as a damage indicator for nonlinear damage identification. The nonlinear damage experiment of three-story frame model in Los Alamos laboratory was used to verify the effectiveness of the proposed method, and this method was applied to the nonlinear damage identification experiment of a transmission tower steel frame model. In the transmission tower model experiment, two kinds of nonlinear damage types are considered: component breathing cracks and joint bolt loosening. The results show that the proposed nonlinear damage identification method can easily identify the nonlinear damage of the frame model and the transmission tower model effectively. The change of floor mass barely has effects on the damage identification results. The damage probability of the damaged stories calculated by the proposed method is significantly higher than that of the undamaged stories, so that it is helpful to find the location of the nonlinear damage source efficiently. And the proposed method is a damage identification method based on sub-structure story, which can identify the transmission tower model with two nonlinear damage sources at the same time.

A novel frequency domain feature-based approach for diagnosis of failure faults in complex structures with interconnected joints

A wealth of complex structures with interconnected joints such as steel truss bridges and warehouses commonly exist in civil engineering, while they are easily subjected to joint faults like bolt loosening, breathing crack and chemical corrosion during their service, which would seriously affect structures’ safety, durability and reliability. Therefore, diagnosis of joint faults, especially at an early stage, would be essential and meaningful for complex structures. To overcome some limitations in existing diagnosis methods, a novel frequency domain feature-based approach for joint faults in complex structures is developed in this paper. In the new approach, complex structures are simplified as some simple and discrete unit substructures. Then, corresponding unit dynamic models are obtained for the dynamic analysis by considering effects of potential faults as additional nonlinear loads. Collecting vibration data of complex structures to be diagnosed only under different levels of harmonic excitations, which have different magnitudes but same frequency components, local frequency domain diagnosis features and indicators based on additional nonlinear loads and transmissibility functions are defined, and detailed procedures of the novel approach are shown accordingly. Finally, effectiveness and availability of the novel approach are verified through some experiments on a steel structure with bolted joints. Moreover, results of comparison study and effects of excitation frequency are discussed to show superiority of the proposed approach further.

Dynamic Modeling and Stability Analysis of a Heavy-Duty Flywheel Rotor-Bearing System with Two Cracks

Cracks have a significant impact on the stability of rotating machinery. However, most studies focus on rotating machinery with only one crack. This paper discusses the influence of two cracks on the stability of a flywheel rotor-bearing system. In this study, the dynamic models of vertically placed flywheel rotor-bearing system with two open cracks and two breath cracks are established using the finite element method (FEM). Floquet theory is used to calculate the stability of the system and the influence of depth and positions of cracks are analyzed. The results show that breathing cracks cause more unstable regions than open cracks, and the range of rotating speeds over which the rotor is unstable increases with increasing crack depth. In addition, it is observed that when the crack locations are adjacent, the unstable region will become very large, covering most of the crack depth range and speed range, making the rotor extremely unstable. Besides, the bearing stiffness causes an offset in the unstable regions, whereas the damping influences the instability value of the rotor.