Cracked Rotor System Research Articles

Remaining useful life prediction for a cracked rotor system via moving feature fusion based deep learning approach

This study proposes a novel approach for predicting the remaining useful life (RUL) of a cracked rotor system by using a moving fusion gated recurrent unit (MFGRU) model. Firstly, 12 multi-domain features were extracted from the raw collected vibration signals, which were then fused and distributed adaptively using bidirectional exponential moving average (EMA) and multi-head attention (MHA). Then a bidirectional gated recurrent unit network combined with moving feature fusion method was proposed to capture the long-term dependence relationship in the monitoring data of the cracked rotor for RUL prediction. Finally, the model’s performance was validated through accelerated life experiments, with the measured values of root mean square error (RMSE) and mean absolute error (MAE) below 3.17 and 2.60, respectively. This study offers a dynamic RUL prediction method with certain significance and valuable reference for designing deep learning models.

Numerical and experimental analysis on the whirl orbit with inner loop in cracked rotor system

Cracks in rotor systems are generated because of internal as well as external heavy loading conditions. The external loading conditions could be attributed to thermal gradients (such as in turbomachinery) or other environmental conditions that result in cracks developments. The internal loading conditions can be attributed to cyclic fatigue loading during continuous and recurrent shaft's running which is the most common cause for cracks propagation. The presence of cracks in rotor systems induces nonlinearities into the system which affects its whirl response. Many published literature on cracked rotors have indicated that when the rotational speed is at sub-critical resonance of order 1/n (1/2, 1/3,1/4, etc.…) of the critical rotational speed, the fundamental whirl orbit takes patterns including inner loop/loops of order (n-1) or outer loop/loops of order (n+1) depending on the critical whirling direction. The present study investigates the strong impact of the magnitude of unbalance force on whirling pattern with inner loop in a cracked rotor. Numerical analysis is carried out on the mathematical model of the considered cracked rotor. The unbalance force magnitude is observed to be the main factor affecting the inner loop pattern in the whirl orbit rather than the ½ of the critical resonance speed. Accordingly, the appearance of inner loop in shaft's whirl orbit due to crack propagation in the rotor system is found here to be present before and after passing through resonance speed. This inner loop whirl orbit pattern is not restricted to be associated with ½ of the critical rotational speed as believed in plenty of literature. This kind of whirling is observed to be strongly depending on the unbalance force magnitude rather than the subcritical resonance speed. The experimental results also validate the numerical simulation findings. Therefore, the whirl orbits of the cracked rotor can be categorized into pre-resonance whirl orbit (Pr-WO), resonance whirl orbit (R-WO) and post-resonance whirl orbit (Po-WO) based on the magnitude of the unbalance force. The resultant numerical and experimental findings on the whirl orbit with inner loop can provide a robust insight into the cracked rotor whirl behavior.

Dynamic analysis of slant cracked rotor system considering nonlinear oil film force.

In this paper, considering the combined effects of nonlinear oil film forces and cracks on the rotor-bearing system, the differential equations of motion with 4 degrees of freedom are established by Lagrangian method. Then, the Lundgren-Kutta method is used to solve them and the results of the model are compared with the experimental data. The study demonstrate that the cracked rotor-bearing system is relatively stable at subcritical speeds, mostly in the period-1 motion. But near 1/3 of the critical speed, there is an inner loop in its whirl orbit and a significant increase in the 2x frequency component. When the system speed rises to the region near 1/2 of the critical speed, though the bifurcation motion and a relatively high 2x frequency can be observed, there are no other reliable fault characteristics. The study proves that the rotor crack fault diagnosis method based on the whirl orbits is convincing for slant cracked rotors.

Vibrational Behavior and Dynamic Analysis of Cracked Rotor Systems during Transient Conditions

Vibrational Behavior and Dynamic Analysis of Cracked Rotor Systems during Transient Conditions

Research on the dynamic characteristics of rotor-bearing-seal system with breathing cracks under steam flow excited force

In order to reveal the influence of breathing-type straight cracks on the motion characteristics and stability of a turbine rotor-bearing-seal system. The study examines the motion characteristic of a cracked rotor system under different loads with different crack depths, the coupled thermal and dynamic loads. The research derives motion differential equations for the cracked system, considering nonlinear dynamic properties such as nonlinear stiffness and damping. The equations incorporate the nonlinear steam flow excited force obtained from numerical simulations. The resulting motion equations are solved using the Runge-Kutta method, and the accuracy of the investigation of nonlinear dynamic characteristics is validated through experimental comparisons. Based on these findings, the motion characteristics and stability of the cracked rotor system under different conditions are analyzed. The results indicate that the motion characteristics of the rotor are progressively altered by the crack depth, and at a certain depth, the motion deviates from the established pattern. The influence of cracks on rotor stability is predominantly notable in the 34–58% THA region and under high load conditions. Moreover, the chaotic characteristics of rotor motion is more significant after applied the coupled thermal and dynamic loads, and the stability of the 34–58% THA region is significantly worse.

Research of energy characteristics and fault position detection for cracked rotor system

Early crack faults will introduce subtle local changes in the whole rotor system, which may bring difficulties to the fault detection process due to external disturbing factors. Meanwhile, judging the damaged position of rotor systems might be tough only through displacement or velocity. To overcome these issues, the harmonic balance-energy power flow analysis (HB-EPFA) is presented to investigate the rotor system with a transverse crack. Besides, a novel indicator (Time-averaged power flow) is proposed to evaluate the crack faults. For the energy characteristic analysis, the cracked rotor appears a special amplitude-jumping phenomenon, even in the case of shallow crack depth. The influence of crack depth on power flow values under different rotating speeds is obtained. Furthermore, the existence of cracks will lead to the rotation shaft presenting an abrupt energy-changing zone, which can be used to detect crack position. Relevant experiments are applied to validate the proposed detection method, and the experimental results agree with the theoretical analysis. The conclusions achieved in this paper can provide a reference for fault diagnosis of rotor systems in engineering practice.

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

PurposeIn this paper, dynamic behavior of a rotor system with an elliptical breathing crack that simulates the real shape of the crack front is investigated.MethodsA finite element model of the cracked rotor system is developed. The crack breathing mechanism is modelled based on an improved breathing model which considers the inclination of the neutral axis of the cracked element cross-section during shaft rotation. Harmonic balance method is used to solve the equations of motion of the rotor system for steady-state response characteristics. The effect of some parameters such as crack depth, crack shape factor and the spinning speed is investigated.Results and conclusionsThe results show that the unique whirl orbits behavior during passage through the subcritical speeds serve as a key indicator of crack presence in the shaft. The effects of the crack front curvature and the breathing model are revealed. The value of shape factor affects the whirl orbit characteristics such as size of the inner or outer loops and the amount by which the orbits rotate while crossing the subcritical speeds. The presented model considering the real crack front shape may contribute towards improved modelling of cracked rotors and better interpretation of measured vibration response.

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.

Novel energy identification method for shallow cracked rotor system

Many factors like period stress or fatigue may lead to cracks in the rotating shaft which can cause economic losses and accidental risk. Early crack faults will introduce very slight local changes in the whole rotor system. And the monitoring data on rotor systems are disturbed by multiple factors. These problems may make subtle fault information be ignored, resulting in the collection of a possible rotor fault becoming tougher. To overcome such issues, novel energy methods including the vibration energy analysis and the 3D energy model representation are presented to investigate the rotor system with transverse crack. For the rotor system with a shallow crack, the energy response analysis shows the existence of shallow cracks mainly affects the peak response values. Meanwhile, the 3D energy model is used to visualize the fault characteristics. The results show that even shallow cracks can cause special phenomena in the 3D energy model, which can promote the identification of crack faults more accurately. The influence of parameters on rotor vibration energy is studied and the corresponding results are obtained. To validate the theoretical analysis results, relevant experiments are applied. The results show that the experimental results agree with the theoretical analysis. The conclusions achieved in this paper can provide a reference for fault diagnosis of rotor systems in engineering practice.

Complexity of periodic sequences of large-scale rotating machinery system coupled by multi-fault

Taking the steam turbine cracked rotor system coupling multi-fault as an example, this paper reports systematic numerical experiments exploring two-parameter periodic complexification cascades. Specifically, we report high-resolution phase diagrams predicting and describing how the periodic sequences unfold over a quite extended range of parameter planes. Surprisingly, such diagrams reveal that the distribution of periodic sequences either agrees well with the characteristics of “eye” of chaos, or is characterized by the derived Farey sum tree and the bidirectional symmetrical Stern–Brocot sum tree. These cascades show that the frequent occurrence of transient multi-period motion is a generic feature for the large rotating machinery system with multi-fault. And the paper obtains a cluster of sequences of the Farey sum tree and the Stern–Brocot sum tree specially suitable for the large nonlinear and nonautonomous systems, which can provide a powerful reference for failure prediction and parameter matching.

Numerical and experimental study on quantitative assessment of multiple fault parameters in a warped internally damped rotor with a transverse fatigue crack integrated with an active magnetic bearing

This work aims to apply experimental data in the multi-fault identification algorithm developed for an internally damped warped cracked rotor system integrated with an auxiliary active magnetic bearing (AMB).A quantitative assessment of additive stiffness due to crack, unbalance, and residual bow with their orientations, multiplicative fault due to residual bow and crack, external and internal (rotating) damping, and AMB parameters that affect the dynamics of the system is done. The rotor experiences multiple harmonics in rotation due to the effect of crack and multiplicative bow-crack fault. To overcome the drawback of removal of residual bow at only 1X harmonic in signal processing, the present work addresses the simultaneous estimation of crack, bow, and multiplicative faults. Measurements of vibrational signalsof shaftand control current from PID controller are taken from the rotordynamic test bench. The multi-harmonic full spectrum amplitudes and phases of forward and backward whirl extracted from the measured test data are fed to theidentification algorithm which estimates fault and system uncertain parameters of fatigue cracked rotor system.This technique can effectively identify simultaneous rotor faults with prior knowledge of some characteristics of the rotor system. The novelty of this work is the identification of shaft residual bow with additive stiffness of crack where the additive crack stiffness is the direct indicator of crack and the magnitude of residual bow is of the permanent bend in rotor defining their severity.

The Improved WNOFRFs Feature Extraction Method and Its Application to Quantitative Diagnosis for Cracked Rotor Systems.

During its operation, a rotor system can be exposed to multiple faults, such as rub-impact, misalignment, cracks and unbalancing. When a crack fault occurs on the rotor shaft, the vibration response signals contain some nonlinear components that are considerably tougher to be extracted through some linear diagnosis methods. By combining the Nonlinear Output Frequency Response Functions weighted contribution rate (WNOFRFs) and Kullback–Leibler (KL) divergence, a novel fault diagnosis method of improved WNOFRFs is proposed. In this method, an index, improved optimal WNOFRFs (IOW), is defined to represent the nonlinearity of the faulty rotor system. This method has been tested through the finite element model of a cracked rotor system and then verified experimentally at the shaft crack detection test bench. The results from the simulation and experiment verified that the proposed method is applicable and effective for cracked rotor systems. The IOW indicator shows high sensitivity to crack faults and can comprehensively represent the nonlinear properties of the system. It can also quantitatively detect the crack fault, and the relationship between the values of IOW and the relative depth of the crack is approximately positively proportional. The proposed method can precisely and quantitatively diagnose crack faults in a rotor system.

Negative potential energy content analysis in cracked rotors whirl response

Appearance 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.

Experimental Comparison of Response for Healthy and Cracked Overhung Rotor System

Online diagnosis of the rotor system has been of great aid for possible detection of crack. In this paper, experimental vibration response of unbalance cracked overhung rotor system with an open crack is compared to the response of a healthy unbalance overhung rotor system for possible indication of the crack presence, due to change in the dynamic response of the cracked rotor system. The experimental modal analysis results have been compared with the finite element results to validate the accuracy of the experimental setup, followed by the comparison of the spectral response for healthy and cracked rotor system. The change in the dynamic behaviour of the cracked rotor system is studied through the waterfall plot and the colour map plot. A noticeable increase of 27.77% in response amplitude for crack overhung rotor system compared to that of healthy overhung rotor system is observed with unbalance provided to disc. The changes seen in both plots can be utilized for the indication of crack presence in the rotor system.

Dynamical analysis of hollow-shaft dual-rotor system with circular cracks

In this paper, we considered a dual-rotor system with crack in shaft. The influence of circular crack in hollow shaft on dynamical response was studied. The equations of motion of 12 elements dual-rotor system model were derived. Harmonic balance method was employed to solve the equations. The critical speed and sub-critical speed responses were investigated. It was found that the circular crack in hollow shaft had greater influence on the first-backward critical speed than the first-forward critical speed. Owing to the influence of crack, the vibration peaks occurred at the 1/2, 1/3 and 1/4 critical speeds of the rotor system, along with a reduction in sub-critical speeds and critical speeds. The deeper crack away from the bearing affected the rotor more significantly. The whirling orbits, the time-domain responses and the spectra were obtained to show the super-harmonic resonance phenomenon in hollow-shaft cracked rotor system.

Torsional vibration characteristics and experimental study of cracked rotor system with torsional oscillation

Root causes of numerous crack failures are attributed to the torsional oscillation between the turbine generator and the grid. To prevent such kind of failures, torsional vibration monitoring system has been intensively installed in reality and the torsional vibration is more and more observed in the operation. However, the mechanism of the characteristics of torsional vibration of the rotor system with and without cracks has not been well explored. Therefore this work presents the dynamic analysis and experimental study on the rotor system with transverse and slant cracks. For simulating the torsional oscillation in reality, excitation device is designed in the experiments and torsional vibration is measured. Based on this, the characteristics of lateral and torsional vibration of the rotor system are compared. The results show that, (i) although the slant crack presents more significant later-torsional vibration (especially for the breathing crack), the transverse cracked rotor system show higher amplitudes in the fundamental frequency and harmonic components (especially for the open crack) and (ii) the torsional excitation introduces more obvious vibration fluctuation in the rotor system with cracks (observed from the orbits and the torsional vibration).

Post-resonance backward whirl in accelerating cracked rotor systems

Rotating machinery are known to exhibit backward whirls (BW), which means that the rotating system precesses in the direction opposite to that of its rotation. Since backward whirl is an important characteristic of the dynamic response that almost always points to significant problems and degradations within the system, it is of high interest to study, characterize and predict this phenomenon. To this end, the Campbell diagram is used to predict BW rotational speeds at steady-state operations of rotor systems to precede the critical forward whirl (FW) rotational speeds (i.e., pre-resonance BW). Still, the BW phenomenon in rotor systems that exhibit recurrent passage through critical rotational speeds during startup and coast down operations has not been fully studied and described in the literature. Notably, a recent study of startup and coast down operations found backward whirl orbits appearing immediately after the passage through the critical FW rotational speed (i.e., post-resonance BW). The difference between the well-known pre-resonance BW and this new kind of post-resonance BW phenomenon is further investigated in this paper for rotor systems with an open crack and anisotropic bearings. In addition, Full Spectrum Analysis (FSA) is employed to capture the BW zones in both numerical and experimental data. A finite element model of the cracked rotor-bearing-disk system is employed here to obtain the linear-time-variant (LTV) equations of motion for the considered system. The whirl response is obtained by the numerical integration of the LTV equations of motion. From results obtained from three different rotor configurations it is observed that the post-resonance BW has a different dynamical behavior compared with the pre-resonance BW. Furthermore, the application of the FSA has confirmed the existence of post-resonance BW zones in both numerical and experimental whirl responses. Successful application of the FSA for capturing the post-resonance BW zones of rotational speeds in the experimental response suggests that it has the potential to be a used as a powerful tool for BW-based crack detection.

Experimental Identification of Internal and External Damping in a Rotor System with a Fatigue-Crack Using Full Spectrum

Demand of higher speeds in rotor systems has elevated the possibility of numerous instabilities. Internal damping is one of the key parameters for instability in such machinery. Its studies are generally conducted for a possible range of chosen internal damping values. Hence, experimental estimation of internal damping along with external damping is very vital for an accurate prediction of rotor stability, which is scarcely addressed in the literature. To fill this gap, current paper presents an experimental identification methodology for estimation of the internal and external damping in a cracked rotor system. Other crucial unknown fault parameters of rotor system, like additive crack stiffness and unbalance, have also been identified. In present work, internal damping due to rub between transverse fatigue crack faces has been envisioned for the first time. Hence, internal damping has been considered due to combined effect of material hysteretic, i.e. the rub between transverse fatigue crack faces, and the rub between disc and shaft during shaft rotation. Measurements much below critical speeds ensures the main contribution of crack in internal damping due to weight dominance effect as compared to shaft material damping. In experimental setup, a hairline fatigue crack was artificially developed by three-point bending procedure in a shaft at a notch location. The opening and closure behavior of crack faces during rotation of the shaft leads to the forward and backward whirls of the rotor at multiple frequencies, which are apparent in the full spectrum. Mathematical modeling of the rotor system for development of identification algorithm is based on these behaviors of cracked rotor system. Experimentally measured responses have been converted into the full spectrum (both amplitude and phase) based on regression analysis and fast Fourier transform (FFT). Earlier, amplitudes of full spectrum have been used for qualitative indication of crack. But in the present work, corresponding phase has also been considered in quantitative estimation of crack parameter along with other system fault parameters. With the help of a multi-frequency reference signal, phase anomalies have been removed during processing of full spectrum. The bow effect of shaft has been removed from full spectrum responses with the help of a slow roll measurement. Estimated parameters are consistent for different sets of rotor speeds and for different frequency ranges of excitation forces due to fatigue crack. Validations of identified parameters have been done by comparing experimental responses with numerically generated system responses. The latter was generated using experimentally identified parameters in the mathematical model of cracked rotor system.

Theoretical and experimental analysis of an unbalanced and cracked cardan shaft in the vicinity of the critical speed

This paper presents a theoretical and experimental analysis of a coupled lateral and torsional vibrations of two identical rotors interconnected by a flexible Hooke’s joint and modelled as a multibody system with a small misalignment angle. Using energy principle and a Lagrangian transformation, the governing equation of the propeller shaft system is established by considering a nonlinear elastic shaft time-dependent perturbation. To study the sensitivity of the crack for a rotating shaft, the model is enriched by considering the periodical feature of the time-varying stiffness deriving from the crack breathing model. The nonstationary response of a cracked rotor system in the presence of unbalance has been evaluated using orbit patterns and Fast Fourier Transform. The highly oscillated feature of the rotors system is theoretically obtained and experimentally analysed. The analysis demonstrated that the crack parameters in the input shaft tend to inhibit the occurrence of unstable oscillations in lateral deflection, orbit and frequency spectrum of the secondary response. It is also found that the passage of the cracked primary shaft near to an integral multiple of the critical speed leads to the phenomenon of sup-harmonic resonance. Subsequently, the experimental analysis conducted equally indicated that the quantitative relation between the faults and the performance of the transmission is impacted by the time-varying stiffness and is the main cause of the frequency-modulated feature in the Cardan shaft system. Finally, the experimental results were informative for the transient response exploration and comparable to the theoretical findings for validating the proposed twin-rotor model.

Dynamic analysis and identification of multiple fault parameters in a cracked rotor system equipped with active magnetic bearings: a physical model based approach

This paper proposes a model-based approach for identifying rotordynamic parameters using full spectrum. First, for developing a mathematical model a cracked shaft system with an offset-disc integrated with an active magnetic bearing (AMB) is considered. Moreover, external viscous and internal (rotating) damping is considered in the mathematical model to analyze their effect on the dynamics of the cracked rotor system. Subsequently, an identification algorithm is developed based on the proposed mathematical model to estimate the critical parameters of the model with the help of displacements and AMB currents obtained from full spectrum analysis. Eight parameters, such as the external and internal damping, translational as well as rotational additive crack stiffness, disc eccentricity and its phase, and AMB parameters, are the main parameters affecting the dynamic behaviour of a rotor system estimated. To overcome the practical difficulty in the measurement of rotational displacements during the identification, a gyroscopic dynamic reduction scheme is used to remove the rotational degrees of freedom. The developed algorithm is tested against various random noise in responses and modelling or bias errors in physical parameters to check the sensitiveness and robustness of the model as in the real case.