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In the propulsion shaft systems, the bearings could support the complicated load conditions due to the unbalanced magnetic pull of the motor together with the propeller thrusts. The contact characteristics and skidding behaviors of balls could aggravate. The previous dynamic models of individual ball bearings subjected to the constant load cannot accurately simulate the phenomenon. To overcome this problem, a tribo-dynamic model of a flexible propulsion shaft system is proposed. The real-time contact characteristics and skidding and spinning behaviors of bearings for a propulsion shaft system are calculated based on Newmark-β and Runge–Kutta methods. The bearings' power losses are numerically estimated. The main power loss components for the system in different rotation speed conditions are located. The effects of the preload and bearing structural parameters (raceway radius, number of balls, initial contact angle) on the bearings' power losses are discussed. The results indicate that applying appropriate preload on the supporting bearings and reducing the ball number of thrust bearings can be efficient methods for system power loss reduction. [ABSTRACT FROM AUTHOR]

The lubrication and dynamic behavior of the orbiting scroll (OS) is crucial to understanding and controlling the leakage between working chambers and the contact between scrolls in the compressor. In this study, a novel comprehensive model consisting of the OS, bearings, rotor, and frames is developed and validated by experiments. This paper demonstrates, for the first time through the tribo-dynamics analysis method, that the rotor dynamics have a significant impact on the flank gap size between scrolls via the interaction of the sliding bearings. The reduction of actual orbiting radii of OS is found to be caused by the bending and tilting of the rotor. However, though increased rotational speeds can narrow the flank gaps, the impact between scrolls should be addressed in these cases. The tribo-dynamic analysis illuminates the direction of the optimal design of compression components in the scroll compressor. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the nonlinear vibration characteristics and stability of a dual-disk rotor-bearing system under multi-frequency excitations. A 4-degree-of-freedom dynamic model is established using the assumed mode method, considering the bearing's cubic nonlinearity. The system is solved using the multiple scale method combined with arc-length continuation. The stability of the system's solutions is determined by solving the eigenvalues of the Jacobian matrix of the averaged equations. The nonlinear vibration characteristics and stability of the dual-disk rotor system under simultaneous resonance conditions are obtained. The results show that changes in system parameters can lead to Saddle-Node and Hopf bifurcations, as well as the occurrence of multi-valued solutions and symmetry-breaking phenomena. Additionally, simultaneous resonance leads to interaction between the two modes, where the relative positions of the resonance peaks of these modes influence the system's dynamic behavior. Variations in system parameters can alter the relative positions of resonance peaks, leading to more complex effects on nonlinear responses. This research provides significant insights into the dynamic behavior of the dual-disk rotor-bearing system under multi-frequency excitations, which is meaningful for designing and optimizing rotor systems. [ABSTRACT FROM AUTHOR]

The turbine disk is the core component of an aero-engine whose position and unbalanced force seriously affect the vibration stability of the rotor system. Ignoring the influence of the offset disk may result in discrepancies between real-world scenarios and numerical simulation results. The present work aims to explore the nonlinear dynamic characteristics of rotor systems under the coupling of bolted joint and offset disk effect, as well as the influence of offset disk position and its unbalanced force on the system dynamic behavior and bending stiffness of bolted joint also investigated. The governing equations of a bolted joint rotor-bearing system with an offset disk were established based on the finite element method and derived as a dimensionless expression in the first. Then, the Newmark method was employed for the numerical solution of the motion equations, and then a bifurcation analysis of the rotor system and the evolution of bending stiffness for the bolted joint was studied. Next, by comparing the frequency-amplitude diagrams, bifurcation diagrams, time history, shaft obits, and bending stiffness diagrams of the bolted joint, the effect of the offset disk position and its unbalanced force on the nonlinear system dynamic was revealed. Finally, an experimental study was carried out to verify the numerical result using the bolted joint rotor test rig with an offset disk. The analysis result of the present work can provide theoretical guidance for structure design and stability analysis on the aero-engine. [ABSTRACT FROM AUTHOR]

This study considers the identification of the Nonlinear Auto-Regressive with eXogenous Inputs (NARX) models of the rotor systems, in which the identified NARX model may sometimes fail. By incorporating rotor response signals at different speeds into the modeling process using an Extended Forward Orthogonal Regression (EFOR) algorithm. This way, the data information involved in identification is more abundant, but this is still not enough. To completely solve the issue, an identification method based on Model Prediction Output (MPO) error is proposed in this paper. Which can filter all possible identification results during the identification process based on MPO error, thereby avoiding potential failed identification results and obtaining the optimal solution. The proposed method improves the accuracy of NARX model identification and reduces the need for professional knowledge. The simulation and experimental cases of a rub-impact rotor system are presented to illustrate the application and the effectiveness of the new identification approach. [ABSTRACT FROM AUTHOR]

Rotor-bearing systems are important components of rotating machinery and transmission systems, and imbalance and misalignment are inevitable in such systems. At present, the main challenges faced by state-of-the-art fault diagnosis methods involve the extraction of fault features under strong background noise and the classification of different fault modes. In this paper, a fault diagnosis method based on an improved deep residual shrinkage network (IDRSN) is proposed with the aim of achieving end-to-end fault diagnosis of a rotor-bearing system. First, a method called wavelet threshold denoising and variational mode decomposition (WTD-VMD) is proposed, which can process original noisy signals into intrinsic mode functions (IMFs) with a salient feature. These one-dimensional IMFs are then transformed into two-dimensional images using a Gramian angular field (GAF) to give datasets for the deep residual shrinkage network (DRSN), which can achieve high levels of accuracy under strong background noise. Finally, a comprehensive test platform for a rotor-bearing system is built to verify the effectiveness of the proposed method in the field. The true test accuracy of the model at a 95% confidence interval is found to range from 84.09% to 86.51%. The proposed model exhibits good robustness when dealing with noisy samples and gives the best classification results for fault diagnosis under misalignment, with a test accuracy of 100%. It also achieves a higher testing accuracy compared to fault diagnosis methods based on convolutional neural networks and deep residual networks without improvement. In summary, IDRSN has significant value for deep learning engineering applications involving the fault diagnosis of rotor-bearing systems.

AbstractMagneto rheological materials are considered as a promising adaptive means of vibration control. This paper proposes a new configuration of smart bearings comprising magneto-rheological elastomer (MRE) layer inserted between the bearing pedestal and the foundation. This configuration provides a directional vibration controllability in both horizontal and vertical directions of a rotor-bearing system. The effect of using MRE layer on the vibration response and the resonant speeds of a rotor-bearing system is investigated. The finite element method is used to derive a dynamic model for the rotor-bearing system using shaft elements based on the Rayleigh beam theory and accounting for the gyroscopic effect and internal damping of the shaft. Simulation results reveal that the use of MRE materials in passive mode leads to downshifting of the first two resonant speeds and the attenuation of the steady state vibration response of the rotor bearing system in the horizontal and vertical directions at the resonance frequencies. When the MRE layer is subjected to a magnetic field generated by an electric current produced in the magnetic coil, the horizontal and vertical vibration responses are increased at the resonant speeds but decreased at other rotational speed ranges. Furthermore, the first two resonant speeds in the horizontal and vertical directions decrease further with the increase of the electric current. [ABSTRACT FROM AUTHOR]

Downhole turbine generators (DHTG) installed within drill-string are susceptible to internal and external excitation during the drilling process, causing significant dynamic loads on bearings, and thereby reducing the bearing's service life. In this study, a finite element model of an unbalanced rotor-bearing system (RBS) of DHTG with multi-frequency excitations, based on the Lagrangian motion differential equation, is established. The responses of the RBS under different drill-string excitations in terms of time-domain response, whirl orbit, and spectrum are analyzed. For a constant rotor speed, lateral harmonic translational and lateral oscillation both transform the whirl orbit to quasi-periodic, while axial rotation only changes the response amplitude. Changing the duration of pulse excitation leads to different response forms. Then, the dynamic characteristics of the RBS supported by a squeeze film damper (SFD) are investigated. The results indicate that SFD effectively reduces the displacement response amplitude and bearing force near the critical speed. As the axial rotation angular velocity of the drill-string increases, the first critical speed and displacement response decrease, while the variation of lateral oscillation frequency and amplitude has limited impact on them. The established model provides a means for analyzing the dynamic characteristics of DHTG's RBS under drill-string excitations during the design stage. [ABSTRACT FROM AUTHOR]

• The dynamic model of the two-span rotor-bearing-pedestal system is established. • A fault characterization model of raceway extension defects is proposed. • The influence of misalignment on bearing defect fault is further discussed. • The system dynamic characteristics during bearing defect extension are analyzed. When the rolling bearing raceway is tilted, the contact load of the raceway increases, which may greatly increase the occurrence of raceway defects. However, the evolution law of the raceway defect extension process on the system dynamic characteristics is not clear when the bearing is tilted. In this paper, considering the influence of rough surface caused by the extension of bearing defects, a mathematical model of raceway extension defects which is more consistent with the actual morphology is proposed. The model can be used to evaluate the damage degree of the bearing raceway of rotating machinery. Taking the two-span rotor-bearing-pedestal system of the test rig as the research object, a nonlinear dynamic model of the system is established considering the nonlinear supporting force of bearings and pedestal, shaft coupling looseness and other nonlinear factors. The effectiveness of the bearing fault characterization model and the system dynamics model is verified by experiments. On this basis, the influence of tilt on bearing fault and the change rule of raceway defect extension on bearing contact characteristics and system dynamic characteristics are discussed. The results indicate that raceway tilt aggravates system vibration caused by the bearing defect. With the increase of the defect range, the impact vibration characteristics weaken, and the roughness of the raceway surface in the defect area has a great influence. However, with the increase of defect depth, the influence law is just the opposite. The research results are expected to provide theoretical support for bearing fault diagnosis of rotating machinery systems. [ABSTRACT FROM AUTHOR]

Disturbances caused as a result of the misalignment and axial motion of the journal affect the characteristics of the rotor-bearing system. This paper aims to propose an algorithm for the theoretical analysis of a rotor-bearing system that considers these disturbances. A theoretical model for a journal bearing considering disturbances is given. The dynamic equations for a rigid rotor-bearing system are introduced. A detailed algorithm that can simultaneously solve the rotor-dynamic equations and the Reynolds equation is proposed. The static performance, such as the bearing attitude angle and the fluid film pressure, are given, and dynamic characteristics such as the nonlinear dynamic responses and the axial orbits of a rigid rotor-bearing system are presented. The hydrodynamic effect of the bearing is enhanced by the axial disturbance. Disturbances in the circumferential and radial directions lead to variations in the fluid film thickness distribution in the axial direction and the offset of the fluid film pressure distribution in the axial direction. When these disturbances work together, the variation trend is more obvious and affects the capacity and dynamic characteristics of the bearing. When the L/D value of the bearing increases, the clearance between the journal and the bearing decreases rapidly. When the value reaches a certain limit, contact and collision might occur. The theoretical analysis method and the algorithm proposed for a rotor-bearing system considering several disturbances could enhance the design level for a bearing and rotor-bearing system. [ABSTRACT FROM AUTHOR]

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Downhole turbine generators (DHTG) installed within drill-string are susceptible to internal and external excitation during the drilling process, causing significant dynamic loads on bearings, and thereby reducing the bearing’s service life. In this study, a finite element model of an unbalanced rotor-bearing system (RBS) of DHTG with multi-frequency excitations, based on the Lagrangian motion differential equation, is established. The responses of the RBS under different drill-string excitations in terms of time-domain response, whirl orbit, and spectrum are analyzed. For a constant rotor speed, lateral harmonic translational and lateral oscillation both transform the whirl orbit to quasi-periodic, while axial rotation only changes the response amplitude. Changing the duration of pulse excitation leads to different response forms. Then, the dynamic characteristics of the RBS supported by a squeeze film damper (SFD) are investigated. The results indicate that SFD effectively reduces the displacement response amplitude and bearing force near the critical speed. As the axial rotation angular velocity of the drill-string increases, the first critical speed and displacement response decrease, while the variation of lateral oscillation frequency and amplitude has limited impact on them. The established model provides a means for analyzing the dynamic characteristics of DHTG’s RBS under drill-string excitations during the design stage.

The dynamic response of rotating systems supported by hydrodynamic bearings considering the journal deformation-induced misalignment has been investigated in recent years. However, most of the previous work studied misaligned angles as fixed configurations, ignoring the variation of misalignment due to the time-varying journal deformation. In this study, a numerical method is proposed to predict the dynamic response of a rotor-bearing system considering time-dependent misalignment. As journal deformation is recognized as a significant factor leading to misalignment, a flexible rotor is considered to determine the misalignment state. The finite element method is employed to calculate the dynamic deformation of the rotor and, hereby, the misaligned angles and film thickness. Subsequently, the pressure distributions of the oil film are calculated using the finite difference method to update the bearing force. The transient lubrication performance and the vibration response of the rotor are discussed based on the numerical computation. In particular, the difference in the oil whip phenomenon is compared between the aligned and misaligned conditions. The results show that the journal orientation varies with time considering the journal deflection. The discussion about the oil whip shows that the misalignment has a significant impact on the stability of the system. In addition, the transient lubrication properties are considerably influenced by the rotation speed and external loading since they affect the magnitude of the resonance vibration and the oil whip. [Display omitted] • Time-varying misalignment is considered in rotor-bearing system dynamic analysis. • The flexibility of the rotor is taken into account to determine the dynamic misaligned angles. • The misalignment significantly influence the stability of the rotor-bearing system. • The vibration response of the rotor considerably affect the transient lubrication performances. [ABSTRACT FROM AUTHOR]

Rolling bearings play a critical role in wind turbine generators, operating continuously in an electromagnetic excitation environment. Their fault vibration characteristics are affected by unbalanced magnetic pull (UMP), which has received little attention in previous studies. Moreover, torsional vibration can provide advantages in bearing fault diagnosis, since it has a good signal-to-noise ratio (SNR) and it can be easily measured by the encoder. However, torsional vibration is rarely considered in the existing model of wind turbine generator. Accordingly, this paper proposes a dynamic model with 8 degrees of freedom to analyze the bearing outer ring fault characteristics of wind turbine generator under the influence of UMP, while also taking into account the torsional vibration in the model. The validity of the model is verified through experiments conducted on a test rig. The results displays modulation of the ball pass frequency outer (BPFO) harmonics with both UMP frequency and rotation frequency in lateral vibration, and this phenomenon can also be observed in instantaneous angular speed (IAS) and instantaneous angular acceleration (IAA) signals that represent torsional vibration. Besides, the lateral vibration spectrum reveals two distinct resonance bands, and simulation analysis suggested that the rotor and bearings give rise to low-frequency and high-frequency resonance, respectively. This study provides a reference for bearing faults diagnosis in wind turbine generator. • A dynamic model of generator bearing outer ring fault is studied considering UMP. • The modulation phenomenon of fault characteristic frequency and UMP is revealed. • The double resonance phenomenon of rotor-bearing system of generator is revealed. [ABSTRACT FROM AUTHOR]

• The gray texture image is used as sample to deal with the motor rotor-bearing system fault diagnosis under variable load conditions. • The proposed method realizes a transfer learning-based fault diagnosis from known to unknown and no-load to on-load conditions. • Compared to the domain adaptation methods, the proposed method can perform an accurate fault diagnosis without retraining under new conditions. Induction motors often operate in variable conditions, and the data distribution of diverse conditions is different. To solve the issue of low accuracy of diagnosis methods caused by large differences in data distribution, an intelligent fault diagnosis method of induction motor rotor-bearing system is proposed. The method combines convolutional neural network with adaptive batch normalization, and the gray texture images transformed from vibration signals are used as the input samples. A total of thirteen conditions including constant and time-varying loads are designed to verify the performance of the method. The average accuracy of the model for thirteen conditions of test set reaches 98.7 %, and the average accuracy for eight unknown conditions of test set is 99.0 %. The proposed method can extract features that are not affected by the variable load conditions, facilitate the transfer from no-load to on-load and known to unknown conditions. [ABSTRACT FROM AUTHOR]

This paper presents a method to reduce lateral vibration amplitudes in large rotating machines. The method is based on avoiding resonances by altering the natural frequencies of the rotor system at each rotating speed during operation. While many research papers have considered altering support stiffness during crossing critical speeds, continuous adjustment methods have received less attention. Continuous on-line adjustment of the natural frequencies of a rotor system is possible to a large range by adjusting the support stiffness of the bearing housings. The optimal foundation stiffness tuning policy can be defined utilizing a rotordynamic model or experimental measurements, effectively creating a resonance-free operating speed region, where vibrations are drastically reduced. It is shown through full-scale experimental laboratory tests, that the subcritical and supercritical response of the rotor system is significantly decreased during run-up and run-down with the optimal foundation stiffness tuning strategy. The developed method can be applied to reduce vibrations in any rotating machinery, where a variable foundation stiffness control can be installed. Moreover, this on-line foundation stiffness tuning strategy could also be applied in combination with resonance crossing methods involving stiffness manipulation. [Display omitted] • A new vibration control strategy is proposed for large flexible rotors. • Natural frequencies are optimized during operation through stiffness adjustment. • A rotordynamic model is used to analyze the control strategy. • Resonance amplitudes are greatly decreased in experiments on a full-scale rotor. [ABSTRACT FROM AUTHOR]

• Oil-film instability in rotor-bearing systems is studied using catastrophe theory. • Finite element model accurately simulates dynamic responses. • Proposed stepwise fitting method establishes precise cusp model. • Catastrophe behaviors of rotor-bearing system are explained by cusp model. The amplitude jumps resulting from oil-film instability are catastrophic events that threaten the stable operation of rotor-bearing systems. In this study, a cusp model was established to investigate the instability boundary and the underlying catastrophe mechanism of rotor-bearing systems. The study presented a finite element model incorporating the nonlinear oil-film force of an experimental rotor-bearing system. The simulated dynamic responses related to oil-film instability, including the amplitude jump and the subsynchronous vibration during the run-up and run-down processes were in good agreement with the experimental data. According to catastrophe theory, the amplitude jump phenomenon can be described by a cusp model. To obtain the cusp model, a stepwise fitting method was proposed based on the dynamic response data. In addition, the topological transformation function, which maps the catastrophe boundaries of the nonlinear dynamic response to the cusp model, was obtained. The checkout results of the validation set confirmed the accuracy of the derived cusp model. The cusp model had upper and lower lobes, representing stable states corresponding to oil whip and no or low excitation of oil whirl, respectively, while the middle lobe represented the unstable state. The transition between these two stable states can explain the catastrophe, bistable, and hysteresis phenomena. The established cusp model can determine the instability boundary and further assist in the dynamic design and control of rotor-bearing systems. [ABSTRACT FROM AUTHOR]

Bolted joint structure is widely utilized in the aeroengine compress rotor systems with convenience in assembly and maintenance. Due to the inherent structure discontinuity and stick-slip behavior at the mating interface, stiffness softening and frictional energy dissipation would be generated at the mating interface, resulting in complex vibration features of the rotor system. In this work, to describe the stick-slip behavior at the mating interface of the rotor system, an Iwan-based model is introduced to describe the contact state of asperities at the multi-scale level. The corresponding model identification method is proposed based on the partial hysteresis curve of the bolted joint. After that, a dynamic model of the bolted joint rotor system is established, and its dynamic response is obtained using the Runge–Kutta method. The effect of preload and friction coefficient on the nonlinear vibration of the bolted joint rotor is evaluated in detail based on the dynamic model. The result indicates that the stiffness softening would lead to the critical speed decreasing and aggravating the vibration response of the rotor system, while the frictional energy dissipation would restrain the response amplitude and induce the self-excited vibration within the super-critical speed range. The higher preload or friction coefficient has little effect on the motion state of the rotor system within the sub-critical speed range and makes system vibration stable between the 1st- and 2nd-order critical speed while unstable at the super-critical speed range. This research helps understand the vibration features of bolted joint rotor systems under the condition of stick-slip behaviors at the mating interface. • A dynamic model of a bolted joint rotor considering mating interface contact is established. • A simplified model of bolted joint to simulate the contact behaviors is proposed. • Dynamic properties of the bolted joint rotor with multi contact state are studied. • Effect of preload and friction coefficient at mating interface on rotor dynamics are investigated. [ABSTRACT FROM AUTHOR]