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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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For rotor–bearing systems, their dynamic vibration models must be built to simulate the vibration responses that affect the safe and reliable operation of rotating machinery under different operating conditions. Single physics-based modeling methods can be used to produce sufficient but inaccurate vibration samples at the cost of computational complexity. Moreover, single data-driven modeling methods may be more accurate, employing larger numbers of measured samples and reducing computational complexity, but these methods are affected by the insufficient and imbalanced samples in engineering applications. This paper proposes a physics-informed hybrid modeling method for simulating the dynamic responses of rotor–bearing systems to vibration under different rotor speeds and bearing health statuses. Firstly, a three-dimensional model of a rolling bearing and its supporting force are introduced, and a physics-based dynamic vibration model that couples flexible rotors and rigid bearings is constructed using multibody dynamics simulation. Secondly, combining the simulation vibration data obtained using the physics-based model with measured vibration data, algorithms are designed to learn vibration generation and data mapping networks in series connection to form a physics-informed hybrid model, which can quickly and accurately output the vibration responses of a rotor–bearing system. Finally, a case study on the single-span rotor platform is provided. By comparing the signal output by the proposed physics-informed hybrid modeling method with the measured signal in the time and frequency domains, the effectiveness of proposed method under both constant- and variable-speed operating conditions are illustrated. [ABSTRACT FROM AUTHOR]

The increasing demand for high-speed rotor-bearing systems results in the application of complex materials, which allow for a better control of the vibrational characteristics. This paper presents a model of a rotor including viscoelastic materials and valid up to high spin speeds. Regarding the destabilization of rotor-bearing systems, two main effects have to be investigated, which are strongly related to the associated internal and external damping of the rotor. For this reason, the internal material damping is modeled using fractional time derivatives, which can represent a large class of viscoelastic materials over a wide frequency range. In this paper, the Numerical Assembly Technique (NAT) is extended for the rotating viscoelastic Timoshenko beam with fractional derivative damping. An efficient and accurate simulation of the proposed rotor-bearing model is achieved. Several numerical examples are presented and the influence of internal damping on the rotor-bearing system is investigated and compared to classical damping models. [ABSTRACT FROM AUTHOR]

Maneuverability is one of the important tactical and technical indexes of fighter aircraft. In this paper, the finite element method is used to establish a dynamic model of the rotor system that can consider arbitrary maneuvering flight form and rotor speed variation during the flight, and the vibration characteristic of the dynamic model is investigated in detail. In addition, the nonlinear forces caused by bearings and oil film are also considered. The Newmark-β method combined with Newton-Raphson method is adopted to solve the dynamic equations. The influences of speed variation, rolling, pitching, and yawing maneuver loads on the vibration responses of the rotor system are also evaluated. [ABSTRACT FROM AUTHOR]

The increasing demand for high-speed rotor-bearing systems results in the application of complex materials, which allow for a better control of the vibrational characteristics. This paper presents a model of a rotor including viscoelastic materials and valid up to high spin speeds. Regarding the destabilization of rotor-bearing systems, two main effects have to be investigated, which are strongly related to the associated internal and external damping of the rotor. For this reason, the internal material damping is modeled using fractional time derivatives, which can represent a large class of viscoelastic materials over a wide frequency range. In this paper, the Numerical Assembly Technique (NAT) is extended for the rotating viscoelastic Timoshenko beam with fractional derivative damping. An efficient and accurate simulation of the proposed rotor-bearing model is achieved. Several numerical examples are presented and the influence of internal damping on the rotor-bearing system is investigated and compared to classical damping models.

Improving the bearing design helps in reducing the negative consequences related to errors in installation, manufacturing, deflections under severe loading conditions, progressive wear of machine elements, and many other aspects. One of the methods of such a design improvement effort is changing the bearing profile along the bearing width to compensate for the reduction in the geometrical gap between the shaft and the bearing inner surface due to the aforementioned causes. Since in all rotating machinery, unbalance usually exists at some level, this paper deals with the response of this modified bearing to unbalanced excitation to evaluate the effectiveness of such geometrical design on the dynamic characteristics of the rotor-bearing system. The numerical solution is performed using the finite difference method by assuming Reynolds boundary conditions to determine the cavitation limits, and the 4th-order Range-Kutta method is used to determine the time responses resulting from the unbalance excitation. The time responses to this type of excitation show that the rotor-bearing with the improved geometrical design is more stable, particularly at high speeds. In addition, this modification leads to an improvement in the lubricant layer thickness and the reduction in the levels of the generated pressure between the surfaces despite the presence of large deviations from the perfectly aligned bearing system. Furthermore, the suggested geometrical design overcomes the problem of asymmetricity in the pressure field resulting from the shaft deviation to a large extent. The results of this work (the enhancement in the level of the film thickness and the improvement in the dynamic response of the system as well as the reduction of the maximum pressure value) extend the range of misalignment in which the rotor bearing systems can operate safely which represents a significant step in designing the rotor-bearing system. [ABSTRACT FROM AUTHOR]

This paper deals with scale-fullscale models of rotor-bearing systems on rotating condition. The investigation is focused on the gyroscopic effect, which causes forward and backward whirl frequencies. When the rotor-bearing system is scaled proportionally in its dimension (height, length, and width), the scaling factor of whirl frequencies can be derived. It depends on the ratio between a transverse and polar moment of inertia on its rotating axis called the gyroscopic factor. The experimental study is conducted to validate it on three scaled rotor-bearing systems, which shifts its disc from the middle of the shaft on the scale of 1:1, 2:1, and 3:1 to clearly show the gyroscopic effect on first bending natural frequency. The scaling factor is then validated using the Campbell diagram by finding its critical speed. From this critical speed, the whirl frequencies along the range of the full-scale model speed can be obtained. The result also shows that the scaling factor remains the same whether it is at rotation or rest condition. Consideration must be made on the effect of the structural design, that is, blade and support, because of its unsymmetric stiffness that can cause backward whirl frequencies. The bearing stiffness must be ensured to be scaled proportionally, especially on journal bearing cases. This finding can be used by engineers to deal with scaling method implementation on rotating machinery design. [ABSTRACT FROM AUTHOR]

A gas journal microbearing and the corresponding rotor-bearing system are studied both theoretically and experimentally for their application in the high-speed air compressor of fuel cell vehicles. The gas microbearing is proved to provide reliable support for the rotor, as it shows both static and dynamic pressure effects under the high operating speed of the on-board air compressor. In order to realize the corresponding theoretical analysis, a new UDF dynamic mesh program is internally developed, with which an original method of CFD transient simulation calculations is proposed. Using this method, the gas microbearing’s load-carrying capacity, stiffness and damping coefficients, and static equilibrium position are analyzed for various fluid fields and under different rotational speeds. Theoretical analysis and experimental tests are performed for the corresponding rotor-bearing system in a high-speed air compressor. The experimental result verifies the practicability of the bearings and agrees well with the simulation results, demonstrating the effectiveness and the high accuracy of the new simulation method using dynamic mesh.

• Benchmark solutions for dynamic analysis of complex rotor systems are derived. • The solutions are applicable to rotor systems with complicated geometries. • Benchmark solutions match well with FEM solutions. • It is convenient for analyzing the influence of arbitrary boundary condition. The rotor unbalance is a major source of rotor vibrations. Rotor vibrations often produce many undesired effects like noise, wear and fatigue, etc. In this paper, we try to seek the benchmark solutions for the unbalance responses of complex rotor-bearing system. The presented approach could be seen as the extension of transfer matrix method (TMM) in some sense. For the TMM, a disk or supporting structure cut off one uniform shaft element into two and someone must use the compatibility condition between these two new elements to derive the transitive matrix. However, for the presented approach, it directly solves the governing equations of uniform shaft elements with consideration of the effects of disks and supporting structures. Thus, this analytical approach is advantageous in reducing the times of matrix multiplication between state matrices and field matrices. One only needs to calculate the inversion of 16 × 16 dynamic stiffness matrix to find the steady state response. It saves the computer memory and is easy to be programmed. In addition, this analytical approach avoids the problems of selecting optimal discretization mesh densities in the case of FEM applications. For arbitrary linear boundary condition, the benchmark solutions are always easy to be obtained. The numerical simulation is carried out and two numerical examples are given to validate the new solutions. In which the finite element method is used as the numerical approach. Simulation results show that the benchmark solutions match very well with the FEM results. The effects of anisotropy in the supporting structures on the rotor's dynamic behavior, which are observed in this work, are also in accordance with many references. This validates the benchmark solutions further. [ABSTRACT FROM AUTHOR]

Under the combined effects of electromagnetic and mechanical excitation, the strong nonlinear and discontinuous characteristics are presented within differential equations of rotor-bearing system for hydraulic generating set. In this paper, the periodic solution of system is derived by means of semi-analytical and semi-numerical harmonic balance method with frequency/time domain technique, which is compared with conclusions obtained through numerical method. On this basis, the system stability is analyzed combined with Floquet theory. The results show that the harmonic balance method with frequency/time domain alternating can accurately reveal the periodic motion form of rotor from the analytical level. Although the method is incapable of presenting the dynamic response of system for the periodic-n and quasi-periodic motion completely, the analytical results acquired can be used to judge the motion trend of rotor as well as the composition of vibration response. The combination of harmonic balance method with frequency/time domain alternating in conjunction with Floquet theory has the ability to obtain numerical/analytical response results of system precisely and quickly, and the motion stability for system can be analyzed and estimated ulteriorly, which could provide useful reference for early fault diagnosis and identification of hydraulic generating shaft system. [ABSTRACT FROM AUTHOR]

Purpose: The design, manufacturing, and operation of high-speed rotor-bearing systems must be accompanied by dynamic analysis and thorough studies of their dynamic behaviors. Bearings are one of the most important components of rotor-bearing systems, and their dynamic characteristics can significantly affect the dynamic behavior of the whole rotating system. Therefore, optimization of dynamic characteristics of bearings may be used as an appropriate tool to achieve the desired dynamic behavior. Methods: The present study considers a hypothetical small high-speed automotive turbocharger, which is modeled as an axisymmetric rotor-bearing system employing the finite-element method. We optimize the dynamic characteristics of the bearings, including stiffness and damping coefficient, using the NSGA-III multiobjective optimization method to minimize the bearing reaction forces and the amplitude of vibrations caused by rotating unbalance. Results: A comprehensive dynamic analysis is performed, and valuable information and graphs, including the Campbell diagram, critical speeds, mode shapes, and the unbalance response at steady and transient operating conditions, are obtained and discussed. Conclusion: The results demonstrate that using optimized bearings can significantly improve the dynamic behavior of the rotor-bearing system, both at steady and transient operating conditions, leading to higher performance and a longer lifetime of the rotor-bearing system. [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.

This paper considers the discontinuous characteristics of a real aero-engine rotor system, that is, the existence of bolted connection characteristics, and establishes a new bolted connection rotor system model. Taking into account the bending stiffness and the nonlinear Hertzian contact force of the rolling bearing, the Newmark- β numerical method is used to solve the system response, and the influence of the bending stiffness on the system is studied. Moreover, the effects of bending stiffness and eccentricity on the system dynamics are analyzed. The results show that the nonlinear phenomena of the system are more abundant and the critical speed of the system is higher when the bending stiffness is involved. With the increase of bending stiffness, the critical speed of the system increases, and the frequency component of the system becomes more complex. Then, the influence of eccentricity on the system is studied based on the bending stiffness. It is found that the greater the eccentricity, the greater the critical speed of the rotor and the greater the amplitude of the main frequency. In the case of the same eccentricity, the main frequency increases as the rotational speed increases, and the frequency doubling component appears in the 2-period motion. This paper provides a basis for predicting the nonlinear response of bolted rotor-bearing system. [ABSTRACT FROM AUTHOR]

In view of the current situation that there are few studies on whether the fault signals that may occur in the rotor bearing system can be identified and analyzed in the sensor arrangement, fault diagnosability is applied to the optimal arrangement of the sensors in the rotor bearing system. The preliminary layout of the multi-sensor is carried out by analyzing the transmission path of the vibration signals in the rotor bearing system and based on the minimum path. Secondly, the nonparametric kernel density estimation method calculates the state information’s probability density function. The K-L divergence value is further used to measure fault detectability, fault separability, and fault diagnosability. Then, the correlation function method is used to fuse the multi-sensor information, and the optimal sensor layout is given with the fault diagnosability as an index. Finally, the validity of the method is proved by the experimental laboratory data and the correlation coefficient. [ABSTRACT FROM AUTHOR]

Axial piston pumps have been widely studied and applied in engineering applications. Generally, traditional simulation models are established to analyze the vibration characteristics of the pump without the churning effect of the gap annular flow. A new vibration model of a rotor-bearing system considering the oil churning effect and time-varying excitation introduced by localized faults on the rolling element bearing is proposed in this work. External forces on rotor-bearing system are solved to obtain time-varying displacement and contact stiffness coefficient based on lump mass method. The dynamic model has constructed to analyze the dynamic characteristics of rotor-bearing system with bearing faults. The validity of the model is verified by comparing the simulation results with the analysis results and the experimental results. The findings reveal that rolling element bearing with localized faults alters the vibration characteristics of the rotor-bearing system. Both the simulation results and the experimental results show the fault characteristic frequency of the rotor-bearing system and the explicit component of its harmonics. The fault characteristic frequency of rotor-bearing system with bearing faults is consistent with the simulation result, and the error is less than 10%. The spectrum of the experimental and simulated signals is similar and indicates the validity of the dynamical model. [ABSTRACT FROM AUTHOR]

The rotor-bearing system is widely used in various high-end electro-hydraulic equipment, which provides specific support, rotation, and other integral functions. However, the fluctuating working conditions of the rotor-bearing system will cause more significant disordered fluctuations in the measured signals. This article proposes a new algorithm called multiscale deep graph convolutional networks (MS-DGCNs) to alleviate this problem. The designed MS-DGCNs algorithm combines a new multiscale intra-class fine coarse-grained processing and multiscale graph convolution kernels. Accordingly, an intelligent fault diagnosis method based on MS-DGCNs for the rotor-bearing system under fluctuating conditions is designed to learn more feature representations and accuracy. First, a sliding window is employed to divide the collected vibration signals into a series of subsignals. The multiscale signal processing is performed to obtain different degrees of the fine-coarse time series. Then, a graph convolution with the multiscale convolution kernel is designed. Finally, the soft-max classifier is combined for intelligent fault diagnosis. The experimental results of the double-span rotor-bearing system under fluctuating conditions well demonstrate that the method has the higher accuracy and generalization. [ABSTRACT FROM AUTHOR]

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]

For rotor–bearing systems, their dynamic vibration models must be built to simulate the vibration responses that affect the safe and reliable operation of rotating machinery under different operating conditions. Single physics-based modeling methods can be used to produce sufficient but inaccurate vibration samples at the cost of computational complexity. Moreover, single data-driven modeling methods may be more accurate, employing larger numbers of measured samples and reducing computational complexity, but these methods are affected by the insufficient and imbalanced samples in engineering applications. This paper proposes a physics-informed hybrid modeling method for simulating the dynamic responses of rotor–bearing systems to vibration under different rotor speeds and bearing health statuses. Firstly, a three-dimensional model of a rolling bearing and its supporting force are introduced, and a physics-based dynamic vibration model that couples flexible rotors and rigid bearings is constructed using multibody dynamics simulation. Secondly, combining the simulation vibration data obtained using the physics-based model with measured vibration data, algorithms are designed to learn vibration generation and data mapping networks in series connection to form a physics-informed hybrid model, which can quickly and accurately output the vibration responses of a rotor–bearing system. Finally, a case study on the single-span rotor platform is provided. By comparing the signal output by the proposed physics-informed hybrid modeling method with the measured signal in the time and frequency domains, the effectiveness of proposed method under both constant- and variable-speed operating conditions are illustrated.

Taking the rotor system supported by angular contact ball bearing as the research object, the dynamic model of rotor bearing system is established by using Lagrange equation. Based on the Archard wear model, the calculation model of wear depth of bearing raceways considering lubrication effects is presented. The wear depth is introduced into the system dynamics model as the bearing clearance. The dynamic characteristics of rotor-bearing system and the evolution of bearing wear are carefully analyzed taking into account the rotor speed, bearing preload and disc position. The results show that the influence of bearing wear on dynamic characteristics of rotor-bearing system is closely related to rotor speed and bearing preload. Changing disc position does not lead to the significant variation of dynamic characteristics of rotor-bearing system with wear depth of bearing raceways. The rotor speed significantly affects the bearing wear, the bearing preload has very limited effect on bearing wear, and the variation of the disc position results in the weak difference of wear depth of bearings.

Rotating machine faults are unavoidable; thus, early diagnosis is essential to avoid further damage to the machine or other machine attached to it. Various signal analysis based conventional techniques have been developed and used in the industries to identify various defects in the rotating machines. In last two decades, researchers have shifted their focus to automated or intelligent fault diagnosis based on Artificial Intelligence (AI) techniques due to a variety of issues in conventional fault analysis techniques, such as a dependence on machine operating circumstances, human interference, and expert abilities. In AI based techniques, various machine learning (ML) and deep learning (DL) techniques have been successfully applied for fault diagnosis of various rotating machines. From last half decade DL have been gaining popularity due to its attractive characteristic of automated feature learning and solving big data, unbalanced data, big computational burden and over-fitting problems of conventional ML techniques. Advances in DL methodologies have prompted interest in DL based intelligent fault diagnosis in the industry in the last five to 6 years. This review paper summarizes recent research and developments on DL based fault diagnosis in the last five to 6 years for various critical rotating machineries in industry such as electric motors, rotor-bearing systems, gear and gearbox, wind turbines, pumps, and compressors. [ABSTRACT FROM AUTHOR]

A gas journal microbearing and the corresponding rotor-bearing system are studied both theoretically and experimentally for their application in the high-speed air compressor of fuel cell vehicles. The gas microbearing is proved to provide reliable support for the rotor, as it shows both static and dynamic pressure effects under the high operating speed of the on-board air compressor. In order to realize the corresponding theoretical analysis, a new UDF dynamic mesh program is internally developed, with which an original method of CFD transient simulation calculations is proposed. Using this method, the gas microbearing's load-carrying capacity, stiffness and damping coefficients, and static equilibrium position are analyzed for various fluid fields and under different rotational speeds. Theoretical analysis and experimental tests are performed for the corresponding rotor-bearing system in a high-speed air compressor. The experimental result verifies the practicability of the bearings and agrees well with the simulation results, demonstrating the effectiveness and the high accuracy of the new simulation method using dynamic mesh. [ABSTRACT FROM AUTHOR]

Improving the bearing design helps in reducing the negative consequences related to errors in installation, manufacturing, deflections under severe loading conditions, progressive wear of machine elements, and many other aspects. One of the methods of such a design improvement effort is changing the bearing profile along the bearing width to compensate for the reduction in the geometrical gap between the shaft and the bearing inner surface due to the aforementioned causes. Since in all rotating machinery, unbalance usually exists at some level, this paper deals with the response of this modified bearing to unbalanced excitation to evaluate the effectiveness of such geometrical design on the dynamic characteristics of the rotor-bearing system. The numerical solution is performed using the finite difference method by assuming Reynolds boundary conditions to determine the cavitation limits, and the 4th-order Range-Kutta method is used to determine the time responses resulting from the unbalance excitation. The time responses to this type of excitation show that the rotor-bearing with the improved geometrical design is more stable, particularly at high speeds. In addition, this modification leads to an improvement in the lubricant layer thickness and the reduction in the levels of the generated pressure between the surfaces despite the presence of large deviations from the perfectly aligned bearing system. Furthermore, the suggested geometrical design overcomes the problem of asymmetricity in the pressure field resulting from the shaft deviation to a large extent. The results of this work (the enhancement in the level of the film thickness and the improvement in the dynamic response of the system as well as the reduction of the maximum pressure value) extend the range of misalignment in which the rotor bearing systems can operate safely which represents a significant step in designing the rotor-bearing system.

A floating raft isolation structure is adopted to reduce the vibration of the marine rotor-bearing system, however, the system on the moving hull will be affected by the ship implicate motion, and its vibration will be difficult to predict. In this study, a dynamic model of the system under heaving and rolling coupled motion is established after considering the nonlinear oil film reaction force, unbalance inertia force, restoring force of the structure and inertia force of the ship motion. A numerical method is introduced to present the responses of the system, such as the amplitude and rotating speed curve, waterfall diagrams, and the rotor orbit and its Poincaré maps, etc. Moreover, the effects of rotating speed, amplitudes and frequencies of the coupled motion on the dynamic behaviours of the system are studied. The results indicate that the unstable region of rotating speed of the system increases under the coupled motion, the vibration of the system is greatly affected by the parameters of coupled motion, and the vibration amplitudes of rotor and raft can be effectively limited due to the displacement restrictor. [ABSTRACT FROM AUTHOR]

Rotor dynamic balancing is a classical problem. Traditional balancing methods such as the influence coefficient method and the modal balancing method, have low balancing efficiency because they need to run many times to add trial weights. Although the model-based balancing method improves the balancing efficiency, it cannot accurately identify the position, amplitude and phase of each unbalance fault for rotors with multi-disc structures, so it is difficult to apply it to actual balancing. To solve the above problems, based on the traditional modal balancing theory, this paper deduces that the continuous and isolated unbalance in the rotor-bearing system can be represented by isolated unbalance on several balancing planes approximately. The model-based method is used to identify the above-mentioned equivalent isolated unbalances, and then the corrected mass is added to the balancing planes so as to complete the balance of multiple flexible rotor without trial weights. Considering the practical situation, the proposed balancing method includes two steps: low-speed balancing and high-speed balancing. The proposed balancing method is verified using three and four-disc rotors. The simulation results show that the balancing method can effectively reduce the vibration of the flexible rotor after low-speed and high-speed balancing, and the amplitude at the measurement point is reduced by 79.74~97.60%, respectively. [ABSTRACT FROM AUTHOR]

Purpose: Nanoparticles have attracted the attention of both academics and industry, especially in the field of lubrication. So, in this study, the effect of base oil containing nano bismuth oxide (Bi2O3) on the dynamic response of a rotor system was investigated experimentally and compared with the addition of nano titanium oxide (TiO2). Methods: The results ofadding nano bismuth oxide particles in various concentrations of 0.5, 1, 1.5, 2, 4, 6, and 8 wt% to the SN500 and SN150 base oils were obtained, and then these results were compared with the pure oil and another type of nanoparticles. Therefore, the effect of different dynamic loads and the concentrations of nanoparticles were tested through monitoring the vibration response on the journal bearing of the rotor-bearing system. Results and Conclusions: This paper concluded that for each speed and for each dynamic load, there were certain concentrations of Bi2O3 in the SN500 and SN150 base oils, at which the vibration response of the system decreased, where each case had its own conditions that necessitated the addition of a certain concentration of nano additives to the base oils. Thus, at higher speed, the addition of (1.5, 6, and 8) wt% to SN500 oil reduced the RMS value by 19%, 30%, and 37%, also, for addition of (2 wt%) to SN150 oil reduced the RMS value by 31%, compared to the pure oil. Additionally, the comparisons between the two nano-additives Bi2O3 with 1, 2, and 4 wt% and TiO2 with 1 and 1.25 wt% were studied experimentally with the3 base oil of SN150. where Bi2O3 has good performance at a wide range of rotational speed and dynamic load, while TiO2 performs better at higher rotational speed and dynamic load. [ABSTRACT FROM AUTHOR]

• A novel double-disc cracked rotor-bearing system is proposed for multi-fault vibration. • The dual-impulse model of rolling bearings is verified and applied to the rotor system. • The multi-fault rotor system can be well distinguished through the vibration signals. • The novel rotor model can capture the coupled fault eigen-signals. • The experimental results are in good agreement with the simulation results. Previous studies have paid little attention to the dynamic modeling of multi-fault systems with both bearing defect and cracked rotor. In the current research, a double-disc rotor model with a breathing crack and fault bearing was established using the finite element method (FEM). The dual-impulse phenomenon associated with inner race defect was addressed as a time-varying external excitation. The effects of varying crack depths and inner race spall lengths were further investigated. The maximum error between simulation and experiment was found to be less than 5% for the dual-impulse time spacing. The calculated results indicate that the inner race defect causes a slight increase in the rotational frequency f rotor and 2 f rotor , followed by a decrease in the 3 f rotor at low speeds, as observed using Fast Fourier Transform (FFT) and Short-Time Fourier Transform (STFT). The influence of changes in crack depth is greater than the bearing defect in the system, a finding that is also confirmed at 1/2 critical speed. The phenomenon of frequency modulation observed in the simulation was also verified experimentally. The ball passing frequency on inner raceway f BPFI , f rotor and mixed frequency components can be used to distinguish whether there is inner race defect. [ABSTRACT FROM AUTHOR]

• The novel CEEMDAN-CWT method eliminates non-rotor vibration interference signal. • A cracked rotor-bearing system with 6-DoFs based on FEM is established. • Jones-Harris model is applied to describe the rolling bearing. • The experimental results have a good similarity with simulation results. In the actual working process, the source of vibration signal is not only the rotor itself, so the detected vibration signal will become complicated. This complex signal makes it difficult to accurately measure the existence of crack. In this paper, a novel method, which includes complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and continuous wavelet transform (CWT), is proposed to analyze the cracked rotor-rolling bearing system. The CEEMDAN-CWT successfully separates the vibration signal of the rotor itself from the original signal and provides results similar to the simulation signal. At the speed below 2000 rpm, the 2X frequency difference between cracked rotor and healthy rotor in CEEMDAN-CWT spectrum is about 1, while the difference of FFT spectrum of original signal is about 0.6, which shows the superiority of the novel method in extracting rotor vibration signals from complex vibration signals. [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]

In practice, the modeling and analysis of nonlinear rotor-bearing systems are difficult due to the nonlinearity and complexity. In the previous studies, finite element simulation and mathematical modeling methods are mostly adopted to conduct the analysis. However, due to the time-consuming problem in finite element simulation and the lack of sufficient prior knowledge in mathematical modeling, the traditional method is difficult to establish the representation model. In order to overcome this issue, in this study, a data-driven model referred to as the NARX (Nonlinear Auto-Regressive with exogenous inputs) model is introduced to conduct the modeling and analysis of the rotor-bearing system. The identification of the NARX model requires random excitation as the system input, while the input signal of the rotor system is harmonics. Therefore, a time-domain frequency sweep modeling method is proposed in this paper by introducing the rotating speed into the coefficients function expression of the NARX model, the system output can be predicted according to the given speed. Moreover, the representation model of the rotor-bearing system obtained by using the proposed method is validated under different rotating speeds, the results show the applicability of the proposed modeling approach. Finally, an experimental case of the rotor-bearing test rig is demonstrated to show the application in practice. Both the numerical and experimental studies illustrate the applicability of the proposed modeling method, which provides a reliable model for dynamic analysis and fault diagnosis of the rotor-bearing system. [ABSTRACT FROM AUTHOR]

In this work, the vibrations in the rotor-bearing system are studied experimentally and theoretically using ANSYS Workbench 2020 R1 software to compute the natural frequencies and mode shapes. In the experimental part, the LABVIEW software was used to examine the signal of the frequency domain values obtained from the accelerometer sensors, based on Fast Fourier Transform (FFT) technology and dynamic response spectrum. in the theoretical part, the natural frequencies are determined based on the finite element method for analyzing the system and knowing its behavior and vibration response level. The results showed that the level of vibration becomes higher at high rotational speeds, and it becomes large when the distances between the bearings are large, according to the bearing position and type used in the system. in this work can be concluded, the system is usually affected by the dynamic response around it and is difficult to separate from it, and the vibrations in the system can be controlled by adding an external damping source, which gives the system more stable. A system operating at high speeds can give a large vibration and an unbalanced response.

Usage of rolling contact bearings in variety of rotor-dynamic applications has put forth a need to develop a detailed and easy to implement techniques for the assessment of damage related features in these bearings so that before mechanical failure, maintenance actions can be planned well in advance. In accordance to this, a method based on dimensional amplitude response analysis and scaling laws is presented in this paper for the diagnosis of defects in different components of rolling contact bearings in a dimensionally scaled rotor-bearing system. Rotor, bearing, operating and defect parameters involved are detailed for dimensional analysis using frequency domain vibration data. A defect parameter for modeling all the three dimensions of the defect as well as the different shapes like square, circular, rectangular is put forth which takes into account the volume as well as the surface area of the defect. Experimental data set is generated for the 'model' bearing (designated as SKF30205J2/Q) using Box-Behnken design of response surface methodology for solution of the theoretical model by factorial regression approach. Obtained metamodel is then used for the prediction of the objective variable, i.e., Vibration acceleration amplitude at the defect frequency component for other types of 'test' bearings (designated as SKF 30305C and SKF 22220 EK) using the developed scaling laws. Confirmation experiments showed that the computable relationship amongst objective variable and the dimensionless parameters can be forecast and correlated. [ABSTRACT FROM AUTHOR]

The vast majority of the existing diagnostic studies using deep learning techniques for rotating machinery focus on the vibration analysis under steady rotating speed. Nevertheless, the collected vibration signals are sensitive to time-varying speeds and the vibration sensors may cause structure damage of equipment after long-term close contact. Aiming at these aforementioned problems, a modified Gaussian convolutional deep belief network driven by infrared thermal imaging is proposed to automatically diagnose different faults of rotor-bearing system under time-varying speeds. First, infrared thermal images are measured to characterize the working states of rotor-bearing system to reduce the impact of changeable speeds. Second, Gaussian units are used to construct Gaussian convolutional deep belief network to well deal with infrared thermal images. Finally, trackable learning rate is designed to modify the training algorithm to enhance the performance. The comparison results verify the feasibility of the proposed method, which outperforms the other methods. [ABSTRACT FROM AUTHOR]