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In this paper, the main excitation sources of micro vibration of spacecraft flywheel rotor systems (SFRSs) are briefly described, and then the research progress is systematically reviewed from four perspectives, including modeling methods, suppression means, vibration isolation techniques, and ground simulation tests. Finally, the existing problems of current research and the direction of further research are given to better serve the micro-vibration prediction and sensitivity analysis of existing models, and provide reference points for the micro-vibration suppression and isolation of the next generation of high-precision spacecraft.

Honeycomb is a splendid kind of structure for aerospace engineering with the advantages of light weight, good shock absorption, and good structural stability. This article aims to provide methods to isolate Pyroshocks based on a honeycomb structure and guarantee the safety of such equipment against a high-frequency shock response. According to stress wave theory, an equation for stress wave transmittance of the honeycomb structure is derived considering the effect of cell wall length and thickness, where desirable honeycomb parameters are obtained. The complexity of the transfer path of the honeycomb structure is exploited to build the spacecraft–rocket interface, which could increase the impedance of the stress wave dramatically. Both finite element analysis and experiments are carried out to validate the shock isolation strategies. The influence of parameters, such as cell wall length and the thickness of the stainless-steel honeycomb, on the isolation performance is analyzed. It is revealed that the honeycomb structure has a significant effect on Pyroshock isolation performance when the wall length of the honeycomb cell is 8 mm and the thickness of the cell is 0.1 mm.

Abstract Dynamic characteristics of large permanent magnet direct‐drive generators (PMDGs) considering electromagnetic–structural coupling effects are analyzed in this study. Using the conformal mapping method, the scalar magnetic potential of the air gap magnetic field considering the slot effect is calculated. On the basis of the discrete current element and magnetic equivalent circuit model, the local magnetic saturation effect of the stator and rotor is quantitatively simulated and the air gap magnetic field intensity distribution is obtained via numerical simulation. A series of uniformly distributed equivalent electromagnetic springs are introduced to develop an electromagnetic–structural coupling finite element PMDG model. The proposed air gap field analysis method is verified by the finite element analysis results. On the basis of the test platform for the Goldwind 1.5 MW PMDG, both modal and dynamic response tests for the stator/rotor coupling system are conducted, and the results are compared with the natural frequencies, mode shapes, and vibration responses obtained using the numerical model. The effects of the air gap length and rotor speed on the natural frequencies of the coupling system are analyzed. The proposed model has the potential to accurately evaluate the PMDG vibration energy, avoiding resonance points, and maintaining stable operations of the unit.

Abstract The rotating parts looseness is one of the common failures in rotating machinery. The current researches of looseness fault mainly focus on non-rotating components. However, the looseness fault of disc-shaft system, which is the main work part in the rotor system, is almost ignored. Here, a dynamic model of the rotor system with loose disc caused by the insufficient interference force is proposed based on the contact model of disc-shaft system with the microscopic surface topography, the vibration characteristics of the system are analyzed and discussed by the number simulation, and verified by the experiment. The results show that the speed of the shaft, the contact stiffness, the clearance between the disc and shaft, the damping of the disc and the rotational damping have an influence on the rotation state of the disc. When the rotation speed of the disc and the shaft are same, the collision frequency is mainly composed of one frequency multiplication component and very weak high frequency multiplication components. When the rotation speed of the disc and the shaft is close, the vibration of the disc occurs a beat vibration phenomenon in the horizontal direction. Simultaneously, a periodical similar beat vibration phenomenon also occurs in the waveform of the disc-shaft displacement difference. The collision frequency is mainly composed of a low frequency and a weak high frequency component. When the rotation speed of the disc and the shaft has great difference, the collision frequency is mainly composed of one frequency multiplication, a few weak high frequency multiplication components and a few low frequency multiplication component. With the reduction of the relative speed of the disc, the trajectory of the disc changes from circle-shape to inner eight-shape, and then to circle-shape. In the inner eight-shape, the inner ring first gradually becomes smaller and then gradually becomes larger, and the outer ring is still getting smaller. The obtained research results in this paper has important theoretical value for the diagnosis of the rotor system with the loose disc.

Abstract The remaining useful life (RUL) estimation of bearings is critical for ensuring the reliability of mechanical systems. Owing to the rapid development of deep learning methods, a multitude of data-driven RUL estimation approaches have been proposed recently. However, the following problems remain in existing methods: 1) Most network models use raw data or statistical features as input, which renders it difficult to extract complex fault-related information hidden in signals; 2) for current observations, the dependence between current states is emphasized, but their complex dependence on previous states is often disregarded; 3) the output of neural networks is directly used as the estimated RUL in most studies, resulting in extremely volatile prediction results that lack robustness. Hence, a novel prognostics approach is proposed based on a time–frequency representation (TFR) subsequence, three-dimensional convolutional neural network (3DCNN), and Gaussian process regression (GPR). The approach primarily comprises two aspects: construction of a health indicator (HI) using the TFR-subsequence–3DCNN model, and RUL estimation based on the GPR model. The raw signals of the bearings are converted into TFR-subsequences by continuous wavelet transform and a dislocated overlapping strategy. Subsequently, the 3DCNN is applied to extract the hidden spatiotemporal features from the TFR-subsequences and construct HIs. Finally, the RUL of the bearings is estimated using the GPR model, which can also define the probability distribution of the potential function and prediction confidence. Experiments on the PRONOSTIA platform demonstrate the superiority of the proposed TFR-subsequence–3DCNN–GPR approach. The use of degradation-related spatiotemporal features in signals is proposed herein to achieve a highly accurate bearing RUL prediction with uncertainty quantification.

An enhanced lightness and thinness is the inevitable trend of modern industrial production, which will also lead to prominent low-frequency vibration problems in the associated structure. To solve the vibration problem of thin plate structures in various engineering fields, the active constrained layer damping (ACLD) thin plate structure is taken as the research object to study vibration control. Based on the FEM method, energy method, and Hamilton principle, the dynamic model of an ACLD thin plate structure is derived, in which the Golla–Hughes–McTavish (GHM) model is used to characterize the damping characteristics of the viscoelastic layer, and the equivalent Rayleigh damping is used to characterize the damping characteristics of the base layer. The order of the model is reduced based on the high-precision physical condensation method and balance reduction method, and the model has good controllability and observability. An LQR controller is designed to actively control the ACLD sheet, and the controller parameters and piezoelectric sheet parameters are optimized. The results show that the finite element model established in this paper is accurate under different boundary conditions, and the model can still accurately and reliably describe the dynamic characteristics of the original system in the time and frequency domain after using the joint reduction method. Under different excitation and boundary conditions, LQR control can effectively suppress structural vibration. Considering the performance and cost balance, the most suitable control parameter for the system is: Q-matrix coefficient is between 1 × 104 and 1 × 105, the R-matrix coefficient is between 1 and 10, and the thickness of the piezoelectric plate is 0.5 mm.

Fault diagnosis technique is the core of Prognostics and Health Management (PHM) system, which plays a crucial role in the intelligent operation and maintenance of various rotating machineries. In this paper, we present a novel sparse representation classification framework with structured dictionary design strategy (SRC-SDD) for intelligent fault diagnosis of rotating machineries. The proposed SRC-SDD method consists of two stages, i.e., the structured dictionary design stage and the sparsity-based intelligent diagnosis stage. In the first stage, the novelty of SRC-SDD lies in the overlapping segmentation strategy for structured dictionary design, which leverages the structured prior knowledge of rotating machinery vibration signals, namely, the periodic self-similarity and shift-invariance properties. In the second stage, SRC-SDD achieves fault recognitions of testing samples using a sparsity-based diagnosis strategy based on the minimum sparse reconstruction error. The proposed structured dictionary design strategy can enhance the representation power of dictionaries and thus promote the recognition performance of the sparsity-based diagnosis strategy. Finally, the effectiveness of SRC-SDD has been validated on the gearbox fault dataset from IEEE PHM society. The diagnosis results show that SRC-SDD achieves the excellent recognition accuracy of 100% for predicting six different gearbox health states. Further, the comparative studies with three conventional SRC methods prove the superiority of SRC-SDD in terms of both the recognition performance and computation efficiency.

Grain boundary structures with high resistance to intergranular fracture are the target of grain boundary design. In this work, grain boundary elimination in front of crack tip is observed in two special bcc iron bicrystals through molecular dynamics simulations under mode I loading. Grain boundary elimination depends on crack advance direction and enhances resistance to intergranular fracture. Direction-dependent elimination leads to directional anisotropy of intergranular crack propagation. By analytical analysis and molecular dynamics simulation, grain boundary elimination is found to be attributed to the activities of twinning and dislocation. All twinning bands are formed by atomic slip along ordinary twinning direction, but all dislocations are nucleated by atomic slip along anti-twinning direction. Mechanisms of twinning formation and dislocation nucleation are revealed by calculating energy barriers of atomic slip and shear stress field. According to the mechanism of grain boundary elimination, conditions for grain boundary elimination are proposed to find all special grain boundaries. Results show that twist grain boundaries cannot be eliminated under mode I loading, while tilt grain boundaries with axes of 〈110〉 can. This work provides a good reference for grain boundary design.

The localization of outer raceway defect plays a significant role in malfunction elimination, failure cause analysis as well as the residual life prediction of ball bearings. Based on the nonlinear dynamic model for a ball bearing and the outer raceway defect model considering the ball finite size, this article employs the detailed mathematical derivation and theoretical analysis of the load distribution for the bearing system with an outer raceway defect located at the different angular positions. Therefore, the essential mechanism of the approximate linear relationship between the proposed indices, namely horizontal-vertical synchronized Peak (HVSPeak) and horizontal-vertical synchronized RMS (HVSRMS), and the defect angular position is explained. More importantly, it is theoretically demonstrated that HVSRMS is approximately a cotangent function with the defect angular position as the only variable, which indicates that the index has excellent anti-interference and practicability. In addition, the superiority and necessity of the HVSRMS index can be seen when compared to HVSPeak, RMS, SampEn and Lemple-Ziv. It is validated through simulation and experiment results that HVSRMS index can efficiently diagnose the angular position of outer raceway defect. Finally, the signal denoising methods for HVSRMS are compared and studied, which indicates the direction for subsequent research.

A finite element dynamic model of the sandwich composite plate was developed based on classical laminate theory and Hamilton’s principle. A 4-node, 7-degree-of-freedom three-layer plate cell is constructed to simulate the interaction between the substrate, the viscoelastic damping layer, and the piezoelectric material layer. Among them, the viscoelastic layer is referred to as the complex constant shear modulus model, and the equivalent Rayleigh damping is introduced to represent the damping of the substrate. The established dynamics model has too many degrees of freedom, and the obtained dynamics model has good controllability and observability after adopting the joint reduced-order method of dynamic condensation in physical space and equilibrium in state space. The optimal quadratic (LQR) controller is designed for the active control of the sandwich panel, and the parameters of the controller parameters, the thickness of the viscoelastic layer, and the optimal covering position of the sandwich panel are optimized through simulation analysis. The results show that the finite element model established in this paper is still valid under different boundary conditions and different covering methods, and the model can still accurately and reliably represent the dynamic characteristics of the original system after using the joint step-down method. Under different excitation signals and different boundary conditions, the LQR control can effectively suppress the vibration of the sandwich plate. The optimal cover position of the sandwich plate is near the solid support end and far from the free-degree end. The parameters of controller parameters and viscoelastic layer thickness are optimized from several angles, respectively, and a reasonable optimization scheme can be selected according to the actual requirements.

This paper deals with the active vibration control of composite cantilever beam. Based on the finite element method and Golla–Hughes–McTavish (GHM) model, the system dynamics equation is established. Models are simplified in physical and modal space because of unobservable and uncontrollable. Based on the particle swarm optimization (PSO) algorithm, the linear quadratic regulator (LQR) feedback gain was optimized. The effect of system vibration damping under different controller parameters, piezoelectric-constrained layer position and excitation signal was studied. The study show that the optimal feedback gain of the controller can effectively balance the control effect and the control cost. The closer the piezoelectric layer and viscoelastic layer are to the fixed end, the better the system control effect and the smaller the control cost. The reduced-order model has a good control effect on different excitation signals.

This paper deals with the active vibration control of piezoelectric sandwich plate. The structure consists of a substrate plate layer sandwiched between two layers of piezoelectric sensor and actuator. Based on laminate theory and constitutive equation of piezoelectric material, the vibration active control dynamic equation of the sandwich structure is established by using hypothetical mode method and Hamilton principle. The Rayleigh-Ritz method is used to solve it. The form of hypothetical solution is used for approximate solution, which is simple and accurate. The method of this paper is verified by several examples. The parametric studies of the sandwich plate structures are carried out. The results show that applying different boundary conditions and piezoelectric patch positions to the structures have a great influence on the natural frequency. When the driving voltage increases, the deflection of the plate structures increase approximately linearly. The active vibration control studies are investigated as well. The results show that within a certain range, the larger the value of the speed feedback coefficient, the better the active control effect. The positions of the piezoelectric patches affect the effectiveness and cost of active control. When the piezoelectric plate is located at the fixed end, the effect and cost of active control are better than that at the midpoint and free end of the plate.

This paper studies traveling wave motions of rotating multi-layered functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical shell under general boundary conditions. Theoretical equations are obtained according to Donnell shell theory, and artificial spring technique, where centrifugal and Coriolis effects caused by rotation are considered. By employing general orthogonal polynomials using a Gram-Schmidt process as admissible functions, solutions are achieved via Rayleigh-Ritz approach. Then, the accuracy and convergence of solutions are validated by the comparison of the obtained results with those reported in literature. Finally, free vibrations of FG-GPLRC cylindrical shells in both stationary and rotating states are investigated. The influences of boundary spring stiffness, GPL weigh fraction, total layer number, and geometry parameters on shell vibration characteristics are evaluated. It is revealed that the frequency variation trends along with material and geometric parameters are consistent for different boundary conditions, while variation rates and frequency values are highly dependent on boundary spring stiffness. Keywords: Rotating cylindrical shell, Functionally graded graphene platelet reinforced laminated composite, General boundary conditions, Traveling wave motion, Rayleigh-Ritz method

In the present work, the nonlinear vibration behavior of elastic-viscoelastic-elastic sandwich (EVES) beams is studied. A finite element (FE) equation taking intoaccount the transverse compression deformation of the viscoelastic core for the EVES beams is derived. In order toaccurately characterize the frequency-dependent feature of the viscoelastic materials layer, athird-order seven-parameter Biot model isused. A 2-node 8-DOF element is established to discretize the EVES beams. The experimental testing onEVES beams validates the numerical predication of the FE model. Numerical and analytical investigations are carried on a series of EVES beams with different thicknesses. The results indicate that the presented FE model has better accuracy in predicting the natural frequency of the sandwich beams, and in predicting damping, the accuracy is related to the thickness of each layer. The results of this paper have important reference values for the design and optimization of the viscoelastic sandwich structure.

This study investigates whether and why spiritual leadership may contribute to enhanced proactive employee workplace behavior. Based on self-determination theory (SDT), we examine the effects of two sequential mediators (i.e., organizational identification and psychological safety) on the relationship between spiritual leadership and proactive workplace behavior. Data collected from 188 subordinate-leader dyads in Chinese firms suggested that spiritual leadership has a significant positive effect on proactive workplace behavior. In addition, both organizational identification and psychological safety mediate the relationship between spiritual leadership and proactive workplace behavior. Furthermore, spiritual leadership positively influences organizational identification, and such identification nurtures psychological safety, which, in turn, fosters the proactive behavior of employees. It extends the existing impact of spiritual leadership to proactive workplace behavior and shed lights on the mediating mechanisms through which spiritual leadership exerts influences on proactive workplace behavior. Finally, it considers the important roles played by leaders in modern organizations.

It is proposed a novel instantaneous frequency estimation technology, multi-generalized demodulation transform, for non-stationary signals, whose true time variations of instantaneous frequencies are unknown and difficult to extract from the time-frequency representation due to essentially noisy environment. Theoretical bases of the novel instantaneous frequency estimation technology are created. The main innovations are summarized as: (a) novel instantaneous frequency estimation technology, multi-generalized demodulation transform, is proposed, (b) novel instantaneous frequency estimation results, obtained by simulation, for four types of amplitude and frequency modulated non-stationary single and multicomponent signals under strong background noise (signal to noise ratio is −5 dB), and (c) novel experimental instantaneous frequency estimation results for defect frequency of rolling bearings for multiple defect frequency harmonics, using the proposed technology in non-stationary conditions and in conditions of different levels of noise interference, including a strong noise interference. Quantitative instantaneous frequency estimation errors are employed to evaluate performance of the proposed IF estimation technology. Simulation and experimental estimation results show high effectiveness of the proposed estimation technology.

Athree-layer composite plate element is developed for finite element modeling and vibration analysis of sandwich plate with frequency-dependent viscoelastic material core. The plate element is quadrilateral element bounded by four-node with 7-degree-of-freedom per node. The frequency-dependent characteristics of viscoelastic material parameters are described using the Biot model. The method of identifying the parameters of the Biot model is given. By introducing auxiliary coordinates, the Biot model is combined with the finite element equation of the viscoelastic sandwich plate. Through a series of mathematical transformations, the equation is transformed into a standard second-order steady linear system equation form to simplify the solution process. Finally, the vibration characteristics of the viscoelastic sandwich plate are analyzed and experimentally studied. The results show that the method in this paper is correct and reliable, and it has certain reference and application value for solving similar engineering vibration problems.

Purpose: summarized and sorted career success evaluation indicators of skilled employees Design/methodology/approach: Based on Grounded Theory, through interviews and questionnaires to railway skilled employees Findings and Originality/value: the study shows that “subjective career success”, including work-family balance, life satisfaction, career satisfaction, perception of career success, “objective career success”, including level of total revenue venue, growth rate of wage and times of promotion, “knowledge and skills career success” including upgrade of knowledge and skills, classification of skills, external competitiveness and job autonomy, are three important career success evaluation indicators of skilled employees. Originality/value: The results show that different age groups, different titles and different positions of skilled employees, there is a significant difference in the choice of career success evaluation indicators. It provides a useful reference to establish a career development system for the skilled employees.

Planetary gear is widely used in engineering and usually has symmetrical structure. As the number of teeth in contact changes during rotation, the time-varying mesh stiffness parametrically excites the planetary gear and may cause severe vibrations and instabilities. Taking speed fluctuations into account, the time-varying mesh stiffness is frequency modulated, and therefore sideband instabilities may arise and original instabilities are significantly affected. Considering two different speed fluctuations, original and sideband instabilities are numerically and analytically investigated. A rotational lumped-parameter model of the planetary gear is developed, in which the time-varying mesh stiffness, input speed fluctuations, and damping are considered. Closed-form approximations of instability boundaries for primary and combination instabilities are obtained by perturbation analysis and verified by numerical analysis. The effects of speed fluctuations and damping on parametric instability are systematically examined. Because of the frequency modulation, whether a parametric instability occurs cannot be simply predicted by the planet meshing phase which is applicable to constant speed. Besides adjusting the planet meshing phase, speed fluctuation supplies a new thought to minimize certain instability by adjusting the amplitude or frequency of the speed fluctuation. Both original and sideband instabilities are shrunken by damping, and speed fluctuation further shrinks the original instability.

In this work, a finite element model was developed for vibration analysis of sandwich beam with a viscoelastic material core sandwiched between two elastic layers. The frequency-dependent viscoelastic dynamics of the sandwich beam were investigated by using finite element analysis and experimental validation. The stiffness and damping of the viscoelastic material core is frequency-dependent, which results in complex vibration modes of the sandwich beam system. A third order seven parameter Biot model was used to describe the frequency-dependent viscoelastic behavior, which was then incorporated with the finite elements of the sandwich beam. Considering the parameters identification, a strategy to determine the parameters of the Biot model has been outlined, and the curve fitting results closely follow the experiment. With identified model parameters, numerical simulations were carried out to predict the vibration and damping behavior in the first three vibration modes, and the results showed that the finite model presented here had good accuracy and efficiency in the specific frequency range of interest. The experimental testing on the viscoelastic sandwich beam validated the numerical predication. The experimental results also showed that the finite element modeling method of sandwich beams that was proposed was correct, simple and effective.

In order to extract and enhance the weak fault feature of rolling element bearings in strong noise conditions, the Empirical Wavelet Transform (EWT) is improved and a novel fault feature extraction and enhancement method is proposed by combining the Maximum Correlated Kurtosis Deconvolution (MCKD) and improved EWT method. At first, the MCKD method is conducted to de-noise the signal by eliminating the non-impact components. Then, the Fourier spectrum is segmented by local maxima or minima in the envelope of the amplitude spectrum with a pre-set threshold based on the noise level. By building up the wavelet filter banks based on the spectrum segmentation result, the signal is adaptively decomposed into several sub-signals. Finally, by choosing the most meaningful sub-signal with the maximum kurtosis, the fault feature can be extracted in the squared envelope spectrum and teager energy operator spectrum of the chosen component. Both simulations and experiments are performed to validate the effectiveness of the proposed method. It is shown that the spectrum segmentation result of improved EWT is more reasonable than the traditional EWT in strong noise conditions. Furthermore, compared with commonly used methods, such as the Fast Kurtogram (FK) and the Optimal Wavelet Packet Transform (OWPT) method, the proposed method is more effective in the fault feature extraction and enhancement of rolling element bearings.

Accurate wind speed forecasting is a significant factor in grid load management and system operation. The aim of this study is to propose a framework for more precise short-term wind speed forecasting based on empirical mode decomposition (EMD) and hybrid linear/nonlinear models. Original wind speed series is decomposed into a finite number of intrinsic mode functions (IMFs) and residuals by using the EMD. Several popular linear and nonlinear models, including autoregressive integrated moving average (ARIMA), support vector machine (SVM), random forest (RF), artificial neural network with back propagation (BP), extreme learning machines (ELM) and convolutional neural network (CNN), are utilized to study IMFs and residuals, respectively. An ensemble forecast for the original wind speed series is then obtained. Various experiments were conducted on real wind speed series at four wind sites in China. The performance and robustness of various hybrid linear/nonlinear models at two time intervals (10 min and 1 h) are compared comprehensively. It is shown that the EMD based hybrid linear/nonlinear models have better accuracy and more robust performance than the single models with/without EMD. Among the five hybrid models, EMD-ARIMA-RF has the best accuracy on the whole for 10 min data, and the mean absolute percentage error (MAPE) is less than 0.04. However, for the 1 h data, no model can always perform well on the four datasets, and the MAPE is around 0.15.

The variations of the supporting condition, which change the stiffness of tilting pad thrust bearing, may alter the dynamic behavior of the rotor system. The effects of supporting condition of thrust pad on the lateral vibration of a hydroelectric generating set are investigated in this paper. The action of a thrust bearing is described as moments acting on the thrust collar, and the tilting stiffness coefficients of thrust bearing are calculated. A model based on typical beam finite element method is established to calculate the dynamic response, and the effects of supporting conditions such as elastic oil tank support, different heights of the thrust pads with rigid support are discussed. The results reveal that the influence of thrust bearing is small when the elastic oil tanks work normally. When the supporting conditions turn to be rigid due to the oil leakage, the differences of thrust pad heights have evident influence on the load distribution of the thrust pads; while the effects on the tilting stiffness of the thrust bearing and the amplitude of the lateral shaft vibration is small when the maximum load on thrust pads is smaller than the allowable value.

The shaft crack is one of the main serious malfunctions that often occur in rotating machinery. However, it is difficult to locate the crack and determine the depth of the crack. In this paper, the acoustic emission (AE) signal and vibration response are used to diagnose the crack. The wavelet transform is applied to AE signal to decompose into a series of time-domain signals, each of which covers a specific octave frequency band. Then an improved union method based on threshold and cross-correlation method is applied to detect the location of the shaft crack. The finite element method is used to build the model of the cracked rotor, and the crack depth is identified by comparing the vibration response of experiment and simulation. The experimental results show that the AE signal is effective and convenient to locate the shaft crack, and the vibration signal is feasible to determine the depth of shaft crack.

Flow induced vibration is an important factor affecting the performance of the rotor-seal system. From the point of view of flow induced vibration, the nonlinear models of the rotor-seal system are presented for the analysis of the fluid force, which is induced by the interaction between the unstable fluid flow in the seal and the vibrating rotor. The nonlinear characteristics of flow induced vibration in the rotor-seal system are analyzed, and the nonlinear phenomena in the unbalanced rotor-seal system are investigated using the nonlinear models. Various nonlinear phenomena of flow induced vibration in the rotor-seal system, such as synchronization phenomenon and amplitude mutation, are reproduced.

Electrical machines are important devices that convert electric energy into mechanical work and are widely used in industry and people’s life. Undesired vibrations are harmful to their safe operation. Reviews from the viewpoint of fault diagnosis have been conducted, while summaries from the perspective of dynamics is rare. This review provides systematic research outlines of this field, which can help a majority of scholars grasp the ongoing progress and conduct further investigations. This review mainly generalizes publications in the past decades about the dynamics and vibration of electrical machines. First the sources of electromagnetic vibration in electrical machines are presented, which include mechanical and electromagnetic factors. Different types of air gap eccentricity are introduced and modeled. The analytical methods and numerical methods for calculating the electromagnetic force are summarized and explained in detail. The exact subdomain analysis, magnetic equivalent circuit, Maxwell stress tensor, winding function approach, conformal mapping method, virtual work principle and finite element analysis are presented. The effects of magnetic saturation, slot and pole combination and load are discussed. Then typical characteristics of electromagnetic vibration are illustrated. Finally, the experimental studies are summarized and the authors give their thoughts about the research trends.

Gearbox and rolling element bearing vibration signals feature modulation, thus being cyclostationary. Therefore, the cyclic correlation and cyclic spectrum are suited to analyze their modulation characteristics and thereby extract gearbox and bearing fault symptoms. In order to thoroughly understand the cyclostationarity of gearbox and bearing vibrations, the explicit expressions of cyclic correlation and cyclic spectrum for amplitude modulation and frequency modulation (AM-FM) signals are derived, and their properties are summarized. The theoretical derivations are illustrated and validated by gearbox and bearing experimental signal analyses. The modulation characteristics caused by gearbox and bearing faults are extracted. In faulty gearbox and bearing cases, more peaks appear in cyclic correlation slice of 0 lag and cyclic spectrum, than in healthy cases. The gear and bearing faults are detected by checking the presence or monitoring the magnitude change of peaks in cyclic correlation and cyclic spectrum and are located according to the peak cyclic frequency locations or sideband frequency spacing.