Bearing Vibration Research Articles

Sparse representations for fault signatures via hybrid regularization in adaptive undecimated fractional spline wavelet transform domain

Recent studies on vibration-based machine diagnostics have highlighted the role played by the wavelet transform (WT). However, common WT-based denoising methods (e.g. wavelet thresholding and non-penalty regularization) are often challenging in attaining accurate sparse representations of fault signatures in practice due to artifacts. In this paper, a method via hybrid regularization in the adaptive undecimated fractional spline WT (AUFrSWT) domain is introduced to achieve the accurate sparse representations of fault signatures from strong noise environments. The method promotes wavelet sparsity by two aspects: wavelet basis design and wavelet coefficient processing. For the former, a new wavelet family, i.e. a fractional spline wavelet, is used, and the AUFrSWT is originally proposed to customize the optimal wavelet basis and meanwhile address the translation-invariant issue. For the latter, the wavelet coefficients are estimated by minimizing a single convex model function with hybrid regularization, where nonconvex arctangent penalty is employed for wavelet sparsity promoting and total variation is used to improve the reconstruction performance of the shrunken coefficients. The method is validated by the analysis of actual bearing and gear vibration data from fault-injection experiments. Analysis and comparison results show great potential for signal sparse representations and machinery fault diagnostics.

Prediction of radial clearance based on bearing vibration using artificial neural network

Artificial neural networks are used for diagnosing of ball bearings condition. They are capable to recognize bearing fault from information extracted from signal of vibration. The aim of the work is to investigate the relationship between vibration velocity in the characteristic band frequencies and radial clearance. Changing the radial clearance during operation may indicate changes in the operation of the rotating system. Experimental research is based on deep groove ball bearings and measuring the vibration of the bearings. The vibration velocities for each bearing were measured under laboratory conditions, and the processed signals were used to train the artificial neural network. An artificial neural network trained in this way can predict the size of the radial clearance based on the vibration of the bearing.

Tuned Positive Position Feedback Control of an Active Magnetic Bearings System With 16-Poles and Constant Stiffness

This paper presents a tuned positive position feedback controller (TPPF) to overcome the dual high peaks of the classical PPF. This control signal is merged with a proportional-derivative (PD) control signal to suppress the vibrations of a constant-stiffness 16-poles rotor active magnetic bearings (AMBs) system. Another benefit of the applied TPPF is turning the rotor’s quasiperiodic unstable motion into a periodic stable motion by eliminating both saddle-node and Hopf points. The whole group equations of motion are derived and their approximate solutions are sought with the aid of the multiple scales method. Different response curves are plotted to clarify the difference between the rotor’s vibratory behaviors before and after PPF and also with TPPF.

The Friction-Induced Vibration of Water-Lubricated Rubber Bearings during the Shutdown Process.

The vibration noise generated by water-lubricated rubber bearings (WLRBs) seriously reduces the concealment of a ship’s navigation. The purpose of this study was to obtain the relationships between friction-induced vibration and the friction coefficient, specific pressure, temperature, and stiffness of the bearing support during the shutdown process of WLRBs. Using transient dynamic analysis (Abaqus/Standard), the shutdown process of the bearing system was simulated by setting a friction coefficient curve, and with the fast Fourier transform (FFT), the data in the time domain were then converted to the frequency domain. In addition, an orthogonal table was applied to select the best level for each factor. The results show that proportionally increasing the friction coefficient and specific pressure caused higher vibrations, and the effect of the specific pressure on vibration is more prominent than that of the friction coefficient. Higher temperatures led to an increase in the peak frequency of noise (squeal) and the virtual value of acceleration. Increasing the stiffness of the bearing support decreased the higher-frequency squeal but dramatically increased the lower-frequency chatter. The results of the study are of guiding significance for the improvement of research methods and the optimization of the materials and structures of WLRBs.

Four-Factor Polarity Switching Control for Synchronous Vibration Suppression of Active Magnetic Bearings Rigid Rotors System in the Full Rotational Speed Range

In order to suppress the synchronous unbalance vibration of the active magnetic bearings (AMBs) rigid rotor system in the full rotational speed range, the polarity switching control (PSC) can effectively suppress the synchronous unbalance vibration of the AMBs-rigid rotor system before and after the rigid cylindrical mode frequency, and the impact of the switching polarity on the system was reduced by using a disturbance observer. However, considering the rigid conical mode, the PSC could not guarantee the synchronous unbalance vibration suppression of the AMBs-rigid rotor system in the full rotational speed range including the rigid cylindrical mode frequency and the rigid conical mode frequency, and the system stability also changes accordingly. This article proposes a synchronous unbalance vibration suppression method based on the four-factor PSC (4-FPSC), which adjusts four polarity factors to suppress the synchronous unbalance vibration before and after two rigid mode frequencies. Besides, the disturbance observer is also avoided. Finally, simulation and experiment results verify the 4-FPSC can effectively suppress the synchronous unbalance vibration of the AMBs-rigid rotor system in the full rotational speed range including the rigid cylindrical and conical mode frequencies.

A comprehensive evaluation of the effect of defect size in rolling element bearings on the statistical features of the vibration signal

A defective rolling element bearing produces a specific vibration pattern that can be used as a diagnostic tool in predictive maintenance. Defect growth from an incipient fault to a fully developed fault alters the vibration pattern significantly. Changes in the statistical features of the acceleration as the defect grows can provide useful information in degradation assessment. The purpose of this paper is to study the trend of the important statistical features in terms of defect size. A physical model with the ability of modeling naturally developed defects has been used for the simulation of the generated vibrations in the rolling element bearings. Defects on the outer race, inner race and rolling element have been considered separately. The vibration signals have been obtained numerically from the model and their statistical features have been calculated for different defect sizes. The behavior of the statistical features including rms, peak, crest factor, kurtosis and level crossing rate have been studied thoroughly and simple relations between the defect size and vibration features have been proposed. Level crossing rate is introduced as a useful feature in the condition monitoring of rolling element bearings. Experimental data of a bearing with a natural defect have been measured using an accelerometer in a test and used to validate the results.

Impulse Response of the Elasto-Hydrodynamic Lubrication Film of a Rolling Bearing to Dynamic Excitation of a Flat Belt Drive.

The impulse response of a rolling bearing and its principal component, the elasto-hydrodynamic lubrication film (EHDL), are analysed. When measuring the vibrations of bearings, we observed that the impulse response was mostly caused by defects (fatigue damage) on the raceways and/or rolling elements. However, this phenomenon can also occur in new defect-free roller bearings, where it is not commonly expected. This study presents an experiment that identifies the conditions of dynamic excitation for the impulse response of the EHDL, the source of which is not defects, but the EHDL itself. The EHDL responds in the form of impulses in case the velocity of its radial deformation is too fast. This is an unfavourable phenomenon that significantly shortens the service life of bearings. To analyse the dynamic excitation conditions, a testing bench at speeds up to 135,000 rpm with a flat belt drive was used. The testing bench enabled the formation of the so-called beat excitation from two harmonic excitation forces close in rotational frequency. The subject of this study is a defect-free high-speed double-row angular contact ball bearing used in the textile industry. We also present other physical conditions for the occurrence of undesired impulse responses that are caused by the EHDL.

Vibration and damping performance of carbon fiber-reinforced polymer 3D double-arrow-head auxetic metamaterials

The vibration and damping performances of carbon fiber-reinforced polymer (CFRP) three-dimensional double-arrow-head (3D DAH) auxetic metamaterials are investigated in this paper. The negative Poisson’s ratio effects of the CFRP 3D DAH auxetic metamaterials are analytically studied by the energy method. 3D finite element models based on Modal Strain Energy approach are developed to analyze their vibration and damping characteristics. To validate the numerical models in the present study, the CFRP 3D DAH auxetic metamaterials are designed and manufactured. The sine-sweep response tests are conducted to investigate their vibration performances. The influence of different inclined corrugated angles, and fiber orientations on the natural frequencies, loss factors and the nominal Young’s modulus are plotted and discussed using validated numerical models. Meanwhile, the effect of Poisson’s ratio on the nominal Young’s modulus, natural frequencies and loss factors is also revealed explicitly. Furthermore, the comprehensive evaluation parameter that simultaneously characterizes the structural bearing capacity and vibration damping performance is further improved through parameter optimization.

EMD and Singular Value Difference Spectrum Based Bearing Fault Characteristics Extraction

Aiming at extracting rolling bearing defect characteristic effectively under strong background noise, a defect diagnosis technique based on empirical mode decomposition (EMD) and singular value difference spectrum is put forward. Firstly, the non-stationary original bearing vibration experimental data is decomposed into several intrinsic mode functions (IMFs) using EMD technique to eliminate the noise influence. Secondly, the effective intrinsic mode functions are selected by using correlation functions to reconstruct the bearing transient vibration signal. Thirdly, the singular value decomposition of the reconstructed signal is carried out to calculate the singular value difference spectrum (SVDS), and the principal components are selected according to the SVDS. Finally, the envelope spectrum of the reconstructed principal components data is calculated, and rolling bearing defect characteristic is picked up according to the envelope spectrum technique. The results of the experiment exhibit that the proposed technique can be effectively applied to rolling bearing defect characteristics extraction.

Suppression of Complex Hysteretic Resonances in Varying Compliance Vibration of a Ball Bearing

It is traditionally considered that, due to the Hertzian contact force-deformation relationship, the stiffness of rolling bearings has stiffening characteristics, and gradually researchers find that the supporting characteristics of the system may stiffen, soften, and even coexist from them. The resonant hysteresis affects the stability and safety of the system, and its jumping effect can make an impact on the system. However, the ball bearing contains many nonlinearities such as the Hertzian contact between the rolling elements and raceways, bearing clearance, and time-varying compliances (VC), leading great difficulties to clarify the dynamical mechanism of resonant hysteresis of the system. With the aid of the harmonic balance and alternating frequency/time domain (HB-AFT) method and Floquet theory, this paper will investigate the hysteretic characteristics of the Hertzian contact resonances of a ball bearing system under VC excitations. Moreover, the linearized dynamic bearing stiffness of the system will be presented for assessing the locations of VC resonances, and the nonlinear characteristics of bearing stiffness will also be discussed in depth. Our analysis indicates that the system possesses many types of VC resonances such as the primary, internal, superharmonic, and even combination resonances, and the evolutions of these resonances are presented. Finally, the suppression of resonances and hysteresis of the system will be proposed by adjusting the bearing clearance.

The effect of outer ring elastodynamics on vibration and power loss of radial ball bearings

Ball bearings are an integral part of many machines and mechanisms and often determine their performance limits. Vibration, friction and power loss are some of the key measures of bearing performance. Therefore, there have been many predictive analyses of bearing performance with emphasis on various aspects. The current study presents a mathematical model, incorporating bearing dynamics, mechanics of rolling element-to-races contacts as well as the elastodynamics of the bearing outer ring as a focus of the study. It is shown that the bearing power loss in cage cycles increases by as much as 4% when the flexibility of the outer ring is taken into account as a thick elastic ring, based on Timoshenko beam theory as opposed to the usual assumption of a rigid ring in other studies. Geometric optimisation has shown that the lifetime power consumption can be reduced by 1.25%, which is a significant source of energy saving when considering the abundance of machines using rolling element bearings. The elastodynamics of bearing rings significantly affects the radial bearing clearance through increased roller loads and generated contact pressures. The flexible ring dynamics is shown to generate surface waviness through global elastic wave propagation, not hitherto taken into account in contact dynamics of rollers-to-raceways which are generally considered to be subjected to only localised Hertzian deflection. The elastodynamic behaviour reduces the elastohydrodynamic film thickness, affecting contact friction, wear, fatigue, vibration, noise and inefficiency.

General Log-Linear Weibull Model Combining Vibration and Temperature Characteristics for Remaining Useful Life Prediction of Rolling Element Bearings

In industrial applications, the vibration and temperature measurements of rolling element bearings are known as two popular condition monitoring methods. The previously published method for remaining useful life (RUL) prediction has been limited to using the vibration signal. However, a single signal source cannot fully reflect the degradation trend of bearings, influencing the RUL prediction precision. In this paper, a novel general log-linear Weibull (GLL-Weibull) model is constructed by considering vibration and temperature condition monitoring signals to estimate the model parameters. During the feature extraction stage, the relative root mean square (RRMS) is derived from the monitored vibration signal, and the relative temperature trend value is extracted from the monitored temperature signal to eliminate individual differences in bearings and random signal fluctuations. Then, a fuzzy operator is introduced to describe the degree of an “overheated bearing” and “excessive bearing vibrations.” During the RUL prediction stage, both the extracted vibration and temperature characteristics are used to create the GLL-Weibull model. The best parameters are attained by employing the maximum likelihood estimation approach. The algorithm performance is checked with criteria like the root mean square error (RMSE) and the mean absolute percentage error (MAPE). The effectiveness and superiority of the presented approach are validated by two real-life prognosis cases. According to the experimental results, the presented approach provides superior prediction precision and lower computational cost than other approaches for bearings under constant or variable operating conditions.

Improvement of the compression ratio of vibratory signals by double pass DWHT

Background/Objectives: The vibratory signals delivered by rotating machines are very important in the maintenance of these machines. For maintenance purposes they are stored or transmitted. The storage and transmission of these signals pose problems of space and bandwidth. To solve this problem compression is a solution. Methods/Statistical analysis: In this work, we compress and decompress the vibration signals formed by variations of the amplitudes vibration of a ball bearing. We used an algorithm based on the Walsh-Hadamard Transform (WHT) in two passes. The coefficients obtained are coded according to Huffman’s coding. An evaluation of performances of this algorithm is made on the basis of the measurements of SNR, MFD,MSE, PRD and CR. Findings: Compression ratios are high when we consider that the reconstruction is almost perfect. Usually, compression methods by transformation have a nonzero reconstructed error. However, this bleaching of vibratory signals both in the temporal and frequency domain, followed by good quantization precision, allowed to cancel this error. In view of these qualitative and quantitative evaluation parameters of the method result, it can be said that the method gives very good results. Novelty/Applications: Improved of Compression Ratio of vibratory signals for maintenance purposes. Keywords: WHT; compression; vibratory signals; storage; bandwidth; rotating machines

Failure Investigation of a Blast Furnace Top Gas Recovery Turbine: Chronology and Mechanism

Top gas recovery turbine (TRT) is used to utilize high top pressure for power generation in modern blast furnaces. A failure occurred in the TRT system that led to interruption in operation and reduced power generation. A large increase in vibration of turbine discharge-side bearing was reported prior to the failure. Failure investigation consisted of collection and analysis of plant data, on-site and visual observations, chemical analysis, microstructural analysis using optical and scanning electron microscope coupled with energy-dispersive spectroscopy and hardness measurements. Both the failed components, that is the connecting piece and the rotor blade, were composed of AISI 420 martensitic stainless steel. In the failed connecting piece, fatigue fracture characterized by ratchet and beach marks were identified to occur from a step, a potential stress concentration site. Analytical scanning electron microscopy revealed that the fatigue cracks originated from the corrosion pits having iron oxide scale rich in sulfur and chlorine. Pitting occurred due to breakage of passive chromium oxide film due to acidic water in the system containing high concentration of chlorine. Crack propagation occurred predominantly along the chromium carbide/tempered martensitic interface. Stator blades failed subsequently in brittle mode. Lower hardness of the connecting pieces compared to the stator blade would have promoted fatigue failure in the former component. Based on the analysis, primary mode of failure is termed as “corrosion fatigue.” Practical recommendations are provided to improve the reliability of the system.

Research on the influence of the normal vibration on the friction-induced vibration of the water-lubricated stern bearing

During the slow voyage of ships, the friction-induced vibration noise often occurs in the contact region of the water-lubricated stern bearing and the tail shaft. The lateral vibration can impact the normal motion of the contact surface, then change the dynamic friction force, finally affect the behaviour of the friction-induced vibration. By adding the movement of the stern shaft journal into the normal load description of the dynamic friction, the equation of friction-induced vibration considering the effect of normal vibration was established. Then the effect law of normal vibration on friction-induced vibration was discussed by numerical simulation and test. The results show that the normal vibration would make the friction-induced vibration appear quasi-periodic, chaotic trend, and narrow the speed range in which the noise of friction-induced vibration appears.

Phase Synchrony Analysis of Rolling Bearing Vibrations and Its Application to Failure Identification

As the failure-induced component (FIC) in the vibration signals of bearings transmits through housings and shafts, potential phase synchronization is excited among multichannel signals. As phase synchrony analysis (PSA) does not involve the chaotic behavior of signals, it is suitable for characterizing the operating state of bearings considering complicated vibration signals. Therefore, a novel PSA method was developed to identify and track the failure evolution of bearings. First, resonance demodulation and variational mode decomposition (VMD) were combined to extract the mono-component or band-limited FIC from signals. Then, the instantaneous phase of the FIC was analytically solved using Hilbert transformation. The generalized phase difference (GPD) was used to quantify the relationship between FICs extracted from different vibration signals. The entropy of the GPD was regarded as the indicator for quantifying failure evolution. The proposed method was applied to the vibration signals obtained from an accelerated failure experiment and a natural failure experiment. Results showed that phase synchronization in bearing failure evolution was detected and evaluated effectively. Despite the chaotic behavior of the signals, the phase synchronization indicator could identify bearing failure during the initial stage in a robust manner.

A Method for Determining Intrinsic Mode Function Number in Variational Mode Decomposition and Its Application to Bearing Vibration Signal Processing

Variational mode decomposition (VMD) method has been widely used in the field of signal processing with significant advantages over other decomposition methods in eliminating modal aliasing and noise robustness. The number (usually denoted by K) of intrinsic mode function (IMF) has a great influence on decomposition results. When dealing with signals including complex components, it is usually impossible for the existing methods to obtain correct results and also effective methods for determining K value are lacking. A method called center frequency statistical analysis (CFSA) is proposed in this paper to determine K value. CFSA method can obtain K value accurately based on center frequency histogram. To shed further light on its performance, we analyze the behavior of CFSA method with simulation signal in the presence of variable components amplitude, components frequency, and components number as well as noise amplitude. The normal and fault vibration signals obtained from a bearing experimental setup are used to verify the method. Compared with maximum center frequency observation (MCFO), correlation coefficient (CC), and normalized mutual information (NMI) methods, CFSA is more robust and accurate, and the center frequencies results are consistent with the main frequencies in FFT spectrum.

Nonlinear dynamic analysis of the bridge bearing and genetic algorithm–based optimization for seismic mitigation

Seismic mitigation for bridges by the specific bearing with highly elastoplastic dissipaters is very important to ensure safety of superstructures exposed to earthquakes. To study the lateral vibration of the bridge bearing, a nonlinear dynamic model is developed while thoroughly considering highly nonlinear mechanical properties of the bearing in this article. The generalized- α method is specifically adapted to solve the nonlinear equations. Moreover, nonlinear behavior of the bearing is fully incorporated through direct path-following of the practical experimental hysteresis curve. The proposed method is validated through careful comparison between the dynamic simulation and the quasi-static experimental results. Mechanical responses of the bridge-pier system under earthquake excitations can be calculated in a more reliable manner. On this basis, a parametric optimization model involving several key parameters of the bearing-pier system is developed. The optimization problem is solved by the genetic algorithm as the searching tool. Numerical examples show that mechanical responses of the bridge-pier system subjected to the earthquake excitations can be effectively mitigated after parametric optimization. The extensive applicability of the proposed method is validated through finding the optimized parameters for the bearing when multiple different earthquakes are considered. Moreover, the accumulative energy absorption of the bearing is also considered to enhance the seismic performance of the bearing. This work provides a reliable way of dynamic performance prediction and seismic mitigation study of nonlinear bridge bearing under earthquake excitations given any complex experimental hysteresis curve.

Influence Investigation of Rolling Bearing Test Conditions on the Informativity Assessment of their Technical Condition

Establishing patterns of the relationship of informative diagnostic parameters signals’s and test modes and operation of rolling bearings is an urgent task of technical diagnostics. The determining factor in the use of certain methods for assessing the condition and bearings faults, as well as the use of certain informative diagnostic parameters, is their sensitivity to changes in the condition of the bearing or to the size and degree of the defect development. The paper presents the results of the dependence study of the rolling bearings vibration parameters on the test and operation conditions: the rotation frequency of the inner ring, axial and radial loads. Numerical values of the listed factors are obtained that are optimal for testing bearings at the input control according to the sensitivity criterion. The study was conducted in accordance with the provisions of the experiment planning theory. It has been established that the magnitude of the vibration parameters and the level of components at the frequencies of bearing defects depend on the speed of rotation in direct proportion and increase with the deterioration of the technical condition of the bearings. It was experimentally confirmed that axial and radial loads significantly affect the values of the controlled vibration parameters only when defects appear in the tested bearings.

Calculation on the radiation noise of ceramic ball bearings based on dynamic model considering nonlinear contact stiffness and damping

Radiation noise (RN) is an important parameter for representing the characteristics of a bearing. By simplifying a ball bearing as a mass–spring–damping system, the differential equations for the vibration of an angular contact ceramic ball bearing (ACCBB) are established from the view of energy conservation considering nonlinear contact stiffness and damping. Then, the RN model of the bearing is constructed by Helmholtz's acoustic theory. The bearing noise is calculated using the proposed model, and the corresponding experiments are performed to confirm the model precision. The bearing noise consists of the noise at the characteristic frequency of each component; the rotational frequency is the primary contributor to the bearing noise. The radiation noise first increases with increasing rotational speed and the sound pressure level (SPL) has a high peak value at a critical speed of 28,000 r·min−1. Then, the noise decreases with increasing rotational speed. The directivity of sound field is discussed at different rotational speed. With increasing the rotational speed, the directivity level (DL) increases and the directivity angle (DA) skews towards the rotation direction. The research provides a theoretical basis to analyze the RN generated by ACCBBs at different rotational speeds.