Vibration Response Of Bearings Research Articles

Numerical simulation and experimental study of the dynamic characteristics of a gas turbine rotor system with beam sea and head sea excitation

Vibration analysis is crucial for studying rotor dynamics. The gas turbine rotor system is subjected to complex alternating loads during navigation, resulting in vibrations transmitted to the bearings that alter the system’s dynamic characteristics. Based on the similarity law of the wave resistance test, a hull model was established. Beam sea and head sea tests were conducted in the towing pool to measure the acceleration response at the key positions. A finite element model of the turbine rotor system was established, and the test data were imported into the model after wavelet noise reduction and resampling to calculate the vibration response at the front and rear bearing points. The vibration responses transmitted to different locations and directions caused by beam sea and head sea conditions were analyzed. A comparison and analysis were conducted on the acceleration responses in various locations and directions under beam sea or head sea conditions. The equivalent von Mises stress distribution of the gas turbine rotor system under beam sea and head sea loads was obtained. The vibration transfer model was verified for accuracy and can be used to quickly analyze the vibration response of bearings under wave load transfer. This study provides a theoretical basis and reference for enhancing the stability of the gas turbine rotor system.

Numerical and experimental investigation on the whirling vibration characteristic of ship propulsion shafting under multi-source uncertainty

Conventional numerical models struggle to accurately capture the whirling vibration characteristics of ship propulsion shafting due to the influence of multi-source uncertainties and gyroscopic effects. Hence, this study develops nonparametric modelling to incorporate multi-source uncertainties into the dynamic equations for shafting. Based on random matrix theory, these uncertainties are represented by random matrices for mass, damping, gyroscopic moment, and stiffness. The whirling frequency under different uncertainties is analysed, revealing that stiffness significantly influences on whirling frequency, followed by mass. Conversely, the gyroscopic moment has the most negligible impact. The range of the first four-order whirling frequencies is estimated accurately using confidence intervals. Additionally, the bearing vibration response is calculated by considering gravity, unbalanced force, and misalignment force. The findings suggest that the time-domain waveform fluctuates within a defined range when considering uncertainty, and unbalance and misalignment are exacerbated, leading to poor stability. Finally, a vibration signal acquisition experiment and modal testing are conducted using a test bench. The experimental results further confirm the effectiveness of nonparametric modelling that considers multi-source uncertainties and gyroscopic effects as more accurate.

A feature vector with insensitivity to the position of the outer race defect and its application in rolling bearing fault diagnosis

The fault diagnosis of rolling bearings is very important in industrial applications, which can avoid accidents and reduce operation and maintenance costs. Although the position of the bearing outer race defect has a significant impact on rolling bearing vibration response, most existing intelligent bearing fault diagnosis methods do not take this into account. In this paper, we establish a dynamic model of rolling bearing to clarify the influence of the outer race defect position on the dynamic response, and propose a feature vector that is insensitive to the outer race defect positions. First, the vibration characteristics of the outer race faults with different defect positions are analyzed, and the impact is evaluated using six indicators. Second, three indicators of insensitivity to the bearing outer race defect positions are constructed as the feature vector for bearing fault diagnosis. Finally, a bearing fault diagnosis method considering the positions of outer race defect is proposed based on the constructed feature vector and K nearest neighbor classifier. The diagnosis results of three datasets formed by experimental signals show that the constructed feature vector can separate different bearing states. Compared with the existing two diagnosis methods, the proposed diagnosis method obtains higher recognition accuracy, in the case of different outer race defect positions of the training set and the testing set. The above research results are expected to provide a reference for rolling bearing fault diagnosis, especially when considering the influence of the outer race defect positions.

Investigating the Combined Effect of Multiple Dent and Bump Faults on the Vibrational Behavior of Ball Bearings

The rolling element bearing is a fundamental component of any rotating machinery. During operation, wear debris and lubricant impurities create dents and bumps on the bearing raceway surfaces. Such localized defects produce transient vibration impulses at one of the bearing characteristic frequencies. Having a combination of multiple types of point defects on the raceway results in superimposed vibration patterns, which reduce the ability to recognize these defects’ effects. In this paper, a 6-DOF dynamic model is developed to accurately investigate the vibration characteristic of a ball bearing with a multipoint defect comprising a dent and bump on its raceway surface. The model considers the effects of time-varying contact force produced due to defects, lubricant film damping, bearing preload, and the inertia effect of rolling elements. The simulation results reveal the vibration behavior of multipoint defect bearings. In addition, bearing vibration response is affected by the number of defects, the angle between them, and the type and size of each defect. Furthermore, it is challenging to predict bearing defects parameters such as the numbers, types, sizes, and angles between adjacent defects from acceleration signal analysis without jerk signal analysis. The validation of the model is proved using signals from the Case Western University test setup.

Simulation of Friction Fault of Lightly Loaded Flywheel Bearing Cage and Its Fault Characteristics.

Because of the operating environment and load, the main fault form of flywheel bearing is the friction fault between the cage and the rolling elements, which often lead to an increase in the friction torque of the bearing and even to the failure of the flywheel. However, due to the complex mechanism of the friction fault, the characteristic frequencies often used to indicate cage failure are not obvious, which makes it difficult to monitor and quantitatively judge such faults. Therefore, this paper studies the mechanism of the friction fault of the flywheel bearing cage and establishes its fault feature identification method. Firstly, the basic dynamic model of the bearing is established in this paper, and the friction between the cage and the rolling elements is simulated by the variable stiffness. The influence law of the bearing vibration response reveals the relationship between the periodic fluctuation of cage-rolling element friction failure and the bearing load. After analyzing the envelope spectrum of the vibration data, it was found that when a friction fault occurred between the cage and the rolling element, the rotation frequency component of the cage modulated the rotational frequency component of the rolling element, that is, the side frequency components appeared on both sides of the characteristic frequency of the rolling element (with the characteristic frequency of the cage as the interval). In addition, the modulation frequency components of the cage and rolling element changed with the severity of the fault. Then, a modulation sideband ratio method based on envelope spectrum was proposed to qualitatively diagnose the severity of the cage-rolling element friction faults. Finally, the effectiveness of the presented method was verified by experiments.

Dynamic simulation of a cylindrical roller bearing with a local defect by combining finite element and lumped parameter models

Rolling element bearings are one of the key components of many rotating machines. Through condition monitoring and vibration analysis of bearings, valuable information about the health status of the machine can be obtained, such as detection of a local fault, unbalance, and misalignment. For more than three decades, various bearing dynamic models have been developed by researchers to simulate the acceleration signal of the bearing and enhance the understanding of bearing vibration response in case of having local defects. Nevertheless, recent studies have shown that measurement of local strain in the bearing can be more effective in fault diagnosis of bearings since local strain signal is less subjected to surrounding noise and non-fault interferences. However, previously developed dynamic models lack a deep study on simulating strain signals at different locations in a bearing. Therefore, this paper presents the result of a combined lumped parameter and finite element models (FEMs) for simulating strain signals of a cylindrical roller bearing in healthy and defective conditions. Contrary to previous combined dynamic models, more realistic modeling assumptions are adopted, such as applying contact pressure to the raceway rather than concentrated nodal forces. The contact pressures are obtained from the lumped parameter model and exported to the FEM for transient analysis. The accuracy of the model in generating stress distribution is validated by a static 2D finite element contact model and theoretical formulas. Dynamic responses of the bearing, such as strain changes at different locations, are investigated in the time and frequency domains to investigate the fault symptoms such as sharp impulses and amplitude modulation. Lastly, the effect of a transmission path on strain measurement and using residual strain signal for fault diagnosis are discussed. Overall, the proposed model is an effective method for strain simulation of healthy and defective roller bearings.

Effect of dynamic misalignment on the vibration response, trajectory followed and defect-depth achieved by the rolling-elements in a double-row spherical rolling-element bearing

Dynamic-misalignment beyond a specific limit suggests some abnormal systems’ behaviour and, if not dealt with appropriately may lead to its sudden breakdown. To address this problem spherical rolling-element bearings are used which have the capacity to encounter such misalignment till a certain limit. Investigating this physical mechanism of such bearing's and quantifying the degree as well as nature of dynamic-misalignment can lead to diagnosing the root cause responsible for it. This paper thus aims at understanding the physics governing the vibration response of spherical rolling-element bearing with a localized defect and subjected to dynamic-misalignment at the same time, using numerical simulations and experimental validation. The numerically simulated results firstly show that an increase in radial and axial loads have a contrasting effect on the acceleration response and contact-load shared by the two bearing rows. Secondly, the rolling-elements while following an offset trajectory, significantly affect the bearing's vibration response as compared to an inclined trajectory and the depth achieved by rolling-elements inside defect also varies with varying misalignment angles. Thirdly. with an increase in misalignment, the strange attractors form intermittent behaviour with outer multi-periodic response having hidden chaos. The behaviour observed from the numerically simulated results was also validated from the vibration data obtained experimentally from the test-rig.

A nonlinear dynamic vibration model of cylindrical roller bearing considering skidding

This paper proposes a dynamic model to investigate the vibration response of a cylindrical roller bearing considering skidding. This model considers the frictional forces and the contact forces between rolling elements and races simultaneously. The interactions between the frictional forces and the dynamic responses of rolling bearing when skidding happens are also included in the model. It improves previous quasi-dynamic models in which the contact forces and frictional forces between races and rolling elements were determined by a separate load distribution model via the static force and moment equilibrium equations for races. The variations of the friction forces in a rotational period are elaborated, and the generating mechanism is also explained. It is found that the existence of skidding may lead to fluctuations and a significant increase of the friction force. The effect of skidding on the bearing vibration is studied by comparing the simulated results with those predicted by previous models under the pure rolling assumption. The results show that the friction forces will increase the vibration level and introduce impact components into the vibration response. It is necessary to consider the influence of skidding on the bearing vibration response using the proposed model, especially for high-speed bearings.

Contact characteristic and vibration mechanism of rolling element bearing in the process of fault evolution

The vibration response of rolling element bearing has a close relation with its fault. An accurate evaluation of the bearing vibration response is essential to the bearing fault diagnosis. At present, most bearing dynamics models are built based on rigid assumptions, which may not faithfully reveal the dynamic characteristics of bearing in the presence of fault. Moreover, previous similar works mainly focus on the fault with a specified size without considering the varying contact characteristics as the fault evolves. This paper developed an explicit dynamics finite element model for the bearing with three types of raceway faults considering the flexibility of each bearing component in order to accurately study the contact characteristic and vibration mechanism of defective bearings in the process of fault evolution. The developed model is validated by comparing its simulation results with both analytical and experimental results. The dynamic contact patterns between the rolling elements and the fault, the additional displacement due to the fault and the faulty characteristics within the bearing vibration signal during the fault evolution process are investigated. The analysis results from this work can provide practitioners an in-depth understanding towards the internal contact characteristics with the existence of raceway fault and theoretical basis for rolling bearing fault diagnosis.

Coupling model and vibration simulations of railway vehicles and running gear bearings with multitype defects

Axle box bearings are important parts of rail vehicle running gear. Currently, there is limited research on the coupling modeling of an axle box bearing and rail vehicle. In this paper, a complete method for bearing modeling with multitype defects is proposed. The bearing kinematics with three translation and one rotation degrees of freedom are analyzed and modeled, and defect modeling algorithms for the inner raceway, outer raceway and rollers are proposed. The theoretical rolling tracks of rollers passing through the defect points are analyzed and formulated. By coupling the bearing model to the motion joint of the shaft end and axle box, a closed-loop bearing-vehicle model is established. Model simulations show that the calculated results for normal bearings, different types of bearing defects and the bearing-vehicle coupling model are consistent with the theoretical values. The novel and complete coupling model proposed in this paper has the advantages of having a simple algorithm, high computational efficiency, and accurate simulation of the bearing vibration response under train running conditions, which can provide important guidance for research on the response of an axle box bearing in train running gear. By establishing a bearing-vehicle coupling model that simulates the bearing vibration response, especially when the bearings have faults, the performance of the defective bearing can be better understood and applied to develop diagnostic algorithms for the condition monitoring of axle box bearings in a rail vehicle.

Dynamic Modeling and Analysis of Rolling Bearing with Compound Fault on Raceway and Rolling Element

Rolling element bearing is a very important part of mechanical equipment and widely used in rotating machinery. Rolling element bearings could appear localized defects during the working condition, which would cause the complex vibration response of bearings. Considering the shaft and bearing pedestal, a 4 degree-of-freedom (DOF) dynamic model of rolling bearing with compound localized fault is established based on time-varying displacement, and the vibration characteristics of rolling bearing with localized faults under different conditions are investigated. The established model is verified by the experimental vibration signals in time domain and frequency domain. The results show that the vibration response of compound fault is the result of the coupling action of a single fault of rolling element and outer race. The influences of compound fault on the vibration signals of the bearing were analyzed under three conditions. With the increasing of radial load, defect size, and rotation speed, the vibration amplitude of bearing would increase correspondently, which would accelerate the failure rate of bearing and reduce the service life of bearing. This model is helpful to analyze the vibration response of the rolling element bearing with single or compound fault.

Experimental and numerical study of an angular contact ball bearing vibration response with spall defect on the outer race

Angular contact ball bearings are widely used in rotary machines for their combined loads capacity, i.e., simultaneously acting radial and axial loads. Spall defect is one of the most important potential failure modes of the rolling element bearings. The main motivation of this study is to achieve a true perception of the spall defect influence on the angular contact ball bearing to predict bearing failure. In this paper, simulation and experimental analysis are performed for an angular contact ball bearing with a spall defect in the outer race. At first, the bearings without and with outer race defect are modeled, and after extracting the governing equations, they are solved using function ODE45 in MATLAB. This function implements a Runge–Kutta method with a variable time step for efficient computation. Then the vibration response in different conditions of rotating speed and axial preload is simulated. A bearing test bench is designed to perform the experimental tests. The defect is contrived in the outer race of a healthy bearing, and the vibration signals at both conditions (healthy and defective) are collected. The spall defect in the outer race is considered to have a cylindrical shape to close the model to real conditions as much as possible. The results are then presented in the form of time-domain signals and fast Fourier transformations (FFT) graphs. The FFT results showed that defect in the outer race produces dominant peaks with a suitable similarity to each other in both simulations and experimental tests.

Online Bearing Clearance Monitoring Based on an Accurate Vibration Analysis

Accurate diagnosis of incipient faults in wind turbine (WT) assets will provide sufficient lead time to apply an optimal maintenance for the expensive WT assets which often are located in a remote and harsh environment and their maintenance usually needs heavy equipment and highly skilled engineers. This paper presents an online bearing clearance monitoring approach to diagnose the change of bearing clearance, providing an early and interpretable indication of bearing health conditions. A novel dynamic load distribution method is developed to efficiently gain the general characteristics of vibration response of bearings without local defects but with small geometric errors. It shows that the ball pass frequency of outer race (BPFO) is the primary exciting source due to biased load distribution relating to bearing clearance. The geometric errors, including various orders of runouts on different bearing parts, can be the secondary excitation source. Both sources lead to compound modulation responses with very low amplitudes, being more than 20 dB lower than that of a small local defect on raceways and often buried by background noise. Then, Modulation Signal Bispectrum (MSB) is identified to purify the noisy signal and Gini index is introduced to represent the peakness of MSB results, thereby an interpretable indicator bounded between 0 and 1 is established to show bearing clearance status. Datasets from both a dedicated bearing test and a run-to-failure gearbox test are employed to verify the performance and reliability of the proposed approach. Results show that the proposed method is capable to indicate a change of about 20 µm in bearing clearance online, which provides a significantly long lead time compared to the diagnosis method that focuses only on local defects. Therefore, this method provides a big opportunity to implement more cost-effective maintenance works or carry out timely remedial actions to prolong the lifespan of bearings. Obviously, it is applicable to not only WT assets, but also most rotating machines.

Transient morphology analysis and sparse representation for bearing fault diagnosis under variable speed condition

Sparse representation has been extensively applied for bearing fault diagnosis under constant speed operation. However, its application to the variable speed case is confined as, unlike the constant speed case, the fault-induced transients under variable speed are more complex and the changing pattern of transient morphology along rotating speed is uncertain. As such, this paper firstly investigates the morphology of faulty bearing vibration response to reveal that the rotating speed variations have negligible effects on morphology of the fault-induced transients. Then an efficient dictionary spanned by a single atom can be constructed, where the optimal wavelet atom is selected by the correlation filtering strategy. The stage-wise orthogonal matching pursuit (StOMP) is subsequently adopted to enable the target signal to be sparsely represented and fast reconstructed. By analysing the characteristic order extracted from the reconstructed signal, the fault diagnosis can be completed. The experimental signals validate the effectiveness of the proposed method.

Fault Detection for Vibration Signals on Rolling Bearings Based on the Symplectic Entropy Method

Bearing vibration response studies are crucial for the condition monitoring of bearings and the quality inspection of rotating machinery systems. However, it is still very difficult to diagnose bearing faults, especially rolling element faults, due to the complex, high-dimensional and nonlinear characteristics of vibration signals as well as the strong background noise. A novel nonlinear analysis method—the symplectic entropy (SymEn) measure—is proposed to analyze the measured signals for fault monitoring of rolling bearings. The core technique of the SymEn approach is the entropy analysis based on the symplectic principal components. The dynamical characteristics of the rolling bearing data are analyzed using the SymEn method. Unlike other techniques consisting of high-dimensional features in the time-domain, frequency-domain and the empirical mode decomposition (EMD)/wavelet-domain, the SymEn approach constructs low-dimensional (i.e., two-dimensional) features based on the SymEn estimate. The vibration signals from our experiments and the Case Western Reserve University Bearing Data Center are applied to verify the effectiveness of the proposed method. Meanwhile, it is found that faulty bearings have a great influence on the other normal bearings. To sum up, the results indicate that the proposed method can be used to detect rolling bearing faults.

Impulse vibration transmissibility characteristics in the presence of localized surface defects in deep groove ball bearing systems

The present study analyzes the impulse vibration transmission through the deep groove ball bearing systems caused by a localized surface defect on the bearing raceways. The analysis is performed to understand the use of vibration signal in rotating machines for condition monitoring and diagnostics. A new dynamic model of a deep groove ball bearing system that accounts for the contact stiffness between the outer race and housing, and includes the effect of a localized defect on raceways is formulated in this study. This model is applied to examine the effect of housing materials on the contact stiffness between the outer race and housing, and the vibration transmission characteristics through the ball bearing systems. A series of parametric studies is also performed to understand the relationships between the material properties, the outer race–housing contact stiffness, and ball bearing vibration response, and as well as the vibration transmission characteristics of the impulse caused by the defects with different sizes. The numerical results demonstrate that the proposed model provides a way for simulating vibration transmissibility characteristics through the ball bearing systems, which was previously not possible. An experimental investigation is also presented to validate the proposed model.

Study on the Disturbance of Rotor-Bearing System Caused by Circumferential Loading Torque

In the rotor-bearing system fault diagnosis, the data mainly come from bearing vibration monitoring. When investigators studied the coupled flexural and torsional vibration, they only took into account the bending vibration, the torsional vibration and swinging vibration. But it’s plagiohedral for them to only monitor bearing vibration signals. This paper presents a circumferential loading system which the torque is imposed on the rotor - bearing system by couplings. On the system we studied the disturbance of rotor-bearing system caused by circumferential loading torque, and observed that the bearing vibration response was inconsistent with the bearing load changes. This provided a new basis for the rotor-bearing system fault diagnosis.

Cyclic bispectrum patterns of defective rolling element bearing vibration response

The vibration signal from a faulty rolling element bearing is not strictly phase locked to the rotational speed of the shaft, due to the variable slip between the bearing elements. For this reason, the classical diagnostic methods, which are based on Fourier analysis, cannot detect clearly the modulation phenomena and the type of the defect, because the relevant information contained in the second order statistic measures is diminished. The main purpose of this paper is the combination of cyclostationary and higher order statistic analysis methods, which can lead to better results, concerning the identification of the status of the bearing. The paper demonstrates that the cyclic bispectral analysis can lead to a discrete spectral structure, enabling the clear detection the type of the bearing fault and the corresponding modulation mechanism, thus significantly overcoming the corresponding problem of other existing methods.

CYCLOSTATIONARY ANALYSIS OF ROLLING-ELEMENT BEARING VIBRATION SIGNALS

Vibration signals resulting from rolling-element bearings present a mixture of physical information, the proper analysis of which can lead to the identification of possible faults. Traditionally, this analysis is performed by the use of signal processing methods, which assume statistically stationary signal features. The paper proposes an alternative framework for analyzing bearing vibration signals, based on cyclostationary analysis. This framework, being able to model, additionally, signals with periodically varying statistics, is better able to exhibit the underlying physical concepts of the modulation mechanism present in the vibration response of bearings. The basic concepts of the approach are demonstrated both in illustrative simulation results, as well as in experimental results and industrial measurements for two different types of bearing faults.