The Analysis of Contact Stresses in Rolling Element Bearings

1979 ◽  
Vol 101 (1) ◽  
pp. 105-109 ◽  
Author(s):  
M. J. Hartnett
Keyword(s):  
Three Dimensional ◽  
Contact Problems ◽  
Rolling Element Bearing ◽  
Rolling Element Bearings ◽  
Algebraic Equations ◽  
Linear Elastic ◽  
Linear Algebraic Equations ◽  
Rolling Element ◽  
Contact Symmetry ◽  
Force Displacement

A numerical solution is presented which can be used to analyze the complete range of frictionless contact problems found in rolling element bearings. A three dimensional, linear elastic solution to the problem is developed by combining the Boussinesq force-displacement relationships for a half-space with a modified flexibility method. In this manner a stable system of linear algebraic equations in terms of the unknown surface pressures is formed, with no restrictions placed upon either contact symmetry or material connectivity. Several numerical examples of common but hitherto unsolved contact problems prevalent in rolling element bearing applications are also presented.

Dynamic Modeling of Rolling Element Bearings With Surface Contact Defects Using Bond Graphs

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Mohsen Nakhaeinejad ◽  
Michael D. Bryant
Keyword(s):  
Three Dimensional ◽  
Surface Profile ◽  
Rolling Element Bearing ◽  
Rolling Element Bearings ◽  
Bond Graphs ◽  
Outer Race ◽  
Proposed Model ◽  
Rolling Element ◽  
Type Size ◽  
Localized Faults

Multibody dynamics of healthy and faulty rolling element bearings were modeled using vector bond graphs. A 33 degree of freedom (DOF) model was constructed for a bearing with nine balls and two rings (11 elements). The developed model can be extended to a rolling element bearing with n elements and (3×n) DOF in planar and (6×n) DOF in three dimensional motions. The model incorporates the gyroscopic and centrifugal effects, contact elastic deflections and forces, contact slip, contact separations, and localized faults. Dents and pits on inner race and outer race and balls were modeled through surface profile changes. Bearing load zones under various radial loads and clearances were simulated. The effects of type, size, and shape of faults on the vibration response in rolling element bearings and dynamics of contacts in the presence of localized faults were studied. Experiments with healthy and faulty bearings were conducted to validate the model. The proposed model clearly mimics healthy and faulty rolling element bearings.

The importance of bearing stiffness and load when estimating the size of a defect in a rolling element bearing

2018 ◽  
Vol 18 (5-6) ◽  
pp. 1527-1542 ◽  
Author(s):  
Francesco Larizza ◽  
Alireza Moazen-Ahmadi ◽  
Carl Q Howard ◽  
Steven Grainger
Keyword(s):  
Large Data ◽  
Rolling Element Bearing ◽  
Static Stiffness ◽  
Data Set ◽  
Rolling Element ◽  
Bearing Stiffness ◽  
Bearing Assembly ◽  
Element Bearing ◽  
Vibration Signatures ◽  
Force Displacement

The change in the static stiffness of a bearing assembly is an important discriminator when determining the size of a defect in a rolling element bearing. In this article, the force–displacement relationships for defective bearings under various static radial loadings at various cage angular positions are analytically estimated and experimentally measured and analyzed. The study shows that the applied load has a significant effect on the static stiffness variations in defective rolling element bearings. The experimental measurements of the effect of the defect size on the varying stiffness of the bearing assembly, which has not been shown previously, provides valuable knowledge for developing methods to distinguish between defective bearings with defects that are smaller or larger than one angular ball spacing. The methods and results presented here contribute to the wider experimental investigation of the effects of loadings on the varying static stiffness of defective bearings and its effects on the measured vibration signatures. A large data set was obtained and has been made publicly available.

Two-step fault diagnosis framework for rolling element bearings with imbalanced data based on GSA-WELM and GSA-ELM

2017 ◽  
Vol 232 (16) ◽  
pp. 2937-2947 ◽  
Author(s):  
Yuan Lan ◽  
Xiaohong Han ◽  
Weiwei Zong ◽  
Xiaojian Ding ◽  
Xiaoyan Xiong ◽  
...  
Keyword(s):  
Fault Diagnosis ◽  
Extreme Learning Machine ◽  
Gravitational Search Algorithm ◽  
Imbalanced Data ◽  
Rolling Element Bearing ◽  
Rolling Element Bearings ◽  
Misclassification Cost ◽  
Weighted Extreme Learning Machine ◽  
Rolling Element ◽  
Learning Machine

Rolling element bearings constitute the key parts on rotating machinery, and their fault diagnosis is of great importance. In many real bearing fault diagnosis applications, the number of fault data is much less than the number of normal data, i.e. the data are imbalanced. Many traditional diagnosis methods will get low accuracy because they have a natural tendency to favor the majority class by assuming balanced class distribution or equal misclassification cost. To deal with imbalanced data, in this article, a novel two-step fault diagnosis framework is proposed to diagnose the status of rolling element bearings. Our proposed framework consists of two steps for fault diagnosis, where Step 1 makes use of weighted extreme learning machine in an effort to classify the normal or abnormal categories, and Step 2 further diagnoses the underlying anomaly in detail by using preliminary extreme learning machine. In addition, gravitational search algorithm is applied to further extract the significant features and determine the optimal parameters of the weighted extreme learning machine and extreme learning machine classifiers. The effectiveness of our proposed approach is testified on the raw data collected from the rolling element bearing experiments conducted in our Institute, and the empirical results show that our approach is really fast and can achieve the diagnosis accuracies more than 96%.

scholarly journals ABOUT WAVELET-BASED MULTIGRID NUMERICAL METHOD OF STRUCTURAL ANALYSIS WITH THE USE OF DISCRETE HAAR BASIS

2018 ◽  
Vol 14 (3) ◽  
pp. 83-102
Author(s):  
Marina L. Mozgaleva ◽  
Pavel A. Akimov ◽  
Taymuraz B. Kaytukov
Keyword(s):  
Structural Analysis ◽  
Three Dimensional ◽  
Grid Method ◽  
Discrete Analogue ◽  
Algebraic Equations ◽  
Initial State ◽  
Haar Basis ◽  
Linear Algebraic Equations ◽  
Gauss Method ◽  
Original Grid

he distinctive paper is devoted to so-called multigrid (particularly two-grid) method of structural analysis based on discrete Haar basis (one-dimensional, two-dimensional and three-dimensional problems are under consideration). Approximations of the mesh functions in discrete Haar bases of zero and first levels are described (the mesh function is represented as the sum in which one term is its approximation of the first level, and the second term is so-called complement (up to the initial state) on the grid of the first level). Special projectors are constructed for the spaces of vector functions of the original grid to the space of their approximation on the first-level grid and its complement (the refinement component) to the initial state. Basic scheme of the two-grid method is presented. This method allows solution of boundary problems of structural mechanics with the use of matrix operators of significantly smaller dimension. It should be noted that discrete analogue of the initial operator equation is a system of linear algebraic equations which is constructed with the use of finite element method or finite difference method. Block Gauss method can be used for direct solution.

Wigner–Ville distribution based on cyclic spectral density and the application in rolling element bearings diagnosis

2011 ◽  
Vol 225 (12) ◽  
pp. 2831-2847 ◽  
Author(s):  
Y Zhou ◽  
J Chen ◽  
G M Dong ◽  
W B Xiao ◽  
Z Y Wang
Keyword(s):  
Fault Diagnosis ◽  
Spectral Density ◽  
Wigner Distribution ◽  
Rolling Element Bearing ◽  
Rolling Element Bearings ◽  
Accurate Analysis ◽  
Time Frequency ◽  
Bearing Fault ◽  
Rolling Element ◽  
Cross Terms

The vibration signals of rolling element bearings are random cyclostationary when they have faults. Also, statistical properties of the signals change periodically with time. The accurate analysis of time-varying signals is an essential pre-requisite for the fault diagnosis and hence safe operation of rolling element bearings. The Wigner distribution is probably most widely used among the Cohen’s class in order to describe how the spectral content of a signal changes over time. However, the basic nature of such signals causes significant interfering cross-terms, which do not permit a straightforward interpretation of the energy distribution. To overcome this difficulty, the Wigner–Ville distribution (WVD) based on the cyclic spectral density (CSD) is discussed in this article. It is shown that the improved WVD, based on CSD of a long time series, can render the time–frequency distribution less susceptible to noise, and restrain the cross-terms in the time–frequency domain. Simulation and experiment of the rolling element-bearing fault diagnosis are performed, and the results indicate the validity of WVD based on CSD in time–frequency analysis for bearing fault detection.

An Experimental Methodology to Determine Components of Power Losses of a Gearbox

2021 ◽  
Vol 143 (11) ◽  
Author(s):  
A. Dindar ◽  
K. Chaudhury ◽  
I. Hong ◽  
A. Kahraman ◽  
C. Wink
Keyword(s):  
Power Loss ◽  
Spur Gear ◽  
Rolling Element Bearing ◽  
Experimental Methodology ◽  
Total Power ◽  
Gear Pair ◽  
Rolling Element Bearings ◽  
Power Losses ◽  
Rolling Element ◽  
The One

Abstract In this study, an experimental methodology is presented to separate various components of the power loss of a gearbox. The methodology relies on two separate measurements. One is designed to measure total power loss of a gearbox housing a single spur gear pair under both loaded and unloaded conditions such that load-independent (spin) and load-dependent (mechanical) components can be separated. With the assumption that gear pair and rolling element bearings constitute the bulk of the gearbox power loss, a second measurement system designed to quantify rolling element bearing losses is proposed. With this setup, spin and mechanical power losses of rolling element bearings used in the gearbox experiments are measured. Combining the sets of gearbox and bearing data, power loss components attributable to the gear pair and rolling element bearings are quantified as a function of speed and torque. The results indicate that all gear and bearing related components are significant and a methodology such as the one proposed in this study is warranted.

scholarly journals Chaotic prediction of vibration performance degradation trend of rolling element bearing based on Weibull distribution

2019 ◽  
Vol 103 (1) ◽  
pp. 003685041989219
Author(s):  
Li Cheng ◽  
Xintao Xia ◽  
Liang Ye
Keyword(s):  
Weibull Distribution ◽  
Relative Error ◽  
High Reliability ◽  
Prediction Method ◽  
Performance Degradation ◽  
Rolling Element Bearing ◽  
Maximum Relative Error ◽  
Rolling Element Bearings ◽  
Rolling Element ◽  
Vibration Performance

Rolling element bearings are used in all rotating machinery, and the degradation performance of rolling element bearings directly affects the performance of the machine. Therefore, high reliability prediction of the performance degradation trend of rolling element bearings has become an urgent research problem. However, the degradation characteristics of the rolling element bearings vibration time series are difficult to extract, and the mechanism of performance degradation is very complicated. The accurate physical model is difficult to establish. In view of the above reasons, based on the vibration performance data of rolling element bearings, a model of bearing performance degradation trend parameter based on wavelet denoising and Weibull distribution is established. Then, the phase space reconstruction of the series of bearing performance degradation trend parameter is carried out, and the prognosis is obtained by the improved adding weighted first-order local prediction method. The experimental results show that the bearing vibration performance degradation parameter can accurately depict the degradation trend of the bearing, and the reliability level is 91.55%; and the prediction of bearing performance degradation trend parameter is satisfactory: the mean relative error is only 0.0053% and the maximum relative error is less than 0.03%.

Rolling Element Bearing Monitoring and Diagnostics Techniques

1989 ◽  
Vol 111 (2) ◽  
pp. 251-256 ◽  
Author(s):  
R. G. Harker ◽  
J. L. Sandy
Keyword(s):  
Case Studies ◽  
Fluid Film ◽  
Rolling Element Bearing ◽  
Rolling Element Bearings ◽  
Film Type ◽  
Rolling Element ◽  
Element Bearing ◽  
Monitoring And Diagnostics ◽  
Bearing Monitoring

Rolling element bearings require distinctly different techniques for monitoring and diagnostics from those used for fluid-film type bearings. A description of these techniques and the instrumentation used to acquire the necessary data is provided for comparison. Also included are some case studies to illustrate how these techniques are applied.

Diagnosis of Rolling-Element Bearings Failure by Localized Electrical Current Between Track Surfaces of Races and Rolling-Elements

2002 ◽  
Vol 124 (3) ◽  
pp. 468-473 ◽  
Author(s):  
Har Prashad
Keyword(s):  
Theoretical Model ◽  
Electrical Current ◽  
Rolling Element Bearing ◽  
Rolling Element Bearings ◽  
Bearing Failure ◽  
Cause Analysis ◽  
Rolling Element ◽  
Rolling Elements ◽  
Dimensional Parameters ◽  
Element Bearing

The diagnosis and cause analysis of rolling-element bearing failure have been well studied and established in literature. Failure of bearings due to unforeseen causes were reported as: puncturing of bearings insulation; grease deterioration; grease pipe contacting the motor base frame; unshielded instrumentation cable; the bearing operating under the influence of magnetic flux, etc. These causes lead to the passage of electric current through the bearings of motors and alternators and deteriorate them in due course. But, bearing failure due to localized electrical current between track surfaces of races and rolling-elements has not been hitherto diagnosed and analyzed. This paper reports the cause of generation of localized current in presence of shaft voltage. Also, it brings out the developed theoretical model to determine the value of localized current density depending on dimensional parameters, shaft voltage, contact resistance, frequency of rotation of shaft and rolling-elements of a bearing. Furthermore, failure caused by flow of localized current has been experimentally investigated.

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