A Nonlinear Model for Structural Vibrations in Rolling Element Bearings: Part II—Simulation and Results

1997 ◽  
Vol 119 (2) ◽  
pp. 323-331 ◽  
Author(s):  
J. Datta ◽  
K. Farhang
Keyword(s):  
Nonlinear Model ◽  
Relative Size ◽  
Operating Conditions ◽  
Rolling Element Bearings ◽  
Governing Equations ◽  
Structural Vibrations ◽  
Outer Race ◽  
Vibrational Response ◽  
Rolling Element

This is the second of two companions papers. In the first paper, “A Nonlinear Model for Structural Vibrations in Rolling Element Bearings: Part I—Derivation of Governing Equations,” equations governing the vibrational response of rolling element bearings were developed. The mathematical formulations are utilized in this paper to study a number of effects on bearing structural vibrations. These include the effects of relative size of roller and inner and outer races, and inertias of inner and outer race assemblies, i.e., inertia of the races plus the components of an external system to which the inner and outer races are attached; the load acting on the bearing, its magnitude and nature (i.e., whether linear, rotational etc.). The studies are made under constant operating conditions (speed, lubrication) and the results obtained are discussed.

Multi-Objective Design Optimization of Rolling Element Bearings Using ABC, AIA and PSO Technique

2013 ◽  
Vol 2 (3) ◽  
pp. 102-125
Author(s):  
Vimal Savsani
Keyword(s):  
High Reliability ◽  
Optimization Technique ◽  
Operating Conditions ◽  
Rolling Element Bearing ◽  
Design Parameters ◽  
Rolling Element Bearings ◽  
Automotive Manufacturing ◽  
Outer Race ◽  
Multi Objective ◽  
Rolling Element

Rolling element bearings are widely used as important components in most of the mechanical engineering applications. These bearings find wide applications in automotive, manufacturing and aeronautical industries. The problem associated with rolling element bearings are that the design and selection are based on different operating conditions to reach their excellent performance, long life and high reliability. This leads to the requirement of optimal design of rolling element bearings. Optimization aspects of a rolling element bearing are presented in this paper considering three different objectives namely, dynamic capacity, static capacity and elastohydrodynamic minimum film thickness. The design parameters include mean diameter of rolling, ball diameter, number of balls, and inner and outer race groove curvature radii. Different constants associated with the constraints are given some ranges and are included as design variables. The optimization procedure is carried out using artificial bee colony (ABC) optimization technique, artificial immune algorithm (AIA), and particle swarm optimization (PSO) technique. Both single and multi-objective optimization aspects are considered. The results of the considered techniques are compared with the previously published results. The considered techniques have given much better results in comparison to the previously tried approaches.

A Nonlinear Model for Structural Vibrations in Rolling Element Bearings: Part I—Derivation of Governing Equations

1997 ◽  
Vol 119 (1) ◽  
pp. 126-131 ◽  
Author(s):  
J. Datta ◽  
K. Farhang
Keyword(s):  
Nonlinear Model ◽  
Contact Region ◽  
Equations Of Motion ◽  
Rolling Contact ◽  
Rolling Element Bearings ◽  
Structural Vibrations ◽  
Nonlinear Springs ◽  
Rolling Element ◽  
Rolling Elements ◽  
Constituent Elements

This paper, the first of two companion papers, presents a model for investigating structural vibrations in rolling element bearings. The analytical formulation accounts for tangential and radial motions of the rolling elements, as well as the cage, the inner and the outer races. The contacts between the rolling elements and races are treated as nonlinear springs whose stiffnesses are obtained by application of the equation for Hertzian elastic contact deformation. The derivation of the equations of motion is facilitated by assuming that only rolling contact exists between the races and rolling elements. Application of Lagrange’s equations leads to a system of nonlinear ordinary differential equations governing the motion of the bearing system. These equations are then solved using the Runge-Kutta integration technique. Using the formulation in the second part—“A Nonlinear Model for Structural Vibrations in Rolling Element Bearings: Part II—Simulation and Results,” a number of effects on bearing structural vibrations are studied. This work is unique from previous studies in that the model simulates vibration from intrinsic properties and constituent elements of the bearing, and takes into account every contact region within the bearing, representing it by a nonlinear spring.

Experimental investigation on time-domain features in the diagnosis of rolling element bearings by acoustic emission

2021 ◽  
pp. 107754632110161
Author(s):  
Aref Aasi ◽  
Ramtin Tabatabaei ◽  
Erfan Aasi ◽  
Seyed Mohammad Jafari
Keyword(s):  
Acoustic Emission ◽  
Condition Monitoring ◽  
Time Domain ◽  
Central Moment ◽  
Rolling Element Bearings ◽  
Test Rig ◽  
Acoustic Emission Sensor ◽  
Outer Race ◽  
Common Time ◽  
Rolling Element

Inspired by previous achievements, different time-domain features for diagnosis of rolling element bearings are investigated in this study. An experimental test rig is prepared for condition monitoring of angular contact bearing by using an acoustic emission sensor for this purpose. The acoustic emission signals are acquired from defective bearing, and the sensor takes signals from defects on the inner or outer race of the bearing. By studying the literature works, different domains of features are classified, and the most common time-domain features are selected for condition monitoring. The considered features are calculated for obtained signals with different loadings, speeds, and sizes of defects on the inner and outer race of the bearing. Our results indicate that the clearance, sixth central moment, impulse, kurtosis, and crest factors are appropriate features for diagnosis purposes. Moreover, our results show that the clearance factor for small defects and sixth central moment for large defects are promising for defect diagnosis on rolling element bearings.

Simultaneous Monitoring of Rolling-Element and Journal Bearings Using Analysis of Structure-Born Ultrasound Acoustic Emissions

2010 ◽  
Author(s):  
A. Albers ◽  
M. Dickerhof
Keyword(s):  
Acoustic Emission ◽  
Acoustic Emissions ◽  
Piezoelectric Sensor ◽  
Journal Bearings ◽  
Rolling Element Bearings ◽  
Acoustic Emission Sensor ◽  
Outer Race ◽  
Rolling Element ◽  
Characteristic Values ◽  
Acoustic Emission Technology

The application of Acoustic Emission technology for monitoring rolling element or hydrodynamic plain bearings has been addressed by several authors in former times. Most of these investigations took place under idealized conditions, to allow the concentration on one single source of emission, typically recorded by means of a piezoelectric sensor. This can be achieved by either eliminating other sources in advance or taking measures to shield them out (e. g. by placing the acoustic emission sensor very close to the source of interest), so that in consequence only one source of structure-born sound is present in the signal. With a practical orientation this is often not possible. In point of fact, a multitude of potential sources of emission can be worth considering, unfortunately superimposing one another. The investigations reported in this paper are therefore focused on the simultaneous monitoring of both bearing types mentioned above. Only one piezoelectric acoustic emission sensor is utilized, which is placed rather far away from the monitored bearings. By derivation of characteristic values from the sensor signal, different simulated defects can be detected reliably: seeded defects in the inner and outer race of rolling element bearings as well as the occurrence of mixed friction in the sliding surface bearing due to interrupted lubricant inflow.

scholarly journals New State Identification Method for Rotating Machinery under Variable Load Conditions Based on Hybrid Entropy Features and Joint Distribution Adaptation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Xiaoming Xue ◽  
Nan Zhang ◽  
Suqun Cao ◽  
Wei Jiang ◽  
Jianzhong Zhou ◽  
...  
Keyword(s):  
Joint Distribution ◽  
Operating Conditions ◽  
Variable Load ◽  
Rolling Element Bearings ◽  
Time Frequency ◽  
Identification Method ◽  
State Identification ◽  
Rolling Element ◽  
Load Conditions ◽  
Testing Set

Fault identification under variable operating conditions is a task of great importance and challenge for equipment health management. However, when dealing with this kind of issue, traditional fault diagnosis methods based on the assumption of the distribution coherence of the training and testing set are no longer applicable. In this paper, a novel state identification method integrated by time-frequency decomposition, multi-information entropies, and joint distribution adaptation is proposed for rolling element bearings. At first, fast ensemble empirical mode decomposition was employed to decompose the vibration signals into a collection of intrinsic mode functions, aiming at obtaining the multiscale description of the original signals. Then, hybrid entropy features that can characterize the dynamic and complexity of time series in the local space, global space, and frequency domain were extracted from each intrinsic mode function. As for the training and testing set under different load conditions, all data was mapped into a reproducing space by joint distribution adaptation to reduce the distribution discrepancies between datasets, where the pseudolabels of the testing set and the final diagnostic results were obtained by the k-nearest neighbor algorithm. Finally, five cases with the training and testing set under variable load conditions were used to demonstrate the performance of the proposed method, and comparisons with some other diagnosis models combined with the same features and other dimensionality reduction methods were also discussed. The analysis results show that the proposed method can effectively recognize the multifaults of rolling element bearings under variable load conditions with higher accuracies and has sound practicability.

Nonlinear Modeling of a Rigid Rotor Supported on Rolling Element Bearings With Localized Defects

2010 ◽  
Author(s):  
Karthik Kappaganthu ◽  
C. Nataraj
Keyword(s):  
Nonlinear Model ◽  
Nonlinear Models ◽  
Nonlinear Modeling ◽  
Rolling Element Bearings ◽  
Rigid Rotor ◽  
Rolling Element ◽  
Localized Defects ◽  
Bearing Race ◽  
Overall Performance ◽  
Bearing System

In this paper a nonlinear model for defects in rolling element bearings is developed. Detailed nonlinear models are useful to detect, estimate and predict failure in rotating machines. Also, accurate modeling of the defect provides parameters that can be estimated to determine the health of the machine. In this paper the rotor-bearing system is modeled as a rigid rotor and the defects are modeled as pits in the bearing race. Unlike the previous models, the motion of the rolling element thorough the defect is not modeled as a predetermined function; instead, it is dynamically determined since it depends on the clearance and the position of the shaft. Using this nonlinear model, the motion of the shaft is simulated and the effect of the rolling element passing through the defect is studied. The effect of shaft parameters and the defect parameters on the precision of the shaft and the overall performance of the system is studied. Finally, suitable measures for health monitoring and defect tracking are suggested.

Feature Selection for Fault Detection in Rolling Element Bearings Using Mutual Information

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Karthik Kappaganthu ◽  
C. Nataraj
Keyword(s):  
Fault Detection ◽  
Mutual Information ◽  
Quantitative Measure ◽  
Rolling Element Bearings ◽  
Outer Race ◽  
Time Frequency ◽  
Rolling Element ◽  
Degree Of Confidence ◽  
Hidden Layer ◽  
Optimal Feature

Rolling element bearings are among the key components in many rotating machineries. It is hence necessary to determine the condition of the bearing with a reasonable degree of confidence. Many techniques have been developed for bearing fault detection. Each of these techniques has its own strengths and weaknesses. In this paper, various features are compared for detecting inner and outer race defects in rolling element bearings. Mutual information between the feature and the defect is used as a quantitative measure of quality. Various time, frequency, and time-frequency domain features are compared and ranked according to their cumulative mutual information content, and an optimal feature set is determined for bearing classification. The performance of this optimal feature set is evaluated using an artificial neural network with one hidden layer. An overall classification accuracy of 97% was obtained over a range of rotating speeds.

scholarly journals Rolling Element Bearing Fault Diagnosis Based on Multiscale General Fractal Features

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Weigang Wen ◽  
Zhaoyan Fan ◽  
Donald Karg ◽  
Weidong Cheng
Keyword(s):  
Fault Diagnosis ◽  
Fractal Dimensions ◽  
Feature Space ◽  
Operating Conditions ◽  
Rolling Element Bearing ◽  
Rolling Element Bearings ◽  
Vibration Signals ◽  
Bearing Fault Diagnosis ◽  
Rolling Element ◽  
Element Bearing

Nonlinear characteristics are ubiquitous in the vibration signals produced by rolling element bearings. Fractal dimensions are effective tools to illustrate nonlinearity. This paper proposes a new approach based on Multiscale General Fractal Dimensions (MGFDs) to realize fault diagnosis of rolling element bearings, which are robust to the effects of variation in operating conditions. The vibration signals of bearing are analyzed to extract the general fractal dimensions in multiscales, which are in turn utilized to construct a feature space to identify fault pattern. Finally, bearing faults are revealed by pattern recognition. Case studies are carried out to evaluate the validity and accuracy of the approach. It is verified that this approach is effective for fault diagnosis of rolling element bearings under various operating conditions via experiment and data analysis.

New Feature Extraction Method for the Detection of Defects in Rolling Element Bearings

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Ling Xiang ◽  
Aijun Hu
Keyword(s):  
Ensemble Empirical Mode Decomposition ◽  
Rolling Element Bearing ◽  
Rolling Element Bearings ◽  
Intrinsic Mode Functions ◽  
Feature Extraction Method ◽  
Outer Race ◽  
Mode Decomposition ◽  
Rolling Element ◽  
Envelope Spectrum ◽  
Detection Of Defects

This paper proposes a new method based on ensemble empirical mode decomposition (EEMD) and kurtosis criterion for the detection of defects in rolling element bearings. Some intrinsic mode functions (IMFs) are presented to obtain symptom wave by EEMD. The different kurtosis of the intrinsic mode function is determined to select the envelope spectrum. The fault feature based on the IMF envelope spectrum whose kurtosis is the maximum is extracted, and fault patterns of roller bearings can be effectively differentiated. Practical examples of diagnosis for a rolling element bearing are provided to verify the effectiveness of the proposed method. The verification results show that the bearing faults that typically occur in rolling element bearings, such as outer-race and inner-race, can be effectively identified by the proposed method.

Evaluation of Factors Affecting the Simulation of Structural Vibrations in Rolling Bearings

1994 ◽  
Author(s):  
Kapil Mehra ◽  
Jayanta Datta ◽  
Kambiz Farhang
Keyword(s):  
High Speed ◽  
Contact Deformation ◽  
Structural Vibrations ◽  
Appreciable Change ◽  
Factors Affecting ◽  
Outer Race ◽  
Nonlinear Springs ◽  
Lumped Parameter ◽  
Rolling Element ◽  
Centers Of Mass

Abstract An analytical model is developed for studying in-plane structural vibrations in rolling element bearings. A lumped parameter approach is employed in developing the model. The mass and moment of inertia of the components comprising the bearing are lumped at their respective centers of mass. The localized stiffnesses due to contact deformation phenomenon are treated as nonlinear springs. The variable spring rates are obtained by application of Hertz equation for elastic contact deformation. Effects of preload, ball rotational speed, and damping are studied using the formulation. An interesting observation is made as to the influence of preload. It is found that in the presence of preload, irrespective of the load magnitude, contact is maintained with both the inner and the outer races. Hence, responses obtained with and without the check for ball/inner race and ball/outer race interferences are identical. In addition, no appreciable change is observed in the responses when the preload value is varied from 10 N to 1N. At high speed of operation, the balls are found to maintain contact with the outer ring, whereas intermittent contact with the inner ring occurs for brief periods of time. Introduction of lubricant is found to dampen the oscillations considerably.

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