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.

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.

Dynamics of Rolling-Element Bearings—Part I: Cylindrical Roller Bearing Analysis

1979 ◽  
Vol 101 (3) ◽  
pp. 293-302 ◽  
Author(s):  
P. K. Gupta
Keyword(s):  
Differential Equations ◽  
Normal Force ◽  
Equations Of Motion ◽  
Roller Bearing ◽  
Rolling Element Bearings ◽  
Analytical Formulation ◽  
Rolling Element ◽  
Cylindrical Roller Bearing ◽  
Cylindrical Roller ◽  
Bearing Analysis

An analytical formulation for the roller motion in a cylindrical roller bearing is presented in terms of the classical differential equations of motion. Roller-race interaction is analyzed in detail and the resulting normal force and moment vectors are determined. Elastohydrodynamic traction models are considered in determining the roller-race tractive forces and moments. Formulation for the roller end and race flange interaction during skewing of the roller is also considered. Roller-cage interactions are assumed to be either hydrodynamic or fully metallic. Simple relationships are used to determine the churning and drag losses.

Rolling Element Bearing Non-Linearity Effects

2000 ◽  
Author(s):  
N. S. Feng ◽  
E. J. Hahn
Keyword(s):  
Equations Of Motion ◽  
Rolling Element Bearing ◽  
Radial Clearance ◽  
Rotor Systems ◽  
Bearing Life ◽  
Rolling Element ◽  
Bearing Load ◽  
Rolling Elements ◽  
Element Bearing ◽  
Negative Clearance

Non-linearity effects in rolling element bearings arise from two sources, viz. the Hertzian force deformation relationship and the presence of clearance between the rolling elements and the bearing races. Assuming that centrifugal effects may be neglected and that the presence of axial preload is appropriately reflected in a corresponding change in the radial clearance, this paper analyses a simple test rig to illustrate that non-linear phenomena such as synchronous multistable and nonsynchronous motions are possible in simple rigid and flexible rotor systems subjected to unbalance excitation. The equations of motion of the rotor bearing system were solved by transient analysis using fourth order Runge Kutta. Of particular interest is the effect of clearance, governed in practice by bearing specification and the amount of preload, on the vibration behaviour of rotors supported by ball bearings and on the bearing load. It is shown that in the presence of positive clearance, there exists an unbalance excitation range during which the bearing is momentarily not transmitting force owing to contact loss, resulting in rolling element raceway impact with potentially relatively high bearing forces; and indicating that for long bearing life, operation with positive clearance should be avoided in the presence of such unbalance loading. Once the unbalance excitation is high enough to avoid such contact loss, it is the bearings with zero or negative clearance which produce maximum bearing forces.

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.

The Monitoring of the Bearing Nodes with Excessive Radial Clearances Using the FAM-C and FDM-A Methods

2009 ◽  
Vol 25 (1) ◽  
pp. 109-127 ◽  
Author(s):  
Andrzej Gębura ◽  
Tomasz Tokarski
Keyword(s):  
Resonant State ◽  
Lubricant Film ◽  
Rolling Element Bearings ◽  
Mechanical Verification ◽  
Macro Scale ◽  
Rolling Element ◽  
Rolling Elements ◽  
Diagnostic Work ◽  
Theoretical Analyses

The Monitoring of the Bearing Nodes with Excessive Radial Clearances Using the FAM-C and FDM-A Methods The paper has been intended to present findings resulting from the monitoring of the bearing support elements with increased radial clearances with the FAM-C1 and FDM-A2 methods. The role the lubricant film plays in this type of the rolling-elements' wear has been described. Discussed are symptoms, parameters, and hazards to the resonant state in bearing nodes, as well as capabilities of diagnosing them with the FAM-C and FDM-A methods. Hypotheses about subsequent stages of the wearing process in aircraft turbojet engine's bearing support assemblies, including how the resonant state occurs, have been presented. The mechanism of the resonance in rolling-element bearings has been described, with particular attention paid to the effects of gyrostatic moments upon the bearing support elements, both in micro- and macro-scale. Theoretical analyses have been supplemented with findings resulting from the diagnostic work carried out by the Authors, and with data from the mechanical verification of engines in the course of the authorised dismantling thereof.

scholarly journals Further understanding of rolling contact fatigue in rolling element bearings - A review

2019 ◽  
Vol 140 ◽  
pp. 105849 ◽  
Author(s):  
Mostafa El Laithy ◽  
Ling Wang ◽  
Terry J. Harvey ◽  
Bernd Vierneusel ◽  
Martin Correns ◽  
...  
Keyword(s):  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Rolling Contact ◽  
Rolling Element Bearings ◽  
Rolling Element

Ceramics in Rolling Element Bearings

1979 ◽  
Author(s):  
C. F. Bersch ◽  
Philip Weinberg
Keyword(s):  
Fatigue Life ◽  
Silicon Nitride ◽  
Cooling System ◽  
Extreme Environment ◽  
Ball Bearings ◽  
Rolling Element Bearings ◽  
Turbine Engine ◽  
Rolling Element ◽  
Rolling Elements ◽  
History Of

The feasibility of using hot-pressed silicon nitride (HPSN) for rolling elements and for races in ball bearings and roller bearings has been explored. HPSN offers opportunities to alleviate many current bearing problems including DN and fatigue life limitations, lubricant and cooling system deficiencies, and extreme environment demands. The history of ceramic bearings and the results of various element tests, bearing tests in rigs, and bearing tests in a turbine engine will be reviewed. The advantages and problems associated with the use of HPSN in rolling element bearings will be discussed.

scholarly journals Component Hardness Differences and Their Effect on Bearing Fatigue

1967 ◽  
Vol 89 (1) ◽  
pp. 47-54 ◽  
Author(s):  
E. V. Zaretsky ◽  
R. J. Parker ◽  
W. J. Anderson
Keyword(s):  
Fatigue Life ◽  
Residual Stresses ◽  
Load Capacity ◽  
Full Scale ◽  
Contact Temperature ◽  
Rolling Element Bearings ◽  
Rolling Element ◽  
Rolling Elements ◽  
Compressive Residual Stresses

The five-ball fatigue tester and full-scale rolling-element bearings were used to determine the effect of component hardness differences of SAE 52100 steel on bearing fatigue and load capacity. Maximum fatigue life and load capacity are achieved when the rolling elements of a bearing are one to two points (Rockwell C) harder than the races. There appears to be an interrelation among compressive residual stresses induced in the races during operation, differences in component hardness, and fatigue life. Differences in contact temperature and plastically deformed profile radii could not account for differences in fatigue life.

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.

An Investigation of Rolling Element Vibrations Caused by Local Defects

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
H. Arslan ◽  
N. Aktürk
Keyword(s):  
Equations Of Motion ◽  
Angular Contact Ball Bearing ◽  
Frequency Spectra ◽  
Rolling Element ◽  
Rolling Elements ◽  
Computer Simulation Program ◽  
Localized Defects ◽  
Spring System ◽  
Mass Spring ◽  
Local Defects

In this paper, a shaft-bearing model is developed in order to investigate the rolling element vibrations for an angular contact ball bearing with and without defects. The shaft-bearing assembly is considered as a mass-spring system. The system shows a nonlinear characteristic under dynamic conditions. The equations of motion in radial and axial directions were obtained for shaft and rolling elements, and they were solved simultaneously with a computer simulation program. Additionally, the effect of localized defects on running surfaces (i.e., inner ring, outer ring, and ball) on the vibration of the balls is investigated. Vibration of rolling elements in the radial direction is analyzed in time and frequency domains. Characteristic defect frequencies and their components can be seen in the frequency spectra of rolling element vibrations. Comparison of the obtained results with similar studies available in literature showed reasonable qualitative agreement.

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