Equilibrium and Associated Load Distribution in Ball and Roller Bearings Loaded in Five Degrees of Freedom While Neglecting Friction—Part I: General Theory and Application to Ball Bearings

1989 ◽  
Vol 111 (1) ◽  
pp. 142-148 ◽  
Author(s):  
J. M. de Mul ◽  
J. M. Vree ◽  
D. A. Maas
Keyword(s):  
General Theory ◽  
Load Distribution ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Contact Analysis ◽  
Hertzian Contact ◽  
Ball Bearings ◽  
Roller Bearings ◽  
Rolling Element ◽  
Bearing Stiffness

A new, general and consistent mathematical model of highly modular character is presented for calculation of the equilibrium and associated load distribution in rolling element bearings. The bearings may be loaded and displaced in five degrees of freedom. High speed rolling element loading is considered, internal friction is neglected, the material is assumed linearly elastic and the bearing rings are modelled as rigid except for local contact deformation. Either classical Hertzian contact analysis or modern non-Hertzian contact analysis of sophisticated or approximate character is used as applicable. The bearing stiffness matrix is computed analytically and used internally in the iterative bearing equilibrium calculation; its final values may be used for other purposes such as (rotor) dynamics analysis. In Part I, the general theory and application to ball bearings is presented. In Part II, application of the general theory to roller bearings and an experimental verification are presented.

Equilibrium and Associated Load Distribution in Ball and Roller Bearings Loaded in Five Degrees of Freedom While Neglecting Friction—Part II: Application to Roller Bearings and Experimental Verification

1989 ◽  
Vol 111 (1) ◽  
pp. 149-155 ◽  
Author(s):  
J. M. de Mul ◽  
J. M. Vree ◽  
D. A. Maas
Keyword(s):  
General Theory ◽  
Experimental Verification ◽  
Load Distribution ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Contact Analysis ◽  
Hertzian Contact ◽  
Roller Bearings ◽  
Rolling Element ◽  
Bearing Stiffness

A new, general and consistent mathematical model of highly modular character is presented for calculation of the equilibrium and associated load distribution in rolling element bearings. The bearings may be loaded and displaced in five degrees of freedom. High speed rolling element loading is considered, internal friction is neglected, the material is assumed linearly elastic and the bearing rings are modelled as rigid except for local contact deformation. Either classical Hertzian contact analysis or modern non-Hertzian contact analysis of sophisticated or approximate character is used as applicable. The bearing stiffness matrix is computed analytically and used internally in the iterative bearing equilibrium calculation; its final values may be used for other purposes such as (rotor) dynamics analysis. In Part I, the general theory and application to ball bearings is presented. In Part II, application of the general theory to ro´ller bearings and an experimental verification are presented.

A General Theory for Elastically Constrained Ball and Radial Roller Bearings Under Arbitrary Load and Speed Conditions

1960 ◽  
Vol 82 (2) ◽  
pp. 309-320 ◽  
Author(s):  
A. B. Jones
Keyword(s):  
General Solution ◽  
General Theory ◽  
High Speed ◽  
Ball Bearings ◽  
Precise Location ◽  
Roller Bearings ◽  
Load Paths ◽  
Elastic Yielding ◽  
Rolling Element ◽  
Rolling Elements

A completely general solution is obtained whereby the elastic compliances of a system of any number of ball and radial roller bearings under any system of loads can be determined. Elastic yielding of the shaft and supporting structure are considered as well as centrifugal and gyroscopic loading of the rolling elements under high-speed operation. The solution defines the loading and attitude of each rolling element in each bearing of the system as well as the displacement of each inner ring with respect to its outer ring. For ball bearings the precise location of the load paths in each raceway are found. Life estimates can be more accurately made since the fatigue effects can be evaluated over known paths in the raceways. The solution, which is accomplished numerically by iterative techniques, has been programmed for an IBM-704 digital computer.

Dynamic Modeling and Vibration Response Simulation for High Speed Rolling Ball Bearings With Localized Surface Defects in Raceways

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Linkai Niu ◽  
Hongrui Cao ◽  
Zhengjia He ◽  
Yamin Li
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Surface Defects ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Hertzian Contact ◽  
Ball Bearings ◽  
Rolling Ball ◽  
Vibration Responses

A dynamic model is developed to investigate vibrations of high speed rolling ball bearings with localized surface defects on raceways. In this model, each bearing component (i.e., inner raceway, outer raceway and rolling ball) has six degrees of freedom (DOFs) to completely describe its dynamic characteristics in three-dimensional space. Gyroscopic moment, centrifugal force, lubrication traction/slip between bearing component are included owing to high speed effects. Moreover, local defects are modeled accurately and completely with consideration of additional deflection due to material absence, changes of Hertzian contact coefficient and changes of contact force directions due to raceway curvature variations. The obtained equations of motion are solved numerically using the fourth order Runge–Kutta–Fehlberg scheme with step-changing criterion. Vibration responses of a defective bearing with localized surface defects are simulated and analyzed in both time domain and frequency domain, and the effectiveness of fault feature extraction techniques is also discussed. An experiment is carried out on an aerospace bearing test rig. By comparing the simulation results with experiments, it is confirmed that the proposed model is capable of predicting vibration responses of defective high speed rolling ball bearings effectively.

scholarly journals Transient Vibration Prediction for Rotors on Ball Bearings Using Load-Dependent Nonlinear Bearing Stiffness

2004 ◽  
Vol 10 (6) ◽  
pp. 489-494 ◽  
Author(s):  
David P. Fleming ◽  
J. V. Poplawski
Keyword(s):  
High Speed ◽  
Roller Bearing ◽  
Transient Behavior ◽  
Rolling Element Bearing ◽  
Ball Bearings ◽  
Transient Vibration ◽  
Vibration Prediction ◽  
Rolling Element ◽  
Bearing Stiffness ◽  
Element Bearing

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic transient analysis requires bearing forces to be determined at each step of the transient solution. Analyses have been carried out to show the effect of accurate bearing transient forces (accounting for nonlinear speed and load-dependent bearing stiffness) as compared to conventional use of average rolling-element bearing stiffness. Bearing forces were calculated by COBRA-AHS (Computer Optimized Ball and Roller Bearing Analysis—Advanced High Speed) and supplied to the rotordynamics code ARDS (Analysis of Rotor Dynamic Systems) for accurate simulation of rotor transient behavior. COBRA-AHS is a fast-running five degree-of-freedom computer code able to calculate high speed rolling-element bearing load-displacement data for radial and angular contact ball bearings and also for cylindrical and tapered roller bearings. Results show that use of nonlinear bearing characteristics is essential for accurate prediction of rotordynamic behavior.

scholarly journals Unbalance Response Prediction for Rotors on Ball Bearings Using Speed- and Load-Dependent Nonlinear Bearing Stiffness

2005 ◽  
Vol 2005 (1) ◽  
pp. 53-59 ◽  
Author(s):  
David P. Fleming ◽  
J. V. Poplawski
Keyword(s):  
Response Prediction ◽  
Rolling Element Bearing ◽  
Response Analysis ◽  
Ball Bearings ◽  
Moderate Amount ◽  
Constant Stiffness ◽  
Unbalance Response ◽  
Rolling Element ◽  
Bearing Stiffness ◽  
Element Bearing

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus, an accurate rotordynamic analysis requires that bearing forces corresponding to the actual bearing deflection be utilized. For this work, bearing forces were calculated by COBRA-AHS, a recently developed rolling-element bearing analysis code. Bearing stiffness was found to be a strong function of bearing deflection, with higher deflection producing markedly higher stiffness. Curves fitted to the bearing data for a range of speeds and loads were supplied to a flexible rotor unbalance response analysis. The rotordynamic analysis showed that vibration response varied nonlinearly with the amount of rotor imbalance. Moreover, the increase in stiffness as critical speeds were approached caused a large increase in rotor and bearing vibration amplitude over part of the speed range compared to the case of constant-stiffness bearings. Regions of bistable operation were possible, in which the amplitude at a given speed was much larger during rotor acceleration than during deceleration. A moderate amount of damping will eliminate the bistable region, but this damping is not inherent in ball bearings.

Theoretische Analyse eines neuen Loslagerkonzepts*/Theoretical analysis of a new floating bearing - The simulated operational behavior of FRB bearings in comparison to reference bearings

2015 ◽  
Vol 105 (05) ◽  
pp. 285-290
Author(s):  
C. Brecher ◽  
M. Fey ◽  
J. Falker
Keyword(s):  
Experimental Investigation ◽  
Theoretical Analysis ◽  
High Speed ◽  
Contact Point ◽  
Ball Bearings ◽  
Roller Bearings ◽  
Cylindrical Roller ◽  
Bearing System

Das Floating-Roller-Ball (FRB)-Lager ist ein Konzept für Radiallager als Loslager für Hochgeschwindigkeits-Motorspindeln, das die Vorteile von Zylinderrollenlagern und angestellten Mehrpunktlagern in einer neuen Wälzkörpergeometrie kombiniert. Zur Auslegung des ersten Prototyps wurde mithilfe eines Berechnungstools das theoretische Betriebsverhalten untersucht. Die Berechnungsergebnisse liefern Randbedingungen als Grundlage zur experimentellen Untersuchung des Lagerkonzepts.   Floating roller ball bearings provide a new floating bearing system for high-speed motor spindles, combining the advantages of both cylindrical roller bearings and elastically mounted multi-contact point bearings in a new roller geometry. To design the first prototype, the operational behavior of the bearing system was analyzed theoretically by a new calculation tool. The results provide the basis for the experimental investigation of the bearing concept.

The Nature of Slip in High-Speed Axially Loaded Ball Bearings

1986 ◽  
Vol 200 (5) ◽  
pp. 359-365 ◽  
Author(s):  
J Dominy
Keyword(s):  
Heat Generation ◽  
High Speed ◽  
Numerical Technique ◽  
Experimental Results ◽  
Ball Bearings ◽  
Roller Bearings ◽  
Axially Loaded

This paper develops a simplified numerical technique for the analysis of heat generation and cage slip in high-speed axially loaded ball bearings. The model compares well with experimental results and has shown the characteristic slip behaviour associated with ball bearings. It has been possible to use the model to investigate the nature and causes of slip in lightly loaded ball bearings and it has been shown that the mechanism is primarily dependent upon the spin power, which falls rapidly as slip sets in. The characteristics of slip in ball bearings are shown to be quite different to those in roller bearings.

An Integrated Approach Toward the Dynamic Analysis of High-Speed Spindles: Part I — System Model

1993 ◽  
Author(s):  
C. H. Chen ◽  
K. W. Wang ◽  
Y. C. Shin
Keyword(s):  
High Speed ◽  
Integrated Approach ◽  
Ball Bearings ◽  
Basic Principles ◽  
Gyroscopic Moment ◽  
High Speeds ◽  
Modeling Process ◽  
Radial Stiffness ◽  
Bearing Stiffness ◽  
Made In

Abstract Experimental evidence [Shin, 1992] has shown that the natural frequencies of high speed spindles with angular contact ball bearings decrease with increasing rotational speed. A recent study [Wang, et al., 1991] illustrated that this phenomenon is caused by stiffness change of the bearings. A simplified approximation was used in the analysis to examine the bearing radial stiffness at high speeds. While the investigation explained the experimental observations in a qualitative sense, the analytical results so far are not sufficient to quantitatively describe the spindle behavior under high speed operations due to the approximations made in the modeling process. This paper presents an integrated approach toward the modelling of flexible spindles with angular contact ball bearings from basic principles. The local dynamics of the bearings are coupled with the global shaft motion. The model derived includes both the longitudinal and transverse vibrations of the shaft interacting with the nonlinear bearings. The influences of shaft speed on the bearing stiffness matrix and the system frequencies have been studied. It is shown that the spindle dynamic behavior can vary substantially as speed increases due to the bearing gyroscopic moment and centrifugal force. These effects have been ignored in most of the previous spindle models. Lab tests were conducted to validate the model. The analytical predictions are quantitatively verified by the experimental results.

Bearing Skidding Detection for High Speed and Aero Engine Applications

2021 ◽  
Author(s):  
Azzedine Dadouche ◽  
Rami Kerrouche
Keyword(s):  
High Speed ◽  
Power Losses ◽  
Severe Damage ◽  
Roller Bearings ◽  
Custom Made ◽  
Rolling Element ◽  
Aero Engine ◽  
Oil Flow ◽  
Rolling Elements ◽  
Surface Distress

Abstract Rolling-element bearings (REB) can develop severe damage due to skidding (slipping) between the rolling elements and bearing races. Skidding can be described as gross sliding between the bearing surfaces in relative motion and can result in significant surface distress such as smearing, especially at light loads and high rotational speeds. Under these conditions, skidding occurs between the rolling elements and the bearing races, leading to increased wear (higher friction coefficient), elevated bearing temperature, significant power losses and reduced service life of the bearing. The main objective of this study is to investigate the significance of various sensing technologies (induction, vibration, ultrasound, acoustic and optical) in detecting skidding in standard series roller bearings as well as custom-made roller bearings for aero engine applications. The bearings have a bore diameter of 60 mm and 90 mm, respectively. Jet and under race lubrication techniques have been used to supply oil to the bearings under test. The custom-made aero engine test bearing features special channels to allow under race lubrication of the rollers/races contacts as well as the cage land. The effect of radial load, rotational speed and oil flow on roller skidding have also been investigated and analyzed. Tests have been performed on a dedicated high speed experimental bearing facility and data was recorded using a commercially-available data acquisition system.

Vibration Monitoring and Damage Quantification of Faulty Ball Bearings

2005 ◽  
Vol 127 (4) ◽  
pp. 776-783 ◽  
Author(s):  
F. K. Choy ◽  
J. Zhou ◽  
M. J. Braun ◽  
L. Wang
Keyword(s):  
High Speed ◽  
Progressive Failure ◽  
Frequency Domain Analysis ◽  
Vibration Monitoring ◽  
Ball Bearings ◽  
Rolling Element Bearings ◽  
Premature Failure ◽  
Damage And Failure ◽  
Rolling Element ◽  
Safety And Reliability

More often than not, the rolling element bearings in rotating machinery are the mechanical components that are first prone to premature failure. Early warning of an impending bearing failure is vital to the safety and reliability of high-speed turbomachinery. Presently, vibration monitoring is one of the most applied procedures in on-line damage and failure monitoring of rolling element bearings. This paper presents results from an experimental rotor-bearing test rig with quantified damage induced in the supporting rolling element bearings. Both good and damaged radial and tapered ball bearings are used in this study. The vibration signatures due to damage at the ball elements and the inner race of the bearing are also examined. Vibration signature analyzing schemes such as frequency domain analysis, and chaotic vibration analysis (modified Poincare diagrams) are applied and their effectiveness in pinpoint damage are compared in this study. The size/level of the damage is corroborated with the vibration amplitudes to provide quantification criteria for bearing progressive failure prediction. Based on the results from this study, it is shown that the use of the modified Poincare map, based on the relative carrier speed, can provide an effective way for identification and quantification of bearing damage in rolling element bearings.

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