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.

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.

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.

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.

Cage Slip in Roller Bearings

1973 ◽  
Vol 15 (5) ◽  
pp. 370-378 ◽  
Author(s):  
K. T. O'Brien ◽  
C. M. Taylor
Keyword(s):  
Fatigue Life ◽  
Heat Generation ◽  
High Speed ◽  
Rolling Element Bearings ◽  
Design Problems ◽  
Adverse Conditions ◽  
Roller Bearings ◽  
Rolling Element ◽  
Low Load ◽  
Rolling Elements

The occurrence of cage and roller slip in lubricated roller bearings has been observed under adverse conditions of high speed and low load. Whilst slip is not normally a problem in roller bearings, in certain applications, for example the bearings supporting gas-turbine shafts, it can pose difficult design problems. For such conditions, bearing distress may occur due to increased wear and heat generation. A reduction of slip may be effected by the use of out-of-round races causing a preloading of some of the rolling elements; this, however, entails a corresponding reduction in fatigue life. Work described in this paper supplements the small amount of existing experimental evidence available concerning slip in rolling-element bearings. As well as a consideration of the effects of load and speed on slip, particular attention is paid to the quantity of lubricant supplied and the degree of misalignment present and the influence of these parameters on slip. Experimental results show a considerable divergence from previous results obtained using a similar bearing.

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.

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.

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.

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.

Intermittent Chaotic Dynamics of Rail Axle Supported by Roller Bearings

2009 ◽  
Author(s):  
S. P. Harsha ◽  
C. ‘Nat’ Nataraj
Keyword(s):  
High Speed ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Radial Clearance ◽  
High Speed Rail ◽  
Frequency Spectra ◽  
Roller Bearings ◽  
Nonlinear Springs ◽  
Rolling Elements

In this paper, intermittent chaotic analysis of high speed rail axle supported by roller bearings has been analyzed. In the analytical formulation, the contacts between rolling elements and races are considered as nonlinear springs, whose stiffness values are obtained by using Hertzian elastic contact deformation theory. The results show the appearance of instability and chaos in the dynamic response as the speed of the axle-bearing system is changed. Period doubling and mechanism of intermittency have been observed which lead to chaos. The appearance of regions of periodic, sub-harmonic and chaotic behavior is seen to be strongly dependent on the radial clearance. Poincare´ maps, time response and frequency spectra are used to elucidate and to illustrate the diversity of the system behavior.

scholarly journals Kinematic Correction for Roller Skewing

1982 ◽  
Vol 104 (1) ◽  
pp. 175-184
Author(s):  
M. Savage ◽  
S. H. Loewenthal
Keyword(s):  
High Speed ◽  
Roller Bearings ◽  
Transverse Curvature ◽  
Constant Radius ◽  
Rolling Elements ◽  
Convex Curvature ◽  
Cylindrical Roller

A theory of kinematic stabilization of rolling cylinders is developed for high-speed cylindrical roller bearings. This stabilization requires race and roller crowning to produce changes in the rolling geometry as the roller shifts axially. These changes put a reverse skew in the rolling elements by changing the rolling taper. Twelve basic possible bearing modifications are identified in this paper. Four have single transverse convex curvature in the rollers while eight have rollers with compound transverse curvature composed of a central cylindrical band of constant radius surrounded by symmetric bands with both slope and transverse curvature.

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