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.

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.

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.

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.

Evaluation of Pivot Stiffness for Typical Tilting-Pad Journal Bearing Designs

1988 ◽  
Vol 110 (2) ◽  
pp. 165-171 ◽  
Author(s):  
R. G. Kirk ◽  
S. W. Reedy
Keyword(s):  
High Speed ◽  
Fluid Film ◽  
Hertzian Contact ◽  
Tilting Pad ◽  
Hertzian Contact Stress ◽  
Bearing Stiffness ◽  
Stress And Deformation ◽  
The Individual ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

The manufacturers of high speed turbomachinery are concerned with the accurate prediction of rotor response and stability. One major factor in the placement of system critical speeds and amplification factors is the stiffness and damping of both the fluid-film bearing and support structure. Typical calculated results for tilting-pad fluid-film bearings have neglected the influence of the point or line contact of the pivot support for the individual pads. This paper will review the equations developed considering the Hertzian contact stress and deformation theory and present the equations for pivot stiffness necessary for inclusion in tilting pad bearing computer programs. In addition, the influence of various standard pivot designs will be compared for typical fluid-film bearing stiffness and damping characteristics.

Research on Numerical Problem in the Simulation Statics Analysis Program of High Speed Ball Bearing

2013 ◽  
Vol 376 ◽  
pp. 248-252
Author(s):  
Ming Yan ◽  
Ming Ming Wang ◽  
Xiang Jun Zhu
Keyword(s):  
Contact Angle ◽  
Fatigue Life ◽  
Load Distribution ◽  
High Speed ◽  
Ball Bearing ◽  
Theoretical Research ◽  
Analysis Program ◽  
Numerical Problem ◽  
Rolling Element

Load distribution, contact angle, rotate speed of rolling element, support stiffness of bearing, fatigue life and other aggregative indicators are got through the simulation statics analysis program of high speed ball bearing. Consequently, it is widely used in the engineering field. The domestic thesis about the simulation statics analysis program of the high speed ball bearing is barely reported, and most of the theoretical research thesis are not specific and have some mistakes. Consequently, aim for programming about a practical suit of the simulation statics analysis program of ball bearing, and the certain numerical problems are studied in the procedure of program.

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.

Bearings Influence on the Dynamic Behavior of HSM Spindle

2012 ◽  
Author(s):  
David Noel ◽  
Mathieu Ritou ◽  
Sebastien Le Loch ◽  
Benoit Furet
Keyword(s):  
Dynamic Behavior ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Experimental Tests ◽  
Operating Conditions ◽  
Design Parameters ◽  
Mechanics Model ◽  
Bearing Stiffness ◽  
Rough Milling ◽  
The Impact

The aeronautic industry requires high speed and high power spindles to obtain high material removal rates during long rough milling operations. The weakness of HSM spindle is the bearings, although high precision hybrid ball bearings have been developed to achieve this critical application. Inadequate use of spindles inevitably leads to shortened lifetimes. Choosing the operating conditions is a required step before machining applications. It can be achieved through either experimental tests or numerical modeling that leads to stability lobe diagrams. Stability of cuts relies on the dynamic behavior of the spindle, which is particularly due to the eigenfrequencies of the tool-shaft assembly. The frequencies depend on bearing stiffness that can change under operating conditions. That is why the impact of cutting conditions and bearing parameters on its stiffness are studied in the paper. A five degrees of freedom model of angular ball bearing is briefly presented. A complete bearing model is introduced. The originality of the approach is the complete technological modeling, notably of the radial expansions of inner and outer rings of bearing. A non-linear expression is established from continuum mechanics model. The influence of geometry of bearing, operating conditions and design parameters of spindle on the bearing stiffness are established and analysed. Then, modal analyses of the tool-spindle assembly are carried out in relation to the varying bearing stiffness. Finally, significance of the approach is demonstrated through the analyses of Frequency Response Function.

Modeling of Crossed Roller Bearings Considering Roller Roundness Deformation

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Van-Canh Tong ◽  
Eui-Wook Jung ◽  
Seong-Wook Hong
Keyword(s):  
Degrees Of Freedom ◽  
Unit Length ◽  
Roller Bearing ◽  
Rolling Element Bearing ◽  
Flat Surfaces ◽  
Roller Bearings ◽  
Proposed Model ◽  
Rolling Element ◽  
Inertial Loading ◽  
Speed Effect

Abstract This paper presents a quasi-static five degrees-of-freedom model of crossed roller bearings that considers roller roundness deformation. The existing models of rolling element bearing do not account for ball and/or roller roundness deformation. However, in the case of crossed roller bearing, roundness deformation of rollers can be significant because of high contact load per unit length of rollers. In this paper, the roller roundness deformation was included by using a formulation of the roller as a cylinder under compression by two flat surfaces. The inertial loading due to rotational speed effect was considered by including the centrifugal force and gyroscopic moment of rollers. Experiments were performed to validate the proposed model, and calculated and measured axial displacements of the bearing under axial loads yielded a good correlation. Extensive simulations were conducted to show the importance of roller roundness deformation and the applicability of the proposed model. The developed model for crossed roller bearing will be useful for the design and extensive analysis of crossed roller bearings.

scholarly journals Research on Gear Tooth Longitudinal Modification of Locomotive Traction Gear with Shaft Structure

2018 ◽  
Author(s):  
Xiaochun Shi ◽  
Riming Zhang ◽  
Weidong He
Keyword(s):  
Contact Stress ◽  
Load Distribution ◽  
High Speed ◽  
Gear Tooth ◽  
Contact Analysis ◽  
Parametric Models ◽  
Heavy Load ◽  
Before And After ◽  
The Ideal

By the contact analysis of the traction gears with shafts of high-speed and heavy-load locomotive, the deformation and load distribution of the Front Guide Surface in starting operation are obtained. According the results, the ideal longitudinal modification curve is fitted out. The gear parametric models were completed, and the load distribution and the contact stress of the gears are compared before and after tooth longitudinal modification in ANSYS. It shows the modification methods and the amount of the modification are reasonable.

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