Dynamics of Rolling-Element Bearings—Part III: Ball Bearing Analysis

1979 ◽  
Vol 101 (3) ◽  
pp. 312-318 ◽  
Author(s):  
P. K. Gupta
Keyword(s):  
Ball Bearing ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Ball Bearings ◽  
Rolling Element Bearings ◽  
Time Simulation ◽  
Rolling Element ◽  
Analytical Development ◽  
Critical Film Thickness ◽  
Bearing Analysis

An analytical formulation for the generalized ball, cage, and race motion in a ball bearing is presented in terms of the classical differential equations of motion. Ball-race interaction is analyzed in detail and the resulting force and moment vectors are determined. The ball-cage and race-cage interactions are considered to be either hydrodynamic or metallic and a critical film thickness defines the transition between the two regimes. Simplified treatments for the drag and churning losses are also included to complete a rigorous analytical development for the real-time simulation of the dynamic performance of ball bearings.

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.

Dynamics of Rolling-Element Bearings—Part IV: Ball Bearing Results

1979 ◽  
Vol 101 (3) ◽  
pp. 319-326 ◽  
Author(s):  
P. K. Gupta
Keyword(s):  
Differential Equations ◽  
Axial Load ◽  
Ball Bearing ◽  
Equations Of Motion ◽  
Rolling Element Bearings ◽  
Dynamic Simulations ◽  
Rolling Element ◽  
Overall Stability ◽  
The Stability ◽  
General Motion

Dynamic simulations of the performance of a ball bearing are presented in terms of the general motion as obtained by integrating the differential equations of motion of the various bearing elements. It is shown that bearing misalignment significantly influences the ball/cage and race/cage interaction and, hence, the stability of cage motion. The increased radial to axial load ratios promote skidding which couples with the lubricant behavior to impose accelerations on the ball which ultimately influence the ball/cage interactions. Hence, the lubricant behavior and the large load variation on the balls play dominant roles not only in determining the extent of skidding but also in establishing the overall stability of the cage motion.

Performance studies of textured race ball bearing

2019 ◽  
Vol 71 (9) ◽  
pp. 1116-1123 ◽  
Author(s):  
Vivek Bhardwaj ◽  
R.K. Pandey ◽  
V.K. Agarwal
Keyword(s):  
Ball Bearing ◽  
Dynamic Performance ◽  
Critical Role ◽  
Operating Conditions ◽  
Frictional Torque ◽  
Bulk Temperature ◽  
Back Side ◽  
Ball Bearings ◽  
Content Type ◽  
Long Duration

Purpose The purpose of this paper is to develop an energy-efficient and dynamically improved thrust ball bearing using textured race. A texture has been used on the stationary race of the test bearing to conduct the long-duration experiment for exploring its tribological and vibrational behaviours under starved lubricating condition using micro size MoS2 blended grease. The performance behaviours of the textured race bearing have been compared with conventional bearing (i.e. having both races without textures) under the identical operating conditions for demonstrating the advantages of textured race. Design/methodology/approach Texture was created on stationary race of the test ball bearing (51308) using nano-second pulsed Nd: YAG laser. Performance parameters (frictional torque, temperature rise and vibrations) of textured ball bearings were measured under severe starved lubricating conditions for understanding the critical role of texture in the long duration of the test. S-type load cell and miniature accelerometer were used for measuring the frictional torque and vibration, respectively. Bulk temperature at stationary races (at the back side) of test bearings was measured in operating conditions using a non-contact infrared thermometer. Findings Significant reduction in frictional torque and decrease in amplitude of vibration with textured ball bearing were found even under the severe starved lubricating condition in comparison to conventional bearing. Originality/value There is dearth of research pertaining to the performance behaviours of ball bearings using textures on the races. Therefore, an attempt has been made in this study to explore the tribo-dynamic performance behaviours of a thrust ball bearing using a texture on its stationary race under severe starved lubricating condition for the longer duration of the test.

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 Influence of raceway waviness on the level of vibration in rolling-element bearings

2017 ◽  
Vol 65 (4) ◽  
pp. 541-551 ◽  
Author(s):  
S. Adamczak ◽  
P. Zmarzły
Keyword(s):  
Ball Bearing ◽  
Correlation Coefficients ◽  
Rolling Element Bearings ◽  
Test Results ◽  
Frequency Bandwidth ◽  
Surface Waviness ◽  
Medium Frequency ◽  
Method Of Calculation ◽  
Rolling Element ◽  
Bearing Vibration

AbstractThis paper provides a quantitative analysis of how raceway waviness (RONt) in 6304-type bearings affects their vibration. The waviness of bearing races was measured at the actual points of contact between the balls and the races. The measurements were conducted in the range of 16–50 undulations per revolution (UPR). The bearing vibration was analyzed in three bandwidths of frequency: low (LB) (50 ÷ 300 Hz), medium MB (300 ÷ 1800 Hz) and high HB (1800 ÷ 10 000 Hz), as well as in the full RMS bandwidth. The paper also presents the procedure used to determine the actual points of contact between the ball and each race to specify the point of waviness measurement. The method of calculation of the contact angle for a ball bearing is also discussed. The Pearson linear correlation coefficients were determined to analyze the relationships between the waviness parameters and the level of vibration. The test results show that an increase in the surface waviness on the inner and outer raceways causes an increase in the vibration level. The influence is most visible for the medium frequency bandwidth.

Dynamics of Rolling-Element Bearings—Part II: Cylindrical Roller Bearing Results

1979 ◽  
Vol 101 (3) ◽  
pp. 305-311 ◽  
Author(s):  
P. K. Gupta
Keyword(s):  
Differential Equations ◽  
Power Loss ◽  
Equations Of Motion ◽  
Roller Bearing ◽  
Geometrical Parameters ◽  
Rolling Element Bearings ◽  
Rolling Element ◽  
Cylindrical Roller Bearing ◽  
Cylindrical Roller ◽  
General Motion

Cylindrical roller bearing performance simulations are expressed in terms of the general motion of the bearing elements as derived by integrating the differential equations of motion. Roller skew as induced by relative race misalignment is simulated. It is shown that skidding can be reduced by using a lubricant providing relatively high traction. However, such a fluid results in increased bearing torque and power loss. The influence of geometrical parameters, such as roller/cage, or race/cage clearance and radial preload, on the roller and cage motion is also investigated.

scholarly journals Demodulation of Vibration Signal Based on Envelope-Kurtogram for Ball Bearing Fault Detection

2020 ◽  
Vol 4 (2) ◽  
pp. 115-123
Author(s):  
Berli Paripurna Kamiel
Keyword(s):  
Ball Bearing ◽  
Vibration Signal ◽  
Rolling Element Bearings ◽  
Central Frequency ◽  
Value Analysis ◽  
Bearing Fault ◽  
Bearing Defect ◽  
Rolling Element ◽  
Signal Demodulation ◽  
Envelope Spectrum

Rolling element bearings often suffer damage due to harsh operating and environmental conditions. The method commonly used in detecting faults in a bearing is envelope analysis. However, this method requires setting the central frequency and the correct bandwidth - which corresponds to the resonance frequency of the bearing - for signal demodulation to be effective. This study proposes a kurtogram to determine the correct central frequency and bandwidth to obtain the frequency band with the highest impulse content or the highest kurtosis value. Analysis envelope is applied to the filtered vibration signal using the central frequency and bandwidth parameters obtained from the kurtogram. The results showed that the envelope-kurtogram method is effective for faulty bearing detection as shown in the envelope spectrum where the peaks coincide with the bearing defect characteristic frequency (BPFO) with high accuracy. Likewise, it can be observed several BPFO harmonics which provide information on the level of bearing fault.

Multi-Objective Robust Optimization of Deep Groove Ball Bearings Considering Manufacturing Tolerances Based on Fatigue and Wear Considerations

2021 ◽  
pp. 1-43
Author(s):  
Md Saif Ahmad ◽  
Rajiv Tiwari ◽  
Twinkle Mandawat
Keyword(s):  
Objective Function ◽  
Ball Bearings ◽  
Rolling Element Bearings ◽  
Objective Functions ◽  
Dynamic Capacity ◽  
Multi Objective ◽  
Design Variables ◽  
Deep Groove ◽  
Rolling Element ◽  
Manufacturing Tolerances

Abstract In designing any machine element, we need to optimize the design to attain its maximum utilization. Herein deep groove ball bearings has been chosen for optimization. Optimization has been done in such a way that the design is robust so that manufacturing tolerances can be considered in the design. Robust design ensures that changes in design variables due to manufacturing tolerances have minimum effect on the objective function, i.e. its performance. Robustness is achieved by maximizing the mean value of the objective function and minimizing its deviation. For rolling element bearings, its life is one of the most crucial considerations. The rolling bearing rating life depends on dynamic capacity, lubrication conditions, contamination, mounting, lubrication, manufacturing accuracy, material quality, etc. and thus the dynamic capacity and elasto-hydrodynamic minimum film thickness has been taken as objective functions for the current problem. Rolling element bearings have standard boundary dimensions, which include the outer diameter, inner diameter and bearing width for the case of deep groove ball bearings. So the performance can be improved by changing internal dimensions, which are the bearing pitch diameter, ball diameter, the inner and outer raceway groove curvature coefficients and, the number of rolling elements. These five internal geometrical parameters are taken as design variables, moreover five design constraint factors are also included. Thirty-six constraint equations are considered, which are mainly based on geometrical and strength considerations. In the present work, the objective functions are optimized individually (i.e., the single-objective optimization) and then simultaneously (i.e., the multi-objective optimization). NSGA-II (non-dominated sorting genetic algorithm) has been used as the optimization tool. Pareto optimal fronts are obtained for one of the bearings. Out of many points on the Pareto-front, only the knee solutions have been presented in the tables. This work shows that geometrically feasible bearings can be designed by optimizing multiple objective functions simultaneously and also incorporating the variations in dimensions, which occur due to manufacturing tolerance.

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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