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.

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.

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 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 Experimental Validation of the DREB and RAPIDREB Computer Programs

1985 ◽  
Vol 107 (1) ◽  
pp. 132-137 ◽  
Author(s):  
P. K. Gupta ◽  
J. F. Dill ◽  
H. E. Bandow
Keyword(s):  
Experimental Data ◽  
Experimental Validation ◽  
Ball Bearing ◽  
Rolling Element Bearings ◽  
Mass Center ◽  
Angular Contact Ball Bearing ◽  
High Speeds ◽  
Rolling Element ◽  
General Motion ◽  
Good Agreement

The general motion of the cage predicted by the computer models in an angular contact ball bearing operating up to two million DN is compared against experimental data. Both the computer predictions and experimental data indicate a certain critical shaft speed at which the cage mass center begins to whirl. The predicted and measured whirl velocities and orbit shapes are in good agreement. The axial and radial velocities of the cage mass center also agree within the tolerance band of the expected experimental error. Due to experimental difficulties the cage angular velocity could not be reliabily measured at high speeds. At low speeds, however, there is a fair agreement between the experimental data and the analytical predictions.

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.

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.

scholarly journals Analytical study of auto-balancing within the framework of the flat model of a rotor and an auto-balancer with a single cargo

2021 ◽  
Vol 2 (7 (110)) ◽  
pp. 66-73
Author(s):  
Gennadiy Filimonikhin ◽  
Lubov Olijnichenko ◽  
Guntis Strautmanis ◽  
Antonina Haleeva ◽  
Vasyl Hruban ◽  
...  
Keyword(s):  
Differential Equations ◽  
Analytical Study ◽  
Rotation Axis ◽  
Equations Of Motion ◽  
The Third ◽  
Rotor Imbalance ◽  
Small Resistance ◽  
The Stability ◽  
Resistance Forces ◽  
Rotor Model

This paper reports the analytically established conditions for the onset of auto-balancing for the case of a flat rotor model on isotropic elastic-viscous supports and an auto-balancer with a single load. The rotor is statically unbalanced, the rotation axis is vertical. The auto-balancer has a single cargo – a pendulum, a ball, or a roller. The balancing capacity of the cargo is equal to the rotor imbalance. The physical-mathematical model of the system is described. The differential equations of motion are recorded in dimensionless form relative to the coordinate system that rotates synchronously with the rotor. The so-called main movement has been found; in it, the cargo synchronously rotates with the rotor and balances it. The differential equations of motion are linearized in the neighborhood of the main movement. A characteristic equation has been constructed. It helped investigate the stability of the main movement (an auto-balancing mode) for the cases of the absence and presence of resistance forces in the system. It was established that in the absence of resistance forces in the system: – the rotor has three characteristic rotational speeds, and the first always coincides with the resonance frequency; – auto-balancing occurs when the rotor rotates at speeds between the first and second ones, and above the third characteristic speed; – the value of the second and third characteristic speeds is significantly influenced by the ratio of weight to the mass of the system; – the second and third characteristic speeds monotonously increase with an increase in the ratio of cargo weight to the mass of the system. Resistance forces significantly affect both the values of the second and third characteristic speeds and the conditions of their existence. Small resistance forces do not change the quality behavior of the system. With high resistance forces, the number of characteristic speeds decreases to one. The paper reports the results applicable to an auto-balancer with many cargoes when it balances the imbalance that equals the balancing capacity of the auto-balancer

scholarly journals Instability Threshold of a Rigid Rotor-Tilting Pad Journal Bearings System

1997 ◽  
Vol 3 (3) ◽  
pp. 199-213 ◽  
Author(s):  
Stefano Pagano ◽  
Ernesto Rocca ◽  
Michele Russo ◽  
Riccardo Russo
Keyword(s):  
Differential Equations ◽  
Numerical Integration ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Stable Operation ◽  
Rigid Rotor ◽  
Tilting Pad ◽  
The Stability ◽  
Tilting Pad Journal Bearings ◽  
Rotor Axis

The stability of a rigid rotor supported on radial tilting pad journal bearings is analysed. This study has been tackled both for small unbalance values by linearising the equations of motion, and also in the case where, because of the high unbalance value, the rotor axis describes orbits with an amplitude such that the system's non-linearity cannot be ignored. In both cases the system's stable operation maps have been obtained and verified through numerical integration of the differential equations of motion.

Floquet Stability Analysis of a Rotor Supported on Rolling Element Bearings With Clearance and Static Load

2013 ◽  
Author(s):  
C. A. Kitio Kwuimy ◽  
A. S. Das ◽  
C. Nataraj
Keyword(s):  
Static Load ◽  
Rotation Speed ◽  
Approximate Model ◽  
Hertzian Contact ◽  
Rolling Element Bearings ◽  
Rotating Shaft ◽  
Second Order Differential Equations ◽  
Rolling Element ◽  
Small Clearance ◽  
The Stability

A rotating shaft supported on rolling element bearings is considered. The system is known to be modeled by a pair of coupled second order differential equations involving Hertzian contact force and thus parametric excitations. In studying the stability of the system, the static equilibrium in the direction of the static load is found to linearly increases with clearance. An approximate model is obtained and conditions of validity of such a model are discussed. Cage rotation speed, static load and clearance are revealed as key parameters. Considering the Floquet formalism for stability, in the domain (clearance,speed), it is found that the domain of stability decreases for large clearance and increases for small clearance. Higher number of rolling element as well as smaller static load positively affect the stability as well.

Influence of Flexibly Mounted Rolling Element Bearings on Rotor Response: Part I—Linear Analysis

1970 ◽  
Vol 92 (1) ◽  
pp. 59-69 ◽  
Author(s):  
E. J. Gunter
Keyword(s):  
Equations Of Motion ◽  
Rolling Element Bearings ◽  
Unbalance Response ◽  
Wide Range ◽  
Rolling Element ◽  
Flexible Supports ◽  
Proper Design ◽  
Support Conditions ◽  
Gyroscopic Effects ◽  
Phase Angles

The paper evaluates the influence of damped, linear flexibly mounted rolling-element bearings on dynamic rotor unbalance response. The system analyzed is treated as a general four degree of freedom unbalanced rotor mounted on damped flexible supports and includes rotor gyroscopic effects. The rotor equations of motion are solved for synchronous precession over a wide range of speeds for various support conditions. Rotor performance curves on bearing amplitude, forces transmitted, phase angles as a function of speed for various values of support damping are computer plotted to illustrate rotor and bearing performance over a wide range of speed and operating parameters. Results indicate that forces transmitted to the bearings by the rotor synchronous unbalance response can be dramatically reduced by proper design of the bearing support characteristics.

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