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Vibration of Bearings

Bearing Engineering and Design Resources

Vibration of Bearings
KAUNSK POLYTECHNICAL INSTITUTE
Central Scientific-Research Laboratory of Vibrotechniques
K.M. RAGULSKIS, A.YU. JURKAUSKAS,
V.V. ATSTUPENAS. A.YU. VITKUTE, A.P. KULVEC
399 page
This book has been translated from Russian
Translator: Dr. N.M. Shivaramkrishnan
General Editor: Dr. V.S. Kothekar
Published for the National Aeronautics and Space Administration, and the National Science Foundation,

Analytical determination of vibrations and friction torque due to rotation, taking into account the hydrodynamic action of a lubricating oil film, and determination of the elastic and damping characteristics of bearings and bearing assemblies are some of the problems considered in this book. The methodology and techniques of measuring the dynamic characteristics of bearings are presented. Experimental data and the methodology of statistical analysis are also given.
The book is intended for scientists and engineers engaged in the instrument manufacturing and machine building industries.

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Introduction:

It is impossible to imagine the progress of modern science and technology without the wide application of bearings, which form an integral part of the majority of machines, instruments and assemblies. The accuracy and sensitivity of the majority of precision instruments and assemblies have improved considerably in the recent past. Tremendous progress has also been made in achieving reduction in the sizes of machines, their weight and power requirements. All this led to the development of new types and designs of mounting and more stringent requirements of the quality of bearings and assemblies. These developments stimulated theoretical and experimental research on the dynamic characteristics of bearings.

The large amount of work (theoretical and experimental) devoted to the study of bearings and their mountings has yet to cover every aspect of the phenomena occurring in this dynamic domain.

In recent times such characteristics of precision mechanisms as spatial vibrations of rings, friction torque and elastic and damping properties have assumed the highest importance. It is necessary to study these characteristics theoretically and experimentally using statistical analysis.

Problems related to the computation of vibrations, friction torque and stiffness of bearings taking into account the enhanced qualitative requirements of bearing assemblies are considered in this book. Methods and experimental setups for the determination of the dynamic characteristics of the mounting are described and the methodology of the statistical analysis of experimental results is given.

Content:

CHAPTER 1. ANALYTICAL DETERMINATION OF FRICTION TORQUE . . .
1.1 Friction Torque in Rolling-Contact Bearings
1.1.1 Rolling friction in bearings
1.1.2 Total friction torque in rolling-contact bearings
1.1.3 Analytical determination of total friction torque in rolling- contact bearings
1.2 Analytical Determination of Variable Component of Friction Torque
1.2.1 Determination of the load acting on the i-th ball bearing
1.2.2 Computation and analysis of variable component of friction torque
1.3 Determination of the Friction Torque in Ball Bearing due to Rolling Friction, Taking into Account Exponential Dependence of Viscosity on Pressure
References

CHAPTER 2. DETERMINATION OF ELASTIC AND DAMPING CHARACTERISTICS OF ROLLING-CONTACT BEARINGS . . . . . . . . .
2.1 Determination of Static Stiffness of Rolling-Contact Bearings
2.2 Errors in Manufacture and Their Effect on the Stiffness of Rolling- Contact Bearings
2.3 Identification of Elastic and Damping Characteristics of Bearings Based on the Results of Vibration Tests
R e f e r e n c e s

CHAPTER 3
ANALYSIS OF RADIAL VIBRATIONS OF BEARING ASSEMBLIES
3.1 Dynamics of Ball Bearing Assembly
3.2 Vibration of the Outer Ring of Ball Bearing and Conservative Friction Torque
3.3 Vibrations of Shaft Rotating in Two Ball Bearings with Preload
3.3.1 Statistical characteristics of vibrations of shaft in standard ball bearings
3.4 Equation of Radial Vibrations of a Shaft in a Bearing During Random Excitation
3.5 General Formulation of the Problem of Probability Modelling

CHAPTER 4. MEASUREMENT TECHNIQUES AND INSTRUMENTS FOR MEASUREMENT OF DYNAMIC CHARACTERISTICS OF BEARINGS
4.1 Measurement of Friction Torque and Vibrations of Bearings
4.2 Setup for the Measurement of Friction Torque in Rolling- Contact Bearings
4.2.1 Electrical instruments for the measurement of friction torque coefficients in bearings
4.3 Apparatus for the Analysis of Friction Torque in Sliding Bearings
4.4 Apparatus for the Measurement of Dynamic Parameters of High-speed Ball Bearings in Specific Conditions

CHAPTER 5. ERRORS IN THE MEASUREMENT OF FRICTION TORQUE AND THEIR REDUCTION
5.1 Additive Error in the Measurement of Friction Torque and Its Reduction
5.2 Dynamic Condition of Correction of Additive Error
5.2.1 Energy spectrum of residual error
5.3 Some Problems of Correction Procedure
5.3.1 Analysis of the effect of interrupting measurement . .
5.3.2 Determination of the parameters of error
5.3.3 Evaluation of the effectiveness of correction
5.4 Friction Torque Measuring Instrument (FTMI) with Correction for Additive Error
5.5 Other Sources of Error in the- Measwenlent of Friction , - . Torque

CHAPTE~ 6. STATZSTICGL ANALYSIS OF EXBRIMENTAL RESULTS OF PRECISION BEARING DYNAMICS
6. l., Reqaifements for .the Evaluation of Statistteal .Characteristics and Preparation of.E&perim,ental Material
6.2 Estimation of Statistical Characteristics 8
6.2.1 Special correlation characteristics of rolling-contact bearing parameters and the dependence of friction torque on different operating conditions
6.3 Determination of Relations between Bearing Parameters

CHAPTER 7. EXPERIMENTAL STUDY OF THE DYNAMICHARACTERISTICS OF PRECISION BEARINGS AND ASSEMBLIES
7.1 Study of Friction Torque in Bearings and Bearing Assemblies
7.1.1 Dependence of friction torque on loading
7.1.2 Study of friction torque in bearing assemblies
7.1.3 Dependence of friction torque (MB) in bearings on other factors
7.2 Effect of Lubricant on Friction Torque in Bearings
7.3 Study of the Dynamic Parameters of High-speed Rotors in Ball Bearing Supports
7.4 Experimental Study of Heating, Friction Torque and Lubricating Conditions of High-speed Ball Bearings
7.5 Investigation of Friction Torque in Precision Slide Bearings .
7.6 Diagnosis of Errors and Mounting-cum-Operational Defects in Bearings according to Characteristics of Friction Torques .
7.6.1 Effect of the shape of bearings
7.6.2 Effect of the cage
7.6.3 Effect of the surface smoothness
7.6.4 Effect of dirt
7.6.5 Effect of lubrication
7.6.6 Effect of ring deformation

CHAPTER 8. WAYS OF REDUCING FRICTION TORQUE AND VIBRATIONS IN BEARINGS
8.1 Effect of Vibrations on Friction Torque in Ball Bearings
8.2 New Designs of Rolling-Contact Bearings and Assemblies with Reduced Friction Torque
8.3 New Designs of Slide Bearings with Reduced Friction Torque

Related:

• Vibration Terms and Definitions
• Shock and Vibration Response Equations
• Vibration Severity Chart
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• Angular / Radial Contact Ball Bearings Static Load Rating Static load rating for Angular / Radial Contact Ball Bearings, use the following the equation:
• Ball Bearings Design, Construction, and Mounting Premium Membership required to access
• Ball Bearings Designations, Loading, Assembly Configurations AFBMA Code and Description - Ball Bearings
• Ball Bearings Fatigue Life Calculations and Load Ratings Fatigue life calculations assume the dispersion in life of identical ball bearings operating under identical conditions, a statistical result is obtained for bearing fatigue life.
• Ball Bearings Application and Standard Designations The single-row deep-groove radial contact ball bearings will take radial load well and some thrust load.
• Ball Screw Support Bearings Ball screw is a mechanical linear actuator that translates rotational motion to linear motion with little friction.
• Ball Bearings ABEC Tolerances The ABEC scale is an industry accepted standard for the tolerances of a ball bearing. It was developed by the Annular Bearing Engineering Committee (ABEC) of the American Bearing Manufacturers Association (ABMA)
• Bearing Application Table Chart Bearing design data presented here provides guidelines and reference for the identification of potential bearing application