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Rolling Element Bearings Analysis

Rolling Element Bearings Analysis
Hamrock, B. J., Lewis Research Center
Anderson, W. J., Bearings and Lubrication
NASA
63 Pages

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Open: Rolling Element Bearings Analysis

PREFACE:

Rolling-element bearings are a precision, yet simple, machine element of great utility. In this report we draw together the current understanding of rolling-element bearings. A brief history of rolling -element bearings is reviewed in the Introduction, and subsequent sections are devoted to describing the types of rolling-element bearings, their geometry and kinematics, as well as the materials they are made from and the manufacturing processes they involve. The organization of this report is such that unloaded and unlubricated rolling-element bearings are considered in the first six sections, loaded but unlubricated rolling-element bearings are considered in sections 7 to 9, and loaded and lubricated rolling- element bearings are considered in sections 10 to 14. The recognition and understanding of elastohydrodynamic lubrication, covered briefly in sections 11, 12, and 14, represents one of the major developments in rolling- element bearings in the last 18 years.

TOC

Symbols 1
1. Introduction 2
1 . 1 Historical Overview 2
1 .2 Conformal and Nonconformal Surfaces 3
1 .3 Bearing Selection 3
2. Bearing Types 4
2. 1 Ball Bearings 5
2.2 Roller Bearings 7
3. Geometry 8
3.1 Geometry of Ball Bearings 8
3.2 Geometry of Roller Bearings 12
4. Kinematics 13
5. Materials and Manufacturing Processes 15
5.1 Ferrous Alloys 16
5.2 Ceramics 16
6. Separators 17
7. Contact Stresses and Deformations 17
7.1 Elliptical Contacts 17
7.2 Rectangular Contacts 20
8. Static Load Distribution 20
8.1 Load Deflection Relationships 20
8.2 Radially Loaded Ball and Roller Bearings 20
8.3 Thrust -Loaded Ball Bearings 22
8.4 Preloading 24
9. Rolling Friction and Friction in Bearings 25
9.1 Rolling Friction 25
9.2 Friction Losses in Rolling-Element Bearings 27
10. Lubricants and Lubrication Systems 27
10.1 Solid Lubrication 27
10.2 Liquid Lubrication 28
1 1 . Elastohydrodynamic Lubrication 29
11.1 Relevant Equations 29
11.2 Dimensionless Grouping 30
11.3 Minimum-Film-Thickness Formula
11.4 Pressure and Film Thickness Plots, Rolling Bearing Fatigue Life 32
12.1 Contact Fatigue Theory 32
12.2 The Weibull Distribution 32
12.3 Lundberg-Palmgren Theory 33
12.4 The AFBMA Method 35
12.5 Life Adjustment Factors 35
13. Dynamic Analyses and Computer Codes 36
13.1 Quasi-Static Analyses 36
13.2 Dynamic Analyses 37
14. Applications 37
14.1 Cylindrical Roller Bearing Problem 37
14.2 Radial Ball Bearing Problem 39

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