Calculation of the Stiffness Matrix of Angular Contact Ball Bearings by Using the Analytical Approach

[+] Author and Article Information
X. Hernot

Institut Universitaire de Technologie de Rennes, Département de Génie Mécanique et Productique, Rennes, France

M. Sartor, J. Guillot

Institut National des Sciences Appliquées, Laboratoire de Génie Mécanique de Toulouse, Toulouse, France

J. Mech. Des 122(1), 83-90 (Jan 01, 2000) (8 pages) doi:10.1115/1.533548 History: Received April 01, 1999; Revised January 01, 2000
Copyright © 2000 by ASME
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International Standards Organization, 1991, International Standard ISO 281/1, “Rolling Bearings-Dynamic Load Ratings and Rating Life-Part 1, Calculation methods.”
Houpert, L., 1995, “Prediction of Bearing, Gear and Housing Performances,” Proceedings of the Rolling Bearing Practice Today Seminar, I. Mech. E., London, February 1995.
Houpert,  L., 1997, “A Uniform Analytical Approach for Ball and Roller Bearings Calculations,” ASME J. Tribol., 119, pp. 851–858.
Palmgren, A., 1959, Ball and Roller Bearing Engineering, Burkbank.
Sjoväll, H., 1933, “The Load Distribution Within Ball and Roller Bearings Under Given External Radial and Axial Load,” Tek. Tidskrift, Mek., h. 9.
Jones,  A. B., 1960, “A General Theory of Elasticity Constrained Ball and Radial Roller Bearings under Arbitrary Load and Speed Conditions,” ASME J. Basic Eng., 82, pp. 309–320.
Andreason,  S., 1973, “Load Distribution in a Taper Roller Bearing Arrangement Considering Misalignment,” Tribology, 6, pp. 84–92.
De Mul,  J. M., Vree,  J. M., and Maas,  D. A., 1989, “Equilibrium and Associated Load Distribution in Ball and Roller Bearings Loaded in Five Degree of Freedom While Neglecting Friction-Part I: General Theory and Application to Ball Bearings,” ASME J. Tribol., 111, pp. 142–148.
Harris, T. A., 1991, Rolling Bearing Analysis, Third Edition, Wiley, New York.


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Angular contact ball bearing geometrical parameters
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Coordinate system and displacements
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Back to back bearing-shaft arrangement
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Displacements versus axial preload
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Axial loads versus axial preload
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Bearing fatigue life versus axial preload
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Coordinate system for the five DOF model
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Variations of Jaa,Jra, and Jrr versus ε



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