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Research Papers: Applications

An Enhanced Study of the Load–Displacement Relationships for Rolling Element Bearings

[+] Author and Article Information
L. Houpert

Senior Scientist
TIMKEN Europe, B.P. 60089
Colmar Cedex 68002, France
e-mail: luc.houpert@timken.com

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received January 15, 2013; final manuscript received September 20, 2013; published online November 13, 2013. Assoc. Editor: Dong Zhu.

J. Tribol 136(1), 011105 (Nov 13, 2013) (11 pages) Paper No: TRIB-13-1023; doi: 10.1115/1.4025602 History: Received January 15, 2013; Revised September 20, 2013

An enhanced analytical approach is suggested for calculating three rolling element bearing loads Fx, Fy, and Fz as well as the two tilting moments My and Mz as a function of five relative race displacements: three translations dx, dy, and dz, and two tilting angles dθy and dθz. A full coupling between all these displacements and forces is considered. This approach is particularly recommended for programming the rolling element bearing behavior in any finite element analysis or multibody system dynamic tool, since only two nodes are considered: one for the inner race center, usually connected to a shaft, and another node for the outer race center, connected to the housing. Also, roller and raceway crown radii are considered, meaning that Hertzian point contacts stiffness can be used at low load with a smooth transition toward Hertzian line contact as the load increases. This approach can be used for describing any rolling element bearing type when neglecting centrifugal and gyroscopic effects and applying the approximation of a constant ball–race contact angle. Deep groove ball bearings (whose contact angle sign follows the sign of the applied bearing axial force) or other ball bearings or spherical roller bearing operating under large misalignment may not support such approximations.

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References

HoupertL., 1997, “A Uniform Analytical Approach for Ball and Roller Bearing,” ASME J. Tribol., 119, pp. 851–857. [CrossRef]
HoupertL., 2001, “An Engineering Approach to Hertzian Contact Elasticity—Part I,” ASME J. Tribol., 123, pp. 582–588. [CrossRef]
HoupertL., 2001, “An Engineering Approach to Non-Hertzian Contact Elasticity—Part II,” ASME J. Tribol., 123, pp. 589–594. [CrossRef]
Eschmann, P., Hasbargen, L., and WeigandK., 1978, Ball and Roller Bearings, Theory, Design and Application, 2nd ed., R. Oldenbourg, München, Germany.
Harris, T. A., and Kotzalas, M. N., 2007, “Essential Concepts of Bearing Technology,” Rolling Bearing Analysis, 5th ed., CRC Press, Taylor and Francis, London.
Hoeprich, M. R., 1986, “Numerical Procedure for Designing Rolling Element Contact Geometry as a Function of Load Cycle,” SAE Technical Paper No. 850764.
CretuS., 1996, “Initial Plastic Deformation of Cylindrical Roller Generatrix Stress Distribution Analysis and Fatigue Life Tests,” Acta Tribol., 4(1–2), pp. 1–6.
HoupertL., 1995, “Prediction of Bearing, Gear and Housing Performances,” Proceeding of the Rolling Seminar Bearing Practice Today, I. Mech. E., London.
Houpert, L., and MercklingJ., 1998, “A Successful Transition From Physically Measured to Numerically Simulated Bearings, Shafts, Gears and Housing Deflections in a Transmission,” Proceeding of the Conference GPC'98 Global PowerTrain Congress New Powertrain Materials and Processes, Detroit, Vol. 4, pp. 131–137.
Hauswald, T., and HoupertL., 2000, “Numerical and Experimental Simulations of Performances of Bearing System, Shaft and Housing; Account for Global and Local Deformations,” Proceeding of the Conference SIA Seminar Fiabilité Experimentale, Paris, France.
HoupertL., 1999, “Numerical and Analytical Calculations in Ball Bearings,” Proceeding of the 8th European Space Mechanism and Tribology Symposium, Toulouse, France.
HoupertL., 2010, “CAGEDYN: A Contribution to Roller Bearing Dynamic Calculations; Part I: Basic Tribology Concepts,” STLE Tribol. Trans., 53, pp. 1–9. [CrossRef]
HoupertL., 2010, “CAGEDYN: A Contribution to Roller Bearing Dynamic Calculations; Part II: Description of the Numerical Tool and Its Outputs,” STLE Tribol. Trans., 53, p. 10–21. [CrossRef]
HoupertL., 2010, “CAGEDYN: A Contribution to Roller Bearing Dynamic Calculations; Part III: Experimental Validation,” STLE Tribol. Trans., 53(6), pp. 848–859. [CrossRef]

Figures

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Fig. 1

Basic tapered roller bearing geometry, relative race displacements, and total roller race geometrical interference

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Fig. 2

Transition from point contact to line contact in a single contact

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Fig. 3

Smooth transition from PC to LC on Fy and local slope in a TRB

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Fig. 4

Study of a truncated point contact [3]

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Fig. 5

Example of variation of coefM, with a transition from PC to LC

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Fig. 6

Comparison analytical results versus numerical results (SYBER)

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Fig. 7

Comparison analytical results versus numerical results (SYBER) in a full system

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Fig. 8

Comparison with SYBER results using a DGBB

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