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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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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