A novel analytical approach is proposed, uniform for ball and roller bearings, which takes into account 5 relative race displacements (3 translations: dx, dy, and dz, and 2 tilting angles: dθy and dθz) to provide simple analytical relationships for calculating directly the resulting 3 bearing loads: Fx, Fy, and Fz as well as the 2 tilting moments: My and Mz. A full coupling between all these displacements and forces is considered. The maximum rolling element load Qmax, the load distribution Q(Ψ) and the 3-D rolling element load distribution dQ(Ψ, x′) at each roller-race contact slice are also given analytically. It will therefore be possible for bearing users, willing to study for themselves a complete statically indeterminate systems including shafts, housing and bearings, to do such calculations using accurate nonlinear bearing forces-displacements relationships suggested in this paper and to predict easily bearing and other system components performances. This approach can also be implemented in any nonlinear Finite Element Analysis (F.E.A.) package for describing a bearing element connecting the shaft to the housing for example. It completes, therefore, the F.E.A. library of elements.

1.
Eschmann P., Hasbargen L., and Weigand K., 1978, Ball and Roller Bearings, Theory, Design and Application, 2nd Edition, R. Oldenbourg Verlag.
2.
Harris T. A., 1991, Rolling Bearing Analysis, Third Edition, Wiley-Interscience, Wiley & Sons.
3.
Hoeprich M. R., 1986, “Numerical Procedure for Designing Rolling Element Contact Geometry as a Function of Load Cycle,” SAE Technical Paper Series 850764.
4.
Houpert L., 1995, “Prediction of bearing, gear and housing performances,” Proceeding of the Rolling Bearing Practice Today Seminar, I. Mech. E., London, Feb. 1995.
5.
Jones
A. B.
,
1960
, “
A general Theory for Elastically Constrained Ball and Radial Roller Bearings under Arbitrary Load and Speed Conditions
,”
ASME Journal of Basic Engineering
, Vol.
82
, pp.
309
320
.
6.
Sjo¨val S., 1933, “The Load distribution within Ball and Roller Bearings under Given External Radial and Axial Load,” Teknisk Tidskrift, Mek., h. 9.
7.
Tripp, J., 1985, “Hertzian Contact in Two and Three Dimensions,” NASA Technical paper 2473.
This content is only available via PDF.
You do not currently have access to this content.