The film thicknesses and pressures in elastohydrodynamically lubricated contacts have been calculated for a line contact by using an improved version of Okamura’s approach. The new approach allows for lubricant compressibility, the use of Roelands viscosity, a general mesh (nonconstant step), and accurate calculations of the elastic deformations. The new approach is described, and the effects on film thickness, pressure, and pressure spike of each of the improvements are discussed. Successful runs have been obtained at high pressure (to 4.8 GPa) with low CPU times.

The lubricant shear modulus G and Ree-Eyring shear stress τ0 are determined in this work by using Roelands’, rather than Barus’, relationship for calculating the lubricant viscosity. When using Roelands’ viscosity, elastic effects in the lubricant tend to be negligible, especially when inlet shear heating and displacement of the center of pressure are considered. These results are illustrated by examples in which inlet shear heating has been calculated, or when the lateral traction force obtained by spinning was known. In some cases, elastic effects are indeed present, though much reduced, and this leads to greater values of the lubricant shear modulus. The Ree-Eyring shear stress found when using the Roelands’ viscosity is also greater.

Results given in this paper are threefold. In the case of Hertzian line contact, a new load/deformation relationship is derived analytically and use is made of the thickness of the outer race section. A minor effect of the section thickness is shown. The exponent on the deformation is 1.074 (instead of 1.1 usually accepted). Results calculated with the new relationship are successfully compared to results calculated with other published relationships and also are compared successfully to some available experimental results. For the case of point contact, useful relationships, obtained by curve-fitting, are given to calculate easily the load versus deformation, maximum Hertzian pressure and ellipse contact dimension as a function of a dimensionless load parameter and ratio k of equivalent radii (instead of sum of curvatures and elliptical integrals before). A large range of k is covered, from 0.05 (found at roller rib contact) to 13,000 to cover all bearing cases, from ball bearings to spherical and tapered roller bearings. Finally, an important analytical relationship, based on curve-fitting, also is suggested to describe a smooth transition from point contact to line contact as the load increases. It is recommended to define bearing setting and bearing preload with the suggested relationship.

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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.

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Rolling contact bearing life is calculated using stresses calculated at the surface and in the volume. Surface stresses account for profile and misalignment as well as asperity deformations. Sub-surface stresses are calculated beneath the asperities (for defining the life of the surface) and deeper in the volume for calculating the life of the volume. The stress-life criterion adopted is the Dang Van one in which the local stabilized shear stress is compared to the material endurance limit defined as a function of the hydrostatic pressure (itself a function of the contact pressure) but also residual stresses and hoop stresses (due to fit). A stress-life exponent c, of the order of 4 (instead of 34/3 in the standard Lundberg and Palmgren model) is used for respecting a local load-life exponent of 10/3 at typical load levels. Life of any circumferential slices of the inner, outer, and roller is defined for obtaining the final bearing life. Trends showing how the bearing life varies as a function of the applied bearing load and Λ ratio (film thickness/RMS roughness height) are given.