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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