This paper presents a solution to the problem of hydrodynamic lubrication of journal bearings taking into account the elastic distortions of the shaft and the bearing. The exact solution for determining the elastic deformation for a given pressure distribution around a bearing is given, together with the reiterative procedure adopted to find the pressure distribution which satisfies both the hydrodynamic and elastic requirements of the system. Results are given which have been derived for a material with a Poisson’s ratio of 0.28, but other values such as 0.33 do not incur substantial errors. The results can be applied to a wide range of operating conditions using the nondimensional group of terms suggested in the paper. The bearing is assumed to be infinite in length, and infinite in thickness. The latter assumption is shown to be valid for a particular case where the outside diameter of the bearing shell is 3.5 times the shaft diameter. A further assumption in the calculation is a condition of constant viscosity of the lubricant existing around the bearing.

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