The design of hydrodynamically lubricated journal bearings against yield

The stress field induced by the half-Sommerfeld pressure distribution in an infinitely elongated bearing is studied in detail. A complex potential formulation for the stress field is employed to solve the elasticity problem, with the intention to compute the required strength according to the classical von Mises criterion. Example contour plots of the yield parameter (root J(2))/p(m) are given and the position and magnitude of the maximum normalized von Mises parameter are determined for a range of working conditions, analytically when they are on the surface, i.e. for eccentricity ratios epsilon < 0.6, and semi-analytically for the cases where they are located subsurface, i.e. epsilon > 0.6. Surprisingly simple results are obtained for eccentricity ratios lower than about 0.7, namely a maximum of the von Mises parameter proportional to the mean pressure, permitting a simple rule to be developed for the design of bearings against yielding: if the bearing works with eccentricity ratios smaller than 0.7, and the average pressure is smaller than 1.22k, where k is the yield stress of the material in pure shear, then yielding is avoided. When bearings are used in the range of very high eccentricity ratios, a more refined calculation is needed, taking into account the actual value of the maximum von Mises parameter and the paper provides design charts for this purpose.