The inclusion of lubricant shear thinning in the short bearing approximation

Abstract

For short journal bearings (defined as those where L/D < 0.5, where L is the length and D is the diameter), such as those used in modern automotive engines, the 'short bearing approximation' is an attractive fast tool for bearing designers to use as a first approximation. The essence of the approximation is that the pressure variation across the width of the bearing is much greater than that around the circumference of the bearing. With this approximation, it is possible to neglect certain terms in the Reynolds equation, and an analytical expression for the pressure variation around the bearing can be written down. By integrating the pressure around the bearing, an analytical expression relating the load, W, to the eccentricity ratio, ε, may be obtained. The standard ‘short bearing approximation’ assumes that the lubricant is Newtonian, and so any variation in the lubricant viscosity with the shear rate is neglected. In this paper, an isothermal analysis is made which uses the short bearing approximation but allows for the possibility of lubricant shear thinning. The variation in the lubricant viscosity with the shear rate is assumed to be as described by the Cross equation, which has previously been shown to give a good fit to measured flow curves. A detailed description of the analysis is given, together with results obtained when the model was applied to a modern automotive con-rod bearing. (Note that the effects of pressure on lubricant viscosity have been neglected.)