The inclusion of lubricant shear thinning in the short bearing approximation

For short journal bearings (defined as those where L/D < 0.5, where L is th e length and D is the diameter), such as those used in modern automotive en gines, the 'short bearing approximation' is an attractive fast tool for bea ring designers to use as a first approximation. The essence of the approxim ation is that the pressure variation across the width of the bearing is muc h greater than that around the circumference of the bearing. With this appr oximation, it is possible to neglect certain terms in the Reynolds equation , and an analytical expression for the pressure variation around the bearin g can be written down. By integrating the pressure around the bearing, an a nalytical expression relating the load, W, to the eccentricity ratio, epsil on, may be obtained. The standard 'short bearing approximation' assumes tha t the lubricant is Newtonian, and so any variation in the lubricant viscosi ty 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. T he variation in the lubricant viscosity with the shear rate is assumed to b e as described by the Cross equation, which has previously been shown to gi ve a good fit to measured flow curves. A detailed description of the analys is 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 l ubricant viscosity have been neglected.)