Optimum design of high-speed, short journal bearings by mathematical programming

Generally, the selection of design variables in bearing design is done by a trial and error method using many design charts. However, it is not so easy to successfully select optimum design variables by such a method, and a considerable amount of working time and cost is needed to complete the optimum design of bearings. In this paper, an optimum design procedure for high-speed, short journal bearings operated in both laminar and turbulent flow regimes is developed based on mathematical programming. Under the short bearing assumption, simplified closed-form design formulas are obtained for the eccentricity ratio, maximum film pressure, fluid film temperature rise, supply lubricant quantity and whirl onset velocity. The radial clearance, slenderness ratio and average viscosity of lubricant, which minimize the weighted sum of fluid film temperature rise and supply lubricant quantity for various combinations of journal rotational speed and applied load, are determined by successive quadratic programming, which is a mathematical programming method. From the optimized results, the characteristics of optimized design variables in both the laminar and turbulent flow regimes were clarified.