Response Surface Mapping and Multi-Objective Optimization of Tilting Pad Bearing Designs

Fluid film bearings for turbomachinery are designed to support the loads applied by the rotor system, often at high speeds when power loss in the bearing becomes significant and bearing temperatures can reach levels that can be detrimental to the long-term reliability of the support system. These requirements of supportive bearings require an intimate understanding of how bearing design variables affect their overall performance. Ideal bearings minimize power loss to increase machine efficiency and maintain low operating temperatures to ensure long-term reliability while meeting other design criteria such as minimum film thickness to provide proper support and avoiding high fluid pressures that can be harmful to the bearing structure. However, real world designs are often forced to sacrifice some of these design goals in order to preserve others. Therefore, further understanding of the relative opportunity costs associated with optimizing the bearing design with differently weighted performance metrics and their relationships to bearing design variables is invaluable to design engineers. This study explores the impact of eight bearing design variables on the performance of two tilting pad journal bearings supporting an eight-stage centrifugal compressor using design of experiments techniques applied to an established thermoelastohydrodynamic (TEHD) bearing model of tilting pad bearing performance. The bearing design variables analyzed include the radial clearance, pad arc spacing, pad axial length, pivot offset, preload, working fluid viscosity and viscosity index, and the number of pads. Each of the design variables — excluding the number of pads which was realistically constrained — were first varied over five levels each in a central composite design. These central composite designs were repeated for each of three values for number of pads. The responses obtained from the TEHD numerical simulations for each bearing design point were power loss, maximum pad temperature, minimum film thickness, and maximum fluid film pressure. The results from the central composite studies were fit with a multivariate least-squares regression model and a secondary series of experimental design studies were simulated around potential optimum design points to obtain a learning set to initialize direct optimization methods. Two direct multi-objective optimization methods, a sequential quadratic programming method and a multi-island genetic algorithm, were performed using Isight, a commercial software. A range of weighting parameters were selected for the optimization functions to find bearing designs that minimized power loss and pad temperature while maintaining pressure and film thickness criteria within acceptable design ranges for fluid film bearings. The resulting optimum design points allowed for a comparison between the design optimization approaches. The various strengths and weaknesses of the different methods are discussed. This study demonstrates how designers can use these approaches to view the relationships between design variables and important performance metrics to design better bearings for a wide range of applications.