Thermohydrodynamic Study of Multiwound Foil Bearing Using Lobatto Point Quadrature

The applications of foil air bearings have been extended for use in a wide range of turbomachineries with high speed and high temperature. Lubricant temperature becomes an important factor in the performance of foil air bearings, especially at high rotational speeds and high loads or at high ambient temperature. This study presents a thermohydrodynamic (THD) analysis of multiwound foil bearing, in which the Reynolds' equation is solved with gas viscosity as a function of temperature that is obtained from the energy equation. Lobatto point quadrature is utilized to accelerate the iteration process with a sparse mesh across film thickness. A finite element model of the foil is used to describe the foil elasticity. An iterative procedure is performed between the Reynolds equation, the foil elastic deflection equation, and the energy equation until convergence is achieved. A three-dimensional temperature prediction of air film is presented, and a comparison of THD to isothermal results is made to emphasize the importance of thermal effects. Finally, published experimental data are used to validate this numerical solution.