A study of thermohydrodynamic features of multi wound foil bearing using lobatto point quadrature

The applications of foil air bearings, which are recognized to be the best choice for oil free applications, have been extended for use in a wide range of turbo-miachineries 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 [1]. However, most of the published foil air bearing models were based on the isothermal assumption. This study presents a thermohydrodynamic analysis (THD) of Multi Wound Foil Bearing (MWFB), in which the Reynolds' equation is solved with the gas viscosity as a function of temperature that is obtained from the energy equation. Lobatto point quadrature, which was proposed by Elrod and Brewe [101 and introduced into compressible calculation by Moraru and Keith [15), 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 deformation equation and the energy equation, until the 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.