Theoretical analysis and numerical simulation of oil lubricated foil bearing with elastic supported bump foil structure

The oil lubricated multi-leaf foil bearing is developed to meet the demand of high rotating speed for hydraulic turbopump, where the lubricated oil is easy to obtain. For the stability of this kind oil lubricated foil bearing needs to be guaranteed, the bearing with elastic supported bump foil structure is proposed to improve the performance of foil bearing. Theoretical analysis and numerical simulation is carried out in this paper. The film thickness expression of multileaf foil bearing is established for the cases with and without top foil deformation. The total flexibility matrix considering elastic supported bump foil structure is developed based on Castigliano's theorem. By employing the Reynolds boundary condition, the oil cavitation effect is presented. The established flexibility matrix is substituting into classical incompressible Reynolds equation, then the deformation equation of the foil and Reynolds equations are solved coupling by successive over relaxation method. The static characteristics such as pressure distribution, bearing load and static equilibrium position are obtained. By employing the perturbation method to Reynolds equations and foil deformation equation, the dynamic characteristics of multi-leaf foil bearing with elastic supported bump foil structure are acquired. The stability of the bearing is analyzed and compared with other type bearings by Routh-Hurwitz method. The effects of bearing load and sommerfeld parameter on the stiffness and damping coefficients are studied. The results indicate that the performance of foil bearing with elastic supported bump foil structure is improved and this kind bearing is suitable for high rotating speed application.