A finite differences approach for fluid-structure interaction in a hydrostatic compliant thrust bearing

It is well known since the pioneering work of Dowson and Castelli that load capacity increases in compliant (elastic pad) hydrostatic bearings, compared to their rigid counterparts. In a recently published paper, a new design solution of a flexible pad hydrostatic bearing was proposed and analysed theoretically. A simplified analytical model was proposed for the fluid-structure interaction. The model was based on two important simplifications: linear pressure distribution on the bearing land, used to calculate the deformation of the pad, and parabolic variation of film thickness in the Reynolds equation. The analysis was made for isothermal conditions and constant pressure in the recess. This new approach relaxes the two simplifications by considering a linearly elastic model for the flexible pad and including its deformation in the Reynolds equation. A finite differences scheme is proposed for both the fluid flow and elastic deformation, considering the flexible plate simply supported. The consistency and convergence of the iterative solution are analysed, and comparisons with previous analytical solutions are shown. These results show the limits of the accuracy of the simplified analytical model and allow the selection of the design parameters of a test rig.