Gas-dynamic foil bearing model

A method is developed to calculate the characteristics of gas-dynamic bearings of rotors of gas-turbine engines and gas-turbine units. The method takes into account the contact interactions between the shaft journal, the fluid film, and the elastic bearing elements. The problem of multidisciplinary mathematical simulation of the elastic gas-dynamic contact is formulated and solved to determine the parameters of lubrication and deformations of the shaft and bearing. The considerable nonlinearity of the problem is governed by the equations describing the fluid flow in the bearing and the features of the elastic contact during deformation of the bearing elements. The calculation of the fluid-film flow in the bearing is based on the solution of the nonlinear two-dimensional Reynolds equation for a compressible fluid. The method of consecutive loading with error correction that within the interval prompts to the linearized Reynolds equation solution for fluid film pressure increment is used. The results of calculation of the fluid-flow parameters in the clearance between the shaft and the bearing are compared with the results obtained by solving the fluid-flow problem in a bearing modeled with the Navier-Stokes equations with the STAR-CD software. The stress-strain state of the elastic bearing elements is studied with the finite element model taking into account the contact interaction between the foils themselves and with the bearing race. The pressure distribution and the clearance in the shaft are determined iteratively by the coupled solution of the fluid flow and bearing foil deformation problems. Bearing stiffness characteristics, its carrying force and attitude angle are determined versus shaft journal displacement value and direction. It is shown that the stiffness characteristics of the bearing depend on the direction of displacement of the shaft journal in the bearing. The influence of the bearing elastic element deformations on the support load carrying capacity and the stiffness characteristics are studied. The results yielded by the calculations with the developed method are compared with those when the fluid-layer thickness in the bearing was calculated using the analytical model proposed by H. Heshmat and co-authors.