Two-dimensional dynamic simulation of a continuous foil bearing

The objective of this paper is to present an integrated procedure which will analyse the dynamics of a foil bearing on elastic supports. A complete time-dependent Navier-Stokes formulation is used to solve for the interaction between the hydrodynamic effects of the fluid lubricant, the motion of the journal, and the deformable foil boundary. The elastic deformation of the foil and its supports are simulated by a finite element model. The steady state, the quasi-transient and the full transient dynamics of the foil-fluid-journal interaction are examined. For the steady state simulation, for a particular journal position, the fluid lubricant pressures are evaluated by means of a joint iterative scheme until convergence is achieved in both the fluid pressure and the corresponding foil deformation. For the quasi-transient case, the transient motion of the journal is calculated using a numerical integration scheme for the velocity and displacement of the journal. The deformation of the foil is calculated through numerical iteration in feedback mode in combination with the fluid film pressure generated by the journal motion, until convergence at every time step is achieved. For the full transient simulation, a parallel real-time integration scheme is used, at each time step, to evaluate simultaneously the new journal position and the new deformed shape of the foil.