Scaling Laws for Radial Clearance and Support Structure Stiffness of Radial Foil Bearings

Design and analysis of foil bearings involve consideration to various physical aspects such as fluid pressure, structural deformation, and heat generation due to viscous effects within the bearing. These complex physical interactions are mathematically governed by highly nonlinear partial differential equations. Therefore, foil bearing design involves detailed calculations of flow fields (velocities, pressures), support structure deflections (structural compliance), and heat transfer phenomena (viscous dissipation in the fluid, frictional heating, temperature profile, etc.). The computational effort in terms of time and hardware requirements make high level engineering analyses tedious which presents an opportunity for development of rule of thumb laws for design guidelines. Scaling laws for bearing clearance and support structure stiffness of radial foil bearings of various sizes are presented in this paper. The scaling laws are developed from first principles using the scale invariant Reynolds equation and support structure deflection equation. Power law relationships are established between the (1) radial clearance and bearing radius and (2) support structure stiffness and bearing radius. Simulation results of static and dynamic performance of various bearing sizes following the proposed scaling laws are presented.