Both AiResearch and Hamilton have modified the polyamide's basic formula and application process to suit their needs. The analysis of foil air bearings requires simultaneous solutions or iteration methods to solve foil elasticity equations and fluid hydrodynamic equations. Foil elasticity equations are nonlinear and involve large-deformation theory. A foil can deform as much as five times its own thickness. Hydrodynamic equations are nonlinear Reynolds equations with continuously changing boundary conditions.
Semiempirical methods seem to provide reasonable results.
Sufficient test data are collected by varying the geometrical parameters and test parameters of the bearing. Results are correlated using a multiple regression method. Then a model is prepared using coefficients of the multiple regression analysis. Hydrodynamic equations are solved using the preferred final geometry. An inverse method is used to design the foil geometry in the unloaded position.