A simplified, new method for evaluating the nonlinear fluid forces in air bearings was recently proposed in [1]. The method is based on approximating the frequency dependent linearized dynamic coefficients at several eccentricities, by second order rational functions. A set of ordinary differential equations is then obtained using the inverse of Laplace Transform linking the fluid forces components to the rotor displacements. Coupling these equations with the equations of motion of the rotor lead to a system of ordinary differential equations where displacements and velocities of the rotor and the fluid forces come as unknowns. The numerical results stemming from the proposed approach showed good agreement with the results obtained by solving the full nonlinear transient Reynolds equation coupled to the equation of motion of a point mass rotor. However the method [1] requires a special treatment to ensure continuity of the values of the fluid forces and their first derivatives. More recently, the same authors [2] showed the benefits of imposing the same set of stable poles to the rational functions approximating the impedances. These constrains simplified the expressions of the fluid forces and avoided the introduction of false poles. The method in [2] was applied in the frame of the small perturbation analysis for calculating Campbell and stability diagrams. This approach enhances also the consistency of the fluid forces approximated with the same set of poles because they become naturally continuous over the whole bearing clearance while their increments were not. The present paper shows how easily the new formulation may be applied to compute the nonlinear response of systems with multiple degrees of freedom such as a flexible rotor supported by two air bearings.

This work presents the comparison between experimental and theoretical results obtained for three straight annular seals. One of the annular seals has smooth rotor and stator while the others have a textured stator; the textures are equally spaced shallow round holes, with two different depths. The experimental results were obtained on a test rig dedicated to the identification of the dynamic coefficients of high Reynolds bearings and annular seals. The test rig uses hot water (<50 °C) as a working fluid. Dynamic excitations imposed by piezoelectric shakers to the rotor enable the identification of dynamic coefficients via complex impedances. Theoretical results compared with experimental findings were obtained by numerically solving the “bulk flow” equations (film thickness averaged equations dominated by inertia effects). The numerical model was extensively validated for smooth annular seals but is less confident for textured surfaces. The present comparisons between experimental and numerical results enable to estimate the accuracy of the numerical model employed for the textured seals.

The present work presents the comparison between experimental and theoretical results obtained for three straight annular seals. One of the annular seals has smooth rotor and stator while the others have a textured stator; the textures are equally spaced shallow round holes, with two different depths. The experimental results were obtained on a test rig dedicated to the identification of the dynamic coefficients of high Reynolds bearings and annular seals. The test rig uses hot water (<50°C) as a working fluid. Dynamic excitations imposed by piezoelectric shakers to the rotor enable the identification of dynamic coefficients via complex impedances. Theoretical results compared with experimental findings were obtained by numerically solving the “Bulk Flow” equations (film thickness averaged equations dominated by inertia effects). The numerical model was extensively validated for smooth annular seals but is less confident for textured surfaces. The present comparisons between experimental and numerical results enable to estimate the accuracy of the numerical model employed for the textured seals.