The Application of the Arbitrary-Order Galerkin Reduction Method to the Dynamic Analysis of a Rotor With a Preloaded Single-Pad Foil-Air Bearing

The compressible Reynolds equation (RE) is typically integrated within a fully coupled dynamical foil-air bearings (FABs)-rotor system via spatial Discretization transformation, e.g., finite difference (FD), finite element (FE). An alternative way of integrating the RE is through Galerkin reduction (GR). The motivation for using GR is the computational benefit coming from the drastic condensation of the problem due to the elimination of the two-dimensional grid used for the air film in FD or FE. This paper presents a novel application of arbitrary-order GR to both nonlinear and linearized analyses of rotor systems supported by single-pad FABs with variable radial clearance (preload). Simulations using FD gave a close correlation with those using GR for all preloads, with discrepancies increasing as the preload approaches the nominal clearance (⁠$c$⁠). The simulations show that the preload has to exceed a certain level in order to delay the onset of instability speed (OIS), and significant delay in OIS and suppression of subsynchronous vibration is possible when the preload is comparable to $c$⁠. Experimental validation is provided.