This paper presents a generic technique for the transient nonlinear dynamic analysis (TNDA) and the static equilibrium stability analysis (SESA) of a turbomachine running on foil air bearings (FABs). This technique is novel in two aspects: (i) the turbomachine structural model is generic, based on uncoupled modes (rotor is flexible, non-symmetric and includes gyroscopic effects; dynamics of support structure can be accommodated); (ii) the finite-difference (FD) state equations of the air films are preserved and solved simultaneously with the state equations of the foil structures and the state equations of the turbomachine modal model, using a readily available implicit integrator (for TNDA) and a predictor-corrector approach (for SESA). An efficient analysis is possible through the extraction of the state Jacobian matrix using symbolic computing. The analysis is applied to the finite-element model of a small commercial automotive turbocharger that currently runs on floating ring bearings (FRBs) and is slightly adapted here for FABs. The results of SESA are shown to be consistent with TNDA. The case study shows that, for certain bearing parameters, it is possible to obtain a wide speed range of stable static equilibrium operation with FABs, in contrast to the present installation with FRBs.
INTRODUCTIONThe dynamics of FAB turbomachinery are governed by the interaction between the turbomachine, air films and foil structures. Due to the computational burden involved, the solution process has been subject to simplifications to three aspects of the problem: The compressible Reynolds equation (RE) governing the air film pressure distribution; The structural model of the turbomachine; The foil structure model. This paper addresses the current simplifications to the first two aspects.