A new Galerkin Reduction approach for the analysis of a fully coupled foil air bearing rotor system with bilinear foil model

The foil air bearing (FAB) is a key enabler of the rapidly expanding technology of oil-free turbomachinery. However, it presents a formidable computational challenge due to the in-tricacy of the mathematical modelling of the nonlinear interaction between the foil structure, air film, and rotor. Galerkin Reduction (GR) allows the integration of the compressible Reynolds Equation within a FAB-rotor model without the need for spatial discretisation, resulting in a considerable gain in computational efficiency relative to grid/mesh-based methods like Finite Difference (FD) and Finite Element (FE). GR has so far been limited to a simple model that ignores the detachment of the top foil from the underlying foil. A new GR approach is developed to overcome this limitation. Following transient and static equilibrium analyses of the nonlinear system, Jacobian-based linearization is used to extract the full mode set, Campbell diagram and linear stability map. The use of GR instead of FD reduced the computational time by over 50% and required 20-60 times less memory for saving the results, without compromising accuracy and reliability. In particular, Jacobian-based linearization using GR retains the ability to detect in-stabilities (like top foil flutter) that are beyond the capability of the traditional linear force co-efficients method.

Automated summary

The foil air bearing (FAB) is crucial for oil-free turbomachinery but is computationally challenging. Galerkin Reduction (GR) allows efficient integration of compressible Reynolds Equation without spatial discretisation. A new GR approach has been developed to overcome limitations, improving computational efficiency without compromising accuracy and reliability.