State of the Art and Dynamic Modelling of Gas Bearings For High Speed Turbomachinery Applications

Gas-film bearings play a crucial role in a multitude of engineering applications, offering advantages such as reduced friction, higher-speed operation, and simpler design than their liquid-film counterparts. This paper explores the current state of the art of gas-film lubrication and gas bearings, as well as a comprehensive study into the field of gas bearing modelling, with a specific emphasis on bump-foil bearings. First, a look is taken into mechanical rotor-bearing systems, as well as different types of bearings and their necessity in such systems. Next, a historical review of fluid dynamics and the subsequent advent of lubrication theory and gas-film bearing development is discussed. Furthermore, an exhaustive detailing of the geometrical and pressurizing mechanism categorizations of gas bearings is conducted. Here, emphasis is placed on compliant-surface dynamic (or selfacting) gas bearings, such as bump-foil bearings. A thorough look into the mathematical modelling of gas-film bearings is demonstrated, deriving the compressible Reynolds equation (the governing equation for gas-film lubrication) from the conservation of mass and momentum for the applicable flow domain. The energy and elastic deformation equations are also introduced, demonstrating their applicability to a bump-foil thrust bearing. A hydrodynamic (HD), thermohydrodynamic (THD), and thermo-elastohydrodynamic (TEHD) approach is shown for the mentioned bump-foil thrust bearing. Additionally, the importance of turbulence modelling, CFD, and FEM to gas bearings is made known. The importance of fast and effective dynamic gas bearing modelling during the design phase was discussed. A simple dynamic, functional gas bearing model was created using MATLAB, employing the MATLAB PDE Toolbox. The successful model accurately predicted the trends of pressure and top foil deformation for a constant rotor rotational speed, eccentricity ratio, and attitude angle, corresponding to those results published by Li et al. ([1]). There is a promising and exciting future for gas bearings, filled with opportunities for further innovation, making this area of study both relevant and essential for engineering advancements.

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