In meeting goals for higher energy density and efficiency for micro-turbomachinery, there is a trend towards higher operating speeds. Gas-lubricated foil bearings historically have provided a key enabling technology for this class of machinery due to their low power loss, high-speed capability in very low to very high temperatures, and process compatibility. Foil bearings have demonstrated very good performance in many rigid rotor applications. To meet future needs, however, micro-turbomachinery will be required to operate above a bending critical speed where shaft flexibility plays a dominant role. Some successes with foil bearing rotors operating in this region have been achieved, indicating that foil bearings can be built with the required dynamic characteristics. However, these efforts have been primarily experimentally driven, and published results indicate attention to such issues as bearing internal friction, rotor balance, rate of rotor speed change, and bearing location are crucial to success. This work presents an analytical examination of these issues. Using a modal solution for the bending critical mode of a simple, symmetric rotor, various relationships between foil bearing parameters and machine design elements are explored.

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