One major challenge for the successful operation of high-power-density micro-devices lies in the stable operation of the bearings supporting the high-speed rotating turbomachinery. Previous modeling efforts by Piekos (2000, “Numerical Simulation of Gas-Lubricated Journal Bearings for Microfabricated Machines,” Ph.D. thesis, Department of Aeronautics and Astronautics, MIT), Liu et al. (2005, “Hydrostatic Gas Journal Bearings for Micro-Turbo Machinery,” ASME J. Vib. Acoust., 127, pp. 157–164), and Spakovszky and Liu (2005, “Scaling Laws for Ultra-Short Hydrostatic Gas Journal Bearings,” ASME J. Vib. Acoust. 127, pp. 254–261) have focused on the operation and stability of journal bearings. Thrust bearings play a vital role in providing axial support and stiffness, and there is a need to improve the understanding of their dynamic behavior. In this work, a rigorous theory is presented to analyze the effects of compressibility in micro-flows (characterized by low Reynolds numbers and high Mach numbers) through hydrostatic thrust bearings for application to micro-turbomachines. The analytical model, which combines a one-dimensional compressible flow model with finite-element analysis, serves as a useful tool for establishing operating protocols and assessing the stability characteristics of hydrostatic thrust bearings. The model is capable of predicting key steady-state performance indicators, such as bearing mass flow, axial stiffness, and natural frequency as a function of the hydrostatic supply pressure and thrust-bearing geometry. The model has been applied to investigate the static stability of hydrostatic thrust bearings in micro-turbine generators, where the electrostatic attraction between the stator and rotor gives rise to a negative axial stiffness contribution and may lead to device failure. Thrust-bearing operating protocols have been established for a micro-turbopump, where the bearings also serve as an annular seal preventing the leakage of pressurized liquid from the pump to the gaseous flow in the turbine. The dual role of the annular pad poses challenges in the operation of both the device and the thrust bearing. The operating protocols provide essential information on the required thrust-bearing supply pressures and axial gaps required to prevent the leakage of water into the thrust bearings. Good agreement is observed between the model predictions and experimental results. A dynamic stability analysis has been conducted, which indicates the occurrence of instabilities due to flow choking effects in both forward and aft thrust bearings. A simple criterion for the onset of axial rotor oscillations has been established and subsequently verified in a micro-turbocharger experiment. The predicted frequencies of the unstable axial oscillations compare well with the experimental measurements.
Discussion: “Static and Dynamic Performance of Externally Pressurized Fluid Film Journal Bearings in the Turbulent Regime” (Heller, S., 1974, ASME J. Lubr. Technol., 96, pp. 381–389)