Hydrostatic Gas Journal Bearings for Micro-Turbomachinery

Several years ago an effort was undertaken at MIT to develop high-speed rotating MEMS (Micro Electro-Mechanical Systems) using computer chip fabrication technology. To enable high-power density the micro-turbomachinery must be run at tip speeds of order $500m∕s$⁠, comparable to conventional scale turbomachinery. The high rotating speeds (of order 2 million rpm), the relatively low bearing aspect ratios $(L∕D<0.1)$ due to fabrication constraints, and the laminar flow regime in the bearing gap place the micro-bearing designs to an exotic spot in the design space for hydrostatic gas bearings. This paper presents a new analytical model for axially fed gas journal bearings and reports the experimental testing of micro gas bearings to characterize and to investigate their rotordynamic behavior. The analytical model is capable of dealing with all the elements of, (1) micro-devices, (2) dynamic response characteristics of hydrostatic gas bearings, (3) evaluation of stiffness, natural frequency and damping, (4) evaluation of instability boundaries, and (5) evaluation of effects of imbalance and bearing anisotropy. First, a newly developed analytical model for hydrostatic gas journal bearings is introduced. The model consists of two parts, a fluid dynamic model for axially fed gas journal bearings and a rotordynamic model for micro-devices. Next, the model is used to predict the natural frequency, damping ratio and the instability boundary for the test devices. Experiments are conducted using a high-resolution fiber optic sensor to measure rotor speed, and a data reduction scheme is implemented to obtain imbalance-driven whirl response curves. The model predictions are validated against experimental data and show good agreement with the measured natural frequencies and damping ratios. Last, the new model is successfully used to establish bearing operating protocols and guidelines for high-speed operation.