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TECHNICAL PAPERS

# Hydrostatic Gas Journal Bearings for Micro-Turbomachinery

[+] Author and Article Information
L. X. Liu, C. J. Teo, A. H. Epstein, Z. S. Spakovszky

Gas Turbine Laboratory, Department of Aeronautics and Astronautics,  Massachusetts Institute of Technology, Cambridge, MA 02139

Geometric asymmetries of the rotors are mostly due to local and global variations in etch depth and out-of-roundness effects are negligible. For a more detailed discussion see (14).

For large departures a numerical simulation of the full nonlinear equations of motion was conducted together with a stability analysis. The results show similar instability behavior such that the linearized stability treatment is suggested to be valid for the bearing operating conditions of interest.

The whirl amplitude of the rotor is negligible at very low speeds and the reference waveform is obtained from measurements at very low speed.

For devices with single wafer rotors, i.e. the micro-bearing rig, wafer misalignment does not yield additional imbalance. Wafer misalignment effects become an issue for multi-wafer rotor designs such as the rotor design of the micro-turbocharger (11).

J. Vib. Acoust 127(2), 157-164 (Aug 05, 2004) (8 pages) doi:10.1115/1.1897738 History: Received January 14, 2004; Revised July 26, 2004; Accepted August 05, 2004

## Abstract

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.

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## Figures

Figure 1

Schematic cross-section of micro-bearing rig with axial flow hydrostatic gas journal bearings

Figure 2

Flow field model for hydrostatic force (left) and hydrodynamic force (right)

Figure 3

Hydrodynamic pressure distribution for eccentricities ϵ=0.2 and ϵ=0.4

Figure 4

Response curves for three different levels of imbalance a=1, 2 and 3μm

Figure 5

Response curves and whirl instability limit for bearing differential pressure settings Δp=1.0, 2.0, 3.0, and 6 psi and an imbalance of a=1μm

Figure 6

Hydrodynamic force comparison between incompressible analytical short bearing solution and SPECTRES (3)

Figure 7

Experimental setup for dynamic imbalance measurements

Figure 8

Experimentally measured response curve for a bearing pressure difference Δp=2.0psi

Figure 9

Experimentally measured response curves for a bearing pressure differences Δp=1.0, 2.0, and 2.4 psi

Figure 10

Behavior of bearing pressure difference at constant bearing flow rate during acceleration to high speed

Figure 11

Comparison of experimentally measured natural frequencies and whirl instability limit with modeling results

Figure 12

Strategies to cross the natural frequency and bearing operating protocol for acceleration to high-speed

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