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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

# Effects of Bearing Stiffness Anisotropy on Hydrostatic Micro Gas Journal Bearing Dynamic Behavior

[+] Author and Article Information
L. X. Liu, Z. S. Spakovszky

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

The scaling law for hydrostatic stiffness is $(Khs)∕(poC)∝(L∕D)(C∕R)−2(Δp/po)$. For a derivation, see (9).

It can be shown that if $kxy$ and $kyx$ were of the same sign, the resulting root occurs at even higher frequency and shows a different dynamic behavior that does not constitute whirl instability.

The vertical dashed line indicates the simple whirl instability criterion for isotropic bearing configurations, $C∕R=2(L∕D)2$, established in (9).

J. Eng. Gas Turbines Power 129(1), 177-184 (Mar 01, 2004) (8 pages) doi:10.1115/1.2180813 History: Received October 01, 2003; Revised March 01, 2004

## Abstract

The high-speed microhydrostatic gas journal bearings used in the high-power density MIT microengines are of very low aspect ratio with an $L∕D$ of less than 0.1 and are running at surface speeds of order $500m∕s$. These ultra-short high-speed bearings exhibit whirl instability limits and a dynamic behavior much different from conventional hydrostatic gas bearings. The design space for stable high-speed operation is confined to a narrow region and involves singular behavior (Spakovszky and Liu, 2005, “Scaling Laws for Ultra-Short Hydrostatic Gas Journal Bearings  ,” ASME J. Vibr. Acoust., 127(3), pp. 254–261). This together with the limits on achievable fabrication tolerance, which can be achieved in the silicon chip manufacturing technology, severely affects bearing operability and limits the maximum achievable speeds of the microturbomachinery. This paper introduces a novel variation of the axial-flow hydrostatic micro gas journal bearing concept, which yields anisotropy in bearing stiffness. By departing from axial symmetry and introducing biaxial symmetry in hydrostatic stiffness, the bearing's top speed is increased and fabrication tolerance requirements are substantially relieved making more feasible extended stable high-speed bearing operation. The objectives of this work are: (i) to characterize the underlying physical mechanisms and the dynamic behavior of this novel bearing concept and (ii) to report on the design, implementation, and test of this new microbearing technology. The technical approach involves the combination of numerical simulations, experiment, and simple, first-principles-based modeling of the gas bearing flow field and the rotordynamics. A simple description of the whirl instability threshold with stiffness anisotropy is derived explaining the instability mechanisms and linking the governing parameters to the whirl ratio and stability limit. An existing analytical hydrostatic gas bearing model is extended and modified to guide the bearing design with stiffness anisotropy. Numerical simulations of the full nonlinear governing equations are conducted to validate the theory and the novel bearing concept. Experimental results obtained from a microbearing test device are presented and show good agreement between the theory and the measurements. The theoretical increase in achievable bearing top speed and the relief in fabrication tolerance requirements due to stiffness anisotropy are quantified and important design implications and guidelines for micro gas journal bearings are discussed.

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## Figures

Figure 1

Singular behavior of whirl instability limit for ultra-short hydrostatic micro-gas journal bearings at different levels of rotor unbalance (SEM photo by (8))

Figure 2

Elimination of singular behavior of whirl instability limit and extension of geometric design space for stable high-speed operation using bearing stiffness anisotropy in ultra-short hydrostatic micro gas journal bearings

Figure 3

Hydrostatic micro-gas bearing configuration with stiffness anisotropy (dimensions are not to scale)

Figure 4

Hydrostatic and hydrodynamic bearing forces for a bearing configuration with anisotropy in hydrostatic stiffness

Figure 5

Whirl ratio for isotropic and anisotropic bearing configurations as a function of C∕R and different levels of unbalance a∕Co. Anisotropic case: numerical solution result (solid line) compared to simple analytical solution (circles).

Figure 6

Stable operating range extension using bearing stiffness anisotropy

Figure 7

Effect of rotor side-load on whirl instability limit of an anisotropic bearing configuration

Figure 8

Effect of eccentricity due to rotor side-load on hydrostatic stiffness anisotropy ∣Kxx−Kyy∣ and hydrodynamic stiffness khd

Figure 9

Experimental verification of natural frequencies in an anisotropic bearing configuration. Measurements are marked by symbols (data by (18)), and the predictions using anisotropic gas bearing theory are marked by lines

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