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TECHNICAL PAPERS

# Analysis of Tilting Effects and Geometric Nonuniformities in Micro-hydrostatic Gas Thrust Bearings

[+] Author and Article Information
C. J. Teo, Z. S. Spakovszky

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

For a $1mm$ radius thrust bearing with a nominal clearance of $3μm$ rotating at a design speed of $1.2×106rpm$, a (large) rotor tip deflection of $1.5μm$ gives rise to a direct-coupled hydrodynamic torque which is approximately $20%$ of the direct-coupled hydrostatic torque at a nominal supply pressure of $4atm$.

Since the thrust-bearing gap is $3μm$, the corresponding maximum tip deflection of the rotor is also $3μm$.

This corresponds to a normalized dynamic imbalance $χ=1.0$.

J. Turbomach 128(4), 606-615 (Feb 01, 2005) (10 pages) doi:10.1115/1.2219761 History: Received October 01, 2004; Revised February 01, 2005

## Abstract

The Massachusetts Institute of Technology (MIT) microengine rotors are supported by hydrostatic gas journal and hydrostatic gas thrust bearings. Due to the low length-to-diameter ratio of the devices, the thrust bearings play an important role in providing sufficient tilting stiffness to resist any tilting motion about the spinning axis of the rotor. The performance of the thrust bearings can be influenced by geometric nonuniformities such as thrust-bearing clearances and orifice diameters, and profiles which arise in the process of micro-fabrication. To enable stable high speed operation of the micro-devices, it is important to quantify these effects. Furthermore, a thrust-bearing analysis tool needs to be developed that is able to explore different thrust-bearing arrangements and configurations. In this work, an analytical model is established for analyzing the effects of rotor tilt and geometric nonuniformities in micro-hydrostatic gas thrust bearings for application to micro-turbomachinery. A previously developed model (Teo and Spakovszky, 2006, “Modeling and Experimental Investigation of Micro-hydrostatic Gas Thrust Bearings for Micro-turbomachines,” ASME J. Turbomach., 128, pp. 597–605) is generalized and extended for application to thrust bearings with orifices arranged in nonaxisymmetric configurations. As a consequence of rotor tilt or geometric nonuniformities, the flow through individual orifices of the thrust bearing becomes nonuniform. The orifice flows are in turn coupled to the hydrostatic pressure field in the thrust-bearing pad, and a Green’s function approach is adopted to solve the coupled system. The hydrodynamic thrust-bearing forces induced by the pumping action of the rotor rotation are determined by solving the Reynolds equation. The model is able to predict thrust-bearing tilting stiffness and variations in the thrust-bearing mass flow rates as a function of rotor tilting angle for a variety of orifice arrangements. The model can be applied to analyze the effects of nonuniformities in orifice diameter and the presence of clogged orifices on tilting and the concomitant reduction in tilting stiffness. In addition, the effects of orifice taper are analyzed using an influence-coefficient method for one-dimensional compressible, viscous flows. Results obtained for various taper ratios are presented and discussed. The model serves as a useful tool for specifying design tolerances during the fabrication of micro-hydrostatic gas thrust bearings and is used in the experiments to estimate the tilting angle of the rotor during operation.

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## Figures

Figure 1

Schematic illustration of three different configurations of hydrostatic thrust bearings: (a) baseline configuration, (b) hexagonal configuration, and (c) annular configuration

Figure 2

Schematic for two degrees-of-freedom rotordynamic model for pitch and yaw dynamics. (a) Rotor at rest. (b) Rotor spinning at speed ω.

Figure 3

Decoupled models for hydrostatic moments (left) and hydrodynamic moments (right)

Figure 4

Mass flow rate versus pressure drop across thrust-bearing orifice

Figure 5

Cross-coupled hydrodynamic torque comparison between incompressible analytical model and CFD calculations

Figure 6

Variation of thrust-bearing tilting stiffness with normalized tip deflection; baseline configuration

Figure 7

Normalized static pressure distribution on thrust-bearing pad for hexagonal thrust-bearing configuration: (a) untilted, (b) tilted

Figure 8

Variation of annular thrust-bearing axial stiffness with compressor rotor outlet static pressure

Figure 9

Variation in tip deflection and tilting stiffness with number of missing orifices

Figure 10

Effects of tapered orifices on thrust-bearing normalized stiffness

Figure 11

(a) Variation of tip deflection with rotational speed for different dynamic imbalance levels χ. (b) Variation of tip deflection with rotational speed for a rotor with normalized dynamic imbalance of 1.0 for different thrust-bearing supply pressures.

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