MEMS turbomachinery rotordynamics : modeling, design and testing

Abstract

One of the major challenges encountered for the successful operation of high-power-density micro-devices lies in the stable operation of the bearings supporting the high-speed rotating machinery. This thesis presents the analysis, design, microfabrication, testing and operation of high speed micro-hydrostatic gas bearings for microturbomachinery in power-MEMS applications. A novel turbine driven microbearing test device for demonstrating repeatable high-speed gas bearing operation was designed, microfabricated and tested. The new microbearing test device incorporates numerous features, including a four plena journal bearing feed system enabling both isotropic and anisotropic journal bearing operation, labyrinth seals for reducing rotordynamic coupling, a redesigned turbine for satisfying power requirements, reinforced thrust bearing structural design, a novel rotor fabrication technology for achieving low radial imbalance and a symmetric feed system to avoid rotor sideloading arising from pressure or flow non-uniformities. 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 microturbomachines.

(cont.) Operating protocols for ensuring thrust bearing static stability have been established and successfully demonstrated on several micro-devices in the MIT Microengine Project. In addition, a simple and useful dynamic stability criterion has been identified: Dynamic instability occurs when the flow through both thrust bearings chokes. A-priori dynamic stability predictions were subsequently verified experimentally for the first time on a micro-turbocharger. A generalized Green's function approach has been successfully implemented for analyzing tilting effects and geometric non-uniformities in micro-hydrostatic gas thrust bearings. The effects of a non fully-developed circumferential flow in low length-to-diameter ratio (L/D << 1) micro-hydrostatic journal bearings are analyzed for the first time. Effects on journal bearing whirl stability and viscous power dissipation are quantified using a simple analytical model and CFD calculations. A dimensionless parameter characterizing the ratio of the flow-through time of the axial hydrostatic flow to the viscous diffusion time was identified to govern the evolution of the circumferential flow field. Singular behavior of the stability boundary or whirl-ratio occurs when the flow through time of the axial hydrostatic flow is approximately half the characteristic viscous diffusion time.

(cont.) Operating conditions for high speed, stable journal bearing operation can thus be ascertained. Experimental techniques and data reduction schemes facilitating the evaluation of key journal bearing rotordynamic information such as the stiffness, natural frequency and damping ratio, as well as the imbalance of the rotor have been successfully implemented. Imbalance-driven whirl response curves for providing an improved understanding of the rotordynamic behavior of micro-hydrostatic gas journal bearings have been obtained for the first time. Effects of journal bearing width and anisotropy are systematically investigated on the redesigned microbearing test device. For low levels of journal differential pressures DP, high whirl ratios ranging between 20 and 40 were achieved. These whirl-ratios were one order of magnitude higher than those encountered in macro-scale journal bearings. Almost all devices tested anisotropically at high values of DP achieved speeds in excess of 1 million rpm. The improvements in bearings and seals design, the high reliability of the novel microfabrication processes, and the repeatability and successful implementation of the operating protocols were vindicated.

(cont.) A first-of-a-kind controlled high speed operation up to 70% of the design speed was also demonstrated. This corresponds to a rotation rate of 1.7 million rpm, a rotor tip speed of 370 m/s and a DN number of 7 million mm-rpm. The technical feasibility of high-speed gas bearings required for achieving high power densities in MEMS-based micro-turbomachinery has thus been experimentally demonstrated.