Gas film bearings offer unique advantages enabling successful deployment of high-speed micro-turbomachinery. Current applications encompass micro power generators, air cycle machines and turbo expanders. Mechanically complex gas foil bearings are in use; however, their excessive cost and lack of calibrated predictive tools deter their application to mass-produced oil-free turbochargers, for example. The present investigation advances the analysis and experimental validation of hybrid gas bearings with static and dynamic force characteristics desirable in high-speed turbomachinery. These characteristics are adequate load support, good stiffness and damping coefficients, low friction and wear during rotor startup and shutdown, and most importantly, enhanced rotordynamic stability at the operating speed. Hybrid (hydrostatic/hydrodynamic) flexure pivot-tilting pad bearings (FPTPBs) demonstrate superior static and dynamic forced performance than other geometries as evidenced in a high speed rotor-bearing test rig. A computational model including the effects of external pressurization predicts the rotordynamic coefficients of the test bearings and shows good correlation with measured force coefficients, thus lending credence to the predictive model. In general, direct stiffnesses increase with operating speed and external pressurization; while damping coefficients show an opposite behavior. Predicted mass flow rates validate the inherent restrictor type orifice flow model for external pressurization. Measured coast down rotor speeds demonstrate very low-friction operation with large system time constants. Estimated drag torques from the gas bearings validate indirectly the recorded system time constant.Copyright © 2006 by ASME

Hybrid Flexure Pivot-Tilting Pad Gas Bearings: Analysis and Experimental Validation

Micro-turbomachinery demands gas bearings to ensure compactness, light weight, and extreme temperature operation. Gas bearings with large stiffness and damping, and preferably of low cost, will enable successful commercial applications. Presently, tests conducted on a small rotor supported on flexure pivot hydrostatic pad gas bearings (FPTPBs) demonstrate stable rotordynamic responses up to 100,000 rpm (limit of the drive motor). Test rotor responses show the feed pressure raises the system critical speed (increase in bearing direct stiffness) while the viscous damping ratio decreases. Predictions correlate favorably with experimentally identified (synchronous) direct stiffness bearing force coefficients. Identified experimental gas bearing synchronous damping coefficients are 50% or less of the predicted magnitudes, though remaining relatively constant as the rotor speed increases. Tests without feed pressure show the rotor becomes unstable at ∼81 krpm with a whirl frequency ratio of 20%. FPTPBs are mechanically complex and more expensive than cylindrical plain bearings. However, their enhanced stability characteristics and predictable rotordynamic performance makes them desirable for the envisioned oil-free applications in high speed micro-turbomachinery.

Rotordynamic Performance of Flexure Pivot Hydrostatic Gas Bearings for Oil-Free 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 500 m/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 microbearing 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.

Hydrostatic Gas Journal Bearings for Micro-Turbomachinery

This paper introduces flexure pivot tilting pad gas bearings with pad radial compliance for high-speed oil-free microturbomachinery. The pad radial compliance was for accommodation of rotor centrifugal growth at high speeds. Analytical equation for the rotor centrifugal growth based on plane stress model agreed very well with finite element method results. Parametric studies on pivot offset, preload, and tilting stiffness were performed using nonlinear orbit simulations and coast-down simulations. Higher preload and pivot offset increased both critical speeds of the rotor-bearing system and onset speeds of instability due to the increased wedge effect. Pad radial stiffness and nominal bearing clearance were very important design parameters for high-speed applications due to the physically existing rotor centrifugal growth. From the series of parametric studies, the maximum achievable rotor speed was limited by the minimum clearance at the pad pivot calculated from the rotor growth and radial deflection of pads due to hydrodynamic pressure. Pad radial stiffness also affects the rotor instability significantly. Small radial stiffness could accommodate rotor growth more effectively but deteriorated rotor instability. From parametric studies on a bearing with 28.5 mm in diameter and 33.2 mm in length, optimum pad radial stiffness and bearing clearance are 1-2 X 10 7 N/m and 35 μm, respectively, and the maximum achievable speed appears 180 krpm. The final design with suggested optimum design variables could be also stable under relatively large destabilizing forces.

Design of Flexure Pivot Tilting Pads Gas Bearings for High-speed Oil-Free Microturbomachinery

Theoretical model of flexure pivot tilting pad gas bearings with metal mesh dampers in parallel

Further advancements in high performance turbomachinery operating at extreme temperatures mandate the development of gas film bearing technology to procure compact units with improved efficiency in an oil-free environment. A novel finite element (FE) procedure to model thin film gas bearings follows. The FE model incorporates a novel class of high order shape functions ensuring computational efficiency and numerical stability even at (infinity) high speed bearing numbers. The method does not rely on cumbersome schemes for evaluation of advection flow terms in the Reynolds equation nor introduces artificial diffusion into the numerical solution. A computational FE program forwards predictions for the static performance and dynamic force coefficients of an externally pressurized gas bearing for ready application to an automotive turbocharger. The predictions show the strong effects of excitation frequency on the dynamic force coefficients and the onset of a hydrodynamic instability at moderately low rotor s...

Finite element analysis of gas bearings for oil-free turbomachinery

Current applications of gas film bearings in high-speed oil-free micro-turbomachinery (<0.4 MW) require calibrated predictive tools to successfully deploy their application to mass-produced systems, for example oil-free turbochargers. The present investigation details the linear rotordynamic analysis of a test rotor supported on externally pressurized gas bearings. Model predictions are compared with the test rotordynamic response determined through comprehensive experiments conducted on a small rotor supported on three lobed hybrid (hydrostatic/hydrodynamic) rigid gas bearings. Predictions for the rotor-bearing system synchronous response to imbalance show good agreement with measurements during rotor coast downs, and manifest a decrease in damping ratio as the level of external pressurization increases. The rotor-bearing eigenvalue analysis forwards natural frequencies in accordance with the measurements, and null damping ratios evidence the threshold speeds of rotordynamic instability. Estimated whirl frequency ratios are typically 50% of rotor speed, thus predicting sub synchronous instabilities at lower rotor speeds than found experimentally when increasing the magnitude of feed pressurization. Rationale asserting the nature of the discrepancies calls for further analysis.Copyright © 2003 by ASME

Deborah A. Wilde

Papers

Finite element analysis of gas bearings for oil-free turbomachinery

Comparison of Rotordynamic Analysis Predictions With the Test Response of Simple Gas Hybrid Bearings