Foil Bearing Design Guidelines for Improved Stability

Abstract

Experimental evidence in the literature suggests that foil bearing-supported rotors can suffer from subsynchronous vibration. While dry friction between top foil and bump foil is thought to provide structural damping, subsynchronous vibration is still an unresolved issue. The current paper aims to shed new light onto this matter and discusses the impact of various design variables on stable foil bearing-supported rotor operation. It is shown that, while a time domain integration of the equations of motion of the rotor coupled with the Reynolds equation for the fluid film is necessary to quantify the evolution of the rotor orbit, the underlying mechanism and the onset speed of instability can be predicted by coupling a reduced order foil bearing model with a rigid-body, linear, rotordynamic model. A sensitivity analysis suggests that structural damping has limited effect on stability. Further, it is shown that the location of the axial feed line of the top foil significantly influences the bearing load capacity and stability. The analysis indicates that the static fluid film pressure distribution governs rotordynamic stability. Therefore, selective shimming is introduced to tailor the unperturbed pressure distribution for improved stability. The required pattern is found via multiobjective optimization using the foil bearing-supported rotor model. A critical mass parameter is introduced as a measure for stability, and a criterion for whirl instability onset is proposed. It is shown that, with an optimally shimmed foil bearing, the critical mass parameter can be improved by more than two orders of magnitude. The optimum shim patterns are summarized for a variety of foil bearing geometries with different L/D ratios and different degrees of foil compliance in a first attempt to establish more general guidelines for stable foil bearing design. At low compressibility (Λ < 2), the optimum shim patterns vary little with bearing geometry; thus, a generalized shim pattern is proposed for low compressibility numbers.

The Effect of Rounding in Bump Foil Structure on the Dynamic Performance of Foil Journal Bearings

“…9. As a summary, the results suggest that increasing the structural stiffness has a beneficial effect on stability for foil journal bearings, which is consistent with the study result conducted by Schiffmann [20]. However, it is noted that a foil bearing with zero compliance defeats the purpose and is not to be compared as a rigid cylindrical bearing is introduced.…”

The Role of Reynolds Number Effect and Tip Leakage in Compressor Geometry Scaling at Low Turbulent Reynolds Numbers

“…This effect describes the non linear dependency of surface friction on Reynolds number. Advancements in dynamic gas bearing technology [1,2], made it possible to realise small scale turbomachines which operate in such regimes. One field of application is domestic heating, where Schiffmann [3][4][5] showed that turbo compressors can provide superior heat pump performance compared to state of the art technology such as scroll, screw or piston compressors.…”

A Review of Grooved Dynamic Gas Bearings

“…With the increasing demand for lighter, more compact, economical, and environmentally-friendly energy conversion systems, gas bearings play a crucial role in oil-free turbomachinery [16][17][18]. Since the first gas-bearing supported turbomachinery delivered by UK Atomic Energy Establishment in 1958, gas bearings have demonstrated their advantages in various applications such as in turbo-compressors, gas turbines and turbochargers/expanders [4,[19][20][21]. As shown in Figure 1, typical applications scale from MEMS-sized gas turbines [20,22], to 10-20 mm tip diameter fuel-cell (FC) application [23], 10-30 mm tip diameter turbomachinery applied for heating, ventilation or air conditioning (HVAC) [1,24,25], and to large size systems such as turbochargers and air cycle machines [26].…”