Fluid film thickness in a compliant foil bearing is greatly influenced by the deflection of the bearing structure. Therefore, in order to properly model performance of a foil bearing, it is mandatory that the deflection of the compliant bearing structure due to the generated hydrodynamic pressure is determined accurately. This article proposes an easy-to-use two-dimensional model, which takes into account detailed geometry of the bump foil-top foil assembly and the interaction between bumps and which can predict the bearing deflection and stresses due to an arbitrary pressure load. The proposed model is first validated using a finite element analysis and the results available in the literature and then used to conduct a parametric study investigating the influence of bump foil geometry, the coefficient of friction between the bearing components, and the type of loading on the structural properties of the bearing. The most important parameters are also identified. The proposed analytical model is completely algebraic and can be easily implemented using any programming language, a spreadsheet, or even a calculator. The resulting solution can also be coupled with the appropriate hydrodynamic model to predict static performance of compliant foil bearings.

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The present paper, which consists of two parts, proposes models of fluid flow in grinding with nonporous wheels. In this first part, a smooth wheel is employed instead of a rough grinding wheel to simplify the analysis. Fluid flow is investigated for laminar and turbulent regimes using the classical Reynolds equation of lubrication and a modified Reynolds equation for turbulent flows, respectively. The applicability of the proposed models is discussed and verified experimentally in terms of the developed hydrodynamic pressure. It is found that the classical Reynolds equation reliably predicts the hydrodynamic pressure if the Reynolds number Re (based on the minimum gap size) is lower than about 300. Experimental results for 300<Re<1500 agree with the proposed turbulent flow model. This suggests that the flow in this range of Re is turbulent, and that the fluid inertia is negligible. The influence of wheel roughness is investigated in Part II.

First gas-lubricated compliant foil bearings (CFBs) were built in the 1950s. Due to their significant advantages, such as oil-free operation, good tolerance to bearing misalignment and very low maintenance, they have been penetrating the bearing applications for high speed compressors, air-cycle machines and gas turbines. The work presented here investigates a novel idea of water-lubricated compliant foil bearings, which could be used in applications where environmentally friendly lubrication is desired, for example in hydroelectric turbines or water pumps. Experimental results collected for three prototype water-lubricated foil journal bearings are presented. The tests were conducted under steady radial load and with the sliding speed varied incrementally. A sequence of design improvements is presented, with the best bearing demonstrating friction coefficient of about 0.01 at the sliding speed of about 4 m/s and the radial load of about 300 kPa. Encountered difficulties, research methodology and the testing equipment are also described.