Structural Properties of Foil Bearings: A Closed-Form Solution Validated with Finite Element Analysis

Abstract

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.

KEY WORDS:

• Compliant Surface Bearings
• Foil Bearings
• Air Bearings
• Structural Stiffness
• Finite Element Analysis

ACKNOWLEDGEMENTS

This work was done under a research project funded by the Polish Ministry of Scientific Research and Information Technology from the budget available for scientific research in the years 2005-2008. The authors would like to thank the Ministry for the funding.

Review led by Waldek Dmochowski

Notes

¹It should be noted that several papers available in the literature (e.g., Le Lez et al. (11)) use the opposite bump foil orientation, with the left end of the bump foil attached to the foundation. The orientation used in this work was chosen to facilitate the model description.

²Because the problem is two-dimensional, all loading terms and reactions are understood to be per unit width of the bump strip (or, in other words, a unit bump width is assumed).

* h and R depend on L and θ: h = 0.5L tan(θ/2) and R = 0.5L/sin(θ)