Compliant Foil Bearing Structural Stiffness Analysis: Part I—Theoretical Model Including Strip and Variable Bump Foil Geometry

Abstract

This paper presents a theoretical model of corrugated foil strip (bump foil) deformation in compliant foil bearings and dampers. The friction forces between bump foils and the housing or the top foil, local interaction forces, variable load distributions, and bump geometries are taken into consideration. Following the trend of earlier published experimental data, the bumps near the fixed end have a much higher predicted stiffness (lower deflection) than those near the free end. Higher friction coefficients tend to increase stiffness and may pin down bumps near the fixed end. An increase in the friction coefficient between the top foil and the bump is a more effective method of achieving both Coulomb damping and higher stiffness. In addition to bump geometry, the load distribution profile greatly influences bump stiffness. A follow-up paper will present the experimental verification and discuss the comparison between theoretical and experimental results.

Numerical and experimental investigation of bump foil mechanical behaviour

“…They predicted that the dynamic coefficients were anisotropic and highly non-linear and that the stiffness and damping was dependant on the pad angle. Bump stiffness under different load distributions along the bump strip was also investigated [1] and the theoretical prediction followed the trend of earlier experimental data, regarding the higher stiffness of the bumps located at the fixed end compared to those closer to the free end. Lower friction coefficients was found to make bumps softer, whereas an increment in friction increased the stiffness and could result in pinned bump ends for the bumps close to the fixed end.…”

“…Then it would increase linearly with the movement of the contact point, which is obviously wrong. However, by choosing the stiffness k to be nonlinear and softening, the reaction force versus deflection can be made constant and fulfilling (1). Choosing a proper stiffness function for k, can even eliminate the problem of determining the magnitude of the friction force F μ when there is no motionẋ r = 0.…”

“…Ku and Heshmat [7,8] performed a experimental investigation of the dynamic behaviour of a compliant foil bearing and compared the results to the mathematical model presented in [1,2,3]. Agreement between the theoretical and experimental results was reasonably good.…”

“…Ku and Heshmat [1,2,3] presented an analytical mathematical bump foil model based on the work of Walowit [4]. The model considered a circular bearing and took into account the effect of the pad location.…”

Experimental and theoretical analysis of a rigid rotor supported by air foil bearings

“…A large amount of the work related to the foil structure modelling has been purely theoretical. However the structural models presented by Ku and Heshmat [22][23][24] were compared to experimental data [25,26] showing reasonably good agreement. Theoretical and experimental investigations entirely focused on the bump foil mechanical behaviour were performed by Le Lez et al [17,18] and Larsen et al [27].…”