Analytical model of bump-type foil bearings using a link-spring structure and a finite-element shell model

A complete analytical model of bump-type foil bearings taking into consideration the effects of four factors, i.e., the elasticity of bump foil, the interaction forces between bumps, the friction forces at the contact surfaces, and the local deflection of top foil, is presented in this investigation. Each bump is simplified to two rigid links and a horizontally spaced spring, the stiffness of which is determined from Castigliano's theorem. The interaction forces and the friction forces are coupled with the flexibility of bumps through the horizontal elementary spring. The local deflection of the top foil is described using a finite-element shell model and added to the film thickness to predict the air pressure with Reynolds' equation. The bump deflections of a strip with ten bumps calculated using the presented model under different load distributions are consistent with the published results. Moreover, the predicted bearing load and film thickness obtained from a foil bearing with a bump circumferential extend of 360 deg also agree very well with the experimental data, especially for predictions with a proper selection of radial clearance (preload of foil structure) and friction coefficients. In addition, the radial clearance and friction force variations in the foil bearing are noted to significantly change the performance of the foil bearing. The predictions demonstrate that the radial clearance of the foil bearing has an optimum value for the maximum load capacity.