Link-Spring Model of Bump-Type Foil Bearings

The field experiences of gas foil bearings (GFBs) from the 1960s prove that GFBs offer several advantages over traditional oil bearings and rolling element bearings. They have the potential to be applied in a wide spectrum of turbomachinery. Bump-type foil bearings, which are considered as the best structure for GFBs, can be simply described as a hydrodynamic bearing utilizing the ambient air as the lubricant and a smooth shell supported by a corrugated bump foil as the bearing surface. However, the performance predictions of bump-type foil bearings are difficult due to mechanical complexity of the support elastic structure, especially for the effects of four factors, elasticity of bump foil, interaction forces between bumps, friction forces at contact surfaces, and local deflection of top foil. In this investigation, an analytical model of bump-type foil bearings considering the effects of all above factors is presented. In this model, each bump of the bump strip is simplified to two rigid links and a horizontally spaced spring, whose stiffness is determined from Castigliano’ theorem. Then, interaction forces and friction forces can be coupled with the bump flexibility though the horizontal elementary spring. The local deflection of top foil is described using a Finite Element model and added to the film thickness for the pressure prediction with the Reynolds’ equation. The bump deflections of a strip with ten bumps under different load distributions are calculated with the presented model and the predictions show consistency with published results. Moreover, the predicted bearing load and film thickness of a full bump-type foil bearing using this model are very close to the experimental data. Also, radial clearance and friction force variations in the foil bearing are noted to change the stiffness of bump significantly. And the predictions from the calculation with a proper selection of radial clearance and friction coefficients show extremely good agreement with the experimental data. The assumption of minimum reachable film thickness is based on experimental data to determine the load capacity of bearing. The results demonstrate that the radial clearance of foil bearing has an optimum value for the maximum load capacity.