Numerical Analysis of the Impact of Manufacturing Errors on the Structural Stiffness of Foil Bearings

The dynamic characteristics of foil bearings operating at high rotation speeds depend very much on the mechanical characteristics of the foil structure. For this reason, the stiffness and damping of the structure of foil bearings are problems that are the focus of many analyses. The mechanical characteristics of the foil structure (top and bump foil) are analyzed either by using a simple approach obtained for an isolated bump modeled as a beam or with more elaborate ones taking into account the three-dimensional nature of the bumps and their mutual interactions. These two kinds of models give different foil structure stiffness, with lower values for the simplified model. However, the published experimental results of the foil bearing structure tend to validate the simplified model. The present paper explains the differences between the simplified and the elaborate models by taking into account the manufacturing errors of the foil structure. A three-dimensional model based on the nonlinear theory of elasticity is developed. The model offers a unique insight into the way the bearing structure deforms when the rotor is incrementally pushed into the foil structure. Three realistic manufacturing errors, bump height, bump length, and radius of the bump foil, are analyzed. Bump height and length vary following a normal distribution with a given standard deviation while the radius of the bump foil is given a waviness form with an imposed peak-to-peak amplitude. Three to five cases were calculated for each kind of error. Results show that only the manufacturing errors of the bump height affect the stiffness of the foil structure by diminishing its values. Height errors of 20 mu m standard deviation (4% of the average bump height and 60% of the radial clearance) may induce a 40-50% reduction of the stiffness of the foil structure, i.e., in the range of the predictions of the simplified model.