A New Structural Bump Foil Model with Application from Start-Up to Full Operating Conditions

The paper presents a new structural bump foil model that can handle all operating conditions from start-up to full speed. The model is based on a non-linear contact algorithm with friction and gaps. The model considers the gaps between the bump foil and the bearing casing, between the bump foil and the top foil and between the rotor and the top foil. Thus, any numerical interference between the rotor and the top foil is avoided. A mixed lubrication model is used for the thin film pressures. Following this algorithm, contact pressures appear if the film thickness is less than three times the equivalent roughness of the rotor and of the top foil. Fluid pressures are calculated from numerical solutions of Reynolds equation while contact pressures, if present, are calculated with the model of Greenwood and Williamson. The model is validated by comparisons with the experimental results obtained for start-up operating conditions of a first generation foil bearing of 38.1 mm diameter with static loads of 10 N to 50 N. Theoretical predictions of the start-up torque and take-off speed compare well with experimental results. It is also shown how manufacturing bump height errors can explain the differences between theoretical and experimental predictions. Further validations are presented for the same bearing operating at high speeds (30, 45 and 55 krpm) and heavy static loads (up to 200 N). The calculated minimum film thickness and attitude angle are compared with experimental data from the literature.