Performance of Heavily Loaded Textured Gas Foil Bearings Based on the Multigrid Method

Abstract Surface texturing technology is a novel avenue for enhancing gas foil bearing performance. For the cases of heavily loaded foil bearing, the static equilibrium eccentricity ratio may exceed 1.0, even 4.0, which will result in poor convergence for the numerical algorithm. The introduction of textures and numerical calculations under heavy load conditions have heightened the complexity of the solution, and the multigrid method offers an efficient resolution to this challenge. This paper established the pressure governing equation considering the effects of gas rarefaction. The cumulative eccentricity method was applied to analyze the bearing’s behavior under heavy-load operating conditions. Additionally, the numerical solution efficiency of the direct, iterative, and multigrid methods was analyzed. Furthermore, the Newton-Raphson method and the perturbation method are utilized to determine the static and dynamic characteristics under large eccentricity conditions. The results indicate that the multigrid method offers up to a 77% increase in computational efficiency compared to the direct solution method. The bearing exhibits maximum load capacity when the axial texture ratio is above 0.7 and the circumferential texture ratio is within the range of 0.3 to 0.4. As the eccentricity ratio increases from 0.1 to 4, the enhancing effect of surface texturing on load capacity decreases by 6.78%, while the friction-reduction effect increases by 4.25%. Furthermore, critical mass calculations indicate improved bearing stability with a large eccentricity. This study shows that suitable texture parameters effectively improve the bearing performance under heavy-load conditions, while the multigrid method can efficiently solve the above problems.