Semi-analytical calculation of stiffness and damping in gas foil bearings

To address the limitations of the traditional Reynolds equation method in terms of model accuracy and generalizability, a semi-analytical method based on the fundamental equations of fluid mechanics was proposed for accurate calculation of the stiffness and damping coefficients of gas foil bearings. First, the fluid-structure interaction between the gas film and the foil structure was established. Then, the eccentricity ratio was continuously varied in order to locate the static equilibrium position of the journal at a determined rotational speed. Subsequently, a first-order eccentricity perturbation was applied to obtain the four stiffness coefficients via steady-state calculations. Finally, the four damping coefficients were determined through transient calculations by imposing two simple harmonic vibrations on the journal. The results showed that as the rotational speed increased, the static equilibrium position of the journal gradually moved closer to the bearing center, the direct stiffness coefficients decreased, the cross-coupled stiffness coefficients increased, and all four damping coefficients decreased. The calculated stiffness and damping coefficients can be used in subsequent rotor dynamics analyses. The stiffness coefficients of the foil bearing were tested experimentally, and the experimental results demonstrated the feasibility of the proposed calculation method.