The Partial Derivative Method for Dynamic Stiffness and Damping Coefficients of Supercritical CO₂ Foil Bearings

Abstract

Supercritical CO2 foil bearings are promising bearing technology for supercritical CO2 high-speed turbomachinery. The partial derivative method including complete variable perturbation of the compressible turbulent lubrication Reynolds equation is effective to predict the frequency dependent dynamic stiffness and damping coefficients of supercritical CO2 bearings. In this research, the structural perturbation of foil dynamic model was introduced into this method and then the dynamic coefficients of supercritical CO2 foil bearings were calculated. The results of parametric analysis show that the structural loss factor has little influence on the trend of dynamic coefficients changing with the dimensionless support stiffness but mainly affects the value of stiffness coefficients as well as damping coefficients. Due to the turbulence effect, the bearing number is not able to directly determine the characteristics of supercritical CO2 foil bearings, which is different from air bearings. Compared to the bearing number, the influence of the average Reynolds number on the change of dynamic coefficients with dimensionless support stiffness is more obvious.

Keywords

• supercritical carbon dioxide
• compressible turbulent lubrication
• real gas effect
• damped elastic support
• structural perturbation
• dynamical deformation