Static and Dynamic Analysis of Gas Foil Journal Bearing for High-Speed Rotor

Abstract

Gas foil bearings (GFBs) are compliant bearings, which provide elastic support to the high-speed rotors. While analysing rotor support system, three key factors play a vital role in bearing performance (i) load carrying capacity (ii) bearing stiffness and (iii) bearing damping capability. The load carrying capacity of the bearing provides the quantitative aspect whereas stiffness and damping provide the qualitative aspect of the bearing. The rotor dynamic performance of the rotor can only be assessed by predicting the bearing dynamic coefficients such as stiffness and damping coefficients. The overall bearing stiffness of a GFB consists of stiffness due to the bump foil, top foil and the bearing gas. The damping occurring inside the bearing is caused by (i) friction between the top and bump foil (ii) friction between bump foil and bearing base.

Reynold’s equation has been used as the governing equation for aerodynamic analysis of the bearing. Non-dimensional Reynold’s equation has been solved by using finite difference approach. Pressure profile, film thickness, load-carrying capacity have been predicted from the numerical solution of the equation. A structural model has been developed for the structural analysis of the bump foil and the top foil. The strain energy of a single bump has been calculated considering three types of forces (Axial forces, Shear forces and Bending moment).The structural stiffness is formulated after finding out the vertical deflection of the bump foil. The variation of bump stiffness with various parameters has been discussed and compared with previous work. A perfect gas is used as the lubricant and its behaviour is studied using Reynold's equation. The perturbation method is used to obtain linearized dynamic coefficient equations. Structural equations coupled with Reynold’s equation has been formulated. Finite difference formulation has been implemented for solving the direct and coupled stiffness and damping coefficients. The effect of bearing compliance and bearing number on bearing dynamic coefficients is discussed.