Analyse Statique et Dynamique des Paliers à Gaz Poreux

Abstract

Increasingly, technological developments impose severe operating conditions for the rotors of rotating machinery due to the increase of rotational velocities, transmitted powers, and loads. These conditions require us to use supporting elements with the best Steady-State and Dynamic performance characteristics. The research study carried out in this report is essentially based on a linear modeling of the dynamic behavior of rotors mounted in porous gas bearings (PGB) operating in a hybrid lubrication regime which is a superposition of aerostatic and aerodynamic effects. The linear approach developed by Stodola and retaken by Hori to study the stability of equilibrium position of the system as it exists thanks to the introduction of eight fluid-film dynamic coefficients, namely: four stiffness coefficients and four damping coefficients. To calculate the Lund’s stability parameters (i.e. the critical mass and the whirl frequency ratio), the eight dynamic coefficients should be determined using an analytical perturbation of the modified compressible Reynolds equation derived for turbulent flow in transient conditions. The first order perturbation process and the adoption of the complex variables technique lead to the writing of three PDEs of order zero and one instead of five PDEs whose unknowns are the static pressure 𝑝0 and the complex dynamic pressures 𝑞𝜀 and 𝑞𝜙. The nonlinear zero-order equation is solved by the central finite differences and the Newton- Raphson methods using two calculation molecules with five and nine points. On the other hand, the two dynamic equations are discretized using the finite differences method and the resulting algebraic equations system by the iterative Gauss-Seidel method with over-relaxation factor. The obtained results highlight the non-negligible effects of the external supply pressure and the fluid flow regime on the steady-state and dynamic behavior of the porous gas bearing operating in hybrid lubrication regime.