Static and Dynamic Analysis of Porous Gas Bearings Lubricated With Air, Refrigerant R-134a, Helium and Hydrogen

Abstract

Porous gas bearings (PGBs) enable high-speed, oil-free operation in modern rotating machinery. This study develops a coupled thermo-hydrodynamic (THD) model for a cylindrical porous gas bearing lubricated with four working fluids—air, R-134a, helium and hydrogen. The modified Reynolds equation is derived by combining the Navier–Stokes and continuity equations with the Morgan–Cameron approximation, Darcy–Forchheimer law and Beavers–Joseph slip condition. Gas compressibility and vapour–liquid transition are represented through the Peng–Robinson equation of state. Steady-state and dynamic analyses are performed to evaluate the influence of permeability and slip on load capacity, pressure distribution, flow rate, friction torque, temperature field and stiffness and damping coefficients. Results show that increasing permeability decreases pressure and load capacity but promotes better thermal uniformity, whilst higher slip coefficients improve film stability and reduce shear losses. Amongst the gases considered, hydrogen exhibits the lowest film thickness due to its low viscosity, whereas helium yields superior thermal behaviour. The combined model provides a reliable computational framework for optimising porous gas bearings under realistic operating conditions.