Modified Reynolds Equation for Aerostatic Porous Radial Bearings With Quadratic Forchheimer Pressure-Flow Assumption

Aerostatic porous bearings are becoming important elements in precision machines due to their inherent characteristics. The mathematical modeling of such bearings depends on the pressure-flow assumptions that are adopted for the flow in the porous medium. In this work, one proposes a nondimensional modified Reynolds equations based on the quadratic Forchheimer assumption. In this quadratic approach, the nondimensional parameter $Φ$ strongly affects the bearing load capacity, by defining the nonlinearity level of the system. For values of $Φ>10$⁠, the results obtained with the modified Reynolds equation with quadratic Forchheimer assumption tend to those obtained with the linear Darcy model, thus showing that this is a more robust and global approach of the problem, and can be used for both pressure-flow assumptions (linear and quadratic). The threshold between linear and quadratic assumptions is numerically investigated for a bronze sintered porous bearing, and the effects of bearing geometry are discussed. Numerical results show that $Φ$ strongly affects the bearing loading capacity and stiffness coefficients.