In porous resistances, Darcy’s law provides a good approximation of mass flow rate when the differences between upstream and downstream pressures are sufficiently small. In this range, the mass flow rates are proportional to the porous resistance’s permeability. For gas bearings, the pressure difference is normally higher, and it is known experimentally that the mass flow rates are lower than would result from Darcy’s law. Forchheimer’s law adds an inertial term to Darcy’s law and, when an appropriate coefficient is selected for this term, provides a good approximation of flow rates for the same applications even with the highest pressure differences. This paper presents an experimental and theoretical investigation of porous resistances used in gas bearing and thrust pad supply systems. The porous resistances considered in the investigation were made by sintering bronze powders with different grain sizes to produce cylindrical inserts that can be installed in bearing supply devices. The paper describes the test setup and experimental results obtained for: (i) mass flow rate through single porous resistances at different upstream and downstream pressures and (ii) mass flow rate and pressure distribution on a pneumatic pad featuring the same porous resistances. The theoretical permeability of the chosen porous resistances was calculated, and the results from setup (i) were then used to obtain experimental permeability and to determine the inertial coefficients. The results, which are expressed as a function of the Reynolds number, confirmed the validity of using Forchheimer’s law. The mass flow rates from setup (ii) were compared to those from setup (i) at the same pressure differentials across the resistance.

Because of their distinctive characteristics, aerostatic bearings are particularly suitable for high-precision applications. However, because of the compressibility of the lubricant, this kind of bearing is characterized by low relative stiffness and poor damping. Compensation methods represent a valuable solution to these limitations. This paper presents a design procedure for passively compensated bearings controlled by diaphragm valves. Given a desired air gap height at which the system should work, the procedure makes it possible to maximize the stiffness of the bearing around this value. The designed bearings exhibit a quasi-static infinite stiffness for load variation ranging from 20% to almost 50% of the maximum load capacity of the bearing. Moreover, the influence of different parameters on the performance of the compensated pad is evaluated through a sensitivity analysis.

This paper proposes a method to experimentally identify the main modal parameters, i.e., natural frequencies and damping ratios, of an aerostatic spindle for printed board circuit drilling. A variety of methods is applied to the impulse-response function of the spindle in the presence of zero rotational speed and different supply pressures. Moreover, the paper describes the non-linear numerical model of the spindle, which consists of a four-degree-of-freedom (DOF) rigid and unsymmetrical rotor supported by two aerostatic bearings. The main goal of the work is to validate the developed non-linear numerical model through the proposed identification procedure and the performed experimental tests. The comparison proves satisfactory, and the possible sources of uncertainty are conjectured.