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Air Bearing Stiffness: Orifice vs Porous Restrictors
Euchang Tech Engineering Team · Technical note · October 2026
Summary. Air-bearing stiffness is the local slope of the load–gap curve. It is not a constant: it depends on gap, supply pressure and frequency. Before comparing datasheet values, check three things: the gap and supply pressure at which stiffness was measured, whether the test frame was stiff enough, and whether the value is static or dynamic. If the displacement measurement includes frame deflection, a 500 N/µm test frame makes a 200 N/µm bearing look like 143 N/µm. Orifice and porous restrictors differ in how the air is fed, and so in their sensitivity to manufacturing variables and their dynamic behaviour.
1. Stiffness is a slope, not a property
An aerostatic bearing carries load on a pressurised air film a few micrometres thick. Its load capacity W falls as the gap h increases. Static stiffness is defined as
Kₛ = −dW/dh, at fixed supply pressure and temperature.
Three consequences matter when you read a datasheet:
- One bearing, many stiffness values. Kₛ changes along the load–gap curve. A value without the gap (or load) and the supply pressure is incomplete.
- A global straight-line fit is not the stiffness. It averages a curved relation. Ask for the local slope at your operating point.
- Static is not dynamic. Under vibration, the air film behaves as a frequency-dependent spring and damper [1]. A static number does not tell you the stiffness at 200 Hz.
Experimental studies compare measured load capacity, gap, static stiffness and air consumption with Reynolds-equation models [2]. This is the right way to validate a bearing: compare whole curves, not single numbers.
2. Orifice versus porous restrictors
Every externally pressurised bearing needs a restrictor between the supply and the film. The ratio of restrictor resistance to film resistance sets the stiffness.
| Orifice (often with a shallow pocket) | Porous (e.g. porous graphite or ceramic) | |
|---|---|---|
| How air is fed | Through one or a few small holes | Through the whole bearing face |
| Pressure distribution | Peaks at the feed holes, falls across the lands | More uniform across the face |
| Key manufacturing variables | Hole diameter, edge shape, pocket depth | Permeability and its uniformity, layer thickness |
| Main modelling uncertainty | Discharge coefficient Cd, which varies with Reynolds number, supply pressure and gap [3] | Permeability of the actual part; flow law through the layer [4] |
| Dynamic risk to check | Pocket volume can promote self-excited vibration ("pneumatic hammer") [1] | No macroscopic pocket, but gas stored in the porous layer is also compressible; stability still needs testing |
Neither type is "stiffer" in general. The result depends on design, gap and supply pressure. What differs is which variables you must control and verify.
Orifice flow: the choked limit
Gas flow through an orifice depends on the pressure ratio r = pdownstream / psupply (absolute pressures). For an ideal isentropic nozzle with air (γ = 1.40), the flow chokes when r ≤ 0.528; below that ratio, mass flow no longer increases as the downstream pressure falls. Real bearing restrictors need validated flow characteristics, including the choking transition. Cd varies with the operating conditions and must be identified for the actual part [3].
Practical point: specify whether supply pressure is absolute or gauge. At typical supply pressures, the difference of about 0.1 MPa changes every calculated flow and stiffness value.
Porous restrictors: permeability is a part property
Porous bearings are modelled with a flow law through the layer, usually Darcy's law as a first approximation [4][5]. The permeability of the finished face governs the result. It varies with material, process and any surface sealing. Treat it as a measured property of each part, not a catalogue constant. Experimental work on porous bearings also stresses the flatness and condition of the opposing guide surface [5].
3. Why test-frame stiffness distorts the result
The frame that loads the bearing in a test is a spring in series with the air film. If the measured displacement includes both the gap change and the frame deflection, the measured stiffness is
1/Kmeasured = 1/Kbearing + 1/Kframe
| True bearing stiffness | Measured with a 500 N/µm frame | Under-reading |
|---|---|---|
| 50 N/µm | 45 N/µm | 9% |
| 100 N/µm | 83 N/µm | 17% |
| 200 N/µm | 143 N/µm | 29% |
| 400 N/µm | 222 N/µm | 44% |
The same applies in your machine. A stiff bearing on a compliant carriage or bracket delivers only the series stiffness. Frame deflection also matters directly: at 1,200 N, a 500 N/µm frame deflects 2.4 µm, a large fraction of an air gap of a few micrometres.
Measuring the gap directly across the air film excludes frame compliance from the load–gap slope. What to ask for, or do yourself:
- the frame stiffness of the test rig, measured, not assumed;
- the gap measured close to the bearing face (several probes to separate tilt from lift);
- loading and unloading curves, to reveal hysteresis.
4. Damping and stability
The damping of an air film comes from squeezing the film and from the delay between a gap change and the pressure response in the pocket and supply volumes. That delay makes stiffness and damping depend on frequency [1][6].
The same delay can turn damping negative. A bearing with too much compressible gas volume behind the film can oscillate by itself. This is pneumatic hammer. In pocketed orifice bearings it depends on pocket volume, supply pressure, gap and the supported mass; porous bearings store gas in the porous layer and are not automatically immune. Stability must be checked by test. A resonance peak in a measured spectrum is not by itself proof of pneumatic hammer. Fixture modes and loose parts can produce similar peaks.
5. When these simple rules do not apply
- Very small gaps. At room temperature and about one atmosphere, the mean free path of air is about 68 nm, so the ratio to the gap is about 0.014 at 5 µm and grows as the gap shrinks. In the pressurised film the local mean free path is shorter; evaluate rarefaction at the local absolute pressure. At the smallest gaps, check whether gas-slip corrections change the prediction.
- Tilted or non-flat films. The analysis above assumes a parallel film. Waviness and tilt of the guide surface change the load–gap curve. Granite guide flatness is part of bearing performance.
- Near the feed holes. Near an orifice exit, inertia and compressibility can invalidate the thin-film (Reynolds) model. Pressure depressions may occur under particular operating conditions [7].
- Temperature. The analysis assumes isothermal flow. Cooling of the expanding air and thermal distortion are not covered here.
6. How Euchang can help
Euchang manufactures air-bearing (air-float) components, porous ceramic parts and granite guide structures. Please provide your load, travel, operating gap, supply pressure and guide-flatness requirement, so that the interface specification can be agreed for the project.
FAQ
Why do two datasheets for similar air bearings show very different stiffness? They are probably measured at different gaps, supply pressures or on test frames of different stiffness. Compare load–gap curves under the same conditions.
Is a porous air bearing stiffer than an orifice bearing? Not in general. It feeds air more uniformly and avoids a pocket volume, but stiffness depends on design, gap and supply pressure.
What is pneumatic hammer? A self-excited vibration of an aerostatic bearing and its supported structure. Compressible gas behind the film (in a pocket or in a porous layer) responds with a delay, which can make the film's damping negative.
Does a stiffer bearing always make the machine stiffer? No. The bearing acts in series with the carriage, brackets and frame. The softest element dominates.
Related technical articles
- Air-Bearing Stages on Granite Bases: Why Flatness and Thermal Stability Matter
- Granite Base Support Points: Airy, Bessel and Three-Point Support
- Passive vs. Active Vibration Isolation for AOI and Metrology Machines
References
- F. Al-Bender, "On the modelling of the dynamic characteristics of aerostatic bearing films: From stability analysis to active compensation," Precision Engineering 33(2) (2009) 117–126. https://doi.org/10.1016/j.precisioneng.2008.06.003
- M. Miettinen, V. Vainio, R. Theska, R. Viitala, "On the static performance of aerostatic elements," Precision Engineering 89 (2024) 1–10. https://doi.org/10.1016/j.precisioneng.2024.05.017
- G. Belforte, T. Raparelli, V. Viktorov, A. Trivella, "Discharge coefficients of orifice-type restrictor for aerostatic bearings," Tribology International 40(3) (2007) 512–521. https://doi.org/10.1016/j.triboint.2006.05.003
- J.-S. Plante, J. Vogan, T. El-Aguizy, A. H. Slocum, "A design model for circular porous air bearings using the 1D generalized flow method," Precision Engineering 29(3) (2005) 336–346. https://doi.org/10.1016/j.precisioneng.2004.11.011
- V. Vainio, M. Miettinen, J. Majuri, R. Theska, R. Viitala, "Manufacturing and static performance of porous aerostatic bearings," Precision Engineering 84 (2023) 177–190. https://doi.org/10.1016/j.precisioneng.2023.06.014
- J. Shi, H. Cao, X. Jin, "Investigation on the static and dynamic characteristics of 3-DOF aerostatic thrust bearings with orifice restrictor," Tribology International 138 (2019) 435–449. https://doi.org/10.1016/j.triboint.2019.06.026
- M. E. Eleshaky, "CFD investigation of pressure depressions in aerostatic circular thrust bearings," Tribology International 42(7) (2009) 1108–1117. https://doi.org/10.1016/j.triboint.2009.03.011
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