Vacuum-preloaded air bearing, simple orifice feed — fixed reference geometry

Reference-geometry calculator (76mm outer diameter, 5µm film, 0.28MPa supply — fixed, matching the original) for a vacuum-preloaded aerostatic thrust collar bearing fed through discrete simple orifices. Vary the remaining diameters and pressures.

✓ validated against legacyoriginal: /calculators/c12_6b.htm

Vacuum-preloaded air bearing, simple orifice feed — fixed reference geometry — original diagram from /calculators/c12_6b.htm

Outer diameter of orifice ring, 2R₁10⁻³ mInner diameter of orifice ring, 2R₂10⁻³ mInner diameter of collar bearing, 2R₃10⁻³ mOuter diameter of vacuum preload, 2R₄10⁻³ mInner diameter of vacuum preload, 2R₅10⁻³ mGroove depth, h₂10⁻⁶ mAmbient pressure, pₐ10⁶ PaVacuum level, p_V10⁶ PaRestrictor pressure, p_R10⁶ Pa

Flow through collar bearing, ṁ_b3.266 10⁻⁶ kg/s

Flow through collar bearing, Q_b164.8 10⁻³ l/min

Flow through vacuum system, ṁ_V0.466 10⁻⁶ kg/s

Flow through vacuum system, Q_V23.5 10⁻³ l/min

Load capacity of collar bearing, F_b70.4 N

Tensile force of vacuum preload, F_V-38.4 N

External load of vacuum-preloaded bearing, F32 N

Axial stiffness, S = −dF/dh36.5 10⁶ N/m

The legacy "please login" demo lock froze D0/H0/pS to these exact values. Per docs/phase6/OWNER-DECISIONS-BACKLOG.md K4, this fixed geometry is kept exactly as in the original and only the inputs that were already free under the lock are exposed. Generalizing it is a deliberate future decision for Anton, not made here. Restrictor pressure pR is clamped to 0.53·pₛ if entered lower (choked flow); solve iteratively (adjust pR) until the external load F matches the intended operating point.

Method & references

The pressure ratio in orifice restrictors is limited at the lower end by choked flow: for air, pR/pS>0.53.
The homogeneous-pressure-over-groove assumption requires a relatively large groove depth (h₂/h₀>40); shallow grooves need finite element analysis.
FIXED GEOMETRY: outer diameter 76 mm, film thickness 5 µm, supply pressure 0.28 MPa — the original demo lock froze these three together.

The computation is a literal port of the original client-side JavaScript from /calculators/c12_6b.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.

Vacuum-preloaded air bearing, simple orifice feed — fixed reference geometry — Engineering ABC