Aerostatic Thrust, Collar, and Vacuum-Preloaded Bearing Suite

Screen circular aerostatic thrust, collar, restrictor, porous-feed, and vacuum-preloaded bearing configurations.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Bearing inputs

Bearing screening result

Net load capacity—N

Equations used

All pressures are absolute and calculations use SI units internally. Positive force is compressive and acts away from the bearing surface; a vacuum contribution is negative.

p(r)=pₒ{(pᵢ/pₒ)²−ln(r/rᵢ)[(pᵢ/pₒ)²−1]/ln(rₒ/rᵢ)}¹ᐟ²

F=Σ∫_rᵢ^rₒ2πr[p(r)−pₐ]dr + ΣAᵣ(pᵣ−pₐ)

ṁ=πh³(pᵢ²−pₒ²)/[12µRT ln(rₒ/rᵢ)]; Q=ṁRT/pₐ

S=−ΔF/Δh, evaluated with the mode’s 0.01% or 0.1% pressure perturbation

pᵣ=β(pₛ−pₐ)+pₐ; F*=F/[πR₀²(pₛ−pₐ)]

ṁ=CᵈAρ{2RTκ/(κ−1)[(pᵣ/pₛ)²ᐟκ−(pᵣ/pₛ)^(κ+1)/κ]}¹ᐟ²

Porous feed: sₚ=kₚAₚ(pₛ²−pᵣ²)/(2ṁµRT)

Shallow pocket: pᵣ/pₐ={[N³ln(R₀/R₁)(pₛ/pₐ)²+ln(R₁/R₂)]/[N³ln(R₀/R₁)+ln(R₁/R₂)]}¹ᐟ²; N=(h₀+h₂)/h₀

Grouped inherent mode: F=F′πR₀²(pₛ−pₐ); S=S′πR₀²(pₛ−pₐ)/h₀

Definitions. R₀ is outer radius; successive R indices define recess, groove, porous-ring, collar, bore, or vacuum boundaries. h₀ is running clearance; h₂ is pocket/groove depth; µ=18 µPa·s, R=287 J/(kg·K), T=293 K, ρ=1.208 kg/m³, and κ=1.4 are fixed dry-air properties. β, F*, F′, and S′ are dimensionless. Cᵈ is discharge coefficient, kₚ permeability, A restrictor area, sₚ porous thickness, ṁ mass flow, Q ambient-referenced volume flow, and S inherent stiffness.

How to use

Select the configuration that matches the feed and bearing geometry: pocket, annular gap, central orifice, grouped inherent restrictors, porous annulus, segmented groove, collar, or vacuum preload.
Enter diameters in mm in strictly decreasing radial order. Enter film thickness in µm and groove/pocket dimensions in their displayed units.
Enter absolute pressures in MPa. Supply pressure must exceed ambient; in vacuum mode pᵥ<pₐ<pᵣ<pₛ. Never enter gauge pressure.
For orifice modes, enter Cᵈ from 0.7 to 0.9 and a positive integer restrictor count. For porous modes, enter positive permeability in 10⁻¹⁵ m².
For grouped inherent restrictors, enter chart- or analysis-derived F′ and S′ for the chosen geometry; the calculator does not derive those two coefficients.
Select Calculate to update net load and secondary pressure, flow, stiffness, restrictor, and dimensionless metrics. Correct any red warning first.
Interpret load as ideal compressive capacity above ambient and stiffness as local clearance sensitivity. Check the supply system against predicted flow and required restrictor size.
Select Reset example to restore the demonstration for the active mode.
Do not use the model for contact, nonparallel surfaces, rarefied gas, high-speed self-acting effects, choking outside the stated restrictor relation, thermal/structural distortion, or safety-critical qualification without higher-fidelity verification.

Worked example

1. Select Shallow pocket. 2. Enter 2R₀=40 mm, 2R₁=32 mm, 2R₂=1 mm, h₂=5 µm, h₀=5 µm, pₛ=0.5 MPa absolute, and pₐ=0.1 MPa absolute. 3. Calculate. Expected results are 240.7 N load, 24.0 MN/m stiffness, 0.399 L/min ambient flow, F*=0.479, and β=0.507. Near this point, a 1 µm clearance increase reduces load by about 24 N; verify flatness, deformation, and supply capacity separately.

Theory and method

The calculator applies the isothermal, laminar, compressible Reynolds solution for steady radial flow between parallel circular surfaces. Pressure-squared varies linearly with logarithmic radius across each annular land. Midpoint integration with the documented radial subdivision converts pressure into force while subtracting ambient pressure. Recess areas add constant-pressure force. Collar modes combine outward and inward flow branches; vacuum preload adds a negative central force to the positive supplied-bearing force.

Restrictor modes balance the land mass flow with a subsonic ideal-gas orifice relation. Porous modes infer a uniform porous thickness from Darcy flow. The grouped-inherent mode intentionally requires dimensionless coefficients obtained for the actual restrictor layout. Results assume rigid, flat, concentric surfaces; uniform clearance and gas properties; negligible inertia; no edge losses beyond Cᵈ; and no thermal coupling. The fixed gas constants represent dry air near 293 K. Predicted stiffness is local, not structural-system stiffness.

Applicability limits. Keep diameter ordering valid, h₀>0, 0<β<1, 0.7≤Cᵈ≤0.9, pₛ>pₐ>0, and pᵥ<pₐ in vacuum mode. Treat restrictor pressure ratios near or below the critical-flow region as a warning requiring a choked-flow model. Verify manufacturable minimum clearance, surface error, contamination margin, gas heating, supply-line losses, and rotor/structure dynamics independently.

References

A. Powell, Design of Aerostatic Bearings, Machinery Publishing, 1970.
B. J. Hamrock, S. R. Schmid, and B. O. Jacobson, Fundamentals of Fluid Film Lubrication, 2nd ed., CRC Press, 2004.

Continue in TriboSolver

Use TriboSolver to refine pressure fields, clearance sensitivity, and coupled structural or thermal behavior when screening assumptions are insufficient.