air-bearing

name	air-bearing
description	Air bearings — hydrostatic vs. aerodynamic, load capacity, stiffness, orifice/porous compensation, squeeze film, precision spindles, cleanroom applications, ISO 12849 design.
metadata	{"priority":7,"promptSignals":{"phrases":["air bearing","aerostatic bearing","aerodynamic bearing","gas bearing","hydrostatic air bearing","porous air bearing"],"minScore":3}}

Air Bearings — Complete Skill

Types of Air Bearings

Hydrostatic (aerostatic): pressurized external air supply; load capacity independent of speed; zero contact at startup/shutdown Aerodynamic: self-generating pressure from rotor rotation; requires minimum speed; no external supply

Hydrostatic Air Bearing Fundamentals

Governing Equation (Compressible Reynolds)

Thin film compressible lubrication: ∂/∂x[(Ph³ ∂P/∂x)/η] + ∂/∂z[(Ph³ ∂P/∂z)/η] = 12 ∂(Ph)/∂t + 6 U ∂(Ph)/∂x

P = absolute pressure; h = gap; η = air viscosity (1.85×10⁻⁵ Pa·s at 20°C); U = surface speed

Compressibility number: σ = 6 η ω L² / (P_a h₀²) [ω = angular speed; L = bearing half-length; P_a = supply pressure; h₀ = nominal gap] For σ < 1: quasi-static; for σ >> 1: compressibility important

Orifice-Compensated Bearing

Flow through orifice (supply to pocket): Q_s = C_d × A_o × √(2(P_s - P_p)/ρ) [m³/s; incompressible; valid for P_s - P_p small] A_o = π d_o²/4 [m²]; d_o = orifice diameter; C_d = 0.6–0.8 (discharge coefficient)

Pocket pressure P_p (equating supply flow to bearing flow): Q_s = Q_bearing = [P_p³ - P_a³] × C_bearing / (P_p) [compressible film flow; C_bearing = geometric constant]

Load capacity (circular pad): W = ∫∫(P - P_a)dA ≈ (P_p - P_a) × A_eff [effective area A_eff ≈ 0.6–0.8 × pad area for typical geometry]

Stiffness (orifice-compensated): k = -dW/dh|_{h=h₀} [N/m; should be positive for stability] Optimal stiffness at: Q_s orifice = Q_bearing [matched at operating point]

Maximum stiffness condition: P_p = √(P_s × P_a) [optimal pocket pressure; P_s = supply; P_a = atmospheric]

Porous-Media Compensated Bearing

Flow through porous pad: Q_porous = (k_p × A / L_p) × (P_s - P_p) [Darcy's law; k_p = permeability [m²]; L_p = thickness [m]] Typical graphite: k_p = 10⁻¹³ to 10⁻¹² m²

Advantages: no orifice clogging; more uniform pressure distribution; better damping Disadvantages: requires clean, dry air (moisture blocks pores)

Aerodynamic Bearings

Spiral Groove Thrust Bearing

Pressure generation from pumping grooves: At rotation speed ω: grooves pump gas inward (or outward) → pressure buildup in land region P_peak = f(σ, groove geometry) → solved numerically

Load capacity: W = (P_peak - P_a) × A_land [approximate; full solution requires Reynolds equation solution]

Stiffness: k_aero ∝ ω × h₀⁻² [stiffness increases with speed and decreases with gap] Minimum speed for load support: ω_min = √(W × k_B / (k_aero_factor × R²))

Journal Aerodynamic Bearing (Foil Bearing)

Foil bearing (compliant): corrugated metallic foils provide structural compliance + damping Load at speed: depends on Sommerfeld number and speed At 50,000 RPM: typical foil bearing capacity 50–500 N Applications: aircraft APU, micro gas turbines, oil-free compressors

Practical Design Parameters

Nominal gap h₀: Typical: 5–20 μm (precision); 10–50 μm (industrial) Smaller gap: higher stiffness, higher load capacity, higher flow rate, more sensitive to contamination

Supply pressure P_s: Typical: 3–8 bar (gauge) Higher P_s → higher load capacity but more flow (air consumption)

Air consumption: Q_air = N_pads × Q_per_pad [slm or L/min; must size filter/dryer + supply] Typical: 10–200 slm for small bearing systems

Cleanliness requirement: Particle size < 1/10 gap (< 1–2 μm for 10 μm gap) ISO 8573-1: particle class 1; moisture < -40°C pressure dew point

Load Capacity — Flat Pad (Hydrostatic)

Circular pad with annular orifice ring: W_max ≈ (P_s - P_a) × A_pad × η_p [η_p = pressure factor ≈ 0.4–0.6 depending on geometry]

Design example: D = 50 mm pad; P_s = 5 bar gauge; P_a = 1 bar abs → ΔP = 5 bar A_pad = π(0.025)² = 1.96×10⁻³ m² W ≈ 5×10⁵ × 1.96×10⁻³ × 0.5 ≈ 490 N per pad

Error Motion and Accuracy

Averaging effect (preloaded air bearing): Position accuracy = h₀ × (δP / P_mean) × (1 / k_normalized) Practical: air bearing achieves 5–20 nm positioning accuracy (surface finish averaging)

Thermal effects: Linear CTE of steel: 11.7 μm/(m·°C); 1°C change in 300 mm span → 3.5 μm gap change Use Invar (1.5 μm/(m·°C)) or temperature control for sub-micron applications

Applications

Application	Type	h₀ [μm]	Load [N]
CMM slides	Hydrostatic	5–10	200–5000
Precision spindle	Hydrostatic	10–20	50–2000
Silicon wafer stage	Hydrostatic	5–8	50–500
Turbine (oil-free)	Foil aero	20–50	100–2000
Gyroscope	Hydrostatic	2–5	1–10

Output

Provide: bearing type (hydrostatic orifice/porous/aerodynamic foil), nominal gap h₀ [μm], supply pressure P_s [bar], pad area and geometry, load capacity W [N] per pad, static stiffness k [N/μm], air consumption [slm], minimum speed for aerodynamic (if applicable), cleanliness class (ISO 8573-1), error motion [nm], temperature sensitivity [μm/°C], and design reference (ISO 12849, bearing manufacturer specs).