| name | gear-lubrication |
| description | Gear lubrication — EHD film thickness (Dowson-Higginson), specific film thickness (lambda ratio), lubricant selection (AGMA viscosity grades), scuffing (scoring), micropitting, thermal rating. |
| metadata | {"priority":7,"promptSignals":{"phrases":["gear lubrication","gear oil","EHD film","elastohydrodynamic","lambda ratio gear","scuffing","micropitting gear"],"minScore":3}} |
Gear Lubrication — Complete Skill
Elastohydrodynamic (EHD) Film Formation
Gear teeth operate under EHD lubrication at contact points
Minimum film thickness (Dowson-Higginson, line contact):
H_min = 2.65 G^0.54 U^0.7 W^(-0.13)
where (dimensionless groups):
G = α_P × E' (materials parameter; α_P = pressure-viscosity coefficient [Pa⁻¹]; E' = reduced modulus)
U = η₀ v_s / (E' R') (speed parameter; η₀ = dynamic viscosity; v_s = mean entraining velocity; R' = reduced radius)
W = F / (E' R' L) (load parameter; F = load per unit length)
Dimensional film thickness:
h_min = H_min × R'
E' = 2 / (1/E₁ + 1/E₂) × (not divided by 2)... = E / (1-ν²) for both steel → E' ≈ 226 GPa
Mean entraining velocity (pitch point):
v_s = π n r_1 (1 + 1/u) / 60 [m/s; u = gear ratio; r₁ = pinion pitch radius]
Specific Film Thickness (Lambda Ratio)
λ = h_min / σ_composite
σ_composite = √(Ra₁² + Ra₂²) [combined surface roughness]
| λ | Lubrication regime | Expected wear/damage |
|---|
| λ < 1 | Boundary lubrication | High wear; asperity contact |
| 1–2 | Mixed lubrication | Moderate wear; micropitting risk |
| 2–4 | Partial EHD | Low wear; some surface distress |
| λ > 4 | Full EHD | No asperity contact; fatigue governs |
Design target: λ ≥ 2 (minimum); λ ≥ 4 preferred for long life
Viscosity Selection
Required viscosity for target λ:
Work backward: set h_min = λ_target × σ → solve for η₀ from H_min equation → get η₀ at operating T → specify ISO VG grade
AGMA viscosity grades for enclosed gears:
| Pitch line velocity | AGMA grade | ISO VG equivalent |
|---|
| V < 5 m/s (low) | 7, 8 | VG 320, 460 |
| 5–15 m/s | 5, 6 | VG 150, 220 |
| > 15 m/s (high) | 3, 4 | VG 68, 100 |
| Hypoid gears | 8A | GL-5 gear oil |
Operating viscosity:
η(T) from viscosity index (VI); ISO VG 150 at 40°C, VG 100 at 100°C → interpolate
Flash Temperature (Scuffing Criterion)
Scuffing (scoring): catastrophic surface damage from adhesion when EHD film collapses
Blok flash temperature:
T_flash = T_bulk + ΔT_flash
ΔT_flash = μ × W_n × v_s × (XΓ) / (thermal coefficient)
XΓ (coefficient for thermal properties):
XΓ = √(E'/π) × 1/√(k₁ ρ₁ c_p1 + k₂ ρ₂ c_p2) (material thermal parameter)
Scuffing temperature criterion (Blok):
T_flash,actual < T_flash,allowable (from SAE J306 or AGMA 925)
T_flash,allowable = T_flash of reference lubricant (scuff failure calibration)
Simplified scuffing index:
Calculate contact temperature; compare to lubricant's scuffing temperature (from 4-ball test)
Micropitting
Small shallow pits (depth 5–20 μm); associated with λ = 1–3
Progressive; can lead to macropitting if severe
Promotion factors: low λ, rough surfaces, slow speed, high pressure, acidic contamination
Prevention:
Increase λ: better surface finish, higher viscosity, EP additives
EP (Extreme Pressure) additives: S-P, S-Cl compounds; form protective film at asperities
Optimize profile (tip relief, crowning) to reduce edge loading
Lubricant Types
Mineral oil: standard; AGMA grades; ISO VG classes
Synthetic (PAO, ester): wider temperature range; better VI; lower traction; premium gearboxes
EP additives (GL-4, GL-5): sulfur-phosphorus for hypoid gears, worm gears, high-load applications
Anti-wear (AW, API GL-4): ZDDP or organic phosphate; less aggressive than EP
Gear Lubrication Methods
Splash/bath: oil level covers lowest gear; adequate for V < 12 m/s
Jet lubrication: pressure-fed jets aimed at mesh exit side; required for V > 12 m/s or critical applications
Jet location: mesh exit side → carry away heat; volume: Q = P_losses / (ρ c_p ΔT)
Grease: open gears, slow speed (<2 m/s), periodic lubrication; NLGI 0-1 for gears
Thermal Rating
Gearbox operating temperature:
T_oil = T_ambient + P_loss / (h_conv × A_case + Q_cooling)
P_loss = P_friction (gear) + P_friction (bearings) + P_churning
Churning losses: significant for high speed splash; reduce by precision oil level control
Gear power loss:
P_gear = μ_m × W_t × V_m / 1000 [kW; μ_m = mean coefficient 0.04–0.12; W_t in N; V_m in m/s]
P_bearing ≈ 1–2% of rated power (typical rolling element bearings)
Max continuous oil temperature: mineral oil 90°C; synthetic 110°C (continuous)
Output
Provide: h_min [μm] at pitch point, λ ratio, lubricant ISO VG grade, AGMA grade, EP/AW recommendation, scuffing risk (T_flash vs. T_allowable), micropitting risk (λ < 2?), oil viscosity at operating temperature [cSt], thermal rating (T_oil expected vs. max).
