gear-lubrication

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).