bearing-fatigue-life

name	bearing-fatigue-life
description	Rolling bearing fatigue life — Lundberg-Palmgren L10 life, ISO 281 modified life with a_ISO factor, dynamic load rating C, contamination and lubrication factors, failure modes, SKF/FAG life methods.
metadata	{"priority":7,"promptSignals":{"phrases":["bearing fatigue life","bearing L10 life","bearing life calculation","ISO 281 bearing","dynamic load rating","bearing life adjustment"],"minScore":3}}

Rolling Bearing Fatigue Life — Complete Skill

Basic Rating Life (Lundberg-Palmgren)

L10 life (10% failure probability): L₁₀ = (C / P)^p [millions of revolutions] C = basic dynamic load rating [N] (from bearing catalog) P = equivalent dynamic load [N] p = 3.0 for ball bearings; 10/3 for roller bearings

In operating hours: L₁₀h = 10⁶ × L₁₀ / (60 × n) [hours; n = rotational speed [RPM]]

Equivalent dynamic load P: Radial bearings: P = X × F_r + Y × F_a [X, Y = radial/axial load factors from catalog; F_r = radial; F_a = axial] Thrust bearings: P = F_a (axial load only) Angular contact: P depends on contact angle and F_a/C₀ ratio (use catalog tables)

Example (deep groove ball bearing): C = 40 kN; F_r = 8 kN; F_a = 0; P = 8 kN; n = 1500 RPM L₁₀ = (40/8)³ = 5³ = 125 million rev L₁₀h = 10⁶ × 125 / (60 × 1500) = 1389 hr

Modified Rating Life (ISO 281:2007)

Modified life L_nm: L_nm = a₁ × a_ISO × L₁₀ [millions of rev or hours]

a₁ — reliability factor:

Reliability %	a₁
90 (L10)	1.0
95 (L5)	0.62
99 (L1)	0.25
99.9 (L0.1)	0.093

a_ISO — life modification factor: a_ISO = f(κ, η_c, C_u/P) κ = viscosity ratio = ν₁ / ν_required [ν₁ = actual oil viscosity at operating T; ν_required = reference viscosity from catalog chart] η_c = contamination factor (0.1–1.0; see below) C_u = fatigue load limit [N] (from catalog; contamination-sensitive threshold)

Viscosity ratio κ: κ = ν₁ / ν [ν = required kinematic viscosity for complete film; from catalog based on speed and bore] κ > 4: excellent lubrication; κ = 1: adequate; κ < 0.4: poor → use additives or EP oil

a_ISO typical range: κ = 2, η_c = 0.7 (clean): a_ISO ≈ 2–5 κ = 0.5, η_c = 0.2 (contaminated): a_ISO ≈ 0.05–0.2

Contamination Factor η_c

Condition	η_c
Extreme cleanliness (filtered recirculation)	0.9–1.0
High cleanliness (ISO 15/12)	0.6–0.9
Normal cleanliness (ISO 17/14)	0.5–0.7
Slight contamination	0.3–0.5
Severe contamination	0.1–0.2
Very heavy contamination	0.05–0.1

ISO cleanliness code (ISO 4406): three numbers for particles > 4 μm, > 6 μm, > 14 μm per 100 mL Target for ball bearings: ISO 15/12/9 (servo); ISO 17/14/11 (industrial)

Required Viscosity (Reference)

Catalog chart correlation (SKF/FAG): ν_required = f(n, d_mean) [cSt at operating temperature] d_mean = (d_bore + D_OD) / 2 [mm]

Approximate formula: ν_required = 45,000 / (n^0.83 × d_mean^0.5) [cSt; n in RPM; valid for 1000–100,000 RPM] At n = 1500 RPM, d_mean = 80 mm: ν_req = 45000 / (1500^0.83 × 80^0.5) = ≈ 15 cSt

Viscosity at temperature (Walther's equation): log log(ν + 0.7) = a - b log T [T in K; ν in cSt] Or use VG46 oil: ν₄₀ = 46 cSt; ν₁₀₀ = 7 cSt; VI ≈ 100

Failure Modes and Their Indicators

Failure mode	Root cause	Indicator
Surface fatigue (spalling)	Overload or contamination	Flaking, pits; noise increase
Fretting corrosion	Micro-slip at fit surfaces	Rust-colored powder at bearing seat
False brinelling	Vibration without rotation	Regular indentations on raceways
Electrical erosion	Stray current through bearing	Frosted/fluted raceways
Cage failure	Imbalance; misalignment; speed	Cage fragment; high vibration
Seizure	Insufficient lubrication	Blue/brown discoloration; welding
Corrosion	Moisture; acid	Pitting; reddish deposits

Static Load Rating (C₀) and Safety Factor

Static safety factor: S₀ = C₀ / P₀ ≥ S₀_min C₀ = basic static load rating [N]; P₀ = static equivalent load

S₀ minimum values: Precision bearings (machine tools): S₀ ≥ 2.0 General industrial: S₀ ≥ 1.0 Vibration loads: S₀ ≥ 1.5–2.0 Shock loads: S₀ ≥ 3.0–5.0

Temperature Effects on Life

Oil viscosity degrades with temperature: Every 15°C increase in oil temperature: viscosity halves → κ halves → a_ISO drops significantly

High-temperature bearing: At T > 120°C: bearing steel may soften → derated rating (typically 10–30% reduction in C per 50°C above 120°C) Use high-T bearing steel (M50 or M62) or ceramic rolling elements for T > 150°C

Standards

Standard	Scope
ISO 281	Basic and modified life rating
ISO 76	Static load rating
ISO 5593	Bearing terminology
ABMA Std 11	L10 life calculation (US equivalent)

Output

Provide: bearing type and designation, C [kN] and C₀ [kN], equivalent load P [kN], basic L10 life [million rev and hours], reliability factor a₁, viscosity ratio κ at operating temperature, contamination factor η_c, a_ISO factor, modified L_nm life [hours], static safety factor S₀, failure mode assessment, lubrication recommendation (viscosity grade and delivery method), and applicable standard (ISO 281).