| 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).
