Bearing Life Theory: L10 and the ISO 281 Rating Life Calculation
The statistical framework that answers 'how long will this bearing last?' A step-by-step look at basic rating life L10, the load-life exponent, and the modified rating life (ISO 281) that accounts for lubrication and cleanliness.
Life Is Not a Single Number
Run several identical bearings under identical conditions and each one lasts a different length of time. Surface fatigue is inherently statistical. So bearing life is treated not as a single value but as a distribution.
Basic Rating Life L10
L10 is the life that 90% of a population of identical bearings will reach without surface-fatigue failure — equivalently, the life at which 10% are expected to have failed. Expressed in millions of revolutions:
L10 = (C / P)^p
- C : basic dynamic load rating (catalog value)
- P : equivalent dynamic load (the real applied load reduced to a single radial value)
- p : load-life exponent — 3 for ball bearings, 10/3 for roller bearings
The exponent p is the crux. For a ball bearing, doubling the load cuts life by 2³ = 8×. A small reduction in load yields a large gain in life.
Converting to Time
Designers usually think in hours. Given speed n (rpm):
L10h = (10^6 / (60 · n)) · (C / P)^p
For example, at the same load, halving the speed doubles the life in hours.
Equivalent Dynamic Load P
A real bearing carries both radial load Fr and axial load Fa. These combine into one equivalent value:
P = X · Fr + Y · Fa
The factors X and Y come from the catalog and depend on bearing type and the load ratio (Fa/Fr). For a purely radial bearing with small axial load, this simplifies to P ≈ Fr.
Why Basic Life Is Not Enough
The L10 formula assumes ideal lubrication and a clean environment. In reality, lubrication condition (λ) and contamination dramatically change life. ISO 281 introduces a modified rating life to capture this:
Lnm = a1 · aISO · L10
- a1 : reliability factor. L10 (90%) is the baseline; for higher reliability (e.g., L5, L1) multiply by a value below 1.
- aISO : life modification factor. It combines the viscosity ratio κ (actual/reference viscosity, directly tied to λ), the contamination factor eC, and the fatigue load limit ratio Cu/P.
aISO can range from below 0.1 to above 50. In other words, lubrication and cleanliness alone can change life by tens of times. Keep the film clean and adequate and aISO rises; let it become contaminated or thin and aISO drops below 1.
The Fatigue Load Limit Cu
Modern clean steel exhibits essentially no surface fatigue below a certain stress level. That threshold is the fatigue load limit Cu. If the applied load is below Cu and lubrication and cleanliness are good, aISO becomes very large and life approaches effectively infinite — at which point other modes (wear, corrosion, contamination) govern the real service life.
Linking Calculation to Reliability
- Define applied loads Fr, Fa and speed n.
- Compute the equivalent dynamic load P.
- Calculate L10 (or L10h) from C/P and the exponent p.
- Find aISO from lubrication (κ), cleanliness (eC), and Cu/P, then correct to Lnm.
- Compare against the required life and reselect type/size as needed.
The value of a life calculation is not the single precise number it produces. It is that it shows quantitatively which variable governs life — usually load and lubrication. That insight is what turns into design margin and maintenance strategy.