Basic rating life L₁₀ is the number of millions of revolutions — or operating hours at constant speed — that 90% of a group of identical bearings can achieve before rolling contact fatigue spalling first appears.
The remaining 10% will fail before this threshold — that is the statistical nature of the definition. According to ISO 281:2007, the basic formula is: L₁₀ = (C/P)^p × 10⁶ revolutions, where p = 3 for ball bearings and p = 10/3 for roller bearings. L₁₀ is the starting point — L₁₀a (adjusted rating life) is more useful for modern design practice, but L₁₀ remains the standard reference for comparison. See step-by-step examples at bearing life calculation guide and choose deep groove ball bearings matched to your L₁₀ requirement.
Formula and Calculation Steps
Step 1: determine the equivalent load P. For pure radial load: P = F_r. For combined loading: P = X·F_r + Y·F_a, where X and Y are read from the catalog as a function of the ratio F_a/C₀.
Step 2: calculate L₁₀ in millions of revolutions = (C/P)^p.
Step 3: convert to hours: L₁₀h = L₁₀ × 10⁶ / (n × 60).
Worked example — bearing 30207 (C = 56 kN, d = 35, D = 72 mm) on a gearbox shaft, radial load F_r = 14 kN, speed n = 1,450 rpm:
L₁₀ = (56/14)^(10/3) = 4^3.33 = 91 million revolutions
L₁₀h = 91 × 10⁶ / (1,450 × 60) = 91,000,000 / 87,000 ≈ 1,046 hours
Under 1,100 hours — well below the 8,000-hour design target. Solutions: reduce load, increase bearing size, or select a bearing with higher C.
The Effect of Load on L₁₀
The power-law relationship makes L₁₀ extremely sensitive to load. Reducing load by 20% (P × 0.8) increases L₁₀ by a factor of (1/0.8)³ = 1.95 — nearly double the life. Conversely, increasing load 20% reduces life to 58% of original.
| Load Change | L₁₀ Multiplier (ball) | L₁₀ Multiplier (roller) |
|---|---|---|
| Reduce 30% (×0.7) | ×2.92 | ×2.50 |
| Reduce 20% (×0.8) | ×1.95 | ×1.72 |
| Unchanged | ×1.00 | ×1.00 |
| Increase 20% (×1.2) | ×0.58 | ×0.63 |
| Increase 30% (×1.3) | ×0.46 | ×0.51 |
This is why controlling load — through dynamic balancing, shaft alignment, and shock reduction — matters more than upgrading to a more expensive bearing.
Practical Example
At a cement plant in Thanh Hoa, the design engineer wanted L₁₀h ≥ 30,000 hours for a fan shaft bearing (n = 740 rpm, radial load 25 kN). Required C:
Required L₁₀ = 30,000 × 740 × 60 / 10⁶ = 1,332 million revolutions
For ball bearing: C = 25 × 1,332^(1/3) = 25 × 11.0 = 275 kN
For roller bearing: C = 25 × 1,332^(3/10) = 25 × 6.44 = 161 kN
Selected 22216 EK/C3 (C = 224 kN) for a 1.4× safety margin. The bearing actually reached 38,000 hours — exceeding the target because good lubrication increased the a_ISO factor in the L₁₀a calculation.