Hong Life CalculatorsUnderstanding the bearing L10 life calculator — concept and principle
Rolling bearings fail by raceway fatigue, and life varies widely even between identical bearings. The basic rating life L₁₀ is the life that 90% of a large group of identical bearings will reach or exceed under the same conditions. This calculator finds L₁₀ in millions of revolutions and in operating hours from the catalogue dynamic load rating C, the equivalent load P and the speed.
How it is calculated
- L₁₀ = (C/P)^p, in millions of revolutions.
- p = 3 for ball bearings and p = 10/3 for roller bearings.
- L₁₀h = L₁₀ × 10⁶ / (60 × n), in hours, with n in rpm.
C and P must be in the same unit (here kN). P combines radial and axial loads into one equivalent radial load using factors from the catalogue.
The principle
The dynamic load rating C is defined in ISO 281 as the constant load under which a bearing reaches a basic rating life of one million revolutions. Fatigue tests show that life falls steeply with load, following a power law: for point contact in ball bearings the exponent is 3, and for line contact in roller bearings it is 10/3. So at P = C the life is 1 million revolutions, and every halving of load multiplies ball bearing life by 2³ = 8. Converting revolutions to hours is just dividing by revolutions per hour, 60n.
Worked example
- Inputs: C = 30 kN, P = 5 kN, 1,500 rpm, ball bearing (p = 3).
- C/P = 30/5 = 6.
- L₁₀ = 6³ = 216 million revolutions.
- Revolutions per hour = 60 × 1,500 = 90,000.
- L₁₀h = 216 × 10⁶ / 90,000 = 2,400 hours.
For a roller bearing with the same numbers, L₁₀ = 6^(10/3) ≈ 392.5 million revolutions, about 4,361 hours.
| Equivalent load P (kN) | L10 (million revolutions) |
|---|---|
| 1.25 | 13,824 |
| 2.5 | 1,728 |
| 3.75 | 512 |
| 5 | 216 |
| 6.25 | 110.592 |
| 7.5 | 64 |
| 10 | 27 |
How to read the result
2,400 hours is roughly one year of single-shift use, short for most industrial machines; makers publish recommended L₁₀h values by application. Because life varies with the cube of C/P, a modestly larger bearing raises life sharply. For higher reliability, ISO 281 multiplies by a factor a₁: 0.64 for 95% and 0.25 for 99% reliability, so the 99% life here would be about 600 hours. ISO 281 also defines a modified life with a factor a_ISO for lubrication and contamination, which can raise or lower life considerably.
Common mistakes
- Mixing kN and N between C and P.
- Using radial load alone when there is a significant axial load.
- Reading L₁₀ as the average life; the median life is several times longer.
- Ignoring shock, misalignment and poor lubrication.
Frequently asked questions
Where do I find C for my bearing?
It is listed in the manufacturer's catalogue for each bearing number, together with the static rating C₀ and the X and Y load factors.
Does L₁₀ apply at very low speed?
For very slow or oscillating motion the static rating C₀ usually governs instead of fatigue life.
Does speed change L₁₀ in revolutions?
No. Speed only converts revolutions to hours, although it affects lubrication and temperature.
Sources: ISO 281:2007, Rolling bearings — Dynamic load ratings and rating life · Lundberg, G. and Palmgren, A. (1947), Dynamic capacity of rolling bearings, Acta Polytechnica, Mechanical Engineering Series