Formula & Calculator
Bearing L10 Life
Estimates the rated fatigue life of a rolling-element bearing, in revolutions, from its dynamic load rating and the actual applied load.
Interpretation
Bearing L10 life is the number of revolutions at which 90% of a group of identical bearings will survive. L10 = (C/P)^p × 1,000,000, where p = 3 for ball bearings. It is a statistical measure of bearing endurance.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| L10 | Rated life (90% reliability) | revolutions |
| C | Basic dynamic load rating of the bearing | N |
| P | Equivalent dynamic load applied to the bearing | N |
| p | Life exponent (3 for ball bearings, 10/3 for roller bearings) |
What it means
The L10 life is a widely used rating for rolling element bearings. It represents the life (in revolutions) at which 10% of a population of bearings would have failed, i.e., 90% survive. The formula is L10 = (C / P)^p × 10⁶ revolutions, where C is the basic dynamic load rating (a capacity of the bearing), P is the equivalent dynamic bearing load, and p is the exponent (p = 3 for ball bearings, 10/3 for roller bearings). This formula is derived from the Weibull distribution and is empirical. It is essential for selecting bearings for a given application, ensuring they last for the required service life. The load P accounts for radial and axial loads combined. Factors like lubrication, contamination, and mounting affect the actual life. The L10 life is often converted to hours based on operating speed. This standardised rating allows engineers to compare bearings from different manufacturers. It is fundamental in machine design for reliability and maintenance planning.
Worked example
Bearing L10 Life – Two Examples
Real‑World| Parameter | Value |
|---|---|
| C | 10,000 N |
| P | 2,000 N |
| p | 3 |
| Parameter | Value |
|---|---|
| C | 20,000 N |
| P | 5,000 N |
| p | 3.33 |
Common mistakes
- Dynamic load P: Use the equivalent dynamic bearing load (radial and axial combined).
- Basic dynamic load C: From bearing catalogue – it’s the load for 1 million revolutions.
- Exponent p: For ball bearings, p=3; for roller bearings, p=10/3 – using the wrong exponent gives a large error.
- Life units: L10 is in revolutions – convert to hours using speed (rpm).
- Reliability: L10 life corresponds to 90% reliability; for different reliability, adjust.
Applications
Bearing L10 life is the number of revolutions at which 90% of identical bearings will survive under a given load. This parameter is used to select bearings for durability and reliability in rotating machinery. It helps engineers choose the appropriate bearing size and type for applications like motors, pumps, and gearboxes. The L10 life accounts for load and material fatigue, and it is a key factor in maintenance planning. By comparing the required life with the application's expected operational hours, engineers can ensure that bearings do not fail prematurely. The formula is also used in quality control and in the development of new bearing materials.
- Selection of bearings for electric motors and generators
- Design of heavy‑duty industrial machinery (crushers, mills)
- Automotive wheel and axle bearing life prediction
- Wind turbine main shaft bearing sizing
- Reliability and maintenance planning for rotating equipment
Frequently Asked Questions
The L10 life is the number of revolutions (or hours at a constant speed) that 90% of a group of apparently identical bearings will survive before the first signs of fatigue (spalling) appear. The formula is L10 = (C / P)^p × 10⁶ revolutions, where C is the basic dynamic load rating, P is the equivalent dynamic load, and p is the life exponent (3 for ball bearings, 10/3 for roller bearings).
- C (basic dynamic load rating) – the constant radial load that would give an L10 life of 1 million revolutions (given in N or lbf by the manufacturer).
- P (equivalent dynamic load) – the constant radial load that would produce the same life as the actual combined radial and axial loads (computed using P = X·F_r + Y·F_a).
- p – exponent: 3 for ball bearings, 10/3 ≈ 3.333 for roller bearings.
- Using the wrong exponent – ball and roller bearings have different exponents; mixing them up gives an incorrect life.
- Using the equivalent load P incorrectly – for combined loads, you must use the appropriate X and Y factors from the bearing catalogue.
- Forgetting to include the axial load – radial bearings also carry axial loads, but they reduce life.
- Using the life formula without adjusting for reliability – L10 is for 90% reliability; for higher reliability, use the adjustment factors (a₁, a₂).
Since L10 ∝ (1/P)^p, doubling P reduces the life by a factor of 2^p. For ball bearings (p=3), life becomes 1/8th of the original. For roller bearings (p=10/3), it becomes about 1/10th. This shows the strong sensitivity of life to load.
For a radial bearing, P = X·F_r + Y·F_a, where X and Y are factors given in the bearing catalogue (depending on the bearing type and the ratio F_a/F_r). For a pure radial load (F_a=0), P = F_r. For a pure axial load on a thrust bearing, P = F_a.
L10 is given in millions of revolutions. To convert to hours of life, use: L10h = (10⁶ / (60·n)) × (C/P)^p, where n is the rotational speed in RPM. This gives the expected life in hours.
C (dynamic) is used for life calculations under rotating loads. C₀ (static) is the load that causes a permanent deformation of 0.0001 of the rolling element diameter. Static loads are checked to prevent plastic deformation, especially at low speeds or during startup.
At elevated temperatures, the hardness of the bearing steel decreases, reducing the dynamic load rating C. Manufacturers provide correction factors (e.g., for temperatures above 120°C, C is reduced). The life formula must be adjusted by using a derated C value.
Adequate lubrication ensures a film that separates the rolling elements from the raceways, reducing wear and preventing premature failure. The L10 life assumes proper lubrication. If lubrication fails, the actual life is much shorter (seizure or early spalling).
Given the required life (L10_target) and the bearing loads, you rearrange the formula to find the required C: C = P · (L10_target / 10⁶)^(1/p). Then select a bearing from the catalogue with a dynamic load rating greater than or equal to the required C.