Rolling Element Bearing L10 Life Equation
Calculates the statistical fatigue rating life of ball or roller bearings in millions of revolutions.
Interactive Calculator Call to Action
Bearing L10 Fatigue Life
Calculate interactively with instant results, step-by-step derivations, and unit conversion. Built on the same engineering standards as this formula reference.
Primary Mathematical Expression
Design Schematic
Nomenclature & Variables
| Symbol | Variable Name | Metric Unit | Imperial Unit | Description |
|---|---|---|---|---|
| L10 | Nominal life | Million Revs | Million Revs | Nominal rating fatigue life in millions of revolutions. |
| C | Dynamic load rating | kN | lbf | Dynamic load rating representing 1 million revolutions life capacity. |
| P | Equivalent dynamic load | kN | lbf | The combined radial and axial dynamic loading force. |
| p | Life exponent | dimensionless | dimensionless | Shape exponent (p = 3 for ball bearings, p = 3.33 for roller bearings). |
Step-by-Step Derivation
- 1
Rolling element fatigue follows a Weibull statistical distribution, where bearing life is related to the applied load.
- 2
Dynamic testing shows bearing rating life varies inversely with load raised to an exponent: L10 \propto (1 / P)^p.
- 3
The proportionality constant is defined by the basic dynamic load rating (C), which is the constant radial/axial load at which 90% of bearings survive 1 million revolutions.
- 4
Setting L10 = 1 when P = C yields the fatigue life formula: L10 = (C / P)^p.
- 5
The exponent p depends on geometry: p = 3 for ball bearings (point contact) and p = 10/3 (approx 3.33) for roller bearings (line contact).
Worked Example Calculation
A roller bearing (C = 35 kN, p = 3.33) operates under an equivalent dynamic load P of 7.0 kN. Calculate its nominal rating life in millions of revolutions.
- •Identify input parameters: C = 35 kN, P = 7.0 kN, p = 3.33.
- •Apply the Bearing L10 Life Formula: L10 = (C / P)^p.
- •Compute the ratio: C / P = 35 / 7.0 = 5.0.
- •Raise to power p: L10 = 5.0^{3.33} \approx 214.6 million revolutions.
Engineering Assumptions
- •90% reliability rate (10% expected fatigue spalling failure rate).
- •Adequate film thickness lubrication and no extreme impact shocks.
- •Proper mounting, alignment, and preload per manufacturer guidelines.
Design Limitations
- •Does not account for reliability requirements higher than 90%, nor does it adjust for environmental cleanliness, temperature limits, or specialized oils (requires ISO 281 adjusted life calculations Lnm).
- •Static load safety factor (C₀/P₀ ≥ 1.0, typically ≥ 2–3 for vibration/shock) must be verified separately.
- •Does not account for misalignment, mounting errors, or false brinelling.
Academic References & Standards
Rolling bearings - Dynamic load ratings and rating life
Global standard for bearing load ratings and dynamic calculations.
Adjusted rating life with a_{ISO} factor
Standard extension for contamination and lubrication effects.
SKF General Bearing Catalogue - Selection Guide
Primary reference for bearing dynamic capacities, life estimation, and selection parameters.
Schaeffler Rolling Bearing Catalogue
Detailed X,Y factors, load ratings, and adjustment factors.