Rolling Element Bearing L10 Life Equation
Calculates the statistical fatigue rating life of ball or roller bearings in millions of revolutions.
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.
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).
Academic References & Standards
Rolling bearings - Dynamic load ratings and rating life
Global standard for bearing load ratings and dynamic calculations.
SKF General Bearing Catalogue - Selection Guide
Primary reference for bearing dynamic capacities, life estimation, and selection parameters.