Engineering · Machine elements

Basic rating life of a rolling bearing

The ISO basic L10 life scales dynamic rating C to equivalent dynamic bearing load P.

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Formula

L_{10} = (\frac{C}{P})^{p}

L10 in million revolutions; C and P in N; p=3 for ball, 10/3 for roller bearings

Variables & units

Variables & units
Symbol	Meaning	Unit
$L10$	Basic rating life reached or exceeded by 90% of a sufficiently large bearing group	million revolutions
$C$	Basic dynamic load rating	N
$P$	Equivalent dynamic bearing load	N
$p$	Life exponent for bearing type	dimensionless

LaTeX

L_{10}=\left(\frac{C}{P}\right)^p

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Derivation & background

The basic relation follows ISO 281 for a dynamically loaded bearing with constant equivalent load. It is a statistical reference, not a guarantee. Lubrication, contamination, reliability above 90%, temperature, fits and varying loads can require modified-life methods; use the applicable manufacturer and standards procedure.

Exam blueprint

Validity range

Derivation steps

The ISO basic L10 life scales dynamic rating C to equivalent dynamic bearing load P.

1State the model assumptions and list quantities with units.
2Substitute into L10 = (C/P)^p; convert quantities to SI first.
3For a ball bearing with C=20 kN and P=5 kN, L10=(4)^3=64 million revolutions.

Rearrangements

Base equation for the target quantity

L_{10}=\left(\frac{C}{P}\right)^p

Preserve signs, boundary conditions and units when rearranging.

Task variant

Work through the numerical example for “Basic rating life of a rolling bearing” and check its unit and magnitude.

For a ball bearing with C=20 kN and P=5 kN, L10=(4)^3=64 million revolutions.

Common mistakes

Substituting a related quantity that shares the same symbol.

Use variable definitions and check: L10 in million revolutions; C and P in N; p=3 for ball, 10/3 for roller bearings.

Exam context

Estimate reference bearing life under a defined dynamic load.

Formula cluster

Machine elements

The ISO basic L10 life scales dynamic rating C to equivalent dynamic bearing load P.

η = Pout/Pin

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M = F·r·sin(θ)

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n₁/n₂ = D₂/D₁

Speed ratio of slip-free belt pulleys

Worked example

For a ball bearing with C=20 kN and P=5 kN, L10=(4)^3=64 million revolutions.

Applications

Estimate reference bearing life under a defined dynamic load.

How do you calculate with Basic rating life of a rolling bearing?

Here is how to work through a typical Basic rating life of a rolling bearing (L10 = (C/P)^p) task step by step:

1
Task
Work through the numerical example for “Basic rating life of a rolling bearing” and check its unit and magnitude.
Solution path
For a ball bearing with C=20 kN and P=5 kN, L10=(4)^3=64 million revolutions.

Frequently asked questions about Basic rating life of a rolling bearing

What does L10 mean?+

L10 is the basic rating life that 90% of a sufficiently large bearing group are expected to reach or exceed. It is a statistical fatigue reference, not a guarantee for one bearing. Scatter and operating conditions can change actual life. This ISO-based reference is statistical and assumes an equivalent constant dynamic load. Application: Estimate reference bearing life under a defined dynamic load. The numerical example For a ball bearing with C=20 kN and P=5 kN, L10=(4)^3=64 million revolutions anchors the idea in a concrete measurement case.

Why are there different p exponents?+

The fatigue-life exponent depends on rolling-element type. The basic relation typically uses p=3 for ball bearings and 10/3 for roller bearings. Check bearing type and governing standard rather than generalizing the exponent. This ISO-based reference is statistical and assumes an equivalent constant dynamic load. The corresponding units are L10 in million revolutions; C and P in N; p=3 for ball, 10/3 for roller bearings. For a ball bearing with C=20 kN and P=5 kN, L10=(4)^3=64 million revolutions. This checks that the reference quantities are compatible.

How can L10 be converted to hours?+

At constant speed n in rpm, divide revolutions by 60n; because the formula returns million revolutions, also multiply by 10⁶. Variable speed and load require an equivalent load cycle. This ISO-based reference is statistical and assumes an equivalent constant dynamic load. Scope: The basic relation follows ISO 281 for a dynamically loaded bearing with constant equivalent load. It is a statistical reference, not a guarantee. Lubrication, contamination, reliability above 90%, temperature, fits and varying loads can require modified-life methods; use the applicable manufacturer and standards procedure. A practical application is Estimate reference bearing life under a defined dynamic load.

How do I check the result and units for Basic rating life of a rolling bearing?+

Write the quantity and unit from the variable list next to every value: L10 in million revolutions; C and P in N; p=3 for ball, 10/3 for roller bearings. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For a ball bearing with C=20 kN and P=5 kN, L10=(4)^3=64 million revolutions. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. This ISO-based reference is statistical and assumes an equivalent constant dynamic load.

Which model limit matters for Basic rating life of a rolling bearing?+

The background states this starting condition: The basic relation follows ISO 281 for a dynamically loaded bearing with constant equivalent load. It is a. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. This ISO-based reference is statistical and assumes an equivalent constant dynamic load.

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Subject references and further reading

This list names subject references and further reading. A page or section number appears when it is part of the reference; these are not verbatim quotations.

[1]SKF, Rolling bearings catalogue, basic rating life and ISO 281.

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Quanta Study editorial team

Symbol

Meaning

Unit

L10

Basic rating life reached or exceeded by 90% of a sufficiently large bearing group

million revolutions

C

Basic dynamic load rating

P

Equivalent dynamic bearing load

p

Life exponent for bearing type

dimensionless

Derivation & background

Exam blueprint

Validity range

Derivation steps

The ISO basic L10 life scales dynamic rating C to equivalent dynamic bearing load P.

1State the model assumptions and list quantities with units.
2Substitute into L10 = (C/P)^p; convert quantities to SI first.
3For a ball bearing with C=20 kN and P=5 kN, L10=(4)^3=64 million revolutions.

How do you calculate with Basic rating life of a rolling bearing?

Here is how to work through a typical Basic rating life of a rolling bearing (L10 = (C/P)^p) task step by step:

Task

Work through the numerical example for “Basic rating life of a rolling bearing” and check its unit and magnitude.

Solution path

For a ball bearing with C=20 kN and P=5 kN, L10=(4)^3=64 million revolutions.

Frequently asked questions about Basic rating life of a rolling bearing

What does L10 mean?+

Why are there different p exponents?+

How can L10 be converted to hours?+

How do I check the result and units for Basic rating life of a rolling bearing?+

Which model limit matters for Basic rating life of a rolling bearing?+