TAHA Engineering Toolsby TAHA Knowledge Lab

Mechanical Engineering

Rolling Bearing Life Calculator (L10)

Basic rating life L10 in revolutions and hours for ball or roller bearings, with reliability factor.

Inputs

Front view of a ball bearing: outer ring, inner ring, ten balls between them, and a load arrow P acting on the shaft.Pnouter ringinner ring
A ball bearing under an equivalent radial load P. L10 is the life in revolutions that 90% of identical bearings reach; it depends on (C ÷ P) raised to the power 3 for ball bearings or 10/3 for roller bearings. Diagram not to scale.

From the bearing manufacturer’s catalogue for the exact bearing.

For combined loads P = X·Fr + Y·Fa with X and Y from the catalogue. For a pure radial load on a radial bearing, P = Fr.

L10 is the life that 90% of a large group of identical bearings reach. Higher reliability gives a shorter life (ISO 281 factor a1).

Result

Rating life
1,071.65million revolutions
Rating life in operating hours
11,907.2
Basic rating life L10
1,071.65million revolutions
Load ratio C ÷ P
10.2333
Working
L10 = (C ÷ P)^3 = (30.7 ÷ 3)^3 = 1,071.6 million rev Hours = 10⁶ × 1,071.6 ÷ (60 × 1,500 rpm) = 11,907 h

The rating life is 1,071.65 million revolutions, about 11,907.2 h at this speed.

Educational estimate — check the assumptions below.

About this calculator

Rolling bearings eventually fail by fatigue of the raceways or rolling elements. Because fatigue is statistical, bearing life is defined for a large group: the basic rating life L10 is the number of revolutions that 90% of identical bearings will reach or exceed under the same load. It depends on the ratio of the bearing’s dynamic load rating C (from the catalogue) to the equivalent load P it carries, raised to an exponent of 3 for ball bearings and 10/3 for roller bearings.

Formula

L10 = (C ÷ P)p   (millions of revolutions)    p = 3 (ball), 10/3 (roller)

L10h = 10⁶ × L10 ÷ (60 × n)    Ln = a1 × L10

C = basic dynamic load rating, P = equivalent dynamic bearing load, n = speed (rpm), a1 = life modification factor for reliability (ISO 281).

Worked example

A deep-groove ball bearing with C = 30.7 kN carrying P = 3 kN at 1500 rpm:

  • L10 = (30.7 ÷ 3)³ = 10.233³ = 1071.6 million revolutions
  • Hours = 10⁶ × 1071.6 ÷ (60 × 1500) = 11 907 h
  • At 99% reliability: L1 = 0.25 × 1071.6 = 267.9 million revolutions (2977 h)

The same load ratio on a roller bearing: (10.233)10/3 = 2327 million revolutions.

Assumptions and limitations

  • Basic rating life only: conventional bearing steel, normal operating conditions. The ISO 281 modified life (factor aISO for lubrication, contamination and fatigue load limit) is not calculated — bearing makers provide tools for it.
  • C and the X, Y factors for P must come from the catalogue of the exact bearing. Calculating P correctly from radial and axial loads is often the largest source of error.
  • The life equation does not cover failures from poor lubrication, contamination, misalignment, wrong fits or overload. Check the static load rating C0 for heavy or shock loads.

References

  • ISO 281:2007 Rolling bearings — Dynamic load ratings and rating life (L10 equation, exponents and reliability factor a1).