Bearing life L10 per ISO 281
Calculate the basic rating life of rolling bearings per ISO 281: load rating, radial and axial force yield the equivalent load P with a transparent e criterion, then L10 in revolutions and L10h in operating hours, including a comparison against application guide values and the static safety factor S0.
Bearing calculator: L10, L10h and S0 (ISO 281 / ISO 76)
P = X · Fr + Y · Fa with X = 0.56 and Y = 1.4566
Fa/Fr > e = 0.3074: the axial force enters P.
Calculation trail of the X/Y determination
Relative axial load f0 · Fa / C0 = 1.38
Linear interpolation between the reference points 0.9 (e = 0.28; Y = 1.58) and 1.6 (e = 0.32; Y = 1.4).
- Life exponent p
- 3
- Basic rating life L10 in revolutions
- 273.4 · 10⁶
- Rating life L10h
- 3,038 hguide value reached
Minimum guide value for normal running: S0 ≥ 1. Use higher values under shock loads or high running smoothness requirements. The largest occurring loads including shock peaks govern.
Basic rating life per ISO 281 (constant load and speed, rotating inner ring). Lubrication, contamination and reliability ≠ 90 % are only covered by the modified rating life Lnm = a1 · aISO · L10. Static verification simplified per ISO 76. X/Y table values for normal clearance CN.
Formulas and fundamentals
The basic rating life per ISO 281 is L10 = (C/P)^p in millions of revolutions. C is the basic dynamic load rating from the manufacturer's catalogue, P the equivalent dynamic load and p the life exponent: 3 for ball bearings, 10/3 for roller bearings. L10 is defined statistically: 90 percent of a sufficiently large group of identical bearings reach or exceed this life before the first material fatigue occurs. With the speed n the life in operating hours follows as L10h = L10 · 10⁶ / (60 · n).
Under combined radial and axial load the equivalent load is P = X · Fr + Y · Fa. Whether the axial force enters at all is decided by the e criterion: as long as Fa/Fr stays below the limit value e, simply P = Fr applies. Only above it do the factors X and Y take effect. For deep groove ball bearings e and Y depend on the relative axial load: the calculator forms f0 · Fa / C0 (with the calculation factor f0 from the product table) or alternatively Fa / C0 and interpolates e and Y linearly between the catalogue reference points – exactly as the manufacturer catalogues require. Both reference points are shown in the calculation trail.
Fixed formula structures apply to the other bearing types: a cylindrical roller bearing used as a floating bearing carries radial force only (P = Fr, axial force only permissible to a limited extent). For tapered roller bearings P = 0.4 · Fr + Y · Fa applies above e, for spherical roller bearings P = Fr + Y1 · Fa below and P = 0.67 · Fr + Y2 · Fa above e. The values e, Y, Y1 and Y2 are bearing specific and are entered directly from the manufacturer's product table.
In addition the calculator checks the static case per ISO 76: the static safety factor is S0 = C0/P0 with the equivalent static load P0. For deep groove ball bearings P0 = Fr applies as long as Fa/Fr does not exceed 0.8, above that P0 = 0.6 · Fr + 0.5 · Fa. Minimum values for normal running are S0 = 1.0 for ball bearings and 1.5 for roller bearings; more under shock loads or high running smoothness requirements.
Two plausibility checks complete the result: if the equivalent load falls below the minimum load (on the order of C0/100 for ball bearings, C0/60 for cylindrical and tapered roller bearings), skidding damage from an underloaded, i.e. oversized bearing is a risk. And at speeds below 10 rpm it is not fatigue but the static verification that governs.
Worked example
Given: deep groove ball bearing 6208 with C = 32.5 kN, C0 = 19 kN and f0 = 13.8 (SKF catalogue data), loaded with Fr = 4000 N and Fa = 1900 N at n = 1500 rpm.
X/Y determination: the relative axial load is f0 · Fa / C0 = 13.8 · 1900 / 19,000 = 1.38. Linear interpolation between the reference points 0.9 (e = 0.28; Y = 1.58) and 1.6 (e = 0.32; Y = 1.4) yields e = 0.307 and Y = 1.457. Since Fa/Fr = 0.475 > e the axial force enters: P = 0.56 · 4000 + 1.457 · 1900 = 5008 N.
Life: L10 = (32,500 / 5008)³ = 273.4 million revolutions, hence L10h = 273.4 · 10⁶ / (60 · 1500) = 3038 h. For intermittently used machines (guide value 3000 to 8000 h) this is just sufficient.
Static verification: since Fa/Fr = 0.475 ≤ 0.8, P0 = Fr = 4000 N, hence S0 = 19,000 / 4000 = 4.75 – well above the minimum value 1.0. The minimum load C0/100 = 190 N is also safely exceeded with P = 5008 N.
Frequently asked questions
What exactly does L10 mean – is it a guaranteed life?
No. L10 is the life that 90 percent of a large group of identical bearings reach or exceed before the first fatigue damage occurs. Statistically 10 percent fail earlier. The actual service life can be considerably shorter due to lubrication, contamination or mounting errors.
Where do I get C, C0 and f0?
All three are product data from the manufacturer's catalogue or online product table (e.g. for a 6208: C = 32.5 kN, C0 = 19 kN, f0 = 13.8). Load ratings are manufacturer specific and not transferable between manufacturers.
When does the axial force enter the equivalent load?
Only when the ratio Fa/Fr exceeds the limit value e. Below it P = Fr applies. For deep groove ball bearings e depends on the relative axial load and is interpolated linearly between the catalogue reference points; the calculator shows the reference points used.
What is the difference between ball and roller bearings in the calculation?
The life exponent: p = 3 for ball bearings, p = 10/3 for roller bearings. Roller bearings therefore reach a longer life at the same C/P ratio, or need a smaller load rating for the same life.
Why does the calculator warn at very low loads?
Rolling bearings need a minimum load (on the order of C0/100 for ball bearings, C0/60 for cylindrical and tapered roller bearings) so that the rolling elements roll instead of sliding. A heavily oversized bearing can fail prematurely due to skidding and smearing – bigger is not automatically better.
Does the calculator account for lubrication and cleanliness?
No, it calculates the basic rating life L10 per ISO 281. The modified rating life Lnm = a1 · aISO · L10 additionally rates lubricant film, contamination and fatigue load limit; that requires viscosity and cleanliness data. Under good conditions the real life is often well above L10, under poor lubrication well below. The factor a1 applies to a reliability other than 90 %; for 90 % a1 = 1 – the default used here. The a1 values themselves differ by source: ISO 281:2007 redefined them, yet current textbooks such as Roloff/Matek (18th edition, 2007) still list the older a1 values (e.g. 0.21 instead of 0.25 at 99 %). Check which set of values your catalogue uses.