Bearing Basic Rating Life (L₁₀)

Rolling bearings do not wear out in the ordinary sense. Kept clean and properly lubricated, a bearing eventually fails by subsurface fatigue: repeated Hertzian contact stress under each rolling element initiates a crack a fraction of a millimetre below the raceway, which propagates to the surface and spalls a flake out. From then on the bearing is noisy and finished. That fatigue process is statistical, not deterministic — identical bearings under identical loads fail at wildly different times — so bearing life is quoted as a probability:

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

$L_{10}$ is the life, in millions of revolutions, that 90% of a large group of identical bearings will reach or exceed. Ten percent will not. $C$ is the basic dynamic load rating from the manufacturer's catalogue — defined as the load that gives exactly one million revolutions of $L_{10}$ life — and $P$ is the equivalent dynamic load your application actually applies. This is ISO 281, and it is the same in every manufacturer's catalogue in the world.

The exponent, and the mistake it invites

\[ p = 3 \ \text{for ball bearings} \qquad p = \tfrac{10}{3} \ \text{for roller bearings} \]

The difference is contact geometry. A ball touches its raceway at a point, which under load spreads into a small ellipse; a roller touches along a line, which spreads into a rectangle. The line contact distributes the same load over more material and its stress rises more slowly with load, and the empirical exponent that comes out of the fatigue testing is 10/3 rather than 3.

Using 3 for a roller bearing understates its life by a wide margin — at a load ratio of 5 the true answer is 214 million revolutions and the wrong exponent gives 125, a 42% shortfall — and on a marginal selection that error sends you to a larger, more expensive bearing you did not need. The error in the other direction, using 10/3 on a ball bearing, overstates the life, and that one matters more.

Steepness is the design lesson

With $p = 3$, halving the load multiplies the life by eight. Nothing else in machine design responds that steeply. It means that small reductions in load pay enormous dividends: taking excess tension out of a belt, correcting a misalignment, removing an unbalanced mass, or shortening an overhang buys far more bearing life than going up a size. It also means the reverse — a bearing running at 25% above its intended load loses about half its life.

Getting hours out of revolutions

\[ L_{10h} = \frac{L_{10}\times 10^{6}}{60\,n} \qquad (n \ \text{in rev/min}) \]

Design targets vary by an enormous range depending on the application: a few thousand hours for household appliances, 20,000–30,000 for general industrial machinery running continuously, 50,000 to 100,000 or more for large fans, pumps and paper machines where a shutdown is unthinkable.

What the number does not include

The equation covers fatigue and nothing else, and fatigue is a minority cause of bearing failure in the field. Contamination, inadequate or wrong lubricant, moisture, misalignment, mounting damage from hammering on the wrong ring, electrical current passage from a variable-frequency drive, and false brinelling in storage or transit account for most bearings that actually fail. ISO 281 addresses this with a modified rating life,

\[ L_{nm} = a_1 \, a_{ISO} \, L_{10} \]

where $a_1$ adjusts for a reliability other than 90% and $a_{ISO}$ folds in the lubrication condition, the contamination level and the bearing's fatigue load limit. That lubrication and contamination term alone can move the answer by more than an order of magnitude — in either direction. A well-lubricated, clean bearing loaded below its fatigue limit can in principle run indefinitely; a contaminated one can fail at a small fraction of its calculated life.

Equivalent load

One more subtlety: $P$ is an equivalent load, not simply the radial force. Where a bearing carries both radial and axial load, it is combined as $P = X F_r + Y F_a$, with $X$ and $Y$ factors specific to the bearing type and the load ratio, listed alongside $C$ in the catalogue. A deep-groove ball bearing carrying significant thrust needs this treatment; a pure radial load does not.