Bearing Life (hours)⚠ unverified
Mechanical / Bearings · Convert rating life to hours at a given speed
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| L10_millions | L10 | — | 1000.0 | Rating life (millions of rev) |
| rpm | n | rpm | 1500.0 | Rotational speed |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| hours | Lh | hour | Rating life in hours |
The science & history
Understanding the Parameters
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Rating life $L_{10}$ — the fatigue life in millions of revolutions, i.e. the raw count of stress cycles the bearing survives with 90 % reliability. It is a property of load and capacity alone and carries no notion of time until a speed is supplied.
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Rotational speed $n$ — the shaft speed in revolutions per minute. It is the bridge between revolutions (what fatigue actually counts) and time (what the operator cares about). The formula assumes $n$ is essentially constant; for a varying-speed duty you must first compute an equivalent mean speed or integrate the damage over the speed history.
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The factor $60$ — converts minutes to seconds' worth of counting, i.e. it turns rev/min into rev/hour ($60\,n$ revolutions per hour). The $10^6$ simply undoes the "millions" in which $L_{10}$ is expressed.
Derivation (Approaching a Proof)
Fatigue life is fundamentally a count of load cycles $N$ (here, revolutions). Time is that count divided by the rate at which cycles accumulate:
$$L_h \;=\; \frac{N}{\text{revolutions per hour}}.$$
The total revolutions are $N = 10^6\, L_{10}$ (because $L_{10}$ is quoted in millions). The revolutions per hour at speed $n$ rev/min are
$$n \ \frac{\text{rev}}{\text{min}} \times 60\ \frac{\text{min}}{\text{hour}} = 60\, n \ \frac{\text{rev}}{\text{hour}}.$$
Dividing gives
$$L_h = \frac{10^6\, L_{10}}{60\, n}.$$
There is no physics beyond the fatigue count itself — this is dimensional bookkeeping — but it is the step that makes the fatigue theory usable in the field.
Dimensional check. $\dfrac{\text{(rev)}}{\text{(rev/hour)}} = \text{hour}$. ✓
History and Development
The revolutions-to-hours conversion has appeared in every rolling-bearing catalogue since the Lundberg–Palmgren rating life was standardised as ISO 281. SKF, Timken, NSK, and FAG selection guides all present it, often folded together with the rating-life formula into a single nomogram or $L_{10h} = \dfrac{10^6}{60 n}\left(\dfrac{C}{P}\right)^a$ expression. The persistence of the "hours" convention reflects that machinery is specified by service intervals (e.g. "40 000 h for a fixed industrial gearbox") rather than by cycle counts.
Related Concepts: Bearing Rating Life L10, Equivalent Dynamic Load Bearing, Minimum Required Dynamic Capacity, Dynamic Load Rating
Notes: Assumes constant speed. For variable-speed duty, combine load/speed bins using an equivalent load and equivalent speed, or sum fatigue damage (Palmgren–Miner) across the duty cycle.