2. From revolutions to hours
L₁₀ comes out in millions of revolutions, which is the honest unit — a bearing does not know what time is. But nobody specifies a machine in revolutions, so:
Note what this does and does not change. Doubling the speed halves the hours and leaves the revolutions untouched. A bearing in a slow robot joint can be tiny and still last decades; the same bearing at 10 000 rpm is a consumable.
What life to design for
| Application | Typical L₁₀h |
|---|---|
| Household appliance, intermittent | 1 000 – 4 000 h |
| Machine tool spindle | 10 000 – 30 000 h |
| Industrial robot joint | 20 000 – 40 000 h |
| Continuous industrial drive, 24/7 | 50 000 – 100 000 h |
Those are conventions, not physics — they encode how much downtime the application tolerates. 8760 hours is one calendar year of continuous running, which is the number worth keeping in mind when a figure like 40 000 h stops meaning anything.
Reliability costs life, steeply
L₁₀ is a 90 % figure. Wanting better multiplies it by a factor well below one:
| Reliability | 90 % | 95 % | 96 % | 97 % | 98 % | 99 % |
|---|---|---|---|---|---|---|
| a₁ | 1.00 | 0.62 | 0.53 | 0.44 | 0.33 | 0.21 |
Going from 90 % to 99 % throws away four fifths of the calculated life. In a robot with six joints that matters more than it looks: if each joint is 90 % reliable over the design life, the arm as a whole is 0.9⁶ ≈ 53 %.
A robot joint bearing at 30 rpm — slow, so the hours pile up even at a modest load ratio.