Design Life

#565 / Mechanical Engineering Easy

Consider a ball bearing is selected for a unique assembly. If the design requires a radial load of 1 N and a minimum basic load rating of 200 N, what is the design life (in millions of revolutions)?

Expand Hint
The minimum required basic load rating (the load in which 90% of bearings from a given lot will survive 1 million revolutions) is:
$$$C=PL^{1/a}$$$
where $$C$$ is the minimum required basic load rating, $$P$$ is the design radial load, $$L$$ is the design life (in millions of revolutions), and $$a$$ is the bearing coefficient.
Hint 2
For ball bearings: $$a=3$$
For roller bearings: $$a=\frac{10}{3}$$
The minimum required basic load rating (the load in which 90% of bearings from a given lot will survive 1 million revolutions) is:
$$$C=PL^{1/a}$$$
where $$C$$ is the minimum required basic load rating, $$P$$ is the design radial load, $$L$$ is the design life (in millions of revolutions), and $$a$$ is the bearing coefficient. For roller bearings, $$a=10/3$$ . However, the problem statement is asking for a ball bearing, so $$a=3$$ . Thus,
$$$200N=(1N)(L)^{1/3}$$$
$$$200^{3}=(L^{1/3})^{3}$$$
$$$L=200^{3}=8,000,000$$$
Because design life is measured in millions of revs, the ball bearing’s design life is 8 .
8


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