Bearing Type
Consider a bearing has a radial load of 1 N and a design life of 10. If the minimum basic load rating is 215.44 N, is the bearing type a ball or roller?
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.
$$$215.44N=(1N)(10\cdot 10^6)^{1/a}$$$
$$$log(215.44)=log(10\cdot 10^6)\times \frac{1}{a}$$$
$$$a=\frac{log(10\cdot 10^6)}{log(215.44)}=\frac{7}{2.33}=3$$$
For roller bearings,
$$a=10/3$$
. For ball bearings,
$$a=3$$
. Because
$$a$$
was determined to be equal to 3 based on the problem statement’s inputs,
the bearing type is ball.
Ball
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