Type of Bearing
Consider a bearing has a radial load of 5 N and a design life of 1. If the minimum basic load rating is 315.48 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.
$$$315.48N=(5N)(1\cdot 10^6)^{1/a}$$$
$$$log(\frac{315.48}{5})=log(1\cdot 10^6)\times \frac{1}{a}$$$
$$$a=\frac{log(1\cdot 10^6)}{log(63.096)}=\frac{6}{1.8}=3.33=\frac{10}{3}$$$
For roller bearings,
$$a=10/3$$
. For ball bearings,
$$a=3$$
. Because
$$a$$
was determined to be equal to 10/3 based on the problem statement’s inputs,
the bearing type is roller.
Roller
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