## Roller Bearing

Consider a roller bearing is selected for a unique assembly. If the design requires a minimum basic load rating of 5.5 N and a design life of 10, what is the design radial load?

##
__
__**Hint**

**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**

**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 ball bearings,
$$a=3$$
. However, the problem statement is asking for a roller bearing, so
$$a=10/3$$
. Thus,

$$$5.5N=P(10\cdot 10^6)^{1/(10/3)}$$$

$$$P=\frac{5.5N}{10,000,000^{3/10}}=\frac{5.5N}{125.89}=0.04\:N$$$

0.4 N