Example

$-$ A single$-$row deep groove ball bearing is used to support the lay shaft of a four speed automobile gear box. It is subjected to the following loads in respective speed ratios

$-$ The lay shaft is fixed to the engine shaft and rotates at $1750$ rpm $.$ The static and dynamic load carrying capacities of the bearing are $11600$ and $17600$ N respectively. The bearing is expected to be in use for $4000$ hours of operation. Find out the reliability

with which the life could be expected.