A gear reduction unit has input shaft AB and output shaft CD with

an input torque of Ti $=200$ lfin at constant speed of $600$ rev$/$min driving

an output load torque To at output speed wo$.$ Shaft AB $($shown separately

with dimensions$)$ is supported by deep$-$groove ball bearings at A and B$,$

which can be treated as simple supports. The pitch radii of the gears are

r$1=1\mathrm{.}0$ in and r$2=2\mathrm{.}5$ in$.$ The pressure angle for the spur gears is $20$

degrees as shown. The targeted combined reliability for the entire set of

four bearings is $92$ percent for a life of $30000$ hours of operation.

a$.$ Determine the target reliability for each individual bearing

b$.$ Determine the radial force to be carried by the bearing A

c$.$ Determine the load rating with which to select a bearing from a catalog that

rates bearings from an L$10$ life of $1$ million cycles.