$2$: $(50$ points$).$ The following figure is a sketch of a rotating shaft supported by two tapered roller bearings

using an indirect mounting. The radial bearing loads are $625$ lbf and $875$ lbf with an axial load of $250$ lbf

as shown. The shaft rotates at $400re\frac{v}{m}in$ and is to have a desired life of $90$ kh $.$

$($a$)$ Which bearing is A and which one B in the Figure as the convention of the design procedure.

$($b$)$ Select a bearing $($by naming its cup and cone numbers for each bearing$)$ using Timken Company

tapered roller bearings data shown in figure $11-15.$ The bore size in the range of $1\mathrm{.}0-1\mathrm{.}5$ inch is

good and a reliability of $90\%$ is desired.

$625$ lbf

$F_{\text{a}\text{c}\text{e}}=250lbf$

$875$ lbf