$11-{31}^{**}$ The shaft shown in the figure is proposed as a preliminary design for the application defined in Problem $3-84.$ The effective centers of the gears for force transmission are shown. The dimensions for the bearing surfaces $($indicated with cross markings$)$ have been estimated. The shaft rotates at $900re\frac{v}{m}in,$ and the desired bearing life is $12$ kh with a $98$ percent reliability in each bearing, assuming distribution data from manufacturer $2$ in Table $11-6.$ Use an application factor of $1\mathrm{.}2.$

$($a$)$ Obtain a Basic Load Rating for a ball bearing at the right end.

$($b$)$ Use an online bearing catalog to find a specific bearing that satisfies the needed Basic Load Rating and the geometry requirements. If necessary, indicate appropriate adjustments to the dimensions of the bearing surface.

Problem $11-31*$

All fillets $2$ mm $.$ Dimensions in millimeters.