Problem # $5(25$ pts$)($open ended$)$

The figure below shows a spindle used in small lathe machines, the drive shaft is mounted using

two similar tapered roller bearings with cup and cone part# $33205.$ The spindle is belt driven, the

tension in the belt creates lateral force in the $-$ve y direction of $200N$ as indicated in the figure. At

the chuck side, the design allows maximum machining loads of; feed force Fx $=-1500$ N$,$ Radial

load $Fz=-750N,$ and cutting force $Fy=2000N.$ Assuming these loads are acting at the center of

chunk at point $C.$

a$.$ Draw F$.$B$.$D of the drive shaft, and determine all bearing reaction forces with exact

locations with respect to given datum.

b$.$ Predict the minimum life of the bearings $($in hours$)$ if you know that the machine operates

at speed of $1200$ rpm $,$ with moderate impact load "use $1\mathrm{.}5$ as application factor"

considering $5\%$ probability of failure of the bearing set.