$10$rmulae sheets are allowed.

Total Marks $100$

A torque $T$ is transmitted by means of system of gears to the shaft shown in Fig. $1.$ If $T=2500Nm,R=0\mathrm{.}08m,a=0\mathrm{.}8m$ and $b=0\mathrm{.}1m.$ Uniaxial yield stress of the material is $500$ MPa $.$ The factor of safety is $2.$ Note that when the torque is transmitted, in addition to the tangential force, there occurs a radial force equal to $0\mathrm{.}5$ F $,$ where F is the tangential force.

The motor power is $25$ kW $.$

i$.$ Determine the diameter of the shaft using maximum shear stress theory. $[10]$

ii$.$ What kind of bearings will you recommend at C and D $?$ If the design life $10,000$ hours, what is the C$10$ catalog entry

Fig. $1$ Transmission shaft and its FBD to be sought $($or exceeded$)$ in a manufacturer's catalog on the basis of ${10}^6$ revolutions for rating life?

$[10]$

iii. If the combined reliability of the two bearings is $0\mathrm{.}95.$ Find the new C $10$ values for bearings $C$ and $D.$ The Weibull parameters are $x_0=0\mathrm{.}02,(-x_0)=4\mathrm{.}439,$ and $b=1\mathrm{.}483.$ The application factor, $a_f,$ is $1\mathrm{.}2.$ The $C_{10}$ for higher reliability