Q$3(10$ Marks$)$

Figure shows a countershaft used in a compound

gear train with $20$ spur gears. Gear A drives with a

speed of $1200$ rpm $.$ Force on each gear are shown

in figure. All gears are of same material. Since gear

$B$ is the smallest gear, transmitting the largest load,

it will likely be critical, so a preliminary analysis is

to be performed on it only. Use a $4$ mm module, a

face$-$width of $4$ times the circular pitch, a Grade $2$

steel through$-$hardened with a Brinell hardness of

$300,$ and a desired life of $1\mathrm{.}1{10}^9$rev with a $90$

percent reliability. Determine factors of safety for

bending and wear.

Use: $$

$J=0\mathrm{.}27,Q_v=6,$ Uncrowned, Commercial enclosed, $Y_N=1\mathrm{.}6831(N{)}^{-0\mathrm{.}0323},Z_N=1\mathrm{.}4488(N{)}^{-0\mathrm{.}023},K_0=K_B$

$=K_T=C_f=1$