A $3-$gear simple train containing a pinion, an idler gear, and a gear. The pinion meshes with

the idler and the idler meshes with the gear. The pinion shaft passes $20$ hp at $2500$ rpm$.$ The

train ratio is $3\mathrm{.}5$:$1.$ The pinion has $14$ teeth, a $25$o pressure angle, and p d $=6.$ The idler has

$17$ teeth. The teeth are standard AGMA full$-$depth profiles. The load and source are both

uniform in nature. A gear$-$quality index of $6$ will be used. All gears are steel with $=0\mathrm{.}28.$ The

service life required is $5$ years of one$-$shift operation with $99\%$ reliability. All gears are steel.

Operating temperature is $200$o F$.$

a$.$b$.$c$.$d$.$Find the gear diameters and the mean and alternating components of transmitted load

on each gear.

Determine a suitable face width and the bending stresses in the gear teeth.

Determine the surface stresses in the gear teeth of the $3-$gear.

Write a computer code to select suitable materials and design for a factor of safety of

$1\mathrm{.}5.$ Calculate the safety factors for both bending and surface stresses.