$)$

The double$-$reduction helical gearset shown in the figure above is driven through

shaft $a$ at a speed of $1200re\frac{v}{m}in.$ Gears $2$ and $3$ have a normal diametral pitch of

$12$ teeth$/$in$,$ a $30$ helix angle, and a normal pressure angle of $20.$ The second pair

of gears in the train, gears $4$ and $5,$ have a normal diametral pitch of $6$ teeth$/$in$,$ a

$25$ helix angle, and a normal pressure angle of $20.$ The tooth numbers are: $N_2=$

$14,N_3=54,N_4=16,N_5=36.$ Find:

$($a$)$ The directions of the thrust force exerted by each gear upon its shaft

$($b$)$ The speed and direction of shaft $c$

$($c$)$ The center distance between shafts

$)$

If the gearset in question #$1$ is to transmit $20HP,$a being the input shaft and shaft

c being the output shaft.

a$)$ What is the type of the gear train shown in figure?

b$)$ Compute the tangential and radial forces acting on each of the gears $2,3$

and $4.$

Question #$3$

Find a suitable diameter of each of the shafts $a,b,$ and $c($in figure of question #$1)$

if the material of the shafts has a yield stress equal to $60{10}^3.$ Make any

necessary assumption.

Question #$4$

For the forces computed in question #$2$ and design life of $3000$ hours.

Compute the design load and

Compute the rating load of the bearings. $($Take rating life equal to ${10}^6$

load cycles$).$