Question

Two gears in a 3: 1 ratio gearset and with a diametral pitch of 4 are mounted at a center distance of 6 in. Find the number of teeth on the pinion. (please note that the smaller gear is the pinion, and the larger gear is the gear)

Answer 1

Answer:

Number of teeth on pinion = $N_{p}$ = 12

Step-by-step explanation:

Given:

Gear ratio = 3 : 1 = 3

Diametral Pitch = P = 4

Center distance = c= 6 in

No. of teeth on Pinion = $N_{p}$ =?

Gear ratio =$\frac{ Number. of. teeth. on. gear}{ Number. of. teeth. on. pinion}$ = $\frac{N_{g} }{N_{p}}$ = 3

As Gear ratio = 3, so

Diameter ratio = $\frac{d_{g} }{d_{p}}$ = 3  

(Note : Diameter Ratio = Gear ratio )

$d_{g} =3d_{p}$                                     Equation 1

Center Distance = c = $\frac{d_{g} + d_{p}}{2}$ = $d_{g} + d_{p}$= 2 (c)

$d_{g} + d_{p}$ = 2 (6) = 12 in

substitute $d_{g}$ from equation 1, here

$3d_{p} + d_{p}$ = 12

$4d_{p}$ = 12

$d_{p}$ = $\frac{12}{4}$ = 3

$d_{p}$ =3in

Now : Diametral Pitch =P= $\frac{N_{p} }{d_{p} }$

$N_{p}$ = $d_{p}(P)$

$N_{p}$  = 4 (3)

$N_{p}$ = 12

Which are the number of teeth on pinion