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

Number of teeth on pinion =
`N_(p)` = 12

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 =
`( Number. of. teeth. on. gear)/( Number. of. teeth. on. pinion)` =
`(N_(g) )/(N_(p))` = 3

As Gear ratio = 3, so

Diameter ratio =
`(d_(g) )/(d_(p))` = 3

(Note : Diameter Ratio = Gear ratio )

`d_(g) =3d_(p)` Equation 1

Center Distance = c =
`(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)` =
`(12)/(4)` = 3

`d_(p)` =3in

Now : Diametral Pitch =P=
`(N_(p) )/(d_(p) )`

`N_(p)` =
`d_(p)(P)`

`N_(p)` = 4 (3)

`N_(p)` = 12

Which are the number of teeth on pinion