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Anettt [7]
3 years ago
15

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 t

eeth on the pinion. (please note that the smaller gear is the pinion, and the larger gear is the gear)
Mathematics
1 answer:
Ivahew [28]3 years ago
4 0

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  

<em>(Note : Diameter Ratio = Gear ratio )</em>

d_{g} =3d_{p}            <u>                         </u><em><u>Equation 1</u></em>

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

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