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GEAR TEETH. 38
I
To Calculate the Number of Teeth when Distance Be=
tween Centers and Ratio of Speed is Given.
Select for a trial calculation, the diametral pitch which
seems most suitable for the work. »
Calculate the sum of the number of teeth in both gears
corresponding to this pitch by multiplying twice the distance
between their centers by the diametral pitch selected.
The number of teeth in each gear is obtained by the follow-
ing formula
:
NX A
T —
t —
n +jV
n XA_
N -r n
T = Number of teeth in large gear.
/ = Number of teeth in small gear.
JV— Number of revolutions of small gear.
n = Number of revolutions of large gear.
A = Number of teeth in both gears.
Example.
The center distance between two shafts is 15 inches. The
small gear should make 126 and the large gear, 90 revolutions
per minute. Calculate the number of teeth in each gear, if 8
diametral pitch is wanted.
Solution:
The number of teeth in both gears is 2 X 15 X 8 = 240.
-
126X240 -140 teeth.
126 + 90
/= 9<>X 240 ^ 100 teeth.
126 + 90
Frequently it is impossible to get gears of the desired pitch
to fit within the given center distance and to give the exact
ratio of speed. Some modifications must then be made ; either
the exact ratio of speed must be sacrificed, the pitch must be
changed, or the distance between centers must be altered.
Note.—The ratio of the number of teeth in the gears can be
seen from the ratio of the speed. For instance, in the above ex-
ample the ratio of speed is 90
/i26, which, reduced to its lowest
terms, is % ; therefore, the number of teeth in the two gears
may, with regard to speed ratio, be any multiple of 5 and 7,
respectively, but in order to fit the given center distance and
also to be 8 pitch, they must be 100 and 140, which is 20 X 5
= 100 and 20 X 7 = 140.
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