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4-00 BEVEL GEARS.
and the total depth to cut the gear at a are 0.098 inch and 0.135
inch, respectively.
These dimensions are found in Table No. 49, as if it was
a spur gear of 16 diametral pitch. All the dimensions of the
tooth decrease gradually toward b, as the whole tooth is sup-
posed to vanish in a point in the center at c. The dimensions
of the teeth at b may be calculated and are always in the same
proportion to the dimensions at a as the distance c b is to the
distance c a ; thus, if the length of the tooth from a to b is made
one-third of the length of the distance c a, the distance b c is
two-thirds of the distance a c, and, consequently, all the dimen-
sions of the tooth at b are two-thirds of the dimensions at a.
Instead of calculating the size of the teeth at<£, the dimensions
may be obtained by careful drawing. The depth of the tooth at
the smallest end is "then measured directly at b, but the thickness
is measured at /; the distance t h is laid off equal to b d.
The length of the tooth from a to b is to a certain extent
arbitrary, but a good rule is seven inches divided by the diame-
tral pitch, but never longer than one-third of the distance from
a to c.
Example.
What is the proper length for the teeth of a bevel gear of 8
diametral pitch ?
Solution
:
Seven inches divided by 8 = % inch, if the gears are of such
diameters that this will not make the length of the teeth more
than one-third of the distance from a to c.
Form of Tooth in Bevel Gears.
Extend the line a (see Fig.12), until it intersects the axial
center line of the gear, as at h ; use/z as the center, and the shape
of tooth at a for the large gear is constructed as if it was a spur
gear having a pitch radius as large as a k.
The shape of the tooth at b is constructed in the same way,
by extending the line b (which always—the same as line #,—is
square to the pitch line of the tooth) until it intersects the
axial center line of the gear, as at d. Using d as center, the
shape of the tooth is constructed as if it was a spur gear having
a pitch radius equal to db. The shape of the teeth of the small
gear is obtained in the same way. which is shown by the drawing.
The form of tooth is shown to be approximately involute,
constructed as explained for spur gears, page 388.
Measuring the back cone radius, a /i, of the large gear, it is
found to be f-§ inch, and the diameter will be f§ inch ; thus, the
shape of the tooth at a for the large gear will be the same as the
shape of the tooth in a spur gear of 58 teeth, sixteen diametral
pitch.
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