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WORMS AND WORM GEARS. 407
Solution
:
In Table No. 47 the pitch diameter of a gear of 68 teeth of
one-inch pitch is given as 21.65 inches; thus, the pitch diameter
for a gear of 68 teeth of %-inch circular pitch will be 21.65 X
0.75 = 16.738 inches.
In column a, of Table No. 5 2 . the addendum for |^-inch
circular pitch is given as 0.2387 inch ; fhis is multiplied by 2,
because it is to be added on both sides of the gear.
Thus, the smallest outside diameter of the gear is 16.738 -+-
0.2387 X 2 = 17.215 inches; or, practically, 17g% inches. If the
gear is to be made hollow to correspond to the curve at bottom
of thread of the worm, make a scale drawing as shown in Fig.
13, and make line^ 17^ inches ; from this drawing the largest
outside diameter may be obtained by measurement.
The diameter of the worm on the pitch line was to be six
times the pitch = 6 X %" — 4>£ inches.
The addendum for the thread on the worm can be obtained
from Table No. 52, column a, and is 0.2387. The outside
diameter of the worm will be 4.5 + 2 X 0.2387 = 4.977 inches, or,
practically, 4|^ inches.
The cutter to be used in roughing out the gear should have
a curve of involute form corresponding to a spur gear cutter for
68 teeth, and its thickness ought to be at least 0.005 inch less
than the width of space as given in column S of Table No. 52.
Therefore the thickness on the pitch line of the roughing cutter
will be 0.37 inch.
The angle of the teeth may be obtained from a drawing as
shown and explained in Fig. 13, or it may be calculated thus :
rj, r 1 c lead of worm
Tangent of angle S = ——-
—
:
-
pitch circumference
Tang. S = 3 X ° 75 = 2 ’ 25
= 0.15915
4.5 x 3-1416 14-1372
In Table No. 21 the corresponding angle is given as 9
degrees and 10 minutes, very nearly.
The depth to which the gear should be cut is given in col-
umn D as 0.515 inch. The gear is finished with a hob, as
described below, which is allowed to cut until it touches the
bottom of the spaces in the gear. The outside diameter of the
hob should be larger than the outside diameter of the worm, in
order that the teeth in the hob may reach the bottom of the
spaces in the gear and leave clearance for the worm, and at the
same time leave the gear tooth of the proper thickness on the
pitch line. This increment is obtained in column k, Table No.
5 2 , and for 34 -inch pitch is 0.075 inch ; thus, the outside diameter
of the hob is 0.075 inch larger than the outside diameter of the
worm, or 4.977 + 0.075 = 5.052 inches. The angle of the finish-
ing threading tool for both worm and hob is 14^ degrees,
making the angle of space 29°, as shown in Fig. 14. The clear-
ance angle of the threading tool must be a little more than the
angle of the thread.
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