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RIMS, ARMS AND HUBS OF SPUR GEARS 393
Example: >
Find chordal pitch in the gear shown in Figure 8 where
the gear has 18 teeth and li inch circular pitch.
Solution:
Pitch radius is 4.295 inches.
Angle a = —- = 10 degrees.
Sine of 10 deg. is found in the table on page 158 to be 0.17365.
Chordal pitch =2X0.17365X4.295 = 1.492 inches.
Thus, we see in this case the chordal pitch is 0.008 inch
less than the circular pitch.
For such a gear all calculations must be made according to
circular pitch, but when spacing off the teeth on the pitch circle
the dividers are, of course, set according to the chordal pitch.
"When a gear has a large number of teeth, the difference between
the circular pitch and the chordal pitch is practically nothing.
Rim, Arms and Hub of Spur Gears.
Figure 9 shows the shape of rim, arms and hub of a cast
iron gear as used in the ordinary mill gearing.
The thickness of the rim of the gear at the edge, as at t, Fig-
ure 9 may be 0.5 X P.
The thickness of the rim at the middle, as at S, may be 2 X /,
or which is the same, equal to the pitch of the gear.
The width of the rim, as at F, Figure 9, may be from two
to three times the pitch of the gear.
The number of arms in large cast iron gears may be
taken as follows : When gears are less than 8 feet in diameter
use six arms; from 8 to 16 feet diameter, use eight arms
and from 16 to 24 feet diameter, use ten arms.
The dimensions of the arms may be calculated by the fol-
lowing formulas:
For 1 in. circular pitch or more, the width of the arm
produced to the center of the gear, as at h Figure 9, may be
3
- V-
D X P X F
m
The width of the arm at the rim as at klt Figure 9, may be
-,, = 0.85 X J. D X P X F
it = width of arm in inches produced to the center of the hub.
&, = width of arm in inches produced to the rim.
D = diameter of the gear in inches.
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