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68
The terminology of bevel gears is illustrated in Fig. IV-5. The pitch of
bevel gears is measured at the large end of the tooth, and both the circular
pitch and the pitch diameter are calculated in the same manner as for spur
gears. It should be noted that the clearance is uniform. The pitch angles are
defined by the pitch cones meeting at the apex, as shown in the figure. They
are related to the tooth numbers as follows:
G
p
N
N
=γtan
p
G
N
N
=Γtan
(IV.1)
where the subscripts P and G refer to the pinion and gear, respectively, and
where γ
and Г are, respectively, the pitch angles of the pinion and gear.
Figure IV-5 shows the shape of the teeth, when projected on the back
cone, is the same as in a spur gear having a radius equal to the back-cone
distance r
b
,. This is called Tredgold's approximation. The number of teeth in
this imaginary gear is
P
r
N
b
π
=
′
2
(IV.2)
where N' is the virtual number of teeth and с is the circular pitch measured at
the large end of the teeth. Standard straight-tooth bevel gears are cut by using
a 20° pressure angle, unequal addenda and dedenda, and full-depth teeth.
This increases the contact ratio, avoids undercut, and increases the strength of
the pinion.
Figure IV-5
Terminology of bevel
gears.
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