T-61
8.1 Development And Geometry Of Bevel Gears
Bevel gears have tapered elements because they are generated and operate, in theory, on
the surface of a sphere. Pitch diameters of mating bevel gears belong to frusta of cones, as
shown in Figure 8-2a. In the full development on the surface of a sphere, a pair of meshed
bevel gears are in conjugate engagement as shown in Figure 8-2b.
The crown gear, which is a bevel gear having the largest possible pitch angle (defined in
Figure 8-3), is analogous to the rack of spur gearing, and is the basic tool for generating bevel
gears. However, for practical reasons, the tooth form is not that of a spherical involute, and
instead, the crown gear profile assumes a slightly simplified form. Although the deviation from a
true spherical involute is minor, it results in a line-of-action having a figure-8 trace in its extreme
extension; see Figure 8-4. This shape gives rise to the name "octoid" for the tooth form of
modern bevel gears.
(a) Pitch Cone Frusta
(b)
Pitch Cones and the
Development Sphere
Fig. 8-2 Pitch Cones of Bevel Gears
Fig. 8-3 Meshing Bevel Gear Pair with Conjugate Crown Gear
Common Apex of
Cone Frusta
Trace of
Spherical Surface
w2
g2
g1
w1
O
O"
O'
P'
O2
O1
P
O2
O1
P
O
