| For intersecting shafts, bevel gears offer a good means of transmitting motion and power. Most transmissions occur at right angles, Figure 8-1, but the shaft angle can be any value. Ratios up to 4:1 are common, although higher ratios are possible as well. |  |
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.
8.2 Bevel Gear Tooth Proportions
Bevel gear teeth are proportioned in accordance with the standard system of tooth proportions used for spur gears. However, the pressure angle of all standard design bevel gears is limited to 20º. Pinions with a small number of teeth are enlarged automatically when the design follows the Gleason system.
Since bevel-tooth elements are tapered, tooth dimensions and pitch diameter are referenced to the outer end (heel). Since the narrow end of the teeth (toe) vanishes at the pitch apex (center of reference generating sphere), there is a practical limit to the length (face) of a bevel gear. The geometry and identification of bevel gear parts is given in Figure 8-5.
