Home Page

8.5 Velocity Ratio

The gear ratio of a worm mesh cannot be calculated from the ratio of the pitch diameters. It can be determined only from the ratio of tooth numbers:

velocity ratio = Z = no. teeth in worm gear =     N_g                              (43)
                              no. threads in worm

9.0 BEVEL GEARING

For intersecting shafts, bevel gears offer a good means of transmitting motion and power. Most transmissions occur at right angles (Figure 1.41), but the shaft angle can be any value. Ratios up to 4:1 are common, although higher ratios are possible as well.

9.1 Development and Geometry of Bevel Gears

Bevel gears have tapered elements because they can be generated by rolling cones, their pitch surfaces lying on the surface of a sphere. Pitch diameters of mating bevel gears belong to frusta of cones, as shown in Figure 1.42. In the full development on the surface of a sphere, a pair of meshed bevel gears and a crown gear are in conjugate engagement as shown in Figure 1.43.
     The crown gear, which is a bevel gear having the largest possible pitch angle (defined in Figure 1.43), 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-S trace in its extreme extension, see Figure 1.44. This shape gives rise to the name "octoid" for the tooth form of modem bevel gears.

T64   Next Page