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extremely high helix angles, there is one continuous tooth or thread. For slightly smaller
angles, there can be two, three or even more threads. Thus, a worm is characterized by
the number of threads, zw.
9.1.3 Pitch Diameters, Lead and Lead Angle
Referring to Figure 9-3:
zw pn
Pitch diameter of worm = dw = ––––––
(9-1)
p sing
zg pn
Pitch diameter of worm gear = dg = ––––––
(9-2)
p cosg
where:
zw = number of threads of worm; zg = number of teeth in worm gear
zw pn
L = lead of worm = zw px = ––––––
cosg
zw m
zw pn
g = lead angle = tan
–1(––––––) = sin–1(–––––)
dw
pdw
pn = px cosg
9.1.4 Center Distance
dw + Dg pn zg zw
C = –––––––– = –––– (––––– + –––––)
(9-3)
2 2p cosg sing
9.2 Cylindrical Worm Gear Calculations
Cylindrical worms may be considered cylindrical type gears with screw threads.
Generally, the mesh has a 90O shaft angle. The number of threads in the worm is equivalent
to the number of teeth in a gear of a screw type gear mesh. Thus, a one-thread worm is
Addendum
Dedendum
dw
pdw
pdw
–––
zw
px zw
L = Worm Lead
pn
px
f
(a)
Tooth Proportion of
Central Section
(b) Development of Worm's Pitch Cylinder;
Two Thread Example: zw = 2
Fig. 9-3 Worm Tooth Proportions and Geometric Relationships
