| 9.1
Worm Mesh Geometry Although the worm tooth form can be of a the most popular is equivalent to a V-type screw thread, as in Figure 9-1. The mating worm gear teeth have a helical lead. (Note: The name "worm wheel" is often used interchangeably with "worm gear".) A central section of the mesh, taken through the worm's axis and perpendicular to the worm gear's axis, as |
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shown in Figure 9-2,
reveals a rack-type tooth of the worm, and a curved involute tooth form
for the worm gear. However, the involute features are only true for the
central section. Sections on either side of the worm axis reveal
non-symmetric and non-involute tooth profiles. Thus, a worm gear mesh is
not a true involute mesh. Also, for conjugate action, the center distance
of the mesh must be an exact duplicate of that used in generating the worm
gear.
To increase the length-of-action, the worm gear is made
of a throated shape to wrap around the worm.
9.1.1 Worm Tooth
Proportions
Worm tooth dimensions,
such as addendum, dedendum, pressure angle, etc., follow the same
standards as those for spur and helical gears. The standard values apply
to the central section of the mesh. See Figure 9-3a. A high
pressure angle is favored and in some applications values as high as 25º
and 30º are used.
9.1.2 Number of
Threads
The worm can be
considered resembling a helical gear with a high helix angle. For
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:
Pitch diameter of worm=dw= ZwPn
(9-1)
p sin
g
Pitch diameter of worm gear=dg= ZgPn
(9-2)
p cos
g
Zw =
number of threads of worm; Zg = number of teeth in worm gear
Pn = Pxcos g
9.1.4 Center Distance
(9-3)
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 equivalent to a one-tooth gear; and two-threads equivalent to two-teeth, etc. Referring to Figure 9-4, for a lead angle y, measured on the pitch cylinder, each rotation of the worm makes the thread advance one lead.
| There
are four worm tooth profiles in JIS B 1723, as defined below. Type l Worm: This worm tooth profile is trapezoid in the radial or axial plane. Type ll Worm: This tooth profile is trapezoid viewed in the normal surface. Type Ill Worm:This worm is formed by a cutter in which the tooth profile is trapezoid |
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