8. Rim diameter
b. Use the following formulas to solve for all
normal tooth dimensions:
a. To find the rim diameter for single- and
double-start worms, multiply the linear
= LPN 0.3183
Addendum normal
pitch by the constant 0.4775 and add the
result of the throat diameter.
= LPN 0.0637 or
Clearance normal
Rim diameter = (LP 0.4775) + Throat diameter
ADDn 0.2
b. To find the rim diameter for three or more
starts, multiply the linear pitch by the
= LPN 0.382
constant 0.3183 and add the result to the
Dedendum normal
throat diameter.
= LPN 0.7
Whole depth normal
Rim diameter = (LP 0.3183) + Throat diameter
Circular thickness normal = LPN 0.5
9. Throat radius
a. To find this radius, subtract one addendum
NOTE: All worm tooth constants are derived from
(normal) from the pitch radius of the worm.
a worm with a l-inch linear pitch.
Throat radius = pitch radius (worm) - 1 ADDn
b. This dimension is taken from the worm but
5. Length of the worm (LOW)
is machined on the worm wheel blank.
a. It is found by using the following formula:
10. Blank width
LOW = [(NT 0.02) + 4.5] LP
a. To find the blank width for single- and
b. The worm is longer than is required for
double-start worms, multiply the linear
complete meshing between the worm and
pitch by the constant 2.38 and add the result
the worm wheel.
to the constant 0.250.
Blank width = (LP 2.38) + 0.250
6. Worm wheel pitch diameter (WWPD)
b. To find the blank width for three or more
a. You learned in spur gearing that for every
starts, multiply the linear pitch by the
tooth in the gear there is a circular pitch on
constant 2.15 and add the result to the
the pitch circle, and for every tooth on the
constant 0.20.
gear there is an addendum on the pitch
Blank width (for three or more starts)
diameter.
= LP 2.15 + 0.20
b. By using this theory, we can derive the
11. Tooth dimensions. These are the same as those
following formulas:
of the worm. The linear pitch and the circular pitch are
(1) WWPC D (real)
of equal value.
12. Number of teeth (NT). Multiply the number of
starts by the ratio of the worm to the worm wheel.
= LP 0.3183 NT
Number of teeth (NT) = No. of starts x ratio of the
worm to the worm wheel.
(2) ADD (real) = LP 0.3183
SELECTING A WORM WHEEL CUTTER
7. Throat diameter
a. It is found by adding the worm wheel pitch
When you machine the throat radius of a worm
diameter and twice the addendum normal.
wheel, select a two- or four-lip end mill with a radius
smaller than the calculated throat radius. You need the
WWPD + 2 ADDn = Throat diameter
smaller radius because as you swivel the cutter from its
b. It is measured at the base of the throat
vertical position to a desired angle, the radius being cut
increases.
radius.
14-24