This, Sk 1c, is a variation on method two but with the teeth on the wormwheel at
an angle enabling the spindles to return to the 90° position, being a major advantage.
Otherwise, its limitations are the same as method two. Incidentally, if you are proposing
to take this route do be aware that the wormwheel has to be slightly larger in diameter
for a given number of teeth than a standard gear having the same number of teeth,
Sk.2 attempts to illustrate this.
This is a variation on method three with the gear not only having its teeth angled
but also having a concave form allowing them to wrap around the worm gear. This is
a must for heavy duty applications and whilst it is not impossible to manufacture
in the home workshop, most will no doubt opt to purchase both the worm and wormwheel
ready made for incorporating into the project being undertaken.
Required Worm Pitch
When needing to determine the pitch for the worm to be made, method one is the easiest.
In this case, as the helix is being ignored, the worm's pitch is equal to gears circular
pitch, that is- Pitch = CP = pi/DP, DP being the diametric pitch.
It will be obvious from Sk1 b and c that with the worm being diagonal with reference
to the wormwheel teeth that the pitch of the worm will increase slightly, as is illustrated
in Sk. 2. The formula therefore becomes- Pitch = pi/(DP x COS hx) where hx equals
the helix angle. Cosine of hx being less than one it can be seen that this increases
the pitch of the worm, or in TPI terms, a reduction.
For gears to the MOD system these formulae become- Pitch = CP = pi x MOD or (pi x
MOD)/COS hx where the helix angle is being taken account of.
As the helix is dependent on the worm's diameter the pitch required will also vary
with diameter. From this it can be seen that there is not one correct value for a
worm gear used with a single DP or MOD size of gear. This then makes it quite impossible
to publish a list of changewheel combinations, not least because of the number of
DP and MOD sizes, far more than there are metric screw thread pitches. What then
is the extent of the problem and how can it be overcome.
First, it should be taken note of the fact that with the mating gear being circular
then the number of teeth that actually mate is much less than the number of pitches
normally engaged with a screw thread. This then means that there is scope for permitting
greater errors than when considering screw threads.
From the formulae above it can be seen that an exact value for the pitch of the worm,
ignoring its helix angle, can easily be calculated from the formula pitch = pi/DP,
that is for 20 DP, 0.15708 inches being 6.36620TPI.
Unlike when using spur gears, where the number of teeth on the gears being used will
fix the shaft centres, a worm gear can be made any diameter that suits the the overall
design. This means that you will often have a choice regarding the worm's diameter.
Providing therefore that the diameter is not unduly small the helix angle will not
be that great and have only marginal effect on the worm's pitch.
If we consider therefore a 20 DP worm of 25 mm diameter this will have a helix angle
of about 3°. The cosine value for 3 degrees being 0.9986. This gives an increase
in pitch of 1.0014 times (1/0.9986), or 0.14%. In TPI terms this is a decrease of
0.14%. Rather than the value above (6.36620TPI that does not take into account the
helix), this will reduce to 6.35729TPI.