Cutting Worm Gears 02

Harold Hall


Method three

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.


Method four

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.


Workshop Processes

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.