Thread: Wormgears (and sectors) without hobbing

In another thread I mentioned some methods for cutting gear sectors (that is, non-complete gears), and ways of getting worm like performance.
For those wanting a good summary of home workshop gear cutting I would suggest starting with Ivan Law's 'Gears and Gear cutting', one of the workshop practice series. He runs through the basics, some of the maths and methods. This is more a short cut...

Background
Cutting a gear is relatively simple. Using a formed cutter, a blank is mounted on a dividing head and indexed around the same number of steps as the number of teeth desired. We talk about cutting gears but really, the thing being cut is the gap between the teeth. There are formulas to determine the depth the cutter must go in and the diameter of the blank, but once those are established, the actual cutting is repetitive but straight forward.

Gears have evenly spaced teeth and on the pitch circle diameter (PCD), the gap between teeth is equal to the thickness of the tooth at the PCD. The distance between teeth on a gear is the circular pitch, which is basically the circumference at the PCD divided by the number of teeth (that is, (Pi x PCD)/n). A worm is basically a screw thread with a tooth pitch equal to the gear circular pitch - as you can probably see, because the circular pitch has Pi in the formula, the pitch of the worm is rarely a nice round number, although some (industrial) lathes can cut them from the box. Most of us have to swap cogs to get there.

However...
We have an advantage cutting a sector. Because the teeth don't have to be a nice even number on a circle, we can make things easy for ourselves. We can cut a worm on the lathe to pitch that the lathe can do easily (for example 12tpi) and then knowing the pitch (1/12 = 0.0833") and the radius of the sector (and the angle of the sector required), we can work out what the sector needs. In the case lets say we want a 90 degree sector and for the sector (pitch circle) radius to be say 2". That means our PCD is 4". Working backwards from the formula above, n=((Pi x PCD)/CP) = 150.857 teeth, and on our 90 degree sector we will therefore have 37.7 teeth. Dividing 360 degrees by the number of teeth means that each tooth is 2.38 degrees on from the next. Therefore to cut the sector we would set it up on a dividing head and after each tooth is cut, index on that angle before cutting the next tooth.

A (involute) gear tooth has a shape though, while a worm is essentially a thread cut with a tool ground to the gear pressure angle, so when using this trick, most people will work it around the gear cutters they have so that the form on the sector is approximately correct and the worm is worked to suit. 16DP is very close to 5tpi (works out to 5.09tpi), so when replicating a sector that looked like 16DP, I was able to cut a worm as 5tpi, adjust the PCD of the sector slightly and was home and hose.

Note that I could do this in metric, but as most of our lathes are set up to cut imperial threads...

Straight vs. Helical
The nicest way to have a worm/ worm gear combination (whether complete or just a sector) is to hob it. There are some alternatives though. A spur gear (that is, one with 'straight' teeth) can work with a worm, provided that the worm axis is inclined so the worm tooth presents as vertical to the gear.
A helical gear with the teeth at the helix angle of the worm will work for positioning purposes. As the helix angle is usually small (a few degrees), the cutting process can be approximated to something similar to cutting spur gears.
worm1.jpg
The other way to produce a worm like profile is to plunge the cutter straight in. In this case the cutter is inclined to the helix angle. If the cutter were the same diameter as the worm, this would be very close to the form you would get if the wormgear was hobbed. It will still produce the form that a worm will work with, but a true wormgear will have a from very close to the work for greater power carrying. For the loads that our projects are likely to see, this will not matter.
worm2.jpg
Both of these methods can be used to either produce a sector or a full gear, although if a full gear the necessary formulas have to be adhered to, to avoid ending up with fractions of teeth

Michael

OK. I followed most of that until the DP acronym.


PCD you explain as pitch circle diameter, CP seems to be Circular Pitch, but what the heck is DP?
Degrees Pitch? Diametric Proportioning? Dyslexic Pantograph?

Hi Nigel,

Nearly "DP" = Diametric Pitch.

I also have a copy of "Ivan Law's book, Gears and Gear cutting" which is quite useful.

Sorry. Yes - diametric pitch. For gears to mesh properly, they must all be of the same dimetric pitch and all of the same pressure angle (which is the angle normal to the tooth surface at the PCD contact point).

When used like that (that is, referring to a 16DP gear), that number is basically a tooth size indicator. When presented with a gear that needs to copy or have something mesh with it, one of the first steps is to determine the DP (or Module if it is a metric gear - similar to DP for metric gears). Most of the formulas for determining blank sizes, depth of cut and all the rest depend on that as a basis.

Michael