worm gear diameter

One of my challenges of understanding these formulas is not knowing what the datum really mean and what is their expected values, I racked my brains until the lights went on. When we look at the worm screw its described as 1/2-13, a screw nominal size and the number of threads per inch (TPI a rate). Additionally we can compute the actual size of a single thread, the pitch or circular pitch (CP a measurement), 1/13 = 0.076923. So when we use a formula DP = pi / CP this results in 3.14 / .0769 = 40.84 But if you use DP = TPI x pi you get 13 x 3.14 = 40.84 its the same value. In my mind the relationship between the worm screw TPI (13) and the worm gear DP (40.84) now becomes very apparent and the computed or derived values are reasonable and make sense.

This thread gave me the opportunity to learn and once understood to be able to apply the knowledge in differing ways.

Thanks,

Caster
 
Caster, I just realized where I was goofing up and it may have made things a bit more confusing. Remember where I said that CP is equal to TPI?? Not correct. In the case of the 1/2-13 tap or worm, the TPI is 13, but the CP is .076923076" In short, now I see why you were saying that the DP = TPI x PI.... because it is! The CP is the inverse of 13 (1/13, or .076923076) so when going directly from TPI (13) to DP we have to multiply, not divide. Don't know why I didn't see that sooner, but thanks for helping me to see it!

Remember when I said this stuff can be confusing??
 
Terry, Once I understand what I am doing I look for tools to validate my knowledge and make the job easier. jocat54 provided a link "(WM BERG Gear Data) http://www.wmberg.com/tools/" to a free downloadable gear calculator that requires DP as an input. Now that we can easily compute the DP of the tap/worm it is a pretty good calculator that provides the data you need and a lot more data to satisfy anyone's curiosity.

Caster
 
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Neat tool, and I have it here too, but it only allows you to calculate for gears of industry standard DP's.

Taps end up creating oddball DP's as we have seen in both cases for Mike and Mark. As a result, we need to be able to thoroughly understand exactly what the various dimensions are and how to calculate them. In my quest to do so, I created an Excel spreadsheet with calculators for spur gears, worm gears, and pressure angle. Additionally there are a couple of pages with common gear data and formulas. I am sharing that spreadsheet here, and those that are interested in having a copy can download it. I would have placed it in the downloads area, but even moderators are not allowed to upload xls files to the upload area.

Check it over and let me know what you guys think. Don't be afraid to post suggestions as I can always make changes to make it easier to use.

View attachment Gear calculator.xlsx
 
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I wrote a program to do gear calculation including circular pitch in both inch and metric, DP and metric MOD. The program does many other useful calculations. Funnily enough it is most popular in Span,Belgium and Holland. I guess because you can get inch or metric results.

Windows (for 32 bit and 64 bit Windows from win2k and later, it still might work on Win98)
Linux 32 bit (use this if you are not sure if you have 32 or 64 bit linux)
Linux 64 bit
 
After applying the math to a 36 tooth wheel and coming up with an OD of 1.065 derived from the following -

OD = .3183 x WP x N +(2xD) = .3183 x 0.076923076 x 36 + (2 x 0.0916) = 0.881446143269 + 0.1832 = 1.06464614327 Rounded to OD = 1.065

I got a worm with some beautiful teeth, all 45 of them! :panic:

With all my attempts so far, I have managed in the middle of it to somehow pull out a 36 tooth wheel that is almost right, or at least close enough to try to use until I can make something better.

I am beginning to suspect the need to sacrifice small furry animals while standing on my head reciting incantations to pull of this bit of black magic. :lmao: There seems to be very little hard math behind it.

Mark
 
Hi Mark,

I assume you are using 1/2-13 tap as your worm or cutter. We worked it out that the DP of the worm is 13*pi or 40.84 thus the OD should be .954 Here is a screen shot of a worm gear calculator with 40.84 DP and 30 deg pressure angle to match the 60 deg threads.

Hope this helps,

Caster

Capture.JPG

Capture.JPG Capture.JPG
 
I think you missed something along the way, Mark. Using a 1/2-13 tap to cut the teeth, the worm will need to be about 0.490" in diameter, maybe only 0.480", but the worm wheel will need to be 1.017" for an OD and the face of it should be 0.433" wide. This was calculated using a tooth depth of .019".

Most important is that you gash the worm wheel before trying to cut the teeth. If you just try to free hob using a standard tap with straight flutes, you will not get the results you expect. To properly gash the blank, you will need some way to index for 40 teeth, then use a cutter to get the teeth started. Use the tap only for the final finishing of the worm wheel.
 
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