Screwcutting Gear Ratio Calculator - About
What
This calculator will go through the various combinations of change gears looking for ratios which deliver a specified thread pitch, or something close to it, if possible.
Copyright ©2011 C. Williams.
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>.
Why
I wrote this shortly after acquiring a mini-lathe ("7x12") and deciding I wanted to cut some thread pitches which weren't in the supplied table - a 27tpi imperial and a few metric threads. To begin with, I wrote a quick hack in C to list all possible combinations of the gears I had, then sorted, winnowed and parsed the output using standard Unix command line utilities. This got me my ratios for 27tpi and 1.75mm. Then I thought someone else might find it useful. Then it occurred to me to look to see if someone else had already published anything which did the same job - indeed they had. W. E. Johns, for example, did something quite similar and wrote a javascript calculator, see here.. Varmint Al has a DOS executable, and also a Visual Basic version by Paul Bussieres. I decided I'd prefer a version that will run for at least Windows, Mac and Linux users, so I re-wrote mine in Javascript. Javascript should run on any modern browser, although I'm willing to bet it messes up comprehensively if used with Internet Explorer. See the bit which reads "as-is with no warranty". There's another implementation which works in your browser, though, by thelittlemachineshop, here and also another CGI version on www.tanj.com, here.
How
To use, first adjust the gear set to match your own (by adding any extra gears you have, and/or setting any you're missing to zero) then check the correct leadscrew is selected, fill in the required tpi or mm pitch and hit the "search for combinations" button. The script attempts to eliminate possibilities which won't physically fit. You might however be interested in them anyway if you're planning to add extra layshafts or make other modifications - pick "eliminate many bad combinations" or "allow combinations which won't fit" instead of "eliminate most bad combinations" if you want to see combinations which would otherwise be screened out. After finding some gear combinations which give thread pitches at or near your target (if any) the list of possibilities appears in the "results" drop-down. Exact matches are shown in bold when the list is dropped down. Pick an option from the list to fill in the coloured table below with the gears, pitch (tpi and mm) and error amounts. The script will also attempt to draw the combination, roughly, so you can get an idea of whether the gears look like they're going to fit - if the combination is too awkward, for whatever reason, the drawing bit will just give up. The validation tries to eliminate combinations which simply won't fit, but occasionally one gets through.
Note: Metric threads with imperial leadscrew or vice-versa
It's generally easiest to get metric threads with an imperial leadscrew if you stir a 127 tooth gear into the mix. Unfortunately, there's not really room for one in an unmodified mini-lathe, plus they're hard to find for this machine. It's often said that a 21 tooth gear will get you closer to some metric threads, but that only really seems to help for 1mm pitch. A 31 tooth provides a few closer matches, but a 63 tooth looks like it'd be worth a try, giving noticably closer to 0.75, 1.0, 1.5 and 1.75 pitches. (A 127 tooth will allow some exact combinations, though, so if you do a lot of both metric and imperial threading, a gearbox modification consisting of an optional auxilliary 100:127 ratio is probably the way to go.)
Final disclaimer
My gear ratio calculator isn't based on anyone else's code, and it hasn't been all that extensively tested. It is licensed to you under the GPL V3. Once again the reader is referred to the "no warranty" clause, above. As custodian of your own lathe, machine shop and person, it is your responsibility to check the sanity and safety of any gear setup you try. I accept no responsibility or liability whatsoever for any damage or loss arising from your use of gear combinations suggested by the output of my gear ratio calculator.
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