Posted by Bob Gitsham on 30/08/2017 11:44:05:
It is my uinderstanding that to cut a metric thread on an imperial lathe or vice versa, you need a127 x 120 tooth gear, as the gender bender gear in the train,
The other gears will then give you the pitch you require. there are other combinations that are used but they only give an approximation of the desired thread pitch.
That's the conventional wisdom Bob, but it's not rock-solid. The magic 127, or slightly less magic 63, toothed gears allow one to calculate a TPI and then convert it to metric, or vice versa. The logic is analogous to 'multiply thou by 25.4 to get mm'.
Calculating ratios with paper and pencil using the method mentioned by John MC is hard work. Having 127 or 63 makes the sums easier. However, we don't have to do it the hard way – a computer can crunch the numbers in nanoseconds and tell you how big the error is. Only if the error was too big would I get a 63 tooth gear. (I would never buy a 127 tooth gear because fitting on the banjo is likely to be problematic – it's too big for comfort!)
Whilst the conversion method might suit the way we do arithmetic, and it gets results, it may not be the only way of producing an acceptable thread. My metric lathe produces more imperial threads than the imperial version and it doesn't have either a 63 or a 127 toothed wheel. What it does have is a set of gears that can be combined in ways that produce thousands of different thread possibilities. Many of them are duplicates or non-standard, but quite a few produce reasonable approximations of imperial TPIs. A quirk of the mathematics means that the gears provided with the imperial model are not quite so productive as it's metric equivalent. Nonetheless, given a calculator like that suggested by Thor, it's well worth checking to see if your existing gear set will do the job without needing a special 63 toothed gear.
Dave