Imperial threads on a Metric lathe.

[DIYSwede]

So - I needed to cut a 12 TPI thread (for a stack of homebrewed 38 DP 20PA gear cutting hobs) on my mini-lathe,
equipped with a 1,5 mm pitch leadscrew...

I won't bore you to death with the math involved, just state the obvious: The inch to mm ratio is 1" to 25,4 mm.
Hence some sort of gear wheel setup in the lathe should provide just that ratio, but as the module for the gears are 1,
a 254 tooth gear would be too "maxi", at least for my mini lathe.
Some kind of divisor for the gear was called for, and quickly halving the 254 gives me 127
(which at 134 mm+/ over 5"1/4 OD still is a bit too big to slip in).
Here my figuring came to a grinding halt, as I realized (apart from you guys, knowing that all along)
that 127 unfortunately is a prime number*. Dang.

-What could be "close enough for comfort", then?
Thinking that "-Being such a powerful stimulant, Spreadsheets isn't merely reserved for the Upper class!", I did this:



Being a simple mind - I also provided the stage gain ratios, the error involved, and its devastating consequences.
Thus you've been warned.
Now - not all these combos are fitting or suitable - the least cumbersome (but perhaps not ideal for "gain distribution")
is the 80-45/50-63 one,which will just fit within the gear cover,
although I also realize that the awkward stock banjo needs a new project of its own...

After getting some help from a student in whipping out a 63 T gear from our (then) new 3D printer at work,
I thought I had solved it.
(Here some of you "Math Reductionists" might wonder why I didn't just went for a small 21 T instead?
Just 1/3 size dia compared to a Biggie 63 T?
-Not being quite sure if the printer was "good enough", thus minimizing any errors to 1/3 of what a 21 T would accomplish.)
-Voila:



As all you wise guys already have seen - I have clumsily turned the 45/50 idlers over, and this config will instead give me a 14,82 TPI...
The nosy ones also probably realized that the spindle hand crank is just an old bike pedal crank with a re-run bakelite handle,
but also that I simply couldn't resist fitting a fused mains switch with a multi outlet strip for lighting & peripherals too...
And what the heck is the lathe sitting on in the pic below?
Unintentional pun: To those of you, I (not being a Doctor either) just humbly say "Be patient."



-Now, that's better! And how did it perform? Check for yourself:



OK - it's just a proof-of-concept hob made outta scrap steel (discarded office hole punch), but the meshing is apparent.
Next up is threading the 14 mm dia silver steel shank from a discarded 500 mm gas spring,
(from which also the tube is used for a 25 dia by 350 mm mold, for casting my own AlSi12 round stock- yet another upcoming project post).
Then slitting, milling, relieving, hardening and finally grinding the hobs-to-be.
Guess it'll be good enough for a card-carrying Swedish Cheapskate?

*Mandatory Math Test: "-As you all already know, the number 13 333 513 is a prime,
but this number is also the sum of two other primes - which ones?"