John – Thank you for the update, I'm very interested to understand the process behind those figures. I think you can guess what I'm planning to do tomorrow!
Brian – Here's my attempt at the arithmetic.
For my old style gearbox, if I replace the 12T gear with a 17 T and select 18TPI, I get 12/17 x 18 TPI = 12.706. Pitch of 12.706 TPI = 1.999 mm.
For 2.5 pitch, I replace the 30/12 pair with a 29/16 combo gear, select 14TPI as per the table above. Now my lathe cuts 12/16 x 29/30 x14TPI = 10.15 TPI, or 2.5025 pitch. Pitch error is +0.1% (contrast error of – 0.2% with 33T gear on new gearbox.)
For 3.5 pitch replace 30/12 pair with 29/16 and select 10TPI. Lathe now cuts 12/16 x 29/30 x 10 TPI = 7.250TPI, 3.5024 pitch. Error is + 0.1%, error on "new" lathe is – 0.2%
So I think we're onto something here.
Obviously multiples and sub multiples of these pitches come out with the same error, so that's OK. Haven't looked at sub 1.0 pitches, probably never going to happen.
Would appreciate your confirmation!
Best rgds Simon