Posted by Ian Parkin on 16/01/2021 12:11:21:
what does all that mean in practice?
Let me preface this by saying I do not have either a Student or Master lathe. Everything I have written is as a result of reading the manual linked above. If you also read it, you will see where the terms come from.
Let us go back to your original post. You say you have a way to cut 3.5mm pitch using 35t, 21t, DA, and 1.5mm gearbox setting. So if you want 1.75mm, that is half (or double) 3.5mm. The easiest thing to do is to change the arrangement of the levers that give you the two letter combination. This is exactly the same as changing the 1.5mm gearbox setting to 0.75mm (or possibly 3mm).
From the manual above, there are two levers, one with A, B and the other with C, D. That gives four possible arrangements of levers. On page 17 of the manual above, it gives a value to be used with each combination. The values are 1, 2, 4 and 8. From page 17, DA corresponds to a value of 2 so for 1.75mm pitch, you would need to try either 1 (AC) or 4 (BC).
The reason I am hesitant to commit myself is that I always get confused over the halving or doubling, especially when metric (pitch) rather than threads per measurement unit are involved. It is a case of try both options: one will be correct.
As to my post above, it is just the results from using the formula on page 17. X is the gearbox position, shown in the manual as (16, 18, 19, 20, 22, 24, 26, 28, 30). To find the 'best' ratio, you have to try all nine possibilities.
The formula tells you to convert your desired metric pitch to an equivalent teeth per inch. If you do that, you end up with a set of nine driver/driven ratios all with a multiple of 127 in their denominator. And you cannot have that because the manual also tells you that the biggest driven gear can only have 64t (and the biggest driver 60t).
So you then find a handy online continued fractions calculator and ask it to give you the closest fraction it can to the exact one, with a maximum denominator of 64. You then back-calculate the teeth per inch each of these nine approximate fractions give and sort from best to worst.
The best, [18, 32, 43] above, gets you 1.7502mm pitch (14.5125 tpi). The worst, [24, 63, 64] gets you 1.736mm pitch (14.6286 tpi).
Edited By DC31k on 16/01/2021 15:02:27