However, the pitch errors are so small that I doubt if anyone would find this unacceptable. If though you are producing an item with metric dimensions you may be prepared to cheat, as I do, and produce threads with metric diameters but having imperial pitches. This is not so uncommon as you may think, screwed shank metric end mills have metric diameter shanks but a 20 threads per inch Whitworth form thread. This no doubt to ease production in the early days of this cutter form.

However, it was having to cut a 1.5 mm pitch external thread to mate with an existing internal thread that I decided to investigate the possibilities and to quantify the errors that would result.

Using Changewheels

I will, first, briefly comment on combinations for cutting imperial threads, so that a viewer new to the process is at home with the procedure.

Questions occasionally surface that lead me to realise that some are unaware that there are, for most pitches, many combinations that will give the same result. The combination published in the lathe's manual maybe the simplest to set up, fewest gears for example, but assumes you have the full set of gears available. Whilst this should be the case with a relatively new machine, missing gears are not unknown, especially with an older lathe. Not therefore having all the gears in the published combinations almost certainly does not mean that the pitch cannot be cut.

The formula for calculating the resulting threads per inch cut is-

1Dn X 2Dn X 3Dn

= TPI of leadscrew X -

1Dr X 2Dr X 3Dr

This where Dn are the driven gears and Dr the drivers. In many cases two pairs of gears will suffice and occasionally,just one pair. Incidentally, 1, 2 and 3, in no way indicates the order in which they are assembled onto the quadrant, any order that is mechanically achievable will give the required result.

There will be two reasons for wanting to use the formula, one easy and one much more complex. Assuming you have been given the values of the gears to use but want to be sure that there has been no error in conveying the information to you, then the formula will easily put your mind at rest. If though you know the TPI required and need to determine the gears to use, then the situation can be much more complex, see my pages elsewhere on the site giving a little more detail.

Even so, for many pitches simple observation will suffice. Consider a lathe having a leadscrew of 8 TPI and wishing to cut a 12 TPI thread. It is obvious that the ratio between the lathe's mandrel and the leadscrew has to be 2 : 3. From this it can be seen that gears of 20 and 30 teeth will give the required result but so will 30 with 45 and 40 with 60. These where the smaller is the driver and the larger the driven.

There would of course be no need to attempt more complex set-

40 x 45

TPI = 8 x -

20 x 60