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.
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- TPI cut equals
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-ups but just as an example
the following would also arrive at 12 TPI. A combination of 20 and 40 would give
16 TPI. Now wishing to achieve 3/4's of this value 45 and 60 would provide this ratio.
Placing these values into the formula as a final check we get -
40 x 45
TPI = 8 x --------- = 12 TPI
20 x 60