Model Engineers’ Workshop – August 2019

62 http://www.model-engineer.co.uk Model Engineers’ Workshop

lathes is not an especially precision item
and usually wears to a certain extent
adding to any inherent inaccuracy. This is
oft en given as a reason not to worry about
slight pitch inaccuracies when cutting
metric threads on an imperial lathe as
such errors will be “absorbed within the
leadscrew wear”.
I am uncomfortable with this reasoning
as:

1. The errors are very likely to add
   together to produce greater than
   expected inaccuracy


2. As model engineers we should try to
   get things as accurate as possible
   The only way to cut accurate metric
   pitches using an imperial lead screw is to
   use a 127 tooth “translator” gear.
   One inch is set internationally as exactly
   25.4 mm. (Take no notice of older books
   that give slightly diff erent conversion
   factors).
   The 127 tooth gear derives from the
   factorisation of 254 into 2 x 127
   As 127 is a prime number this is the
   lowest number of teeth that can be used
   on a translator gear.
   This brings a number of practical
   problems (described below) so Drummond
   and other manufacturers introduced gears
   of 63 teeth which enabled the user to
   get ratios that gave more accurate near
   misses.
   Table 1 shows my screw cutting chart
   using standard Drummond gears and
   quantifies the pitch errors which are quite
   small and frankly quite good enough for
   all practical purposes.
   A college lecturer was very fond
   of using the phrase “for all practical
   purposes” The lack of precision in this
   phrase puzzled one of the students who
   asked the lecturer to explain what it
   meant. After thinking for a few moments,
   he said
   Suppose all the young ladies lined up

on one side of an empty room and the

young gentlemen did the same on the

opposite side facing them. Then at my

signal they all moved forward enough

to exactly halve the distance between

them. No matter how many times this was

repeated theoretically they would never

meet, but after only a few moves they

would be close enough together “for all

practical purposes”.

If you do use a near-miss set-up it is

best to leave the thread fairly full and

then finish it with a die as this gives

some improvement over short lengths of

thread.

Problems with 127 tooth

wheels

The fi rst problem is fi nding one for your

lathe!

They may be available for current lathes

if you are very lucky, but it will be diffi cult

with older and obsolete machines.

The second problem is the diameter

3

4

The “wonderful” gear and its mate.

Gear train set up for metric screw cutting.