Calibrated Dial Connected to
Metric Lead Screw.
Note the 22 and 28 tooth pulleys reducing the feed of the leadscrew
to 1mm for each turn of the dial.
The Metric leadscrew has a pitch very nearly the same as the pitch of the 1/4"-20TPI
leadscrew used to cut US/English threads. It is however of a very slightly coarser pitch
but so close that it can be used with the same split nuts as the 1/4-20 leadscrew.
The pitch of the US/English leadscrew is 1/20 of an inch, or 1/20". This is equal to
50 tousandths (50 *0.001) of an inch, or 0.050". This is easy to see since 1/20 =
50/1000. Since there is, by international convention, exactly 25.4000 millimeters in one
inch then the 0.050 inch is the same distance as .050*25.40 or 1.27 millimeters. This long
winded statement can be abbreviated to simply saying that 0.050" = 1.27mm is the
pitch of the 1/4-20 leadscrew.
Since the pitch of the Metric leadscrew is a little coarser than that of the US/English
one, we would expect the number to be slightly larger than 0.050" or 1.27mm. In fact
the pitch of the metric leadscrew is 1.2727272...mm (the series goes on forever). This
nonending decimal is however very nicely the ratio of the two rather small numbers 14/11.
In other words 14/11 = 1.27272.....
This is a rather odd screw pitch to be considered for a leadscrew and is not one of the
standard Metric screw pitches but it is a very nice number for working with the change
gears (pulleys) on a lathe. This is because the advance of a nut running on the thread can
be converted to the standard Metric screw pitches by a simple set of gear ratios. In this
sense it is just as good as a leadscrew with a 1.0mm pitch would be but has the advantage
that it can be used with the same split-nuts that are standard for the 1/4-20 leadscrew.
The pitches of the 1/4-20 leadscrew and the 14/11mm pitch leadscrew are so close that if
long lengths of the threaded material are held next to each other it takes 23.33 inches
for the thread on one to fall back one complete thread compared to the other. Since there
are 20*23.333 = 467 threads in this 23.33 inches then the difference in their pitches is 1
part in 467 or 1/467. This fraction 1/467 is about 0.0021 or less than 1/4 of 1 percent
since 1/4 of one percent (1/4%) would be 1/4 divided by 100 or 0.0025.
The point of the percentage argument just made is that any error made by using the
"wrong" leadscrew but having the right set of gears to cut a metric thread will
produce a thread or feed less than 1/4% in error. The same applies to the feed set by the
calibrated dial using the (N3/N4) gear ratio of (22/28) = (11/14) to turn the Metric
leadscrew.
The Metric leadscrew has a pitch of (14/11)mm as just stated. If it is turned only (11/14)
of a revolution then a nut would advance exactly (11/14) times (14/11) millimeter or
exactly 1.000 millimeter. Thus the calibrated dial advances the carriage exactly one
millimeter when rotated one complete revolution since the leadscrew is only turned 11/14
of a revolution. If you divide the dial into 100 equal increments then you advance
the carriage 1/100 of a millimeter or 0.010mm per increment.
Now, getting a little carried away here, if you do not have the 14/11mm metric leadscrew
mounted but have the 1/4-20 leadscrew mounted and proceed as if you had the Metric screw
mounted then you will be off 1/4% in your settings. For a dial with 100 subdivisions then
you would be off less than 1/4 of a division if you turned it completely through the 100
divisions. Further one can say that since the 1/4-20 leadscrew has finer threads than the
14/11mm leadscrew than you would be 1/4% too short in the carriage mevement. You could
then compensate by turning the dial an extra 1/4 division.
This is just to show that in some case where one might happen to have the required pulleys
but not the right leadscrew, that one might possibly get by on short threading jobs by
using either leadscrew and using the gear (pulley) setups for the appropriate thread
One last point is that the difference in pitches between the two leadscrews is LESS
than 1/4% and closer to 1/5% of their basic values.
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