magic 127 TOOTH ?

I've heard the magic number of 127 in the context of metric threads and understand it is half of 254 but how does it work ?

An imperial lathe cuts threads in turns per inch. So to have it cut metric pitch threads, it's handy for the change gears to convert inches to millimetres. Or in reverse for a metric lathe to cut imperial threads.

Say a 12 tpi thread is needed.  To cut that the spindle has to turn 12 times whilst the saddle moves one inch.  Gears are used to make the leadscrew turn in time with the spindle in the ratio needed to cut the thread.

As there are exactly 25.4mm per inch, 127 teeth can be arranged with other gears to include exactly the right ratio to convert inches to mm. Unfortunately 127 toothed gears are uncomfortably big and might not fit in the space available . So common to use a more manageable 63 toothed gear instead - the approximation is still reasonably good.

Although having 127 or 63 teeth simplifies the maths when setting up a thread cutting gear chain, it's possible to cut metric and imperial threads without them. (My lathe doesn't have either.) The threads may be worse approximations than 63 would do, but still be acceptable for most practical purposes. But if you have an old imperial lathe or metric only lathe, it will be easier to use a conversion gear.

Dave

Edited By SillyOldDuffer on 11/01/2020 18:59:51

As you have noted 127 is half of 254. 245 teeth would convert 25.4mm to inches for a metric lathe or vice versa for an imperial item, but 254 teeth would be a bit crowded! So half that number will work just as well - as Dave SOD says - with other gears.

Why did they made 1 inch equal to 25.4 mm, would 25.6 mm not be a better choice, or was it done deliberately to make conversion difficult? Niko

Edited By speelwerk on 11/01/2020 19:25:21

Um. Well originally a metre was some small fraction of the distance from Paris to the North Pole and a millimeter was a thousandth of that. An inch was 1/36th the distance from Henry VIII's nose to the tip of his middle finger (or something like that). When you compared them an inch was about 25.399999.. mm or something similar.

**LINK** actually shows that the old UK inch was 0.0000017 shorter than 25.4 mm!

Later on when they standardised lengths internationally it was hard enough just having a standard metre without having to maintain a standard inch as well, so at some stage (in the 1930s I think?) it was decided that the imperial world would move towards an inch being DEFINED as 25.4 mm exactly, which was pretty close to the "old inch". Had they decided to make it 25.6 mm it would have been nearly 1% different which is a lot in precision measurement. Actually conversion is very easy, 25.6 would only have been useful for some binaary divisions.

So the Inch got there first. Pity that no one standardised on ten inches to the foot. Would have made life so much easier..

Howard

The American and Scottish inch were longer and the French pouce was even longer at 27mm!

Thankyou gentlemen for your answers ! I work in many facets of engineering and have to say that far from being dead The imperial system is used far more than you may think - even IF the size is expressed in metric !!! eg "I"beams at 254mm, 104mm Etc Steel pipe at 48.3.. Hydraulic pipe at 12.7mm Waterloo should have been the end of it ! Ah well. Noel

Wot like this?

Far too obvious!

Pedant Alert, there is no standard inch. The Imperial Standard was the yard, divided by 3 to give feet and by 36 to give inches.

The US Yard has been defined as a division of the International Standard Metre since 1893. In the UK BSI adopted inches of 25.4mm in 1930 and the USA followed in 1933. This "Industrial Inch" was slightly different from the inch used by the man in the street, but not many noticed.

In 1946, the Commonwealth Science Congress adopted a yard consistent with 25.4mm inches based on the unchanged International metre. Canada shifted to this system in 1951, the UK in 1964. There hasn't been a physical Standard Yard for about 70 years: in fact all imperial units have long been derived from ISO (metric) standards. In a very real sense, an inch is 25.4mm and nothing else.

The metre was first defined as the length of a seconds pendulum (half period) because it was possible to measure time far more accurately than anything else. Unfortunately pendulum time depends on gravity, which was then assumed to be identical throughout the world: it isn't, varying enough to render pendulums unsatisfactory as a way of defining a high accuracy Length Standard. Next attempt was in terms of a great circle quadrant; this came unstuck because the earth is an oblate spheroid, not a true sphere. Whilst it might be assumed from these mishaps that the metric system is foolishly flawed, these early metre standards were both far more accurate than the yard. At the time the Standard Yard was a length of old Brass Rod kept in a cellar...

Dave

Broadly speaking, the length of the metre (meter) hasn't changed, unlike the inch, though the means of defining it has been updated over the years.

Perhaps the best explanation I've seen is HERE

Sorry to the folks over the pond, but it seems the US inch is actually metric.

Bill

So with global warming, the globe must be expanding and the metre getting longer all the time. Ditto the metre and its fractions. Whatever will the micron-chaser's do? They'll be spending all their time -- which is also speeding up due to the greater distance needed to be travelled to complete one revolution of the Earth -- recalibrating their bipolar microscopes and things.

.

I presume [or at least hope] you realise that the metre has not been defined that way for decades. ... Quite a lot of them.

MichaelG.

.

Edit: meaningless quantifier included especially for you, Hopper

Edited By Michael Gilligan on 12/01/2020 08:24:02

Noel,

I have sent you a PM - please look for the flashing " inbox" button near the top left of the page.

Eric

I think we should all work in the FFF System (Furlong, Firkin, Fortnight) would be much better than all this metric stuff

John

A 127 tooth gear will produce metric threads with zero error but it is difficult to incorporate it into a practical gear train on most lathes. In the real world there are many gear trains that will cut a metric thread that is close enough for all practical purposes, the error will not be measurable unless you have access to a serious metrology lab. There are many documented gear trains for metric threads which will save the bother of working them out for yourself.

Mike

I cant remember where I heard this, but the inventor of slip gauges Carl Johansson was Swedish, and wanted to sell them to America so started making US inch gauges. Great idea not a great salesman and his company got into trouble and was bailed out by Ford. Ford could see the benefit of the accuracy for manufacturing and reaped the $$$$

Other manufacturers soon followed and the Johansson gauge (Jo Blocks) become the defacto standard eventually adopted by the US government. Little did they know that Johansson worked in metric and to make life easy had approximated the US 1" gauge to 25.4mm instead of 25.4000508, well before it was standardised to 25.4

Adrian

Just in case anyone thinks 63 is a 'good enough' approximation to 127/2=63.5, it is probably OK for a rough and ready fixing with 4 or 5 threads engaged, but see the extract below from an article I wrote back in the mists of time...

What if we want to cut metric threads on an imperial machine, or vice versa? One can change over the leadscrew, but this takes time, as the apron must be removed and the clasp nuts replaced and adjusted as well. Is there an easier way?

One inch equals precisely 25.4 millimetres (though at various times in the past it has not!) If we had a 254 tooth changewheel in our set-up, we could convert precisely between the two systems. There is a problem though, a 1-module 254-tooth gear is 256mm in diameter! A 127 tooth gear could be used, as it is exactly half of 254, but it would still be about 5” across. You could accommodate such a gear by making a new mounting banjo, but you would also need to add further idler gears. The whole set-up would be rather clumsy.

The answer is a 63-tooth gear. It may seem that 63 is ‘close enough’ to half of 127 to do the job, but it isn’t – it would produce errors of around 2%, acceptable for some purposes, but not for many others. The 63 tooth gear arises from another, fortuitous bit of maths.

1mm pitch is 25.4 threads per inch. To cut 25.4 tpi on a 16 tpi leadscrew we need a ratio of 16:25.4, this works out at 0.62992:1, or almost exactly 63:100. If we introduce the ratio 63:100 into our gear train then a 16 tpi leadscrew will cut a 1mm pitch thread well within the tolerance of any other aspect of the process. To translate this into standard change wheels we can use:

63/100 = 63/50 *1/2=63/50 x 30/60

Conversely, a ratio of 100:63 will allow a 1mm metric leadscrew to cut a 16tpi thread with the same accuracy. In fact, the standard metric leadscrew for mini lathes has a pitch of 1.5mm, which would therefore cut 16 x 1.5 = 24 tpi, but this is dealt with by putting the ratios 2/3 and 100:63 in series.

(typo 127/2=63.5)

Edited By Neil Wyatt on 12/01/2020 18:57:32

That's an interesting point I hadn't realised Neil. In which case, for my 10 tpi leadscrew lathe that I printed a 63 tooth gear for years ago (which has stayed as it worked very well for a feed and my lathe is too old and not posh enough for a separate power feed shaft) it looks like I would be better off printing a 39tooth for metric cutting if I ever need one (although, looks like 79 fits a bit better, I'll have to see if the diameter fits). I had solely thought of it in terms of an approximation of half 127.

Thank you!

I use a combination of a 127T and 50T gear on a Myford ML7 to cut metric threads as this gives a ratio of 2.54 to 1.

The setup has to be run without the gear guard though!

Gordon.

It might be easier to understand Neil's explanation above if you realise that when using 127 it is a Driven gear, and when using 63 it is a Driver which is why it is not trying to replace the 127, just the lucky bit of maths he mentioned.

As 63 is not prime you might be able to get the 7x9 factors in with other gears. If you can fit another stud on the banjo you might be able to use a 6 gear combination instead of finding a 63 tooth gear.
eg 63, 60, 30, 100 to get 1mm with an 8tpi leadscrew can become
35, 60, 45, 50, 30, 50 with the same accuracy.

However sometimes the maths can work with 63 driven - so 25, 63, 25 ,35 ,50, 45 is half the error of the above.

Given that lathes already existed when metric was invented it is really remiss of them not to have thought of all this and tweaked the figures to make the ratio 256. Napoleon would never have realised.