Boxford aud metric gears

[Clive Brown 1Participant @clivebrown1]

3mm x 127/135 = 0.111111 inches; 9 tpi

3mm x 135/127 = 0.1256 inches; ~8 tpi

Take your pick

[HopperParticipant @hopper]

OK. Very cunning. But yes, have to wonder why Boxford did not do like Southbend, Hardinge and others and use one of the sets of much smaller gears to achieve a quite acceptable result, albeit not perfect like the 127/100.

[Neil WyattModerator @neilwyatt]

I was going to make the same comment on Howard’s post (sorry Howard!)

As I wrote many years ago for my articles/book on thread cutting on Mini Lathes:

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. To get standard changewheels:

100/63 x 2/3 = 50/63 x  4/3 = 50/63 x 4/3 = 50/63 x 40/30

From these basic ratios, it is possible to derive a ratio for any other metric or imperial thread. Armed with a 63-tooth wheel and the right changewheel ratios you can cut almost any standard thread.

Of course this is not necessarily of any benefit to Boxford owners, but I like to get the facts straight!

Neil

[Michael GilliganParticipant @michaelgilligan61133]

Thanks for re-posting that, Neil … If there was ever a Post that deserved to be made ‘sticky’ then that is surely it.

MichaelG.

[Neil Wyatt]

On Neil Wyatt Said:

I was going to make the same comment on Howard’s post (sorry Howard!)

As I wrote many years ago for my articles/book on thread cutting on Mini Lathes:

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. To get standard changewheels:

100/63 x 2/3 = 50/63 x  4/3 = 50/63 x 4/3 = 50/63 x 40/30

From these basic ratios, it is possible to derive a ratio for any other metric or imperial thread. Armed with a 63-tooth wheel and the right changewheel ratios you can cut almost any standard thread.

Of course this is not necessarily of any benefit to Boxford owners, but I like to get the facts straight!

Neil

To translate 16TPI leadscrew minilathe language into Boxford/Myford 8TPI language, that would be:

The magic ratio of 16/25.4 = .6299 becomes 8/25.4 = .3149

Which is as close as dammit to 63/200 = .3150, an error of .0001.

Myford’s 21T metric conversion gear, to cut a 1mm thread with an 8TPI leadscrew, is used in a gear train of driver/driven = 45 x 21/40 x 75     = 945/3000 = .3150, ie an error also of just .0001.

So while the 21T is oft pooh-poohed as an “approximation only” it, like its triplicate brother the 63T, it is plenty good enough for most practical applications within a ratio error of 0.0001.

This of course all applies to change-gear lathes and not gearbox lathes. Gearboxes add an extra layer of complexity because you are limited to using the 8 or so pairs of gears inside the gearbox as part of the overall calculation, and using different stud gears to make up the difference. Hence perhaps, manufacturers using the 100/127T combo instead of the seemingly more obvious 80/127T combo that would give the same magic ratio of .6299 as 16/25.4 .

I don;t know. But my head hurts thinking about it. And it’s time for lunch and an afternoon in the shed welding up the legs for my Stirling engine fan. No numbers or calculations involved.

Its in the back of my mind somewhere that John Stevenson conceived, made and sold a special 30-something Myford stud gear for gearbox metric conversion and I am sure there was  thread on teh old forum about it somewhere. Might have a search later on.

 

[Michael GilliganParticipant @michaelgilligan61133]

Hopper

Hopefully this will link you to a post by Roderick Jenkins:

https://www.model-engineer.co.uk/forums/topic/thread-cutting-2/#post-204892

MichaelG.

[Brian WoodParticipant @brianwood45127]

How interesting all this exchange has now become. Like Hopper, I too puzzled periodically over the choice of 135 teeth in a conversion wheel set; thank you Pete Rimmer for lifting the curtain to reveal the secret.

Likewise, Neil Wyatt’s elegant explanation for the use of 63 teeth, I have been aware of that since he first postulated it.

Brian

[SillyOldDufferModerator @sillyoldduffer]

Makes my brain hurt too!  Consider the requirements.   The boss sends for his senior designer, and says:

1. I’m going to make a lathe in two versions.  One will be sold to customers mostly producing Imperial TPI threads, and the other to customers mostly producing Metric Pitch Threads.  The main difference is the lead-screw; which will be either metric or TPI.
2. As the market is brutally competitive, the lathe must be cheaper to make than the opposition, but equally featured.
3. The machine will have a simple 1:2, 1:1, 2:1 gearbox between the banjo output and the lead-screw.
4. To improve sales appeal, the imperial version must be able to cut all common metric threads, and the metric version must be able to cut all common imperial threads.  (In both cases with acceptable accuracy.)
5. Do not suggest gear combinations that won’t fit in the space available on the banjo.
6. Your mission is to identify the minimum number of gear combinations that meet the requirement.  Ideally the Imperial and Metric gear sets should have many gears in common.

Various ways of tackling this requirement:

1. An ELS eliminates the need for most of the gearing and is almost infinitely flexible.   But the development and production cost might easily break Requirement 2.   Worth keeping an eye on, because the cost of the technology needed to implement ELS is falling, whereas the alternatives are static.  At some point in the future, ELS is likely to displace gears because it’s cheaper.  Not yet though!
2. The maths is kept simple by specifying a 127 toothed gear,  because it allows an obvious and accurate conversion 1″ = 25.4mm.  But a 127 toothed gear costs money, breaking requirement 2, and, because it’s a big gear, it might also break requirement 5.
3. A well-known alternative is the 63 toothed gear.  As explained by Neil, 63 teeth don’t simply approximate half of 127.  Used appropriately in combination with the other gears, it can get closer to spot on than might be expected.  Requires more sums.   Potentially this is a good answer – only one special conversion gear is needed, but this bumps into requirement 2.  21 toothed gears are an alternative, but I don’t see much advantage compared with 63T, especially as it’s likely to need more gears in set.  21T solutions are more likely to break requirement 2.
4. Calculate the minimum number of gear combinations needed to produce all the required metric and imperial thread ratios that will fit on the banjo.  This approach needs a lot of calculation, but minimises production cost.

Most lathes designed after about 1960 take option 4, almost certainly because it reduces production costs by accepting some loss of accuracy in the other system.  The loss may not be significant in comparison with the overall inaccuracies inherent in real lathes.   Using a 127 toothed conversion gear on a machine with a worn lead-screw will not produce accurate threads!!!

My metric WM280 does metric and imperial with 11 gears:  20, 30, 45, 50, 60, 60, 65, 70, 75, 80, 85 toothed gears.   The Imperial WM280 does the same with 13:  20, 25, 30, 40, 45, 50, 55, 60, 63, 70, 75, 80, 80.  A cost saving is that eight gears are common to both imperial and lathes: 20, 30, 45, 50, 60, 70, 75 & 80.       I’ve not attempted a detailed comparison, but I suspect the Imperial WM280 does a few more accurate TPI threads than a metric 280 can manage, whilst the metric machine does a few more accurate metric pitches than the imperial can do.

In theory the Imperial WM280’s need for extra gears should make it more expensive than the metric machine.  Tried to check that, but Warco are only advertising the metric version.   Oddly, no-one seems to be selling Imperial-first Chinese hobby lathes in the UK at the moment.  Could be a container full of them is en-route, or maybe most new customers are going metric, accepting that a metric machine is ‘good enough’ if they happen to need an imperial thread.

Dave

[Michael GilliganParticipant @michaelgilligan61133]

I think the most intriguing thing about the 135 gear is that it seems rather ‘extravagant’ to make it in that physical form.

Its factors just comprise a bunch of threes and five, which are commonly available.

MichaelG.

[Clive FosterParticipant @clivefoster55965]

Michael

The 127 gear does the conversion magic.

The other gears are chosen to get the desired pitches / TPI in sensible places on the gearbox tumbler setting. Official factory conversion sets seem always to be chosen to give a nicely linear arrangement of pitches / TPI by either changing gears in the drop train in sequence or simply resetting the tumblers.

From what I’ve seen the, usually computer calculated, “funny” ones using other gears hop around the box like demented flea. Some seem to want both stud driver and gearbox driver to be changed for certain threads. An absolute recipe for confusion for anything approaching general work. But acceptable if needs must and you can use what you have for “just this one” job.

In the Boxford case where the stud drive gear is changed the 135 tooth gear is chosen to work with the 40 tooth gearbox drive gear and the 18 – 30 tooth pair at the gearbox input that drives the Norton gearcone that sets the basic pitch /TPI sequence. If I read the parts book correctly, Boxford use the same cone for both imperial and metric boxes.

I’m pretty sure you need a factor of 8 in there hence changing the gearbox drive gear from the standard metric 45 teeth to 40.

My metric Smart & Brown 1024 uses a 120/127 conversion gear and changes the gearbox input driver in sequence to generate a range of pitches / TPI for given tumbler (dial and lever) settings.

Clive

[Clive Foster]

On Clive Foster Said:

Michael

The 127 gear does the conversion magic.

[…]

Yes, Clive … I am well-aware of that

I was merely commenting upon the strangeness of providing a 135

MichaelG.

[Clive FosterParticipant @clivefoster55965]

I know you know Michael.

Just making a rather clumsy attempt at pointing out that the 135 gear driving a 40 tooth gear was chosen so as to work well with the whats in the gearbox.

I suspect the main reason why the other part of the compound gear is given a tooth count close to 127 is to ensure the train can be assembled with gear, or gear and shaft, clearance for all combinations needed.

Clive

[Michael GilliganParticipant @michaelgilligan61133]

Thanks, Clive … Yes I would support your suspicion

There can really be no other reasonable justification for having such a large gear

MichaelG.

[Michael Gilligan]

On Michael Gilligan Said:

Hopper

Hopefully this will link you to a post by Roderick Jenkins:

https://www.model-engineer.co.uk/forums/topic/thread-cutting-2/#post-204892

MichaelG.

Thanks MG. That’s the one I was thinking of.

[Craig BrownParticipant @craigbrown60096]

This chart gives the information required for cutting imperial threads on a metric Boxford. I had ment to post it sooner but I had forgotten about it until I saw it in my cupboard tonight

[Author]

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