Lathe gear calculation

[duncan webster 1Participant @duncanwebster1]

deleted whilst I sort out the formatting

Edited By duncan webster on 07/07/2021 20:03:52

[duncan webster 1Participant @duncanwebster1]

This just run and runs!

I've taken SODs Python rewrite of the original Basic program and added a couple of bells/whistles. Ian's printout is Driver/driver/driven/driven, but it doesn't say so. Here's the output from python

In IanT's version it potentially prints the same set of gears 4 times, as (CD)/(AB) is the same as (DC)/(AB) and so on.

Note how the 63 tooth driver gives the best results

Next step is to convert it into an exe so that anyone who wants it can have a copy. I know this can be done, but my computer is not playing ball. Any volunteers?

What a performance to get this on here. If I just copy/paste the python output this site screws up the column separation, so I had to screendump, convert to JPG and put it in as a photo. There must be an easier way?

[GeorgineerParticipant @georgineer]

I'm afraid you're all overthinking it by my lights.

I've downloaded a copy of Duncan Munro's ML7 gear calculator and I use that. Although it is psecifically set up for the ML7, it includes a tutorial and offers the possibility of using it on other lathes too.

https://metal.duncanamps.com/software.php

It works for me.

George B.

[CalumParticipant @calumgalleitch87969]

Duncan, perhaps the best thing would be to rewrite it in Javascript and encapsulate it in a web page, which will ensure it will run on any machine for a very long time to come. An exe will only run on the architecture and operating system for which it is made. I'd be happy to give it a go if you like.

[duncan webster 1Participant @duncanwebster1]

Callum, pm sent

[BevelParticipant @bevel]

Back again

This is the illustration I have on my lathe, in charts quoted by your kind selves there are only 4 gears quoted when mine contains 5?

My understanding is z1 + z3 are drivers as they are transferring rotation onto other gears but where does this leave L as it transfers rotation to leadscrew?

Also never fully understood this one either, does it mean I can literally select any point on threading dial to cut these thread ranges? What does Mn relate to and is z =32T referring to the gear on end of leadscrew?

[SillyOldDufferModerator @sillyoldduffer]

Posted by Bevel on 08/07/2021 08:56:24:

Back again

This is the illustration I have on my lathe, in charts quoted by your kind selves there are only 4 gears quoted when mine contains 5?

Confusing isn't it!

It's to do with how Bevel's particular Imperial lathe is set up to cut metric threads. In imperial mode the lower TPI table shows the expected 4 gears, plus two 'H' spacers. And the same is true of the metric threads on the right of Bevel's table. However, to get some metric pitches, his particular lathe adds a 5th gear.

It's a matter of mechanical convenience. Lathe designers have many gear combinations that could be used to generate a particular ratio, and they choose them to comfortably fit in the space available, whilst keeping cost down by minimising the number of gears needed to cover the lathe's design range. Usually, combinations involving very big or very small gears are avoided to reduce wear and tear.

My metric WM280 always uses 4 gears to get metric and imperial, and does so without 63 or 127 toothed gears. The designer achieves this magic by suggesting gear combinations that are close approximations rather than spot on. The imperfections don't matter unless very long threads are cut (longer than the lathe can manage!), or are worse than the lead-screw error. (Which is bad enough for precision screws to be ground rather than turned. Lathe cut threads are 'good enough' rather than highly accurate. )

Calculating the gear combination needed to produce a particular thread is challenging. (Well, I think so.) The easiest way to do it is to write (or find) a computer program that generates all the possible ratios that can be produced from the available gears and ignore all the unwanted answers. Or sort the list by TPI/pitch and use it to look up the gears needed. The table on a lathe is a much shortened version of the full list. Although the maths is simple (see the various programs mentioned recently), the sums have to be repeated thousands of times. It's too much work for a human unless started by finding a near combination and moving in by trial and error. The second way of doing it, which is more practical for paper and pencil methods provided the maths is understood, involves Continued Fractions. Still tedious, and best done with a computer.

Note that although all lathes are similar, the actual implementation varies. Without checking carefully, I couldn't be sure a program written for an Imperial Super 7 was right for my Chinese metric lathe. For the same reason, the tables printed in books, on the web, or on various headstocks are as likely to confuse as clarify. Necessary to swot up I fear to grip the sums. lathes.co.uk is worth a look and various books have already been mentioned.

Dave

[BevelParticipant @bevel]

Thanks very much Dave, just ordered the aforementioned literature by Mr Cleeve

[Howard LewisParticipant @howardlewis46836]

From your picture of the chart on your machine it looks as if to cut a 2 mm pitch thread, the gear train is set up

A 55T is compounded with a 50T, driving a 60T compounded with a 39T, which drives a 75T on the Leadcsrew.

So the solution was there all the time!

Once you have absorbed the content of Martin Cleeve's book, things will be so much clearer and straightforward.

Howard

[BevelParticipant @bevel]

Afraid not Howard mate if it was that simple we wouldn't be discussing it lol.

That is what this is all about in first place I only have a limited number of gears and unfortunately 39T isn't one of them.

[IanTParticipant @iant]

I believe you have 40t, 50t, 55t & 70t change gears Bevel?

Regards,

IanT

[BevelParticipant @bevel]

I most certainly do Ian buddy

[SillyOldDufferModerator @sillyoldduffer]

Posted by Bevel on 08/07/2021 16:01:03:

… I only have a limited number of gears …

What gears have you got Bevel? Might be able to crunch an alternative combination for you from a full list. Is it only 39T that's missing?

For fun we can have a competition. Nigel and Howard will apply pen and paper to simple fractions, Ian will adapt his BASIC program, and I will apply Python. Show working. Winner gets duffed up after school for being a nerd!

Dave

[Howard LewisParticipant @howardlewis46836]

ANY chance that someone, like Home and Workshop Machinery, mor whoever might have a 39T gear for this machine.

There must have been one originally.

Would one be available for any of its clones ? Warco wouldn't be the only company selling that model (Grizzly perhaps?

If so, might be worth getting any others that are missing.

may be expensive but worth it when you come against a job that calls for the missing gear, as in this case.

Howard

[Pete RimmerParticipant @peterimmer30576]

You could use one of the several ready-made calculator options listed on this page:

**LINK**

[BevelParticipant @bevel]

Posted by SillyOldDuffer on 08/07/2021 16:46:43:

Posted by Bevel on 08/07/2021 16:01:03:

… I only have a limited number of gears …

For fun we can have a competition. Nigel and Howard will apply pen and paper to simple fractions, Ian will adapt his BASIC program, and I will apply Python. Show working. Winner gets duffed up after school for being a nerd!

Dave

Haha LMAO great Dave love it!!

Looks like Ian has already done it chaps.

Never was a 39T Howard mate, bought machine brand new and only comes with what I listed in first post.

Just 20, 30, 40, 50, 55, 60, 63, 70,75 + 80.

Still chuckling here Dave

Thanks Pete I will keep them for future ref

[CalumParticipant @calumgalleitch87969]

Well, I have done some code-bashing with the equivalent of a gas torch and a large hammer, and the results of my labours may be seen here:

https://u38cg.github.io/geartrains.html

I have run it against Duncan's results and I get the same (note though the results may come in a different order), and I have calculated a couple by hand and agree with them, but of course I can't guarantee it against all the many wonderful ways computer programs can manage to fail.

I would welcome comments and suggestions for improvements – for my own benefit, I intend to add options for a screwcutting gearbox, and perhaps options to enter information in metric form. Would anything else be useful?

[Nigel Graham 2Participant @nigelgraham2]

Just a gentle reminder gents…

Bevel's original query was an explanation of how the gear-train quoted is calculated to cut a 26TPI thread on a lathe with an 1/8" leadscrew.

Not metric.

Usually that is a simple arrangement but may need a compound train if the headstock pinion is large and the cut thread fine. This example looks very complicated in comparison, but we now know this is a function of the machine's design.

[duncan webster 1Participant @duncanwebster1]

Nigel, you should look at Calum's link, it sorts out the gears to cut tpi, if you want metric you have to convert it yourself. 1mm pitch is 25.4 tpi. It will work out 26 tpi just a quickly, or even 27 if you were so inclined

[SillyOldDufferModerator @sillyoldduffer]

Posted by Calum Galleitch on 08/07/2021 22:48:31:

… the results of my labours may be seen here:

…

I have run it against Duncan's results and I get the same (note though the results may come in a different order)…

I think Calum's offering is the best program so far because it's web-enabled and everyone can try it. Javascript and HTML run in a browser so the user doesn't need to worry about how the magic is done.

I suspect the order of results difference is caused by the incantation that assembles the HTML table. It starts:

document.getElementById('results' .insertAdjacentHTML('beforeend'

Try 'afterend' rather than 'beforeend', or maybe one of the other insert position controls.

Finally, if anyone wants to 'View Source', it depends on the Browser. On Firefox, it's ctrl-u, or accessed from the 'Web Developer' menu.

Dave

 

edit: pesky Smiley removed.

 

Edited By SillyOldDuffer on 09/07/2021 09:37:18

[CalumParticipant @calumgalleitch87969]

The other thing I was careful to try to do was to make it all a single file, so you should be able to right-click and save it and it will work for as long as web browsers continue to support Javascript…

> Try 'afterend' rather than 'beforeend'

I thought this as well, but it turns out that 'afterend' means to place it after the closing tag of the HTML that you are referring to – in other words it writes the results outside the table! Useful I'm sure for some purposes, but not here.

It's not impossible to write a bit of code to sort the results afterwards – I thought about trying to sort by the size of the error, but then it occurred to me that probably the most useful metric is the practicality of the gear train, and I'm not sure if there's a sensible way of calculating this: perhaps the sum of squares of the differences of the compound gears? Suggestions welcome.

[JourneymanParticipant @journeyman]

The program writing is a bit beyond me but I just about understand the principle. The output from these programs is I feel a little confusing, especially for someone setting up change gears for the first time. For the example given to cut a 26TPI thread using a machine with 8TPI leadscrew the output from Calum's program for example is:-

Not entirely clear which line to choose or where to start the gear train. Part of the problem is that the plate on the lathe for this solution shows 4 gears but ignores the 40 tooth gear fixed to the lathe spindle. Now the programs do include the 40 tooth spindle gear and in fact you must start with this so any selection of gears that does not include 40 is not useable. The following image may help:-

It may not be apparent but in all the selections with 4 gears the second in line (meshed with the spindle) is an idler and serves only to make the gear train long enough to reach from spindle to leadscrew (on this type of lathe) it also reverses the direction of the leadscrew. The ratio calcs are shown for the 26TPI example.

John

[Nigel Graham 2Participant @nigelgraham2]

I must admit I find it easier to use tooth- and turns- counts than decimal ratios, for most inch threads, because the sums are direct and clear, and don't invoke error bands, but as long as it works. Using decimals comes into its own for calculating for metric threads on an Imperial lathe, and that was the approach my spreadsheet uses.

More importantly though…

To clarify your last paragraph there though, there should be a reverser, probably within the headstock on Bevel's lathe and as on my Harrison, (external on the Myford 7) to nullify the reversal introduced by a 4-shaft set-up. I think his photos do show this.

'

An artificial tooth-count of 1 (not 0 obviously!) for an idler cancels that middle calculation and any potential rounding-error completely. I never calculate the idler but select any wheel that fits sensibly. My Myford's own chart shows an idler by just a hyphen.

[JourneymanParticipant @journeyman]

Posted by Nigel Graham 2 on 09/07/2021 21:56:51:

To clarify your last paragraph there though, there should be a reverser, probably within the headstock on Bevel's lathe and as on my Harrison, (external on the Myford 7) to nullify the reversal introduced by a 4-shaft set-up. I think his photos do show this.

The WM250 (and similar) lathes have a small gearbox between the change gears and the leadscrew. This is able to change the ledscrew direction and also gives 3 effective ratios between the change gear setup and the leadscrew ie. 1:1, 2:1 and 0.5:1

John

[CalumParticipant @calumgalleitch87969]

John, I quite take your point about the output requiring some intelligent interpretation. There's a balancing act between making such a tool capable of handling every case correctly, and it becoming too difficult to use for anyone but an expert – who probably doesn't need such a tool to begin with!

(Also it might be worth hiving off this software discussion to a separate thread?)

I'm more than happy to do some work on the tool to make it more generally useful/applicable, though I probably need some advice on how to do so. But as I see it, some immediately useful enhancements would be:

• Entering an initial ratio (for example on my lathe, the first wheel revolves at 1/4 spindle speed)
• Specifying the first wheel tooth count, if it is fixed
• An option to account for an idler wheel?
  • And tracking leadscrew rotation direction?
• Accounting for any quick change ratios present.
• Distinguish between "actual" zero error and error less than tolerance.

I think these are all easy enough to code. What else would be useful?

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