Lathe gear calculation

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?

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.

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

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

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.

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

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.

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

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?

I have written an online computer program for calculating gear trains to cut metric or imperial threads on metric of imperial lathes. You might find it helpful. This is the URL link:

RideTheGearTrain.com

I would love to hear whether people find it useful.

Where you website says "link to program" it does not for me as it goes to RideTheGearTrain.com

Hi Evan,

There is no link that works for me in your " 05/04/2022 10:26:05 " post, I guess it should be?:

***Link***

 I have just checked a few gear-trains and they seem to agree with my Chinese lathe. Thanks for sharing.

Thor

Edited By Thor 🇳🇴 on 05/04/2022 11:21:57

JasonB,

Yes it looks as though you found RideTheGearTrain OK. It should even turn up on a Google search, as long as you don't insert spaces.

It has now had 1.2 million page loads. One company reported selling 10 million mini-lathes, and that was just one Chinese company!

Thanks Thor,

Your ***Link*** works. I just couldn't see how to insert an active link, but I just found that funny looking icon that looks like the back and of a petrol tanker doing 10 km/h. So here is another link to my program.

**LINK**

There was on older link via one of my other web sites HeroSteamEngine.com. But the program has been moved to its own site. The old address should forward you to the current address.

It is listed on www.lathes.co.uk/latheparts/page14.html but unfortunately they copied some of my very old code onto their web site. But when you try to run their program, it forwards to the correct site RideTheGearTrain.com.

Hope that is not too confusing!

Extensive help files have been written, with help buttons beside most entries. This includes a discussion of the weird method used to label gears in the gear trains of Chinese lathes.

You will see I have written some other apps on the same site. See the menu items with orange buttons. The app to calculate drill sizes based on % depth of thread is perhaps unique. After you specify the size of your thread it lists a range of metric, imperial and 'number' drills and calculates the percent thread depth for each one. The idea is that you might not have the exact recommended drill but can probably find one in your kit that gives a reasonable percentage.

Another set of apps are for cutting speeds. It shows tables of recommended speeds and provides a calculator and table generator.

Cutting speeds are dependent of hardness so there is a section on the hardness of various metals and then hardening and tempering of steel.

Another app is for calculating the tailstock offset required to cut a taper (eg Morse taper) by the tailstock offset method.

The next update will remove text from entries that should be numeric. I found people were trying to include units such as mm.

Evan

PS For Programmers:

You may be interested to know that RideTheGearTrain was written using PHP. This is a general purpose programming language that runs on nearly all servers. It generates HTML code which is sent back to the users computer to display a web page. If the user responds to a question (or data INPUT) on the web site, the program has to run again from scratch, but the new and old data is transmitted back to the server in the URL. It gets very cumbersome, but has the advantage that the user can save the URL and use it again at any time. It means that the user does not have to run any code or run plugins. But it requires the user to be online.

With great respect this thread on threads puzzles me.

Why do people keep re-inventing the [change-]wheel?

Or are they trying to cut very odd threads on lathes made to cut standard threads from standard lead-screws?

My Myford 7 and Harrison L5 came with change-wheels and tables for a wide range of Imperial and metric threads; but the sums are all simple. The ML7 can use its normal wheels for the smaller, common mm pitches, tabulated on a printed plate inside the guard; but I have treated it to an extra, 63T, wheel. The Harrison has a 127T wheel in a change-wheel set further enhanced by a 3-speed feed-shaftl/lead-screw gear-box..

I know many people use the small lathes sold by the likes of Axminster Tools, and I have one not yet "commissioned", These are metric but I believe you can buy additional wheels for cutting Imperial threads if wished. (I am not sure if Axminster still sells metalworking machines, though.)

For anything else, hardly likely more than once in a Blue Moon Leap Year, the calculator would suffice, but I did create an MS 'Excel' spreadsheet to determine close BA and ISO-M threads for my third lathe, an EW Stringer, with its own 25 to 65 X 5T wheel set.

No need to write computer programmes unless you enjoy programming for its own sake, and arithmetically all my spreadsheet does that would be time-consuming by calculator or slide-rule, is facilitate homing in on least-error wheel combinations for cutting up to perhaps 10 turns to acceptable accuracy - so covering the majority of tasks. I simply, manually tweaked the tooth-counts by "inspection" and rejected those results too inaccurate for fine work. Oh - and it then lets me print it.

'

*Holtzappfel also recognised chasing-lathes, which basically copy the thread from a master-screw rather than generate it by gearing; and a cam-type fitting for short thread-lengths, The latter controlled the tool travel by a cam plate or bar set at the appropriate angle across the spindle axis, but I don't know how it related that to the spindle revolution. I have a copy of ME from sometime in WW1, in which a contributor describes a chasing attachment he made for his simple lathe, from a length of threaded bar.

26.000000 -0.000000 n[40] n[50] n[25] n[65]
26.000000 -0.000000 n[40] n[60] n[30] n[65]
26.000000 -0.000000 n[40] n[65] n[25] n[50]
26.000000 -0.000000 n[40] n[65] n[30] n[60]
26.000000 -0.000000 n[40] n[65] n[35] n[70]
26.000000 -0.000000 n[40] n[70] n[35] n[65]

Nigel, I think a lot of people have, or are going to get, second hand lathes that are missing some gears and almost certainly missing the original manuals. Added to this is the fact that some old lathes were never intended to cut metric thread pitches. So there is a constant demand for information on how to do this with either what people have got or what is the minimum they need to buy or make to enable them to do what they want.

Martin C

In this instance, the requirement is to cut a 26 tpi thread.

The picture of the chart on the lathe seems to show that 26 tpi is one of the pitches available on line. A.

All that is needed is to set up a gear train as the chart indicates.

Howard

Can you share your method please Nigel? I for one don't find the sums simple!

For example, if my lathe has:

H A
... |
C B
|
D H

Leadscrew 3:1
Headstock 40t
Gears Available: 20, 30, 45, 50, 60, 60, 65, 70, 75, 80, 85

What's the closest gear combination you would recommend for:

• 2BA 0.81pitch 31.25tpi
• 3.25tpi BSW?

Which of the two example does my lathe get closest too?

And, for extra points, what gear(s) should be bought for my lathe to get the threads spot on?

Please show all your workings!

Dave

Hi Nigel,

Yes, despite being retired, I am a programming addict like others on this thread on threads. Of course many absolute beginners using lathes don't know how to calculate the gear train gear ratio. That included me when I started on this path.

Martin Conelly pointed out a common use for the programs. People often have missing or damaged gears and manuals and want to find the best and cheapest way to cut metric on an imperial lathe etc.

A number of users have contacted me and I have helped them out by adding their lathes with gearboxes. This included a 16 foot imperial lathe being used to overhaul metric hydraulic cylinders for diggers up to 800 tonnes in Canadian open caste oil-sand mines...etc.

But probably the most common use is trying to cut odd threads on minilathes, eg a camera thread 27 TPI.

The problem is the weird labelling used on minilathes. It is OK if you just want to do exactly as they say, but if you want to actually understand what it is doing, it is extremely confusing. As mentioned above, they never mention the spindle gear that has been machined into the spindle (usually 40 teeth). If the user is not aware of this, it is impossible to calculate gear ratios.

Secondly, they do not label the gears in the order that power is transmitted through the gear train. Instead they are labelled by the order in which you mount the gears on the studs. So you cannot simply say that eg Z2 drives Z3 because that may not always be the case. It is so confusing that I recommend minilathe users who want to use my program should give up on that crazy labelling and use the labels shown in my program, which are in the correct order for calculating the gear train ratio.

I have extensive discussions of these issues, and many others, in my help files (probably too verbose).

I had even forgotten why I started writing RideTheGearTrain. I suddenly remembered! I was considering making an Archimedes Screw for the Hero's Steam Engine and wanted to know the maximum pitch that could be achieved with the gears I had. It grew like Topsy!

Many users contacted me wanting special features and most of these have been added, including how to cut worm gears to a particular modulus or diametric pitch. I had to teach myself.

Feed rates are less important but have been included.

The ability to look up various metric and imperial standard threads from tables has been added, eg bicycle threads, Tyre valve threads, Edison light bulbs etc (just for fun). These tabels gave a lot of extra information in the specifications and these have been used to calculate torque/stress etc as shown in the results.

Any further suggestions for RideTheGearTrain.com ?

Nigel

I found your note about a system using a leadscrew set at an angle to the axis of the lathe to modify the effective pitch of the leadscrew. At least I assume that is how it works, but I had never heard of it. I suppose the effective pitch would be the cosine of the angle times the pitch of the leadscrew. The variation in pitch would be limited by the offset angle that could be achieved. Perhaps they had a range of leadscrews to choose from. VERY INTERESTING ! Of course, very early lathes had a range of leadscrews and did not rely on the gear train. It may have been easier to produce leadscrews than gears. A cam system might just use a cam to nudge the carriage a bit further as the half-nuts move along the leadscrew. Again I am guessing.

Evan