Lathe gear calculation

Right.:

Starting from the top of the lathe, the leadscrew is driven from a pinion on the spindle (sometimes immediately following the tumber-reverse gear).

So that gear is a Driver.

It rotates another wheel, so that second is Driven.

That is common to any pair of gears: the one providing the motion drives the driven, but in the opposite direction.

Now, in a change-wheel set-up the spindle has to drive the leadscrew in the same direction. Therefore we interpose a third gear that does not rotate a shaft but passes the Driver's rotation to the Driven one; and in doing so it makes the Driven turn in the same direction as the Driver at the top.

That intermediate gear is called an Idler, or Stud, wheel, although the former term seems very hurtful because it is by no means "idle" ! It means simply that it is not rotating a shaft. Its teeth count does not matter as long as it fits between the other two wheels - in a simple train. It does matter in a compound train.

Now the calculations come down to matching the ratio between the thread to be cut and the thread of the leadscrew.

On an inch-dimensioned lathe with an 1/8" TPI leadscrew, if the thread you are cutting is an even number of turns per inch, the fractions are quite straightforward and you normally need use only one Driver (that up at the top on the spindle output) and one Driven (that on the leadscrew), linked by just one idler, on the stud somewhere in between them.

If we call the threads to be cut T and the leadscrew thread L, then L/T = Driver / Driven.

Make the two numbers small but even (as I did with 8/26 = 4/13) Then multiply both by 5: so 20/65 if the Driver pinion is of 20 teeth, making it a 65T wheel on the leadscrew.

'

I tried to understand that list you gave of 4 wheels but I'm afraid it flummoxed me and I wonder why it was so complicated. 70,65,30,60.

Sorry - if that is the correct order going down from the spindle, I could not make those figures fall out at all! I've tried various combinations of those but then I twigged 2 things:

- Have you quoted one extra: the 70T wheel?

- Does you lathe's driver pinion have 40 teeth?

For then, as you do not have a 130T wheel, you will need a compound train. It now falls into place:

The 40T pinion drives the 65T which is keyed with the 30T together on the stud. That 30T the drives the 60T on the lead-screw: Now use the (driver/driven) X (driver/driven) formula:

(40/65) X (30/60) = 0.3077. Which equals our original 8/26.

Eureka! If I have diagnosed the machine correctly, and that 70T wheel stays off the lathe.

Even-number threads with even-number leadscrews usually work out quite simply, and many need only a Driver-Idler-Driven trio. Fine threads do start to need compound trains and it looks as if this the case on your lathe.

So now: 8/26. Multiply by 5. (40/130) but to compensate for having no 130T wheel, we divide the work into 2 steps hence :

= (40/65) X (30/60)

A 46/65 duo with idler would cut a 13tpi thread, of course. That's not a standard inch thread but it is extremely close to 2mm pitch (45/65 inch = 1.954mm). Worth bearing in mind if you need cut a short M14 or M16 ISO coarse thread!

++++

One point regarding setting the wheels: do not push them into tight mesh but allow a very slight play between them. The favoured dodge is to put a strip of ordinary thin printer-paper between them, lock them into mesh then gently rotate the machine by hand to eject the paper.

Brian Wood's "Gearing of Lathes for Screwcutting" quotes, to cut a 2 mm pitch thread, on a mini lathe with a 16 tpi Leadscrew 63T / Idler / 50T, resulting in an error of < 0.001 mm

Essentially the ratio is 63:50, with the idler to change the direction of rotation.

If your lathe has a 8 tpi Leadscrew, slightly modifying this by making the Idler a compound, it becomes

63T / (50T + 35T ) / 70T. The 50T+35T Compound meshing with the 70T halves the speed at which the Leadscrew revolves relative to the chuck, since the pitch is twice as coarse..

This should be possible, since it does not involve using any more than one gear of each tooth count.

Howard

Oops - yes, less speed more haste. There should obviously be four gears in a compound train.

I'd edited my programme to remove some comments and make it the same as published for my first post - and seem to have deleted a bit of the programme listing too. Here's the first few lines as it should have been...(without 65t gears...)

Input required TPI 12.7
Input deviation 0.03
20 55 70 25 12.72727273
55 20 70 25 12.72727273
20 55 50 35 12.72727273
55 20 50 35 12.72727273
30 55 75 35 12.72727273
55 30 75 35 12.72727273
20 55 35 50 12.72727273
55 20 35 50 12.72727273
40 55 70 50 12.72727273
55 40 70 50 12.72727273

Apologies..

IanT

Aha the penny dropped, Nigel you were spot on with your calcs I have a 40T pinion.

Guys ALL your help is invaluable and very much appreciated.

I will get that book/books for sure and further my understanding. All these machines I have used for so many years and never given any thought to what was actually occuring within. Until now as you are all most probably aware it's been a simple case of following chart and selecting levers to correspond, and to be frank if Warco gave a better selection of change gears with their lathes then I most probably would never have looked any further.

Hats off to you gents, this knowledge will eventually wilt in the age of CNC and mores the pity cos once it's gone it won't return. Excuse my pesimism but I see it every day, young men today are not as skilled as previous generations gone by, not thru any fault of their own but via a massive leap forward in technology.

A massive thanks to you for taking time and explaining it all in such great detail.

Regards

Bevel

deleted whilst I sort out the formatting

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

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?

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.

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.

Callum, pm sent

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?

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

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

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

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.

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

Regards,

IanT

I most certainly do Ian buddy

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

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

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

**LINK**