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Lathe gear calculation

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Bevel06/07/2021 21:25:40
33 forum posts
5 photos

Hi All,

Asked a similar question some time ago but forgotten the answer.....doh!

Could some kind soul take 5 minutes and enlighten me on how to calculate lathe gear changes required for selective pitches please?

I can see on machine what gears I need but how exactly does this work out eg. my machine has 8tpi leadscrew, I have 20,30,40,50,55,60,63,70,75 + 80 gears. For a 26tpi thread I would need 70, 65, 30 + 60 gears but how does the maths work here exactly?

My previous thread a gentlemen mentioned the 127/100 rule, what does that mean and what bearing does it have on change gears?

Many thanks once again guys

HOWARDT06/07/2021 21:56:03
908 forum posts
39 photos

If the ratio between the spindle and the lead screw is 1:1 then with an 8 tpi lead screw the saddle will move 1/8 inch. So for other pitches you have to calculate a ratio that gives you the pitch you require. To get 16 tpi the ratio is 2:1, 2 revolutions of the spindle to one of leadscrew, and so on. When you try to get the ratio for metric the ideal gear set would include a 254tooth gear, one inch is 25.4mm, when using a imperial leadscrew. Because 254 gear is too big you can opt to use 127 or 63, this however causes a bigger pitch error than 254. By selecting different compound gear sets you can get within acceptable pitch errors.
I spent most of my design life calculating these sorts of things and I quite enjoy them.

others will no doubt come up with the gears you need for all pitches as there are numerous charts around.

Pete Rimmer06/07/2021 22:11:46
1233 forum posts
65 photos

127 does not give a pitch error for metric conversion. 63 does though.

Bevel06/07/2021 22:14:23
33 forum posts
5 photos

Hi Howard,

Many thanks for the reply but I've only partly got it.

I undertstand the ratio bit and also the conversion to metric to explain the 127 rule but in simpleton terms (sorry) if I was looking for 26tpi thread how would I calculate the nearest I could get with gears to hand?

How do I know in what order to place the gears etc as example below?

x - 70

30 - 65

60 - x

This is illustrated on lathe itself so I know it's correct.

Chris Crew06/07/2021 22:45:19
201 forum posts

It doesn't matter what order you place the gears on the banjo, provided that the 'drivers' remain drivers and the 'driven' remain driven. You may find that you have to re-arrange the gears on the banjo in order to actually get them in the space available but you must observe the above rule on the studs. If you invest a few pounds in one of the many excellent publications that are available, and personally I think Martin Cleeve's 'Screw-cutting in the Lathe' is one of the best, you will have all the answers you need at your fingertips. Ivan Law's 'Gears and Gear Cutting' provides excellent easy to understand information for calculating change-wheel combinations for 'odd' threads contained in worms etc. which can also be used for screw-cutting purposes.

Edited By Chris Crew on 06/07/2021 22:46:22

Bevel06/07/2021 22:59:12
33 forum posts
5 photos

Ok guys many thanks for the advice, think a little browse for literature is called for eh Chris yes

Nigel Graham 206/07/2021 23:13:55
2132 forum posts
29 photos

The underlying rule is that the Ratio of the change-wheel train = Ratio of the leadscrew TPI / cut TPI.

To take your example (and this is one I had to do myself recently). You don't tell us your lathe's headstock pinion tooth-count, and I am afraid I can't work out what that combination you show gives. If though the pinion is of 20Teeth the ratio works in a single step and uses what you have:

Leadscrew: 8

Cut thread: 26

8 / 26 : you can work from that but I prefer to halve both numerator and denominator first to bring it closer to the wheel counts, as this shows:

So 8 / 26 becomes 4 / 13.

Now with a 20T driver; multiply both numbers by 5 (because the wheels are in counts of 5)

(4 X 5 ) / (13 X 5) = 20 / 65.

The 20 Tooth wheel is the driver, up on the output of the reverse tumbler

The 65T wheel goes on the leadscrew.

Then put an intervening idler wheel on the banjo stud to connect them and make the work and leadscrew run in the same direction (assuming a right-hand thread).


In general form

LS / Cut thread = Driver (on headstock) / Driven (on leadscrew)


However, as you don't quote the headstock pinion (usually called the spindle):

If that driving pinion is not 20tpi, then you will need re-calculate to suit that; and this may mean a compound train as your question describes.

So if that wheel is of 40tpi you would need effectively a 130T wheel on the leadscrew to gain that 8:26 ratio. Not possible so we split the gearing into two sections; and the most likely is:

8/26 = 40/130 = 40/65 X 30/60 =

40T driver; meshed with a 65T wheel keyed to a 30T wheel on the banjo stud. The 30T then meshes with the 60T wheel on the leadscrew.

And so on for other driver-pinion counts: equate the overall gear ratio to the thread ratio.


In general form:

LS/ Cut threads = (Top Driver / 1st stud wheel) + (2nd stud wheel / leadscrew wheel)


To answer your other question. 100 and 127T.

The 127T wheel allows cutting metric threads on a lathe with an inch-fraction leadscrew. So if we want a 1mm pitch thread; 1mm is equivalent to 25.4TPI

LS/Cut = Driver/Driven

8/25.4 = 40 / 127 (multiplying numerator and denominator by 5).

If we need a millimetric thread of different pitch we would therefore modify the upper part of the change-wheel train but the leadscrew wheel is still the 127T wheel. In practice, this is physically too large for some lathes and a 63T wheel can be used instead, with due consideration of the cumulative pitch error this will introduce.

I must admit I am puzzled by the " 100 / 127 Rule " you quote. I have not encountered that previously.

My Myford ML7's change-wheel guard conveniently holds a chart showing the wheel-trains for most common inch and some metric pitches, and fine feeds, with the standard wheel set. Do you have a manual for your lathe? That ought include a similar chart.

duncan webster07/07/2021 00:13:01
3984 forum posts
65 photos

I think the 63t gear in metric setups should be a DRIVER. Why? Well100:127 is very near to 63:80, accurate to 1 part in 10000

Bevel07/07/2021 07:47:34
33 forum posts
5 photos

Reason I asked the question in first place was yes I do have the chart and I know how to use it but the chart states the combination listed above.

Trouble is I don't have a 65T gear and I need to cut a 2mm pitch thread. I need to cut a M14X2 thread and have a finishing die but need a base thread first. Hence the query.

I asked a similar question previously and the forum answered in spades and allowed me to cut a thread of 1.5mm pitch with the change gears available to a close enough tolerance for job in hand.

With that much more experience now I would like to learn the reasoning behind the calculations enabling me, hopefully, to work out myself what is possible for future projects. Even tho I am time served some 30 years ago I have always had use of geared lathes so change gears are relatively new to me tbh.

Nigel, to answer your question the lathe is a Warco WM250v in English and it has a 40T pinion.

Bevel07/07/2021 09:31:18
33 forum posts
5 photos

Still don't understand where the second combo of 30/60 comes from?

Sorry it's most probably so simple but I can't see correlation at all smile d

Martin Connelly07/07/2021 09:41:23
2137 forum posts
222 photos

Howard stated in the first reply that if you have a 1:1 ratio between the spindle rotation and the leadscrew rotation then your 8tpi leadscrew will cut an 8tpi thread. He then pointed out that changing this 1:1 ratio to 2:1 and slowing down the leadscrew by a factor of 2 gives a thread pitch of 2 x 8tpi ie 16tpi. Inversely speeding up the leadscrew with a ratio of 1:2 halves the tpi being cut to 4tpi.

That is the basic principle so how do you put it into practice seems to be your question. You will probably have two ways of setting up change gears.

The first is a driver, an idler, and a driven gear. The idler can be any size gear that makes the setup easy. The driver and the driven gear give the ratios that are important for the tpi calculations. Starting with the setup that gives you an 8tpi thread if you double the tooth count of the driver gear then the leadscrew will double its speed relative to the 8tpi setting and the carriage will travel twice as far per spindle revolution and you will end up with a 4tpi thread. Conversely if you half the driver tooth count then the leadscrew moves at half the rpm and the carriage will travel half as much per spindle revolution giving a 16tpi thread.

Since it is the ratio between the driver and driven that is important you can achieve the same thing by halving the driven gear tooth count or doubling it.

If you look at your setup chart the manufacturer will have done a lot of calculations for you and picked setup that are easy to assemble in the available space. The chart may have setups for 8, 12, 16, 24 tpi. If you look at the ratios of the driver and driven gears the ratios will be 1:1, 3:2, 2:1, 3:1. Knowing this the chart should start to make sense to you.

The second type of setup is where there are 2 driving and 2 driven gears with the first driven and second driving gear compounded on the same shaft as the idler was on with the simple setup. This is done when the ratios are a little more complicated or will not easily fit in the space. For example the 24tpi above may require two gears that are not in the set but can be achieved another way. The two sets of ratios from this tpi could be 3:2 and 2:1 which together give 3:1.

It is easy with a spreadsheet to create a table with all possible ratios that can be put together with a full selection of change gears that can be fitted into the space. With a limited choice a table of all possible combinations with available gears can be used to find approximations for metric pitch on an imperial leadscrew.

So you have an 8tpi leadscrew and a number of change gears and a manufacturer's chart. If you post the available gears you have and the setup for an 8tpi thread (a picture is best) I, or others, can create a spreadsheet for all possible combinations (and probably some impossible to assemble ones) to allow you to pick the nearest approximation to a metric pitch thread. It can also be used to try other gear tooth counts to see if buying or making another gear improves the approximations.

There is another thread somewhere where this was done for (I think) a Chester lathe.

Martin C

Martin Connelly07/07/2021 09:51:54
2137 forum posts
222 photos

Is your chart the same as the one in this thread?

WARCO WM-250 lathe family and WM16 mill | Model Engineer (

Martin C

IanT07/07/2021 10:00:21
1992 forum posts
212 photos

A 2mm pitch is a 12.7 TPI thread (25.4 / 2) Bevel...

So using the MEW277.BAS programme that I posted here recently, you can calculate the gears required.

(assumes 8 TPI lead screw)

Input required TPI 12.7
Input deviation 0.012
30 75 65 12.71111111
45 50 65 12.71111111
50 45 65 12.71111111
75 30 65 12.71111111
40 65 75 12.69230769
65 40 75 12.69230769
30 75 55 12.71111111
45 50 55 12.71111111
50 45 55 12.71111111
75 30 55 12.71111111
40 65 55 12.69230769
65 40 55 12.69230769



Nigel Graham 207/07/2021 10:57:51
2132 forum posts
29 photos

I can't help thinking there is a heck of lot of over-thinking going on here, of what has been and still is, a basic part of the art since the 19C!

The calculations for cutting a thread to the same units as the lathe (TPI on an inch lathe, mm pitch on a metric) are simple fractions; whether needing a single step or compound train, which is normally 2 but occasionally 3, fractions multiplied.

Cutting a thread of differing pitch-type (mm on inch and vice-versa) is a little trickier by usually needs a conversion 127 or 63T wheel, prime numbers; but not always. My Myford ML7's own chart gives several mm pitches with the "ordinary" wheels. Yet the arithmetic is the same.

Nor do you need know computer languages and programming for what is frequently a pencil, paper and calculator (or mental arithmetic) task.

The computer is valuable for creating tables made once and printable for workshop reference, but still only by ordinary "sums" in a spreadsheet. Mine, in MS 'Excel', gives metric and even BA threads, on an 8tpi-lead lathe with a simple 5-increment wheel range, to a fair degree of accuracy; by normal divisions and multiplications. It was a bit fiddly because I had to swap values around to narrow the errors, but a one-off that did not need compilers and languages, just the standard 'Excel' tools. It also shows the cumulative errors to assess maximum practical non-inch screw-cut lengths, usually longer than necessary anyway; and which may be impractical.

Engineering is performing physical, creative tasks in the best, simplest and most efficient ways, not adding work to make the most complicated ways!

IanT07/07/2021 11:26:05
1992 forum posts
212 photos

No one needs to know anything about computer programming (or languages) to copy and paste a text file into Basic Graham. If Bevel wants to dig into Excel or sharpen his pencil (and mental skills) - then I guess that's up to him.

Personally, nor do I care about the "purity" of one computer language over another, or whether I could make Excel do the same thing. I much prefer things that are convenient, simple and work.

Mike published a small Basic programme to calculate change gear combinations and I typed it (from MEW) into my PC. Others can now simply copy and paste it from my earlier thread. It's just taken me about two minutes to load the programme, run it, copy the results and then paste them here. Nothing complicated about it at all.

But folk can do this whatever way they prefer - I'm just suggesting a way I find convenient.



Howard Lewis07/07/2021 12:55:49
6104 forum posts
14 photos

As Howard T said, some time ago, you are looking to set up a suitable ratio between the Mandrel and the Leadscrew, depending upon what pitch of thread you wish to cut, and the pitch of the Leadscrew..

You would do well to buy and study Martin Cleeve's book "Screwcutting in the Lathe" No.3 in the Workshop Practice Series, or Brian Wood's book, "Gearing of Lathes for Screwcutting".

This is an easier task if you are looking to cut an Imperial thread on a machine with an Imperial Leadscrew, or a Metric pitch on a machine with a Metric leadscrew.

The rule for PITCH is Drivers over Driven.

The usual Driver / Idler /Driven set up will move the Saddle TOWARDS the Headstock if the lathe has a LEFT Hand thread Leadscrew.


Cutting an Imperial thread on a machine with an Imperial Leadscrew.

Cutting a 16 tpi thread on a lathe with a 8 tpi Leadscrew.

(NORMALLY a left hand thread, BUT not on every machine! CHECK )

The Leadscrew needs to rotate at half the speed of the mandrel, so assuming a 20T driver, you need a 40T on the Leadscrew. The space between can be filled with any suitable Idler (It will not affect the overall ratio, only the direction of rotation ) 0.125 x 20 / 40 = 0.625 A 8 tpi Leadscrew has a pitch of 1/8" or 0.125"

To cut a 12 tpi thread, you would use a 40T Driver onto a 60T on the Leadscrew. 8 x 60 / 40 = 12

(HERE we are talking tpi, not Pitches. Pitch is the inverse of tpi, so the formula becomes Driven / Drivers )

IF the Leadscrew is Right Hand Thread a second Idler will be required.

Cutting a Metric Thread on a machine with a Metric Leadscrew.

To cut a 1.5 mm pitch thread on a machine with a 3 mm pitch Leadscrew , the driver could be a 20T driving a 40T on the Leadscrew, with an Idler in between.

To cut a 1.75 mm pitch, you would use a 35T driver, Idler, 60T, so that the Leadscrew rotates a little faster than in the previous example.

If you wanted to cut a 0.8 mm pitch thread, on a machine with 1.5 mm pitch Leadscrew, you would need a compound Idler, starting with a 40T Driver onto a 50 / 40 Idler onto a 60T on the Leadscrew.. So the calculation becomes 1.5 mm x 40/50 x 40/60 = 0.8

All the above are based on the Leadscrew being a Left Hand Thread. With that, IF you wanted to cut a Left hand thread, you would need to insert an additional Idler. The exact tooth count does not matter, the idler is merely there to reverse the direction of rotation of the Leadscrew.

IF then lathe has a Right Hand thread Leadscrew, to cut a Right Hand thread, again a second Idler is required.

The Calculation for the overall ratio is the same..

Hope that this clarifies the position.


duncan webster07/07/2021 13:04:18
3984 forum posts
65 photos

As I pointed out in the other thread, the program referred to by IanT does not print out one of the gears, it also does not tell you which are drivers or driven

For example, the first row above would be

Drivers = 30, 75 Driven = 55, 65

tpi is then 8 *(55*65)/(30*75) = 12.711

it would not be difficult to make the program differentiate, but I don't do basic anymore

Howard Lewis07/07/2021 13:46:03
6104 forum posts
14 photos


I omitted a Zero in the 16 tpi example. 16 tpi is 0.0625" pitch

Proof reader required!


Bevel07/07/2021 15:08:35
33 forum posts
5 photos

Holy Sh*t guys, technical overload! crookcrook

Many thanks to you all for your input much appreciated.

Even tho I have a GCSE in mathematics and never been considered a dullard this is all completely over my head if I'm honest.

Ian T's computer program/ excel file formula sounds just the ticket but I'm lost there as he only lists 3 gears, where have the others gone lol?? How exactly do you set them up?

Nigel Graham 2 writes that this is just simple arithmetics but all this talk of drivers and driven, ratio's etc etc has my head swimming.

Must be simpler way to work out what I can achieve with what I have to hand and where I position everything surely.

Martin C my chart is slightly diifferent, I will take a pic and post it shortly

Howard Lewis07/07/2021 16:38:19
6104 forum posts
14 photos

Buy Martin Cleeve's book and you will understand what is needed. Once you have grasped the basics, it just becomes a matter of simple Multiplication and Division. Calculus does not come into it!


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