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Find the gears needed for the gear train
to produce any screw thread on an engineer's lathe.

A PHP program by Evan Lewis: Contact Us
Link to this program: www.RideTheGearTrain.com
The author describing the program: Video about Ride The Gear train
The authors' lathe videos: Evans YouTube Playlists
This includes a video: Understanding Geartrains
INSTRUCTIONS & INFORMATION: About 'Ride The Gear Train'
Lathe project-2000 year-old steam engine: HeroSteamEngine.com

Recommended:

Boxford Users Group
Blondihack's: Quinn Dunki's supurb mini-lathe channel
Winky's Workshop: Engineering YouTube channel
Keith Appleton: Model Engineering
Enots Engineering: Alan demonstrates engineering methods
Alan talks about this program
Joe Pieczynski: Joe Pie's channel-excellent engineering demonstrations by a professional
Tony Griffith's Lathes.co.uk: has detailed information about every lathe you could imagine.


RideTheGearTrain Tutorial
Part 1A for Mini-Lathes

RideTheGearTrain Tutorial
Part 1B for all other lathes
including South Bend Clones

RideTheGearTrain Tutorial
Part 2 for all users








  • FREE ONLINE SOFTWARE
  • CALCULATES THE GEARS REQUIRED TO CUT ANY THREAD
  • FIND SOLUTIONS WITH THE GEARS YOU HAVE, OR PLAN TO GET
  • CUT A METRIC THREAD ON AN IMPERIAL LATHE (WITHOUT SPECIAL GEARS?)
  • CUT AN IMPERIAL THREAD ON A METRIC LATHE
  • ENTER YOUR OWN SET OF GEAR WHEELS
  • LIST ALL THE THREADS POSSIBLE WITH YOUR GEARS.
  • CAN BE USED ON ALMOST ANY LATHE WITHOUT A LEAD-SCREW GEARBOX
  • CHANGE THE LEAD-SCREW PITCH
  • GEARBOX FOR ALL SOUTH BEND 9 inch CLONES INCLUDED (eg BOXFORD)
  • GEARBOXES FOR MANY OTHER BRANDS AND MORE ARE BEING ADDED
  • INSTRUCTIONS FOR ADDING YOUR GEARBOX TO THE SOFTWARE
  • LIST FEED RATES POSSIBLE WITH YOUR GEARS.
  • ENTER COMPOUND GEARS IN PAIRS 127/100, 80/63 OR SINGLY 127,100
  • SPECIAL CALCULATIONS FOR MAKING WORM GEARS
  • ADD A FUDGE FACTOR FOR ODD-BALL MACHINES
  • RUN IT ON YOUR PHONE OR TABLET IN THE WORKSHOP
  • RETAINS ALL YOUR DATA IN THE URL ADDRESS - SAVE AS A BOOKMARK
  • DISPLAY PAIRS OF GEARS FOR A GIVEN GEAR RATIO (eg metric imperial conversion).
  • TABLES OF RECOMMENDED CUTTING SPEEDS.
  • PRODUCE TABLES OF RPM, DIAMETER AND CUTTING SPEED.
  • CALCULATOR FOR CUTTING SPEED FROM DIAMTER AND RPM.
  • EFFECT OF MATERIAL HARDNESS ON CUTTING SPEED.
  • COLORS OF STEEL WHEN HEATED FOR HARDENING AND TEMPERING.
  • CALCULATE TAILSTOCK OFFSET FOR TURNING TAPERS.
  • A RANGE OF DRILL SIZES FOR TAPPING THREADS.
  • CAN BE FOUND USING GOOGLE: SEARCH FOR RideTheGearTrain



At each point where you can enter data there is a HELP button; a colored circle with a question mark in the middle (?). Simply clicking the help button takes you to the help file. It then asks you to click a link to take you to the paragraph you requested. When you have read the help, just click any button labelled 'Return to Program'. This takes you back to the page you had been working on, and any data you entered should still be visible (except for drop-down menus eg thread references).

Colour Coded Help Buttons: Starting a new section such as 'Choose your Lathe' there may be a blue help button about that section. Each data entry has a green help button explaining what should be entered. If there are other sections of the help file that are related to this step, they are shown in yellow.

Missing Links: Occasionally you may find a help button that takes you to the help file, but there is no paragraph on that topic. That is because it is still under construction. The help file is still evolving. Using the browser's search feature (Command F or Control F) may find related help notes.



The main menu has 6 numbered entries or 'steps'. Start by going through these in order. However, you can come back and alter the entries in any order. You can choose RUN without entering any data, just to see what the results might look like. Pay special attention to the instructions for step 5. Click on the yellow or green help buttons for more extensive help.



NO GEARBOX: If you cannot find a lathe that exactly matches yours, you may be able to find something similar and adapt it using Optional Entries. Otherwise use the Custom Lathe or Custom Gearbox options in the main menu or at the bottom of the list of lathes. Custom Gearbox: Enter data from the label on your gearbox

If you do not have a gearbox, and it is not a mini-lathe choose one of the first two items. One is for metric lathes without screw-cutting gearboxes using pitch in mm and the other is for imperial lathes without screw-cutting gearboxes using inches and threads per inch (TPI). Check that the pitch of the lead-screw is correct. There is an input box at the beginning of Step 2 so that you can check it and make changes if necessary. The program assumes that metric lathes have 3mm lead-screw pitch and imperial lathes 8 TPI. Leadscrew pitch can also be changed in Optional Entries.

Chinese lathes If yours is a Mini-lathe scroll down further to find one that appears to match yours.
have some peculiarities and users should review the questions in Optional Entries and you can make changes to suit your lathe if necessary.

WITH GEARBOX: The data for many lathe models have been added to the program. If your lathe does have a leadscrew gearbox for cutting threads the program will need to know the gear ratios in the gearbox. If you are lucky you will find your lathe on the list. In that case the gear ratios are included in the program and all you have to do is select the lathe.

If your lathe and gearbox are NOT on the list you can still use the program by setting up a Custom Gearbox. The Custom Gearbox program calculates the gear ratios in the gearbox from the thread cutting label that is normally found on the gearbox. Typically this will show rows and columns based on the positions of various gear levers. Within the table you will see the pitch or threads per inch (TPI) that can be obtained with these lever positions. Sometimes there are also smaller numbers on the table representing carriage feed rates but you can ignore these. The program also needs the standard gear train used with the tables and the pitch of the lead-screw.) Full instructions can be found in this help file: 'Custom Gearbox'. After entering the data, contact the author to have your lathe added to the program (AEDLewis at gmail dot com).

VARIABLES THAT COULD CHANGE WHEN CHANGING LATHE MODELS

The program keeps a list of specifications for each lathe and these specifications will change when you choose a different lathe. However, data from your personal selection
of thread size and output method as well as preferences should be retained. Specifications that change include your set of change gears and compound gears, the stud and lead-screw gears, power feed gear ratios for the cross-slide and carriage, the pitch of the lead-screw and all gearbox specifications.

After running the program save the URL which contains your data including your personal set of change gears. The program looks up your IP address to make sure it is not me doing test runs, but the IP is not recorded and there are no personal data or cookies kept by the program.


Compound Gears: First you have to decide whether you will be using compound gears. These are made from two gears joined together. At this stage you are designing the type of gear train but you will not enter the actual gears in this question. You can choose to keep things simple by selecting NO compound gears are included in this gear train design. If the program does not provide a suitable solution, and you have compound gears available, you might want to add ONE compound gear is included in this gear train design, or in extreme cases TWO compound gears. Consider increasing the acceptable error mentioned below.

If you are cutting a metric thread on an imperial lathe, or if you are cutting an imperial thread on a metric lathe, you may find a solution with no compound gears, but it is likely that you will need a compound gear of some kind. The best solution is to use a 'transposing' compound gear such as 127/100 which provides the conversion factor for converting between metric and imperial (1.27x2=2.54). For more thorough discussion see the following sections on converting between metric and imperial:
"When to engage the Half_Nuts"
How does conversion from imperial to metric work?
Converting Metric lathes to cut imperial threads
Converting Imperial Lathes to cut metric threads 'List all compound gears for converting between metric and imperial'


You would only need TWO compound gears if you have not been able find a solution with one compound gear. This may occur when you are using a lathe without a gearbox and is more common in Chinese lathes if you cannot change the stud gear and lead-screw gear (see "Optional Entries" in the menu.

Automatic Compound Gears is the next option. If your lathe allows you to use your set of change gears in any location in the gear train, then you should use automatic mode. In this case the list of compound gears, (mentioned below), is completely ignored. The program automatically generates every possible compound gear by selecting any two gears from your list of change gears. So all you have to decide is whether you want to design a gear train with two, one, or no compound gears, as mentioned above.

No Automatic Compound Gears: Many older lathes, eg Boxford and other clones of the South Bend lathes were designed with two sets of gears. One was a set of 'change gears' that could be used as stud gears or lead-screw gears. These gears have keyway slots so that they can be driven by the stud shaft or lead-screw/gearbox shaft. The other set had a larger hole bored through the center and no keyway because they were designed to spin freely, but with two gears joined together. An idler gear is similar, but is a single gear that has the larger hole bored through the center, and no keyway, so that it can spin freely. Often compound pairs of gears were permanently riveted together. If your lathe has this arrangement you cannot use automatic mode and need to enter your list of compound gears separately.

HOWEVER, there is an adapter (designed by Bob Townsend) which allows you to use automatic mode, and you could make it quite easily. See the photo shown below.

Enter your own list of change gears:
Just enter the number of teeth on each gear and separate the numbers with commas. These are all single gears, not compound pairs, and generally have keyways.

Enter your own list of compound gears:
Finally you can enter a list of compound gears. You do not need to use this list if you chose automatic. Otherwise you can enter your compound gears as permanent pairs as numbers of teeth separated by a slash eg 127/100. If these gears can be easily taken apart and mixed and matched as pairs you can enter this as a plain list of numbers eg 127, 100, 78, 18.





Basically this allows you to choose either metric or imperial (inch) units. For example you can click a button to select a metric thread (mm pitch) or imperial thread (TPI). It doesn't matter what kind of lathe you have. It may have a metric or imperial leadscrew.

However, there are several other options besides threads that are described in more detail below. (See the index tabs down the left side of this page, or click the links here.)

There is an option to calculate the carriage feed rates, or power feed rate for the cross-slide instead of thread pitches. These can be calculated in imperial or metric units. There is also the option of calculating gear trains for making worm gears using diametral pitch (DP) in imperial units or modulus in metric units. You can also request a gear train with a specified gear train ratio (GTR). This can be used in other machine tools such as milling machines. Finally you can generate a list of compound gears with a specified gear ratio. There are hundreds of combinations that could be used as 'transposing' gears for converting between metric and imperial.



Acceptable Error: If you enter an error of zero, the program will only display gear trains that will give the exact thread. However, if there is no solution you may be willing to accept a small error and enter 0.25 or 0.5%. Then you are likely to find a lot more solutions to your problem. You can even try 2% to produce even more results. If you get too many results you can reduce the error. There is a much more detailed discussion of Error below. Click on the link: Error.



This is where you enter the actual number you are looking for. It is called a 'value' in the menu. The question is based on the choice you made in step 3: If you requested a metric thread you will be entering its pitch in mm. If you requested an imperial thread you will be entering threads-per-inch or TPI. In step 3, you may have chosen some other calculation such as feed rate, modulus etc rather than a thread. They all work the same way and the program will tell you what kind of value you are expected to enter.

There are three buttons in the menu that provide different ways to enter this value. Only use ONE of these options: 5A, 5B, or 5C. By far the simplest way is to choose 5A and enter a single value.



Initially you will want to enter just a single value such as a thread pitch/TPI to have the program work out all the ways that your personal list of gears can be arranged to produce the required result. The program simply asks for the required information eg pitch or TPI of the thread you want to make.




The 'Range' feature can be used to select a range of values (such as thread or feed rate etc) so that you can generate a table.

You may want to produce a list of all the common threads you can produce. This can result in long lists. This is similar to entering a single pitch or TPI in 5A but instead of a single number, you enter a range of numbers by filling in 3 boxes: The starting value,
The ending value
and the interval between values

eg from 1 to 3 with interval 0.5 would display threads of 1.0, 1.5, 2.0, 2.5, 3.0 and you would enter
STARTING VALUE 1, ENDING VALUE 3, INTERVAL 0.5.
Do not include zero in your range because it may result in divide by zero error.




This option allows you to look up tables to find out the pitch or TPI of a standard thread such as the course or fine versions of Metric threads (ISO), Whitworth, UNC and a lot of weird and wonderful standards. If you chose metric threads in step 3 it only shows metric standards and of course imperial only shows imperial standards. If you chose a feed rate etc the menu does not display option 5C at all.

The main purpose is to find the pitch/TPI, but since the standards include a lot of other information the program takes advantage of this to display things like the 'Calculation of thread depth and angle',
and how far to advance the compound slide when single point threading. The program also produces tables of drills recommended for internal threads. The extra details can be accessed using a separate orange button.

With regard to use of the dial on the cross-slide see: Cross-slide dials calibrated for radius or diameter



At last you are ready to run the program. When you click 6. RUN, it will display the combinations of gears that will solve your problem. The main table of results shows sets of gears to use in the gear train and the pitch or TPI of the thread it will produce. It includes the percentage error comparing the actual thread with the requested thread.

There may be additional information marked FYI (For Your Information). These items are additional information that may be of interest, including the gear train ratio (GTR) and the gear ratio of the gearbox. The 'gearbox ratio' includes the lead-screw pitch so that you can multiply GTR by the 'gearbox ratio' to get the pitch or TPI. Calculation of TPI is the inverse of pitch (inches per thread, or mm per thread). For that reason for imperial threads the gearbox ratio is multiplied by the 'inverse GTR' ie 1/GTR and that is what is displayed.

If you have too many or too few results you can scroll down to the bottom of the page and click the button to return to the main menu and alter any of the parameters. eg You may want to adjust the acceptable error. Then click 6. RUN to run the program again with your new data.




You may be in a situation where you need to make or buy new gears. The best way is to choose new gears to add to your list and see what happens. You may want to combine this with the '5B. RANGE of values' option.

'Recommend new gears' is designed to give you some suggestions of gears that may be helpful, but is quite limited and often comes up with no results. Start by going through items 1-5 in the menu. When it comes to entering a thread pitch or TPI, choose a single value (5A) not a range. Then choose this step. It does not use your full set of gears, but asks you to choose the number of teeth on the gears you would like for your gear train (there may be 2, 4 or 6 boxes to enter the gears depending on how many compound gears you chose in step 2.)

If you have a gearbox it goes through every gearbox setting and calculates the gear train ratio (GTR) required to get the exact thread you requested.

If there is no gearbox it calculates a single required GTR.

When you click RUN the program should show a list of possible gear combinations.

The program displays a recommended new gear which is also a blue link. If you click this, it does not delete your data. Instead it adds the new gear to your list and automatically jumps to RUN the program and displays EVERY gear combination and gearbox setting that will produce the requested thread. You can repeat this process adding yet another gear without deleting the previous addition.

The GTR is also displayed as a blue number which is a link. If you click that, it will show all the gear combinations that will produce that GTR and thread. But it is only valid for the one gearbox setting. It also deletes most of the data you entered earlier so you may prefer not to use it.




Most users of western lathes will not need this, but should take a quick look to see what the options are.
• You may need to specify the pitch or TPI of the lead-screw.
• Some lathes do not have a stud gear that can be changed, instead the first gear in the gear train is machined into the spindle. The program allows you to enter the fixed number of teeth on this gear.
• Similarly the gear on the lead-screw shaft, or input to the gearbox, (lead-screw gear or LSG) may not be changeable and the user can specify the number of teeth on that fixed gear too.
• Finally there is a fudge factor. Every result calculated may be multiplied by this fudge factor to correct for unusual problems. All of these items are in the "Optional Entries" page and are described below.




(This item is in "Optional Entries").
If the user has a very large set of gears, perhaps including a gearbox, and especially if the 'acceptable error' is set high, the number of results can be very large. For that reason there is a limit on how many results are displayed for you to read . The results limit can be adjusted here in Optional Entries.



(This item is in "Optional Entries").
The carriage power-feed gear ratio can be changed here. Not all lathe models have power feed but if a ratio of 1 is entered the program will display the feed rate when you use the lead-screw instead.

In order to calculate carriage feed rates the program needs to know the gear ratio for the carriage feed. There is usually an extra gear in the apron of the carriage that slows down feed rates, usually by about 1/3. This means that the feed rate will be about 1/3 of the thread pitch that would be obtained with the same gear train and gearbox setup and the half-nuts engaged. So the feed rate is the feed ratio multiplied by the pitch. The program records the feed ratios in the lathe specifications for each lathe. There is more information about feed rates and gear ratios below.

This ratio is usually constant for a given lathe and remains the same whether you are cutting metric or imperial threads. But a metric lathe may have a different ratio to an imperial lathe. (That is the case for Boxford A and B models where the carriage feed ratio is 0.34 for imperial lathes and 0.361 for metric lathes.)

Some lathes may have a lever for changing this ratio. Myford lathes use a ratio of 1/9 or 0.1111, but this is set up in the gear train which has an ingenious system which reduces the gear train ratio by 1/9 when a compound gear is slid on its shaft. See the diagram in the Myford section.




(This item is in) "Optional Entries").
The cross-slide power feed gear ratio can also be changed here. It works exactly the same way as the carriage feed described above. There is one difference which I will describe using the Boxford as an example. In my Boxford A imperial lathe the carriage feed ratio is 0.34 and that is multiplied by 0.3 for the cross feed ratio. The overall ratio we need to calculate the cross feed as the distance fed per revolution of the chuck is 0.3 x 0.34 =0.1. So when the ratio is reported it is necessary to know whether it is relative to the carriage feed rate or relative to revolutions of the chuck.




(This item is in "Optional Entries").
In most European and American lathes the stud gear is designed to turn at the same speed as the chuck, and it can be easily changed. So that is the most commonly changed gear. The reversing tumbler gears are usually positioned between the spindle gear and stud gear but they act as idler gears and do not affect the gear ratio. They also act as spacers between the spindle gear which is machined into the spindle, and another gear at the base of the stud. Both the spindle gear and the gear at the base of the stud shaft have thge same number of teeth, and that is why they turn at the same speed. The stud gear is keyed to this other gear at the base of the stud shaft. Technically, the stud gear pair is actually a compound gear, but since it turns at the same speed as the spindle and chuck we do not include the gear at the base of the stud when calculating the gear train ratio.

So on most lathes the stud gear can be changed. But most Asian/Chinese lathes do not have a stud gear so it is NOT changeable. They leave out the reversing tumblers and put a reversing lever on the front of the gearbox. This means that the gear machined into the spindle now serves the role of a stud gear, but it cannot be change. However, we do need to know that it is not changeable, and how many teeth there are on the spindle/stud gear and this is entered in Optional Entries.




(This item is in "Optional Entries").
The lead-screw gear or LSG is normally connected to the lead-screw or the input shaft for the lead-screw gearbox. Asian/Chinese lathes may be designed in such a way that this gear cannot be changed. The program needs to know that it cannot be changed, but it also needs to know how many teeth it has to calculate the overall gear train ratio. These are entered here.

With the loss of the stud gear and lead-screw gear, and a very limited gearbox, it becomes necessary to use two compound gears in many cases. Then the number of gears that can be altered is 4, which is the same as a conventional lathe with a stud gear, LSG and one compound pair.



(This item is available in "Optional Entries").
For lathes with gearboxes the TPI or pitch of the lead-screw is recorded with the lathe specifications. So you should not have to change it unless you have a non-standard lead-screw.

It is the leadscrew that tells us whether it is a metric or imperial lathe. For a lathe without a gearbox the program assumes the lead-screw has 8 TPI for imperial lathes or 3mm pitch for metric lathes. If that is not correct, it can be changed here. For example mini-lathes usually have lead-screws with 16 TPI, 1.5mm or 2 mm.


ADVANCED SETTINGS IN OPTIONAL ENTRIES

Is the lead-screw metric or imperial?

(This item is in "Optional Entries").
If you specify a metric lead-screw the type of lathe is set to metric, and of course an imperial lead-screw implies an imperial lathe. If the lathe has a gearbox it is assumed that it is the same type as the lead-screw.

I have heard of a very rare case where a metric gearbox was fitted with an imperial lead-screw, it is generally assumed that they match! If not you could contact the author for a special lathe set-up.



(This item is in "Optional Entries").
This should be self-explanary. Many lathes have a gearbox fitted to the end of the lead-screw, between the last gear of the gear train (the lead-screw gear) and the lead-screw itself.

There should be a table attached to the lathe showing how to set up the gearbox to cut a particular thread. Some lathes have several knobs and levers which have to be turned to a particular position to create the required thread. The Norton style of gearbox has two levers. One marked with letters of the alphabet, and each step increasing the gear ratio by a factor of two, eg 2,4,8,16. The other lever is marked with numbers.

There should be documentation to tell you how to set up the gear train when you are expecting to use the table provided. From this 'standard gear train' we can calculate the primary ratio. The primary ratio is the gear ratio which all the gearbox ratios have to be multiplied by. There is further discussion about the primary ratio below.


(This item is in "Optional Entries").
All the gearbox ratios have to be multiplied by this primaryRatio constant. If there is no gearbox it is set to one and the Ffactor mentioned below is also one. In that case without a gearbox:

TPI = leadscrewTPI / GTR

Generally the user does not need to know about the primary ratio, because it has been entered into the program when each of the lathes was set up. However, the option of changing it is given for the advanced user whose lathe is not already listed but is similar to another lathe that is listed. It may be possible to alter a number like the primary ratio to make it work. For example, there may be a user with a SouthBend 9" clone that has been built using a different primary ratio. This can be recognized when the so called 'standard gear train' that is used with the standard gear chart is different to normal. In that case the user can choose a lathe that is otherwise the same, and adjust the primary ratio. Having done that a couple of threads can be checked to ensure that the primary ratio has been calculated correctly.

I will try to explain briefly and summarize here.

The story started with the imperial Boxford lathe with a gearbox. It was realized that with an imperial lead-screw with 8 threads per inch (TPI), the user could cut a thread with 8 TPI making a one-to-one copy of the lead-screw. To do that required an overall gear ratio of 1:1. But the manufacturer said you had to use the 'standard gear train' with a 40 tooth stud (driver) gear and 56 tooth (driven) lead-screw gear (LSG). This produced a gear train ratio of 40/56 = 1/2.8. So, when the gearbox was set up for 8 TPI it was not providing a 1:1 gear ratio but rather a gear ratio of 2.8 to compensate for the gear train ratio of 1/2.8 giving an overall gear ratio of 1.0. So that is where a primaryRatio was born. However there is a snag here, which is described in more detail below. In imperial lathes TPI is inversely related to the gear ratio, and the primary ratio used in our equations is related to 1/GTR. So the primary ratio has to be inverted to 1/2.8 rather than 2.8.

It is easiest to explain the equations for a metric lathe and then come back to the imperial lathe later. So let's switch to the metric lathe with a gearbox where thread pitches are in mm and the lead-screw pitch is quoted in mm. In that case the pitch of the thread is related directly to the gear ratios. If the gear ratio is increased it will cause the lead screw to rotate faster, producing a longer pitch. As shown in the 'EQUATIONS' box after the results, the equation we use to calculate pitch of a metric thread from the gear train ratio (GTR) is:

ThreadPitch = primaryRatio x Ffactor x leadScrewPitch x GTR

Ffactor (sometimes called factorF) is the gear ratio provided by the gearbox, or a multiple of the ratio. Since we are going to multiply it by a constant (primaryRatio) we can generally adjust the Ffactors to look the same as the gear table provided by the manufacturer. Then we calculate the primary ratio which will always be used with this Ffactor table. To do this calibration we can use any thread pitch from the table with the Ffactor assigned to that pitch and the standard gear train ratio. By rearranging the above equation:

primaryRatio = ThreadPitch /(Ffactor x leadScrewPitch x GTR)

In this case we have to use the GTR of the standard gear train. Once we have determined the primaryRatio in this way we can use it with any GTR. So let's look at how the program uses it.

When the program needs to loop through all the threads that can possibly be made, it loops through all the possible combinations of gears in the gear train and calculates all the GTR values. Then it loops through all GTR values, and for each one loops through all the Ffactor values in the table, and for each combination calculates the ThreadPitch using the above equation. It compares this with the required thread and calculates the percentage error. If the error is within the acceptable limits set by the user, it keeps that result and displays it later.

The system for imperial threads is similar but it is all based on the following equation. The most obvious difference is that it is divided by GTR instead of being multiplied by GTR.

TPI = primaryRatio x Ffactor x leadscrewTPI / GTR

In this case the Ffactors from the manufacturers label are not pitches, but TPI which is the inverse of pitch. Whereas pitch is proportional to the overall gear ratio, TPI is its inverse ie instead of using a pitch in inches per thread we use threads per inch. So the primaryRatio is also proportional to TPI, not pitch.

We have to remember that these primary ratios are not identical. If we have an imperial lathe and want to calculate the primary ratio from a metric pitch we have to convert the metric pitch into TPI and use the imperial equations, not metric equations.

The equation for calculating the primary ratio for an imperial lathe is obtained by rearranging the above equation for TPI:

primaryRatio = TPI x GTR / (Ffactor x leadscrewTPI)

This can be calculated from any valid thread on the manufacturers table. The primary ratio is often a long decimal number but it can be interesting to calculate its inverse ie 1/primary ratio which may be a simpler number. It may be further revealing to divide this by the standard gear train ratio and divide by the lead-screw TPI and see if you get an integer.

To calculate primaryRatio for a particular gearbox I like to use the settings where TPI is the same as the leadscrewTPI. Then they cancel out and the equation becomes:

primaryRatio = GTR / Ffactor

The use of the primary ratio is scattered all through this help file and it may be worth using these internal links to read more about it. There is bound to be some repititition.
How was the 'Primary Ratio' discovered?
How was the 'Primary Ratio' calculated for metric lathes
Method for calculating TPI with an imperial gearbox
More about the method for calculating TPI with an imperial gearbox



(This item is in "Optional Entries").
A few rare and unusual lathes may need to have the calculated pitch or TPI adjusted by multiplying by a 'Fudge Factor'. The primary ratio is multiplied by this fudge factor and in fact we could just change the primary ratio instead.

eg if the stud gear turns twice as fast as the spindle you would need a fudge factor of 0.5 to halve the pitch, or 2.0 for imperial to double the TPI.

The stud gear is usually a compound gear but only the outer gear is usually changed. However there have been cases where people have an old lathe where the inner gear has been changed to the wrong size. Generally it should have the same number of teeth as the spindle gear so that the outer stud gear turns at the same speed as the spindle. If this is incorrect the fudge factor can be used to correct it.

On the Boxford A,B,C series the spindle has 24 teeth and the inner stud gear should also have 24T. In two cases I know of, a 25T gear had been substituted. In these case the fudge factor would be 24/25. This correction can usually be built into the software by altering the 'primary ratio' for your lathe. Contact the author using the email listed at the top of the menu page.

There are rare lathes where an adjustment is required and it is necessary to include the gear ratio in this section (or its inverse). This is done with the fudge factor.

(For both metric and imperial lathes the program multiplies the primaryRatio of the gearbox by the requested fudge factor, and this means the pitch or TPI are effectively multipled by this factor. If the lathe does not have a gearbox the primaryRatio is 1.0 unless it has been multiplied by the fudge factor.)

The role of the stud gear and tumblers has been described above, under the heading Can the stud gear be changed?

If the spindle gear has 32 teeth and the stud base gear has 16 teeth then the stud shaft will spin twice as fast as the spindle ie driver/driven=32/16=2. If you are calculating the pitch it will be twice as long and you would need a fudge factor of 2.

In imperial lathes the TPI is also proportional to the primaryRatio used for that type of lathe. But with the lead-screw spinning twice as fast in the above example, the TPI will decrease. So the primaryRatio should be multiplied by a fudge factor of 1/2 or 0.5.

USE OF THE FUDGE FACTOR FOR COMPLEX GEAR TRAINS:
Towards the end of this document is a section about the Logan 200 Lathe which gives another example of a use for fudge factors.


This is a 'stand alone' program that does not need any of the lathe specifications in steps 1-6. Just click the button labelled Drill Sizes in the main menu. This presents you with a list of standard reference threads (like those used in step 5C), but it includes both metric and imperial standards. Look for the type of thread you want (eg UNC or ISO) and then use the drop-down list to find the required size of thread. This also includes the pitch or TPI. When you have selected the size, click the 'RETURN' button.

The program will display tables of recommended drill sizes. These tables are quite unusual - possibly unique. Most tables recommend one drill size - take it or leave it. If you don't have that drill size you must find the nearest size you have. The recommended size to be used with ordinary fluted taps would be expected to leave a thread 75% of the full thread depth. However, one proposed argument is that these taps tend to push metal up into the crest of the profile 'forming' a thread with increased depth.

This is not an exact science unless you have precise information about the material you are working with, and usable threads can be produced over a range of percentages. For example softer materials like aluminium form a full thread more easily than hard materials like stainless steel.

If you are making a thread that is not required to handle a heavy load you might accept a thread with less than 100% depth. It would certainly be easier to cut. This is somewhat controversial as conventional taps are primarily considered cutting tools.

In fact, the main reason for recommending 75% depth of cut is that high percentages require a considerable amount of torque, and could easily break the tap, resulting in severe headaches!

Also the strength of the thread may not be increased significantly by increasing the percentage of thread depth. Beyond 75% depth of thread the strength of the hole does not increase much, yet the torque required to tap the hole rises considerably. This is confirmed by the following quote:
www.regalcuttingtools.com: Increasing the thread depth from 60% to 72% in 1020 steel requires twice the torque, but with the same length of engagement, the strength of the thread only increases 5%.


The tables displayed by this program show the % depth for a range of common drill sizes including metric sizes in steps of 0.1mm, which of course includes the common 0.5mm step sizes. The imperial drills are in steps of 1/64 inch. These can be useful for the hobbyist who may not have a huge range of drills. Numbered drills or letter drills could be included.

Quoting Wikipedia regarding number and letter gauge drill sets: The gauge-to-diameter ratio is not defined by a formula; it is based on—but is not identical to—the Stubs Steel Wire Gauge, which originated in Britain during the 19th century... Number and letter gauge drill bits are still in common use in the U.S. and to a lesser extent the UK, where they have largely been supplanted by metric sizes. Other countries that formerly used the number series have for the most part also abandoned these in favour of metric sizes.

Since we are talking about threads there is a discussion here about single point thread cutting on a lathe and why we often use the compound slide set at an angle of 29.5 degrees. See 'Why 29.5 degrees'.



As described earlier, these drop-down menus allow you to choose one of the thread standards (eg ISO, BSW or Panzerrogr Gewinde). The drop-down menu will show you a list of available sizes. Choose one. Then click a 'Return' button. In this case you do not have to click RUN. The program runs automatically and shows you a lot of detailed information about that thread. This includes the depth of thread and how far to advance the compound slide if you are single point cutting the thread on a lathe. It is all based on the standard specifications.




By using the Preferences button in the menu you can turn off a lot of the explanatory text, tables and other details.




Please don't hesitate to contact me at the above email address (AEDLewis at gmail dot com) if you:

(a) have any questions or suggestions

(b) find any errors

(d) would like to add other brands of lathes

(e) tell me how you used it



The purpose of this online computer program is to search through all the possible combinations of gear wheels in the gear train, and gearbox settings, looking for the best combination which will produce the required thread. It will list the gear combinations that will give the perfect thread with 0% error, but it will also list gear combinations that give a close approximation. The percentage error is displayed and the user can choose how much error they are willing to accept.

If you have a lathe without a screw cutting gearbox it is assumed that standard metric lathes have a lead-screw pitch of 3 mm and imperial lathes have a lead-screw with 8 threads per inch. However, you can change the lead-screw pitch (in "Optional Entries" and that allows the program to work on any lathe without a gearbox.

When we come to lathes that do have a gearbox, things get more complicated because the gear ratios they provide vary and it is necessary to include gearbox data for specific lathes. Although this software was originally written for South Bend Clone lathes which have a Norton gearbox, such as Boxford model A, and others listed below, other gearboxes are being added as people send in the data needed.

'Ride The Gear Train' allows you to cut metric threads on an imperial lathe and imperial threads on a metric lathe. It can display results for a single thread pitch or TPI, or for a range of values. You can specify your own selection of gears and try out a new gear before you buy it. It can be used for unusual cases such as pipe threads. Special features allow the user to select a power feed rate in metric or imperial, as well as diametral pitch or modulus for making worm gears.

Boxford and many other lathes have two different kinds of gears which fit on different sized shafts or studs. The program therefore allows for two sets of gears. One is known as the set of "change gears" or "change wheels", generally used for the stud gear (which is the first gear in the gear train) and for the lead-screw gear (which is connected to the lead-screw or the gearbox when fitted. This is the last gear in the train). The second set of gears have a larger hole drilled in the center. These are the "compound gears" which allow two gears to be connected together on the central shaft with a key, or permanently riveted together.

If you have a lathe that does not have two different kinds of gear you can ignore the list of compound gears. In that case you use the "automatic compound" gear option, which will automatically work out every possible way that your gears can be paired together to make a compound gear.

In many cases it is not necessary to use compound pairs of gears at all, and in others cases one compound gear is required. Although it is rare to require two compound gears in a row, there are some lathes (eg Asian/Chinese mini lathes) that require two compound gears. The program allows you to choose 0,1 or 2 compound gear pairs (Step 2). If you include a stud gear and lead-screw gear with two compound pairs there are 6 gears making up the gear train, and with a large collection of gears it can produce millions of possible combinations.

Most lathes have the stud gear shaft turning at the same speed as the spindle, but there are some exceptions. There is an optional fudge factor to take this or other quirks into account (see "Optional Entries" ).




If you are setting up the gear train to cut an imperial thread the only thing you need to know about the thread for RideTheGearTrain is the number of threads per inch (TPI). The diameter and depth of cut etc do not affect the gear train. The following is a YouTube video I made about single point screw cutting. In this case I am talking about cutting a metric thread on an imperial lathe, but I use the same method for metric and imperial threads. I make extensive use of the variable speed DC motor to slow down and stop at precisely the correct point, and the reverse the motor rather than disengaging the half-nuts from the leadscrew and fiddling around with a thread dial indicator. Since my lathe has a screw-on chuck I rarely use the reverse screw cutting technique, with the tool upside-down, as recommended by Joe Pie. (I have recently made a chuck clamp to allow reverse threading.) See also the section on engaging the half-nuts
and TDI (Thread Dial Indicator) below. Following that is a section about setting the depth of cut: 'Calculation of thread depth',



Lets review the data entry process focusing on making a thread. In step one of the menu you will have selected the type of lathe you are using. This can be either a metric or imperial lathe. In step 2 you will have entered the change gears that you have available and the type of gear train you intend to use. In step 3 you would select 'imperial thread' from the top of the list. In step 4 you decide on how much error you are willing to accept in the TPI. In step 5A you enter the TPI you require. You can skip steps 5B and 5C unless you want these special features. It might be worth taking a look at 5C using reference tables for standard imperial threads. Finally in step 6 you actually run the program using the data you have entered. The program evaluates all the possible gear ratios between the spindle shaft (chuck) and the lead-screw. For each one it calculates the TPI of the thread produced and compares it with your required TPI. If they are not exactly the same, but the error is within your acceptable range, it will be reported as a suitable gear setup and the percentage error will also be displayed.

In most cases there are a lot of possible solutions and you can choose whichever is most convenient or most accurate. If there are too few results you can go back to the menu to increase the acceptable error and run the program again, or add another gear to your set to see whether you need to buy or make one. If there are too many results you can decrease the acceptable error, or even reduce it to zero.



If you are planning to cut a metric thread the only thing you need to know about for RideTheGearTrain is the thread pitch in mm. Lets review the data entry process focusing on making a thread. In step 1 of the menu you will have selected the type of lathe you are using. This can be either a metric or imperial lathe. In step 2 you will have entered the change gears that you have available and the type of gear train you intend to use. In step 3 you would select 'metric thread' from the middle of the list. In step 4 you decide on how much error you are willing to accept in the pitch. In step 5A you enter the pitch you require. You can skip steps 5B and 5C unless you want these special features. It might be worth taking a look at 5C using reference tables for standard metric threads. Finally in step 6 you actually run the program using the data you have entered. The program evaluates all the possible gear ratios between the spindle shaft (chuck) and the lead-screw. For each one it calculates the pitch of the thread produced and compares it with your required pitch. If they are not exactly the same, but the error is within your acceptable range, it will be reported as a suitable gear setup and the percentage error will also be displayed.

In most cases there are a lot of possible solutions and you can choose whichever is most convenient or most accurate. If there are too few results you can go back to the menu to increase the acceptable error and run the program again, or add another gear to your set to see whether you need to buy or make one. If there are too many results you can decrease the acceptable error, or even reduce it to zero.



It is probably best to use the search function built into the browser. This will take you to an appropriate place on this page without losing the data you have entered. On Windows eg Chrome try Control F for the first occurrence of a word and Control G for subsequent occurrences. On Mac Safari or Chrome use Command F to open the search box at the top right, and Command G after that.



Definitions can vary so let\'s introduce the terminology I use. Lathes generally rely on using "change wheels" or "change gears" in the gear train to select the gear ratio required to make the lead-screw turn at the speed necessary to produce the desired thread pitch or power feed rate. Clock makers and other engineers often refer to gears as 'wheels'.

The "gear train" generally consists of the "stud gear" first (sometimes referred to as the "tumbler stud gear" or "mandrel" and in some cases it is machined into the spindle shaft). The "lead-screw gear" (LSG) is last in the train and is considered a "driven"gear. LSG is the gear wheel mounted on the lead-screw or gearbox input and Myford sometimes refer to this as the 'Input' gear or gear 'L' or even gear 'X' !.

On most lathes "tumbler gears" are used for reversing the direction of rotation and they act as idlers that do not affect the overall gear ratio of the gear train. They can be ignored and the stud gear comes after the tumblers. The number of teeth on the stud gear divided by the teeth on the lead-screw gear provide the main gear ratio of the train. In between these "end gears" there may be an "idler wheel" which just fills the space but does not alter the overall gear ratio. It does reverse the direction of rotation.

For a wider range of threads the idler gear may be replaced by one or two "compound gears". Each compound gear is a pair of gears connected together by a keyway or rivet etc.

The general convention for defining "driver" and "driven" gears is as follows: As power is transmitted from the motor to the lead-screw the first gear to receive the power, and pass it on, is called the "driver". It passed power on to the attached gear known as the "driven gear". When a compound gear is inserted in the gear train the gear that is driven by the stud gear is naturally called the "driven" gear. It is physically connected to another gear which will drive the next gear down the train, so it is known as another "driver". When calculating gear ratios the rule is always that the RATIO = DRIVER/DRIVEN.

When calculating the gear ratio of the gear train we calculate a ratio for each point where one gear meshes with the next. This is an important point. We write down the gear ratio at each point where gears mesh, and multiply them all together to get the overall gear ratio. Idler gears are ignored in this process, as explained above.

If we want to look at the contribution that a compound gear makes to the overall gear ratio of the gear train (GTR) we realize that the first gear in the compound pair (eg the one that receives power from the stud gear) is a DRIVEN gear as described above and the second gear of the pair is a DRIVER gear. The contribution of the compound gear to the overall gear train ratio is the number of teeth on the driver gear divided by the number on the driven gear. That means the contribution is the second compound gear divided by the first gear in the pair. This may seem counterintuitive. So although it is not really the conventional way of calculating gear trains I think of the basic ratio being STUD/LSG and when a compound gear is included I multiply that basic ratio by the contribution of the compound gear which is second compound gear (driver) divided by the first compound gear(driven).

There is some variation in preferred terminology between manufacturers e.g. MYFORD refer to several different numbered stud shafts where the compound gears and idlers can be mounted.

More complex gear trains are less common, but they may use "two compound gears" in series producing a huge range of ratios and this can result in too many results to display. For this reason RideTheGearTrain divides the gears into two sets: the "top set" contributes to the top line of the overall gear ratio and the "bottom set" contributes to the bottom line of the ratio. The gear train ratio is calculated by multiplying all the TOP numbers together to make the top line of the ratio. These are all the driver gears. Then we multiply all the bottom numbers together (the driven gears) to calculate the bottom line of the ratio. Then we divide the top line by the bottom line and we get the overall gear train ratio (GTR). Asian/Chinese mini-lathes may use two compound gears.

If we have a gear train with 6 gears in it, there will be 3 TOP gears and 3 bottom gears. These can be put together is 12 different ways but all 12 have the same GTR. If there are say 100 different ways of producing the desired thread there would be 1200 different ways of arranging the gears. Instead the program displays the 100 unique solutions and displays SOLVE beside each one. When the user clicks SOLVE the program displays the 12 solutions all having the same GTR. Beside each solution is the DRAW button. Clicking DRAW produces a scale drawing of the gear train.

On some lathes including Boxford the compound gears have a larger shaft diameter than the change gears and therefore they are treated as two separate sets of gears. Other brands are sensibly designed so that all the gears can be interchanged. This program has an " Automatic Compound Gears " feature to put together all possible combinations for this type of lathe, but it cannot be used for the older Boxford lathes unless an adapter is used. In a later section there is a photo of the adapter which can be made quite easily to allow any pair of gears to be used as a compound pair on the Boxford lathes.

All of the above refers to the "gear train" but most modern lathes also have a screw cutting "gearbox" to provide a wider range of gear ratios without physically handling the gear wheels. This software will work for virtually all lathes without a gearbox.

However, gearboxes come in a wide variety of designs and they have to be built into this program. The most common type is known as the "Norton gearbox" invented by W.P Norton about 1886. It was used in the early South Bend lathes in 1933 and large numbers of other lathe manufacturers made copies known as "South Bend clones". The design is used in Boxford lathes and about 22 other brands. These include: Ace, Asbrinks, Blomqvist, Boffelli & Finazzi, Boxford, David,Demco, Harrison, Harmal, Hercus, Fragram, Grizzly, Joinville, Lin Huan(Select), Moody, NSTC, Parkanson, Purcell, Sanches Blanes, Sheraton, Smart and Brown, Storebro, TOS, UFP. (This list and other information courtesy of Lathes.co.uk).

Other companies use a very similar design with slight variations and this includes the popular Myford lathe company who removed the 11.5 TPI position and replaced it with 9.5 TPI.

There are increasing numbers of Asian and Chinese lathes on the market. They often have a very limited lead-screw gearbox e.g. gear ratios 0.5, 1, 2. The "stud gear" may be part of the spindle and cannot be altered. The "OPTIONAL ENTRIES" section of "DATA ENTRY" allows the user to specify whether the stud gear and lead-screw gear can be changed.



In the Introduction I described how some lathes allow you to use any two of the change gears to make up a compound pair and the way the 'Automatic Compound Gears' mode looks at every possible combination. However, Boxford and some other clones of the South Bend lathe, require two different kinds of gears. The adapter shown below (designed by Bob Townsend) solves this problem allowing any two gears to be combined. The 'studs' that are placed on the banjo for mounting gears are really bolts with T-shaped heads. This device is similar, but the diameter of the bolt is smaller to allow a sleeve to slip over it and rotate freely. That sleeve has a key attached to it and this fits the standard change gears in such a way that they must turn together on the key, thus becoming a compound pair. This photo is provided courtesy of Bob Townsend who made it and provided the design to the Boxford Users Group online.

Photo Section of Boxford Users Group. You may need to register and log in.

A photo in a set of photos of the compound gear adapter for Boxford

A photo in a set of photos of the compound gear adapter for Boxford

A photo in a set of photos of the compound gear adapter for Boxford

A photo in a set of photos of the compound gear adapter for Boxford

A photo in a set of photos of the compound gear adapter for Boxford

A photo in a set of photos of the compound gear adapter for Boxford

A photo in a set of photos of the compound gear adapter for Boxford

A photo in a set of photos of the compound gear adapter for Boxford

A photo in a set of photos of the compound gear adapter for Boxford

Bob Townsend's adapter designed to use the keyed change-wheels to make up compound pairs.

A photo of the compound gear adapter for a Myford lathe

This compound gear adapter is the type used on Myford lathes. The photo was kindly provided by Geoff Rose from the Myford User's Group.



Although the data you enter is lost when you quit the web page, it is retained in the web address (URL). It is recommended that you make a 'favorite' or 'Bookmark' after running the program. This will permanently save all the data you entered. ('favorite' for American PC users, 'favourite' for British Commonwealth PC users or 'Bookmarks' for Mac users.)



If an error of zero is reported the gear set gives an exact result. An error of +0.5% produces one extra thread in 50 turns and may be OK for short threads eg a nut with 5 turns of thread. Enter the error you are willing to accept. If you have a limited selection of gears the program may produce too few results. For that reason the default acceptable error may be set quite high such as 2%. However plenty of results are generally produced with 0.5% or less, and choosing a smaller error produces fewer results. If you set the required error to zero you only get exact solutions. If you leave the error entry blank the program uses its default error. Results are rounded to 4 decimal places before being displayed. Calculations later in this section suggest that an error of 0.22% would be a conservative error that could be taken up by clearances in a high grade nut and values up to 0.88% may be work as well. If fact you can increase the clearance by turning the thread a little deeper than normal.

An error of 0.5% means that a thread with 200 turns would have an error of one turn ie 201 turns. But you don't usually use a nut with 200 turns on it. About 5-10 turns would be more typical. A thread of 20 turns would only be in error by one tenth of a turn and a nut with 10 turns of thread would be in error by one 20th of a turn. If the pitch is 2mm, one 20th of a turn is 0.10 mm which can probably be taken up by normal thread clearances.
Hi Evan, I just read yr contribution to Myford User group, followed it up and kept reading Riding the Gear Train. I found this: Choosing an acceptable error. Para. 3: If the error is 0.2147mm in 50 turns, it will only be 0.043 mm in 10 turns and that is about 17 thousandths of an inch. But 0.043mm /25.4 = 0.00169" - 1.7 thou, not 17 ! Sorry, makes me feel back in the classroom! Alan
For example, one of our users has a lathe 16 feet (4.8 meters) long and wanted to know how much error there would be in a 200mm long thread. The program reported an error of 0.2147% for his solution for a 2 mm pitch. Since this is a percentage it means it will have an error of 0.2147 mm in 100mm or 0.43mm in a 200mm long thread at 2mm pitch. In his case 0.43mm was considered too much error. He decided to use a 127/100 conversion gear which results in 0% error. It is a bit unusual to have a nut that long. Most ordinary nuts are only about 4 to 6 turns of the thread. If the error is 0.2147mm in 50 turns, it will only be 0.043 mm in 10 turns and that is about 1.7 thousandths of an inch. For a nut with 5 turns it is half as much. These numbers are similar to standard tolerances in thread specifications and are probably acceptable.

I have worked this argument backwards and calculate from the published tolerace what % error would be acceptable. The following calculations suggest that a safe acceptable error for a standard nut would be 0.22% and possibly up to 1.75% for a nut with high tolerance and 5 turns in length.

I looked up ISO metric specs for a 2 mm course male thread.   The tolerance in diameter may be -0.038 to -0.071 mm.   The nut may be over-sized by a similar amount so these could add up to 0.14mm between the internal and external threads. These tolerances depend on the grade of thread. The tolerance increases for larger threads but not in exact proportion to pitch.

https://www.accu.co.uk/en/p/134-iso-metric-thread-tolerances

I used triangle geometry to calculate that the tolerance in diameter would translate into a longitudinal movement equal to the tolerance divided by 0.866 (see the aside below).   I used a 2mm pitch as a random example. The worst case would be the smallest tolerance in the diameter which was 0.038 or 0.019 in radius. This would be expected to allow the nut to move along the axis of the thread by 0.019 / 0.866 = 0.022 mm.   This is an absolute tolerance in mm.

Most nuts are about 4 to 6 turns. If we assume the nut has 5 turns of the thread, and there is an error in the pitch, that exactly takes up the standard tolerance in the thread (0.044mm), what is the percentage error? With a 2 mm thread the thickness of the nut would be 10 mm.  

Error = 0.022 mm / 10 mm = 0.0022 or 0.22% error. 

Actual tolerance in the male thread may be nearly double this amount in lower grade threads and when you include tolerance in the female thread it could double again. So the tolerable % error could be 4 times higher, ie 0.88%. This means users can type into my program an acceptable error of 0.22 % and the thread should be able to accommodate a high grade nut (with about 5 turns of thread). This is a conservative estimate and it is probably safe to go up to 2 to 4 times this error especially with lower grade nuts.

A rough guide of 0.2 to 0.5 % seems reasonable.

ASIDE:

So how do these tolerances translate into longitudinal tolerance in the pitch? The thread is a triangle with 60 degree angles.   Actually the three sides will be equal in length (an isosceles triangle).   If the base of this triangle is y, the height is

y root(3)/2   or  

1.732 y / 2 = 0.866.

The thread has two such triangles, one on each side of the thread, so the height must be doubled and is 1.732 y.   Now the base of the triangle (y) is actually the pitch of the thread.  So the depth of the thread is 1.732 times the pitch.  In this example the pitch is 2mm and the minor diameter of the thread will be 3.464 mm less than the major diameter.   A tolerance of 't' in the diameter would allow a slightly bigger movement in pitch. So the tolerance must be divided by 0.866.   In real thread specifications the triangular thread profile is clipped off at the crest and root, but it wouldn't have much effect on these calculations.



Step 2 in the data entry is designing the gear train and entering your set of gears. The first thing we have to decide is how many compound gears can be included in the gear train. The simplest gear train may have no compound gears at all. For example in the Boxford style of lathe, the standard gear train has a stud gear and lead-screw gear, both of which may be changed. Between these is an idler gear which does not affect the gear ratio. One or even two compound gears can be inserted in place of the idler gear and since they do alter the gear ratio they dramatically increase the number of solutions to your problem.



As described above, this design usually includes an idler gear. If you are not cutting a metric thread on an imperial lathe or an imperial thread on a metric lathe, this may be all you need. Try this first and if you do not find the result you want, then add a compound gear.



If you don't get a satisfactory result without compound gears it is time to add one compound gear.

If you are converting between metric and imperial you will probably need a compound gear. Try any compound gear you have available and you may find that it solves your problem without buying special gears.

A special 'Transposing' compound gear can give very accurate conversion. In fact the standard 127/100 compound transposing gear gives zero error in the conversion. This is because 127 can be multiplied by 2 using other gears and 127/100 = 1.27. Multiplying by 2 gives 2.54 which is the conversion factor for converting cm to inches and vice versa. This is commonly used in imperial lathes to cut metric threads and could be flipped over to convert a metric lathe to cut imperial threads. However, there are many other alternative gear combinations used in all kinds of lathes. This is descussed in detail later.



With a conventional European, British or American lathe with stud and LSG that can be changed, it is unlikely that you will need to use two compound gears in series. However, this option is available if necessary to produce an unusual thread. Two compound gears may be necessary when you have no gearbox or a limited gearbox such as the three speed model. If you get no results with one compound gear you may need to advance to two. In this case there are two pairs making 4 compound gear wheels plus the stud gear and leadscrew gear with a total of 6 gears There are so many possible combinations that it can produce a very large number of results and many sets produce the same gear ratios. In this case the user may be given lists of gears to choose from. There is a list of gears for the top line of the equation for the gear train ratio and another list for the bottom line. But no need to panic! Each line of results includes a SOLVE button. This shows you all the different ways you can put these together. If there are 6 gear positions it may result in a list of 36 solutions, all with the same gear ratio and thread pitch. Beside each of these you will see a DRAW button which produces a scale diagram of the gear layout. Some solutions did not really need six gears and replaces some with the word ANY. In these cases the diagram is reduced to one or zero compound gears. With six gears the program became so complicated I used binary numbers to ensure I found all combinations. The diagram below shows what a gear train with two compound gears might look like. Four gear wheels are put together to make two compound pairs. The stud gear at the top (shown in blue) and leadscrew gear at the bottom are included in the gear train. There is also an idler wheel to correct the direction of rotation.

Asian/Chinese lathes (especially mini-lathes) may be designed in such a way that you cannot change the stud gear and on some lathes you cannot change the lead-screw gear (LSG). Furthermore, they may have a gearbox limited to 3 gear ratios instead of 30 to 40. This severely limits the number of results unless you use two compound gears. In this case the number of solutions can become so large that it is not practical to display them all. The method used to display the results for two compound gears is described in the section terminology.



In the terminology section I described the reason that older lathes like the Boxford had two sets of gears: viz. change gears and compound gears. However more modern lathes, including Asian/Chinese lathes allow you to use any of the change gears to make up compound gear pairs in any combination. The Auto_Compound mode was designed for these more modern lathes. In this mode the program automatically puts together every possible combination of gears, two at a time, to make a wide range of compound gears. In this case it does not use the list of compound gears at all. You can ignore any numbers that appear in the compound list if you select automatic.

Earlier I described an adapter that can be made for the older lathes to allow it to work the same way. If you make this adapter you can choose automatic mode in RideTheGearTrain.



If you have one of the older style lathes like the Boxford or other South Bend clones with two sets of gears, (a set of change gears for the stud and LSG positions, and a set of compound pairs to place between the stud and LSG gears) then you should use the "No Automatic Compound Gear" mode and enter two lists manually as described below.

It would be worth considering making the adapter shown here, especially if you don't have a gearbox. This adapter allows you to put together any two of your change gears to make up a compound gear.



In this box you can enter a list of your change gears. They are entered as a simple list of numbers (representing the number of teeth on each gear), separated by commas. You can edit the list and add your own gears easily while deleting the existing lists so that you only see results that are possible with the gears that you actually own. Sometimes it is interesting to enter only a few gears. Or if you are thinking of obtaining an extra gear to your set, you can add it to the list to see how much it helps. This is where 5B Range Entry may be useful. The range option produces results for a range of different thread sizes or feed rates etc.

The program originally provided a long lists of change-wheels, and compound gears, with each lathe by default, but this created thousands, sometimes millions, of possible combinations for the program to work through, producing thousands of results. The lists have been reduced to a more realistic number based on the gears that were sold with the lathes originally. However, it is quite likely that you have a different set of gears.



Like the list of Change Gears above these gears are entered as a list of numbers (representing the number of teeth on each gear), separated by commas. The only difference is that you are permitted to enter compound gears as pairs eg 127/100, or singly 127,100. The slash indicates that these two gears are connected permanently and cannot be taken apart. Gears separated by commas can be mixed and matched any way to make pairs.

In the introduction we talked about the reason for having two sets of gear wheels called "change gears" and "compound gears". You can enter a list of compound gears which are generally necessary when you want to cut a metric thread on an imperial lathe or vice versa. The above notes on entering change gears also applies here. The only difference is that compound gears can be entered as pairs or singly. The difference between compound gears and change gears is that the compound gears often have a larger hole bored in the center so that they can run freely on a sleeve or bearing. This means they are not generally interchangeable with the change gears above. The compound gears are usually connected together in pairs eg one pair on an imperial lathe is likely to be for metric conversion, consisting of a 127 tooth gear connected to a 100 tooth gear, so that they both rotate together with the larger gear driving the smaller one. These conversion gears are sometimes referred to as 'transposing' gears. This connected pair can be flipped over for special purposes so that the smaller gear drives the larger gear. The program tries both possibilities automatically. Now you may have other compound gears as well and it might even be possible to separate them and connect them together in unusual combinations. eg I have the 127/100 pair and another metric conversion pair 80/63. Now we could make odd-ball combinations like 127/63 and 127/80 producing even more interesting gear combinations, but in practice it may be difficult to get them apart, so they can be added as "fixed" pairs, like this 127/100 or as individual gears like this 127,100, 80, 63 which can be combined in any order. The following is an example with fixed and single compound pairs of gears:

45, 72, 127/100, 63, 80

This will allow combinations like 63/45 with the individual gears, but not 63/127 because the 127 wheel is permanently connected to the 100 tooth wheel.

The following is a photo of my collection of change-wheels or change-gears which can be used to cut various threads.

A photo of my collection of gear change wheels for the imperial Boxford A Lathe



This software can be easily used on any lathe without a gearbox. The only value that varies between lathes is the lead-screw pitch. It is assumed that the standard metric lead-screw has a pitch of 3mm and the standard imperial lathe has a lead-screw with 8 threads per inch, but this can be changed by entering the lead-screw pitch after selecting "Optional Entries" in the menu.




Unfortunately the name for the first important gear in the gear train has been given various names. I call it the stud gear. Myford lathes call it the 'mandrel gear' or 'Tumbler gear' or 'first stud gear'. In some cases it is called the spindle gear, which I will explain below.

All lathes with a gear train have gear teeth machined into the spindle shaft. That is the shaft that has the chuck on the other end. This is the spindle gear. The spindle gear drives two gears on a rocker arm called the 'Tumbler Gears' which can be set to forward or reverse rotation of the leadscrew. Reverse rotation is used for cutting left-hand threads and forward for right-hand threads. (This is not the same as reversing the motor.) The tumbler gears are actually idler gears that do not affect the overall gear ratio.

These tumbler gears mesh with a gear that can rotate freely on a short shaft called a stud. It is keyed to a second gear on the same stud shaft and that second gear (furthest from the head casting) is the famous 'stud gear'.

Thus the stud gear is normally a compound gear ie two gears keyed together. Usually the gear at the base of the stud shaft has the same number of teeth as the spindle gear. Since the tumblers are idler, the stud shaft turns at the same speed as the spindle and the stud shaft is used as a substitute or surrogate for the spindle. This means you can ignore all the gears above the stud shaft. The stud gear can then be considered the first gear in the train when calculating the gear ratio of the whole gear train.

In most lathes this stud gear can be changed by undoing a nut, pulling the gear off and replacing it with another gear having a different number of teeth. Often this is the only gear that needs to be changed to cut the desired thread. If the lathe has a gearbox, the thread chart on the gearbox may indicate the size of the stud gear e.g. it may have a 20 tooth stud gear for fine threads and a 40 tooth stud gear for course threads.

LATHES WITHOUT A STUD GEAR - e.g. CHINESE LATHES
And now for exceptions to this fairly standard setup. This mainly concerns Chinese and other Asian lathes, particularly the popular mini-lathes. Although early models had tumbler gears, and a conventional stud gear, more recent models do not. Instead they have a reversing gear in the gearbox or leadscrew drive.

These lathes use the spindle gear (with teeth machined into the spindle shaft) as the first gear in the gear train. This is like having a stud gear that cannot be changed. Because it cannot be changed it is not even mentioned of the diagrams of gear trains that are usually printed on the lathe. And yet, we have to know the number of teeth on this spindle/stud gear if we want to calculate the gear ratio of the whole gear train (GTR) to check the pitch of the thread being produced.

The gear train diagrams and peculiar labelling of the gears in the gear trains of these lathes are described in detail here: Chinese mini-lathes and how gears are labelled The gear labelling can be recognized by the use of the letter Z. The above link explains why I suggest that if you use RideTheGearTrain.com you scrap the Chinese labelling system and use mine.

The main difference is that I label the gears in the order that power is transmitted through the gear train, and that is the way gear ratios are calculated. The Chinese method (which may have originated in Germany or Austria) labels the gears according to the order they are placed on the stud shafts and this has nothing to do with the way power is transmitted.

If you have one of these lathes with a leadscrew gearbox you may need to interpret the Chinese labelling system to work out the gear ratios used in the gearbox.



The entries of compound gears depends on how you designed your gear train in Step 2 where you were asked whether you want zero, one, or two pairs of compound gears in your gear train.

Each pair alters the gear ratio, and having more pairs gives a much wider range of possible gear ratios and therefore a lot of possible threads. But it does make things more complicated and it is best to keep the number low. If you are cutting a standard imperial thread on an imperial lathe you can probably find all the solutions you need with zero compound gears.

With ZERO compound gears you generally have a large idler gear simply to fill the gap between the stud gear and leadcrew gear. Adding an idler gear does not affect the gear ratio, but does change the direction of rotation of the leadscrew. Of course the number of teeth on the stud or spindle gear and the leadscrew gear DO affect the gear ratio. In fact the gear ratio of the whole gear train
GTR = Stud / LSG where LSG is the leadscrew gear.

If you requested ONE COMPOUND PAIR, it will be made up of two gears joined together with a key or rivet, and these are labelled Comp_1 and Comp_2 in this program. The effect on the gear train ratio is Comp_2 / Comp_1.

Similarly if you requested TWO COMPOUND GEARS, you will have Comp_1 and Comp2 as the first pair and Comp_3 and Comp_4 as the second pair. The effect of the second pair on the gear ratio is Comp_4 / Comp_3. When these ratios are multiplied together you can see how you could end up with a lot of combinations, especially if you have a large number of gears to choose from.



You will only see this if you selected one or two compound gears in Step 2.

Compound gear one is of course the first compound gear and is usually labelled Comp_1. It is paired with Comp_2 affecting the GTR by a factor of Comp_2 / Comp_1.

Gear ratios are actually calculated at the points where gears mesh, so Comp_1 is driven by the stud gear with the stud as the 'driver' and Comp_1 as driven. Comp_1 is connected by a key to Comp_2. Then Comp_2 drives the leadscrew gear. So Comp_2 is a driver and LSG is a driven gear. Gear ratios are calculated as driver over driven. That is how we get Comp_2 (driver) / Comp_1 (driven).



Comp_2 is the second gear in the first compound pair described in the section on Compound_1. If you selected ONE compound pair Comp_2 drives the leadscrew gear. If you selected TWO compound pairs, Comp_2 drives Comp_3 of the second compound pair.



You will only see this if you selected two compound gears in Step 2.

Compound gear three, or Comp_3, is the first compound gear in the second pair. It is driven by compound gear 2 (Comp_2). Comp_3 is connected by a key to Comp_4. This pair of gears affects GTR by a factor of
Comp_4 / Comp_3 as explained above.



Compound Gear 4 is connected by a key to Comp_3. Comp_3 was driven by Comp_2. Comp_4 drives the leadscrew gear. That is why its effect on GTR is
Comp_4 / Comp_3.



LSG is the last gear in the gear train. It is physically connected by a key to the leadcrew, or if there is a leadscrew gearbox it connects to the input shaft of the gearbox.

It is always a driven gear. So if the number of compound gears in the gear train is zero, The stud gear (which is always a driver) effectively drives the leadscrew gear, so
GTR = stud/LSG.



After doing any kind of calculation, fitting gears or adjusting the gearbox, it is important to do a light scratch cut and check the pitch or TPI before making a deeper cut.

A helpful hint is to cover the surface where you plan to cut the thread using a marker pen or layout ink. Then when you make a scratch cut it really stands out with the high contrast. When you have finished cutting the thread there should be a narrow band of ink still visible at the crests of the threads because the thread profile normally has a small flat at the crest of the thread. An alternative is to manually turn the chuck say 5 or 10 turns and measure how far the carriage moves.



If you request a single thread pitch or TPI the results will be automatically sorted so that results with zero error are listed first and then results with increasing levels of error.

If you have requested a range of values they will remain in the order of thread sizes.

If you select a single thread with 0% error the results will be sorted with the lowest gear ratios first. It is thought that lower ratios results in a quieter gear train.



Sometimes a large collection of gears can result in thousands of suitable gear combinations. You probably don't want to look through a list of more than 2000. In "Optional Entries" in the menu, you can change the maximum number of results that can be displayed.

The number of results and computation time vary with the number of possible gear combinations. The number of combinations possible with a set of gears increases rapidly as more gears are added. If you are selecting only 2 gears from a set of n gears, the number of combinations is n.(n-1) = n squared minus n. It is possible that the operators who run our server will kill the program if it runs too long. So far this has not been a problem, even with 3.7 million combinations of gears.



Idler gears do not affect the gear ratio, but they are used to help solve problems with fitting the gears together on the gear train, as outlined in the next paragraph. They also swap the direction of rotation of the lead-screw and alter the positions of the reversing lever.

The question has arisen whether these idler gears should be included in your list of change gears or compound gears. The answer depends on the type of lathe. In most modern lathes all the gears can be used in any role, (stud, LSG, compound pairs or idlers). In that case all the gears should be listed in the change gear list and 'automatic compound gears' selected, while the manual list of compound gears is completely ignored.

However, older lathes including the Boxford and other South Bend clones, used two or more different types of gear. The change gears had a smaller hole bored and fitted with a keyway so that they could be used on the stud shaft or lead-screw shaft. Other gears had a larger bore and no keyway so they could spin freely and used as either idler gears or compound pairs joined together. Often the gear set would include an 80 tooth single gear with a large bore, to be used as an idler gear to help fit the other gears together on the banjo. This was not designed to be used as a change gear or as a compound gear. In that case it should not be included in either list! But once the gears have been chosen the user may add an idler to help fit the gears together. It can be ignored by the program because idler gears do not alter the gear ratio.



This is an FAQ. For the mathematically inclined the short answer is this: Lets look at a simple gear train with the spindle or stud gear driving an idler gear which then drives the leadscrew gear. How does the idler gear affect the overall gear ratio of the gear train.

Rl = Rs x Ns/Ni x Ni/Nl Note that Ni cancels out.
Rl = Rs x Ns/Nl
GTR= Rl / Rs
GTR= Ns / Nl but this equation does not include Ni for the idler.

Where:
Rl is RPM of the leadscrew gear (if there is a gearbox this is its input shaft)
Rs is RPM of the spindle or stud gear
Ns is the number of teeth on the spindle or stud gear
Nl is the number of teeth on the learscrew gear
Ni is the number of teeth on the idler gear, but this term cancels out
GTR is the gear ratio of the Gear Train.

EXPLANATION:
But for most of us an explanation may be helpful:
Imagine making a compound gear from two gear wheels having the same number of teeth, say 80. This would alter the gear ratio of the gear train by 80/80=1. That means it would have no effect on the gear train ratio. That is what an idler is like. We can analyze this more thoroughly.

Let's use the standard imperial gear train as an example: I use T as shorthand for teeth. N is the number of teeth and R is RPM.
Stud gear Ns = 20T (initial driver)
Idler gear Ni = 80T (ignored)
rh lead-screw gear Nl = 56T (driven)
This is where the idler is a bit peculiar. It is driven by the stud gear and must be considered a 'driven' gear. But the lead-screw must be a driven gear, and in relation to that the idler is acting as a driver. Remember the comparison with a pair of compound gears with both having the same number of teeth? The compound pair has a driver gear connected to a driven gear, but in our example they have the same number of teeth.

The stud gear turns at the same speed as the spindle and chuck. lets call that Rs for stud RPM or spindle RPM. How fast will the idler turn? Ri = Rs x Ns/Ni where Ns and Ni are the number of teeth on stud and idler gears. In our example Ri = 20/80. Does this make sense?

COUNTING TEETH PASSING FROM ONE GEAR TO THE NEXT
Each time the stud turns around 20 teeth are passed to the idler. But when the idler moves 20 teeth it is only 20/80 or one quarter of a turn ie Ns/Ni. Now as the idler turns a quarter turn it passes 20 teeth to the lead-screw gear (LSG) which has 56 teeth. How far will the LSG turn? It will not do a complete turn because it requires 56 teeth to make a full turn. It will only turn 20/56th of a turn. That is an interesting ratio because it is the same as 20T/56T ie Ns/Nl. This indicates that the overall gear ratio of the gear train is Ns/Nl and the number of teeth on the idler gear is not mentioned at all. Now lets write down the calculations for the whole gear train. What we want to know is" How fast does the lead-screw turn when compared with the stud gear?

Rl = Rs x Ns/Ni x Ni/Nl
But you can see that Ni cancels out leaving
Rl = Rs x Ns/Nl

and the overall gear ratio of the gear train is Ns/Nl. Again the size of the idler gear has disappeared and has no effect. That means the idler could have ANY number of teeth and it would not affect the gear train ratio.

Another way of thinking about the idler is to ask whether it is actually doing anything. Since it is not connected to a shaft that drives another gear, or anything else, it is not really doing anything useful! The stud gear and lead-screw gear ARE connected to shafts and transmit power. In the compound gear, one gear is connected to another and alters the number of teeth that are being passed from one gear to the next.

TUMBLER GEARS Most newer Chinese lathes do not have reversing tumbler gears and owners of these lathes can ignore the following comments.

The tumbler gears in the reversing tumblers are not connected to anything on their shafts either. They are also idler gears and have no effect on the gear ratio. In that case the gears that matter are the spindle gear (machined into the spindle shaft), and the gear at the base of the stud or 'inner stud gear'. This is connected via a keyed shaft to the 'outer stud gear' which is the one you can change. The number of teeth on the inner stud gear should be the same as the number of teeth on the spindle gear. Then, since the two tumbler gears are idlers, the gear ratio between spindle and stud shaft is 1:1. The stud turns at the same speed as the spindle. That is why we can ignore all the gears above the stud gear.

One thing the idler does do is reverse the direction of rotation of the lead-screw. This may cause the reversing lever positions to be flipped, so that forward becomes reverse and vice versa. If an extra compound gear has been added to the gear train it has the same effect, and an idler gear may be added just to make the reversing lever function normally.

The main reason for adding an idler gear is to make it easier to fit gears together. See the next section.



The program does some basic tests on each result to see whether gears are likely to interfere with each other. If it passes this crude test the program displays ** to indicate a preferred result.

The diameter of a gear is proportional to the number of teeth, so regardless of the distance between teeth (see diametric pitch or modulus) the number of teeth can be used as a substitute for diameter or radius. For example, if the stud gear has 20 teeth, we can assign the radius a value of 20. If it connects to a compound gear with 40 teeth on the first compound gear (comp1) and 60 on the second gear (comp2), the program calculates the difference between the two compound gears 60-40=20 and finds that it is equal to the radius of the stud gear which is 20. It is therefore likely that the larger gear will hit the shaft or nut that the stud gear is mounted on. In that case the result would not be given the preferred rating with **. This kind of problem can be resolved by placing an idler gear between the stud and compound gears. This reverses the direction of rotation of the lead-screw so that the lever positions for forward and reverse will be swapped (switched).



When the program runs it displays DRAW beside each result. If you click DRAW the program displays scale drawings of the gear train. Below that there is a box reporting whether these gears are likely to fit together. The program also provides extra drawings showing how idler gears can be inserted into the gear train if there is any difficulty getting the gears to fit.

Whether or not problems occur depends on how the gears are arranged. In the drawings produced by the program the gears are arranged in 3 planes so that each gear remains visible (not hidden behind a bigger gear), but some lathes only allow you to use two planes. In that case compound gears can be flipped over as long as they still connect together in the correct order. This can eliminate or cause interference between gears. (When you flip over a compound gear it will affect the gear train ratio unless you have the gears meshing in the same order as the original design.)

There is no guarantee that any of these gear combinations will actually fit on their mounting bracket known as a quadrant or banjo shown below. This bracket usually has a screw clamp where it is mounted, and this can be loosened to alter its position, so that the gears mesh well.

The gears mount on the banjo or quadrant.



If you do not include the two standard gears in your change wheel set, you may be surprised that there are certain threads you cannot cut. The thread that causes the most problems is one equal to the lead-screw thread. Without a gearbox you need a 1:1 gear ratio for the gear train, and this often requires you to have two identical gears in your list. With a gearbox it is less obvious because the gearbox does not have a 1:1 gear ratio on any of its settings. Myford lathes (1956 and later) are an exception to this rule. Their standard gear train has a gear train ratio of 1.0 For a Boxford lathe standard gears are: Stud=20 and lead-screw=45 for metric lathes and Stud=20 with lead-screw=56 for imperial lathes.

Other errors should be self explanatory. If you see any that need better explanation, or appear to be programming issues please don't hesitate to send me an email and I will try to fix the problem ASAP. The program was released in June 2020 and the initial bugs have been gradually ironed out.



If you run RideTheGearTRain requesting a range of threads, as described in the previous paragraph, and find that there are holes in the range of threads you can cut, you might want to obtain an extra gear or two. Of course you can add a proposed new gear to the list of your gears in this program to see how it improves the range of threads you can produce. If you decide to order a new gear check it out with the Boxford Users Group listed at the top of this page or other groups. There you can learn about the specifications of the gears. For example all the gears in a set have to have the same spacing between the teeth, and this is described by the "diametric pitch" and for Boxford lathes DP=18. The Mark 1 models had a pressure angle of 14.5 degrees but it is possible that later versions used 20 degrees. See the next section.
All about Diametral Pitch (DP) and Modulus

People have been making gears successfully in plastic with 3D printers and CAD software to draw the involute curves. There may also be some second-hand gears available. You may even find that you can buy new ones. In New Zealand try www.chevpac.co.nz and in UK check out lathes.co.uk.

Since this was written I have developed the 'New Gear' button which can be used to recommend a new gear to add to your set in order to add a specific thread:
6. Recommend new gears.



All the gears in the Boxford gear train have a diametral pitch of 18 with a pressure angle of 14.5 degrees so that they can all mesh together regardless of how many teeth there are. The pressure angle used on more modern gears is often 20 degrees due to increased strength of materials and quieter operation. Just as a matter of interest, the pressure angle is analogous to the sliding angle of a wedge. It allows one tooth to slide against the next while still transmitting power efficiently without putting excessive load on the teeth or bearings of the gears. Why are the teeth shaped using an involute curve? This curve on the teeth ensures that the pressure angle should not change excessively as the teeth slide over each other and remains relatively constant if the gears are not meshing perfectly. In an involute curve (Archimedes spiral) the radius of the spiral increases in proportion to the angle of rotation. In fact the point of contact of the gear teeth is moving to a greater radius in proportion to the angle of rotation, so the effective pitch diameter is increasing as the teeth move past their point of maximum contact.

The diameter of each gear has to be adjusted to give the required diametral pitch. It is based on the pitch diameter which is the contact point roughly half way between the root diameter and the outside diameter. This is the diameter at which the teeth make contact. If fitted correctly the pitch diameter of one gear should just contact the pitch diameter of the next gear. The DP is the total number of teeth divided by the pitch diameter giving units of teeth per inch but since it is based on diameter rather than circumference it does not give the actual spacing between teeth. In most cases this is all you need to know. For specifications on a wide range of lathes, an excellent pdf has been produced by John Bates in Australia: Lathe Change Gears

The actual pitch diameter varies depending on the design of the gear teeth. When meshing correctly the pitch diameter circles just touch each other. Since radius is diameter divided by 2, the distance between the centers of the gears is half the pitch diameter of one gear, plus half the pitch diameter of the gear it is meshing with. The Diametral Pitch can be estimated from the outside diameter of the gear (Do) by adding 2 to the number of teeth (T). So pitch diameter is DP=(T+2)/Do .

eg the 60 tooth Boxford change gear is about 3.2 inches diameter at the root of the gear teeth and 3.4 inches outside diameter. We know DP should be exactly 18 so the pitch diameter is 60/18=3.333 inches. That will give DP=18.0. This is similar to threads per inch (rather than pitch), but the circumference of the gear at this mid-point is Pi.D so diametral pitch, DP of 18 is equivalent to 18/Pi = 5.73 teeth per inch. Inverting this number gives 0.175 inches pitch or 4.433 mm pitch. The program can be used to design a worm gear with DP=18 by requesting an imperial thread with 5.73 TPI. The program will accept non-integer values and this calculation is now built into the program. Let's check the above equation by subtracting 2. The pitch diameter estimated from the outside diameter of 3.4 inches is (60+2)/3.4=18.235 which is not very accurate.

You may come across the 'modulus' of a gear which can be used in a similar way to DP. The modulus is the pitch diameter divided by the number of teeth, so the 60 tooth gear would have a modulus of 3.333 inches/60 = 0.5555 = 1/18. ie modulus is the inverse of DP:
MOD=1/DP
However this can be misleading because daimetric pitch is usually used in imperial units and modulus is used in the metric system.

Equations:
DP = T / PD
PD = T / DP
DP =(T+2) / Do (approximately)
T = DP x PD
P = DP / Pi
MOD= 1 / DP

DP is the diametral pitch
PD=pitch diameter
Do=outside diameter of the gear wheel T = number of teeth on the gear wheel
P = Actual pitch in inches
Pi is 3.1415926



A worm gear is essentially a thread which turns a gear wheel. If the gear wheel has a standard diametral pitch you will need to make a thread to match. The section above explains the diametral pitch. eg the gear wheels in the Boxford gear train have a diametral pitch of 18. The diametral pitch (DP) is the number of teeth (T) on a gear divided by the pitch diameter (PD). If you choose diametric pitch or modulus from the "thread type" options in the program, it will tell you what gears to use to produce the required screw pitch.
Incidentally I have a YouTube video showing a very simple method for making both parts of a worm gear using a thread cutting tap (which is a substitute for a tool known as a hob). See the links in the intro/header above.



When this option is selected in step 3 of the data entry menu, the program will calculate the gear train and/or gearbox setting required to provide the feed rate you requested in imperial units: inches per turn of the chuck. Each time the chuck or spindle turns the carriage will advance by the requested amount in inches.

If you are using a lathe without a lead-screw gearbox, specific information about your lathe is not recorded by RideTheGearTrain. In this case you will need to go to "Optional Entries" in the menu to enter the appropriate power feed gear ratios for the carriage and cross-slide in your lathe. Once you save your data it should not be necessary to enter it again. See 'Saving your data'.

Further details about feed rates and feed gear ratios are provided below under the heading 'Display Feed Rates'.

Instructions for changing the gear ratios for power feed are provided in "Optional Entries".




When this option is selected in step 3 of the data entry menu, the program will calculate the gear train and/or gearbox setting required to provide the feed rate you requested in imperial units: inches per turn of the chuck. Each time the chuck or spindle turns the cross-slide will advance by the requested amount in inches.

If you are using a lathe without a lead-screw gearbox, specific information about your lathe is not recorded by RideTheGearTrain. In this case you will need to go to "Optional Entries" in the menu to enter the appropriate power feed gear ratios for the carriage and cross-slide in your lathe. Once you save your data it should not be necessary to enter it again. See 'Saving your data'.

Further details about feed rates and feed gear ratios are provided below under the heading 'Display Feed Rates'.

Instructions for changing the gear ratios for power feed are provided in "Optional Entries".



When this option is selected in step 3 of the data entry menu, the program will calculate the gear train and/or gearbox setting required to provide the feed rate you requested in metric units: mm per turn of the chuck. Each time the chuck or spindle turns the carriage will advance by the requested amount in mm.

If you are using a lathe without a lead-screw gearbox, specific information about your lathe is not recorded by RideTheGearTrain. In this case you will need to go to "Optional Entries" in the menu to enter the appropriate power feed gear ratios for the carriage and cross-slide in your lathe. Once you save your data it should not be necessary to enter it again. See 'Saving your data'.

Further details about feed rates and feed gear ratios are provided below under the heading 'Display Feed Rates'.

Instructions for changing the gear ratios for power feed are provided in "Optional Entries".



When this option is selected in step 3 of the data entry menu, the program will calculate the gear train and/or gearbox setting required to provide the feed rate you requested in metric units: mm per turn of the chuck. Each time the chuck or spindle turns the cross-slide will advance by the requested amount in mm.

If you are using a lathe without a lead-screw gearbox, specific information about your lathe is not recorded by RideTheGearTrain. In this case you will need to go to "Optional Entries" in the menu to enter the appropriate power feed gear ratios for the carriage and cross-slide in your lathe. Once you save your data it should not be necessary to enter it again. See 'Saving your data'.

Further details about feed rates and feed gear ratios are provided below under the heading 'Display Feed Rates'.

Instructions for changing the gear ratios for power feed are provided in "Optional Entries".



In Step 3 of the main menu you can request feed rates instead of a thread pitch or TPI. Some lathes only have power feed to drive the carriage along the length of the lathe bed and this may be called longitudinal feed. Most lathes will also have power feed on the cross slide, causing the tool to move at right angles to the bed or lateral feed, which can be used for facing procedures.

If your lathe has 'power feed' provided in the apron you can request a power feed rate for the 'lateral' movement provided by the cross-slide, or 'longitudinal' movement provided by the carriage. This feature can be selected during data entry by choosing the appropriate buttons instead of choosing a thread type.

Feed rates can be selected in imperial units of inches per turn of the chuck, or spindle, or in metric units of mm per turn of the chuck (It doesn't matter whether it is a metric or imperial lathe). The program will then calculate the gear train setup and gearbox settings required.



In most cases you want to produce a smooth surface finish and the power feed should be slower than the feed you use for cutting threads. For that reason most lathes include gears that slow down the power drive to about one third of the leadscrew speed, and the cross slide is about one tenth of the leadscrew speed. These gear ratios cannot be changed on most lathes and this program requires the gear ratios if you want to calculate feed rates as described under the heading Feed Rates.

If you are using a lathe without a lead-screw gearbox, specific information about your lathe is not recorded by RideTheGearTrain. In this case you will need to go to "Optional Entries" in the menu to enter the appropriate power feed gear ratios for the carriage and cross-slide in your lathe. Once you save your data it should not be necessary to enter it again. See 'Saving your data'.

Of course the actual speed of movement varies depending on how fast the spindle/chuck is turning (RPM). The feed rate determines the width of the cut and the rate that metal is removed depends on the feed rate, RPM, and depth of cut.

Most lathes provide power feed through a system that is separate to the lead-screw thread. This saves the thread from excessive wear. The Boxford uses a keyway cut into the lead-screw to provide power feed through the apron and carriage. Other lathes have a shaft that is completely separate from the lead-screw. In most cases there are gears in the apron that provide feed rates that are slower than thread cutting speeds.

The feed rates are a simple fraction of the pitch expressed as a gear ratio. The gear ratio built into the program for South Bend 9" imperial clones including Boxford lathes provides a cross feed rate at 0.1 times the pitch and carriage feed rates are 0.34 of the pitch. eg if the lathe is set up for 8 TPI, that is 1/8 inch per turn, the cross feed rate will be 1/10 or 1/80th inch per turn to give a better finish. These power feed gear ratios can be changed in the "Optional Entries" in the menu. The standard values are different in Boxford imperial and metric lathes.

Boxford Model A had the thread cutting gearbox and power feed on the cross-slide and carriage. The Model B had no gearbox but retained power feed. Model C had neither. If anyone has a Boxford 'A' like mine that came from a New Zealand high school after being partially converted to metric, the plate on the gearbox does not show thread pitch, but rather feed rates. This can be confusing to the beginner attempting single-point thread cutting, but the original gearbox label and a metric version were attached to the gear train cover.



This is probably the most common use of compound gears. They are used to cut metric threads on an imperial (English) lathe which has a lead-screw measured in threads per inch. In the photos (further down this page) there is a 127 tooth gear driving a 100 tooth gear (as a compound pair). Two times 127/100 is 2.54 which gives an exact conversion of inches to cm metric measurements. The conversion is explained more fully later in this section. This gear combination gives an exact conversion with 0% error. (One inch is 2.54 cm or 25.4 mm and this is an exact conversion as defined by the International Bureau of Weights and Measures.)

Since 127 is a prime number it cannot be divided by anything to create smaller gear combinations with 100% accuracy. There are several other compound gears that can be used instead, but they introduce a slight error. An 80 tooth gear driving a 63 tooth gear is quite common. 80/63=1.2698 which is almost the same as 127/100=1.27 with an error of only 0.01575%. And a 47 tooth gear driving a 37 tooth gear gives 1.270270 with an error of 0.021%.

It may be convenient to think of the imperial lathe with a lead-screw having 8 TPI plus a metric conversion gear as being the same as a metric lathe with a lead-screw pitch of 2.5mm.

There is a huge number of gear combinations that can be used for imperial to metric conversion and it is probably simplest to let RideTheGearTrain find a combination for you. In fact you may not need a special 'transposing' conversion gear at all.

It is reasonably straightforward to find compound gear combinations that will provide a gear ratio approximating 1.27 like the 127/100 gear. I have written a separate little program to do this, and it is included in RideTheGearTrain: 'List all compound gears for converting between metric and imperial'

ALTERNATIVE WAYS OF USING RIDE THE GEAR TRAIN FOR IMPERIAL TO METRIC CONVERSION: If you have an imperial lathe without a gearbox, you can tell the software that you have a metric lathe and change the lead-screw pitch under 'optional data entry' to 2.5mm as described above. The program will not know that you are using this conversion compound gear, and it will not show in the scale drawings of the gear train.

HOWEVER, if you have any trouble getting the metric thread you want, or if you do not have a conversion gear, (especially if your lathe has a gearbox) it IS worthwhile telling the software that you are using an imperial lathe and let it find out what gear selections will give you a pretty good approximation to the metric thread you want, without even using a conversion gear. The results are often surprising.

If you tell the software that you are using a metric lathe with a lead-screw pitch of 2.5mm and you need to cut a thread with a pitch of 2.5 mm you need the stud gear to have the same number of teeth as the lead-screw gear ie 1:1 gear ratio of the gear train ignoring the conversion gear. If you then get the program to select a compound gear you would actually end up with two compound gears in your train - the gears suggested by the software in addition to the metric conversion gear which you hid from the software. You can switch around the stud and lead-screw gears to get various threads in just the same way as you would for a metric lathe with this unusual lead-screw. (Smaller metric lathes like the metric versions of the South Bend 9" have 3 mm lead-screws.)

If you do not have a gearbox it does give the computer program more power if you tell it that you have a metric lathe and change the lead-screw pitch to 2.5 mm and use one compound gear. This way the metric conversion compound gear remains fixed. When the program adds another compound gear it thinks there is only one that it can vary (when there are really two) to produce all kinds of weird and wonderful threads - assuming you have more compound wheels and change gears to choose from. It might actually pay to run the software both ways. First as an imperial lathe (with the conversion gear included in your list of compound gears) and again as a metric lathe with a lead-screw pitch of 2.5. But on this occasion you would not include the metric conversion gear in your list of compound gears, because you are already using it.


Half-nuts must be kept engaged and the thread dial indicator cannot be used for cutting metric threads on an imperial lathe or imperial threads on a metric lathe, except...

Generally it is agreed that you cannot use the conventional method to disengage the half-nuts when cutting a metric thread on an imperial (inch) lathe or an imperial thread on a metric lathe. The thread dial indicator cannot be used. However there are several solutions to this problem:

If you have a reversing motor, run the motor in reverse to return the tool to the starting point and keep the half-nuts engaged at all times. However, there will be some backlash or slack in the leadscrew drive mechanism, so when winding back the tool will follow a different path. So you have to make sure the tool is completely out of the groove when rewinding. Furthermore, you have to make sure the backlash is taken up before the tool engages back in the groove for the next cut. Starting the forward motion well before the tool engages in the groove gives it time to take up the slack. You can also give it a helping hand by applying a little friction on the big wheel used for moving the carriage along the bed.

Many lathes are fitted with a Thread Dial Indicator or TDI to allow you to re-engage the half-nut in the correct position on the lead-screw. However use of the dial indicator does not work when you are mixing imperial and metric systems.

You cannot use the reverse lever in the gear system because this alters the relationship between the lead-screw position and the spindle/chuck position. This lever is used for making left-hand threads.

Use of a variable speed motor (described in the next section) is very helpful in allowing you to slow down and stop cutting precisely before the tool hits a shoulder at the end of the thread.

Another variation was provided by Chris Armstrong of the Boxford User's Group, who credited Max Grant, so it is going around the community.

When cutting a metric thread on a lathe with an imperial lead-screw, you can actually disengage the half-nuts at the end of the thread. The sequence is:
1. Take note of the number on the threading dial when you engage the half-nuts.
2. Take a threading pass and dis-engage the half-nuts at the end of the pass. (The dial starts turning)
3. Stop the lathe before the threading dial has done a full turn, withdraw the tool and re-start the lathe in reverse. Don't manually move the saddle !
4. Re-engage the half-nuts when the threading dial first returns to the original number (in step 1).

Having said this I would recommend an excellent YouTube video which explains a slight variation allowing you to disengage the half-nuts briefly to allow a sudden stop at the end of the thread.
1. When the half-nuts are disengaged the dial starts turning. You watch how far it moves as you stop the motor.
2. Then wind the motor back just enough to reach the exact point where you disengaged.
3. THEN you can wind the motor in reverse to the beginning of the thread with the half-nuts engaged.
Using this method you can re-engage in the same spot at the end of the thread. It is just as though you never disengaged the half-nuts. This method is demonstrated in the following embedded YouTube video: (If I was Sir Fred Dinbar I would say it was de-MONSTER-ated.)



You still need to reverse the motor using the lead-screw to move the carriage back.

Another method described by Joe Pieczynski can be found amongst his many excellent videos using the link below. The method is to turn the tool upside-down and run the lathe motor in reverse while cutting the thread. That way you never have to worry about hitting the shoulder at the end of the thread. However, if your chuck screws on you should make a chuck clamp to prevent it from unscrewing. (It happens quickly, don't ask how I know!) This applies to the early Boxford lathes and other South Bend clones.

The following embedded YouTube video shows Joe Pieczynski's demonstration of reverse threading. It is a favourite!





Something to be aware of is that there are two ways that the cross-slide dial can be manufactured. The old British lathe I am using has the dial calibrated in thousands of an inch which is the actual distance the tool advances. The diameter of the work decreases by double that amount. This is a radius dial. However, the American lathes that you often see on YouTube have the cross-slide dial calibrated to indicate the change in diameter of the part, so it indicates half the true movement of the tool. Either way I think you have to multiply or divide by two to keep track of what you are doing. In the next section I mention that the zero position of the protractor angles on the compound slide can also vary from one manufacturer to another.



There are additional benefits to using option 5C to look up a thread using reference tables in RideTheGearTrain. These tables include additional thread specifications which can be used to calculate drill sizes and depth of cut.

One specification that is useful is the 'included angle' of the thread profile. The old British Standard Whitworth (BSW) thread angle was 55 degrees, but this has largely been superseded by metric and UNC threads. Most modern thread standards have a thread angle of 60 degrees. If you set the compound slide at half that angle, eg 30 degrees, the tool will only cut on one side of the thread groove and this produces a cleaner cut with less chatter.

One reason is that the actively cutting edge is reduced to half of the edge when cutting on both sides during a plunging cut with the cross-slide. Chatter tends to be worse with wider cuts.

The second reason is that chips are forming only on one side and can escape the thread groove more easily. Otherwise chips from one face will collide with chips coming from the other side and may even pile up and damage the thread surface. Both of these factors may be more critical when cutting hard materials or deep threads.

Most people actually set the angle at 29 or 29.5 degrees to give a slight polishing effect on the other face of the groove. It also ensures that the angle doesn't go over 30 degrees if there is an error in measuring the angle and this is the third reason for using this angle.

Note that the protractor engraved on the compound slide can be manufactured with its zero point in different places, so that it can differ by 90 or 180 degrees. Chinese lathes in particular may have the protractor shifted by 90 degrees, so instead of choosing 30 degrees you need 60 degrees. When this is correct the travel of the compound slide should coincide with the edge of the thread cutting tool.

Since the tool is being advanced at an angle the compound-slide dial does not indicate the depth of the thread along a true radius line. You could use trigonometry with a cosine function to calculate how far to advance the tool with the compound slide. RideTheGearTrain does this for you so you can simply read off the distance to advance the tool with the compound slide.

Having said that, Joe Pieczynski made a video in 2016 showing how you can set the depth of cut using the cross-slide without using any calculations. All you need to know is the depth of the thread which is measured along a true radius.

He sets the compound slide to zero, then registers the tool on the surface of the part using the cross-slide. Then moves the carriage away from the surface so that he can advance the tool to the required depth using the cross-slide (not the compound slide). Now the compound slide, which is still set on zero, has the tip of the tool at full depth. Lock the cross-slide in place and don't move it again. Now you can wind the compound slide back and forth and cut the thread until the dial on the compound slide reads zero again. Then you know the tip of the tool is at full depth.

To give the thread a final polish Joe does a couple of 'spring passes' without changing the depth. These are called spring passes because when making a deep cut the tool and its mounting tend to spring away from the surface. If you repeat the cut without changing the tool depth it will still make an additional shallow cut as the tool springs back. This may actually take several spring cuts, especially if you are using a long, thin boring bar.

Then he unlocks the cross-slide, advances the tool a few thousandths of an inch using the cross-slide this time, so that the tool cuts the groove on both sides for a finishing pass. To finish the surface of the thread and remove burrs he uses a file and then a ScotchBrite (or 3M pot scrubber) pad.

Quinn Dunkie of BloniHacks demonstrated a simpler method in her thread cutting video shown in the section about the 'Precision Mathews lathe'. She simply sets a dial gauge (commonly called a clock in USA) on the carriage to measure movement of the tool post. Then she can simply advance the angled compound slide until the dial indicates the required depth of cut. This is great if you don't bump the dial gauge!

Another common method is to register the tip of the tool on the surface and set the cross-slide dial to zero and set the compound slide to zero. After each cut withdraw the tool with the the cross-slide. Before starting the next cut advance the tool back to its zero setting on the cross-slide. Then advance the compound slide to the desired depth of cut. The disadvantage of this method is that you need your cosine function, tables or calculator to find out how far to advance the compound slide. Since 1/cos(30)=1.154700 you could look up the depth of cut and multiply it by this constant (assuming 30 degree angle). But whatever method you use you need to look up reference tables to find the depth of cut. So why not look it up with RideTheGearTrain and it will tell you how far to advance the cross-slide.

Coating the part with a Sharpie felt-tip marker, or marking out dye, is very useful for revealing how much flat remains on the crest of the thread, and this gives a rough guide to determine whether you have reached full depth. If there is no ink left you have gone too deep and the crest will be sharp instead of flat.

In this video Joe also discusses cutting a flat on the tip of the tool to match the thread standard which is also displayed by RideTheGearTrain. For most threads this is 1/8th of the pitch, but if it cannot be ground on the tip of the tool accurately it is better to have it a bit too sharp (with a smaller flat) than having the flat too big.



https://www.youtube.com/watch?v=nLHXSXzQP3U


There is an interesting thread on thread cutting on the Myford Users Group. Rather than pirate their content I will give you the link to this discussion about why we use the 29.5 degree compound slide angle for cutting threads. It is quite a long series of messages started by someone who set the 29.5 degrees relative to the lathe bed instead of 29.5 degrees relative to a line perpendicular to the axis of the lathe. This led to another user providing the following link to Joe Pieczynski who says he "debunked the idea that using 29 or 30 degrees means the tool is ONLY cutting on one side". Yes he proved that but unfortunately it is only half the answer.

This is my view: If we used a 30 degree angle the left edge of the tool would be doing almost all of the cutting, but the right edge slides down the right face of the groove polishing off the right face and preventing the stair-step effect that Joe demonstrated so well. At 29.5 degrees the "polishing effect" on the right side is improved.

There is nothing magical about 29.5 degrees which has become so engrained. When I was in school we were told just subtract a couple of degrees off 30. That is probably still good advice. To the purist this could lead to the wrong depth of cut if measured on the cross slide alone, unless it was recalculated from the angle actually used. But this error is minuscule and can be avoided by measuring with the cross-slide. There is a technique for using the cross slide movement to set a zero point on the compound slide. Cut until you reach zero. Another way is to use a dial gauge to measure depth.

It is often said that it really isn't necessary to set the angle on the cross-slide for small screw threads. But I don't think there is really any disadvantage either.

MYFORD GROUP DISCUSSION

JOE PIE's VIDEO




My Boxford motor was not wired to run in reverse, so I made a YouTube video about how to rewire the single phase AC 'condenser motor' or 'capacitor motor' to run in reverse. This just involved changing some connections in the junction box on the side of the motor.



Later I converted my lathe to a DC motor which operates with variable speed in forward and reverse. This gives very convenient control for cutting a thread up to a shoulder. I used a second hand treadmill motor 2.5 horsepower (1.86 kW) 4000 RPM DC motor with a low cost Chinese pulse width modulator (PWM) speed controller. This allows you to smoothly vary the voltage from 0 to 180 volts DC. This works by turning the power on and off at a high frequency and varying the percentage of time it receives full power.

A popular alternative is to use a 3 phase motor with VFD (Variable Frequency Drive) electronics which can also be obtained from China quite cheaply. This takes the single phase power supply, converts it into direct current and then back into 3 phase AC with variable frequency. The AC motors tend to lock into a speed matching the frequency provided. This provides excellent smooth speed control.

Both of these options usually come with programmable features such as ramp up time when you first switch it on, ramp down when switching off, current limit, short circuit and overheating protection. The early Boxford lathes and other brands have chucks that are screwed onto the spindle. Care must be taken to ensure the chuck does not come unscrewed when run in reverse. Consider making a chuck clamp.







How did I discover the pitch of 2.5 mm? If the imperial lathe has a lead-screw with 8 threads per inch (like all the South Bend clones, and many others) that is a pitch of 1/8 inch. Multiply by 2.54 which is the number of cm in an inch we get a pitch of 2.54/8 cm. Now look at the metric conversion gear with a 127 tooth gear driving a 100 tooth driven gear. It is going to slow down the lead-screw, so we multiply by 100/127 or 1/1.27. Put these together and we have 2.54/8 x 1/1.27. We know that 1.27 is exactly half of 2.54 so this simplifies to 2/8 = 1/4. So the pitch of 1/8 inch translates to 1/4 cm = 2.5 mm. I did the calculation this way to emphasise that 1/8 inch neatly translates to 1/4 cm. A slightly simpler way is to say 1/8 inch pitch is 0.125 inches x 25.4 mm/inch = 3.175mm actual pitch. Multiply 3.175mm by the conversion gear ratio of 100/127 = 2.5mm. So we now have a metric lathe with a lead-screw having an effective pitch of 2.5 mm.

There is one more fly in the ointment that may go unnoticed. We cannot tell the software that we have a metric lathe if it has a gearbox because the imperial gearbox is different to the metric gearbox. However, it is interesting to look at the equivalent lead-screw pitch. When they move from a lathe without a gearbox to the Boxford Model A with a gearbox they change the standard stud wheel from 20 teeth on imperial lathes to 40 teeth with metric conversion. This produces twice as many teeth whizzing past with every turn and speeds up the lead-screw, causing the carriage to move twice as fast, so it appears to have double the pitch and our effective pitch changes from 2.5 mm to 5 mm.

We do not intend to continue with using only the standard 20 and 40 tooth stud gears. Instead the program will vary both stud gear and lead-screw gears. (If you are not using automatic compound gears, don't forget to tell the program what selection of compound gears you have, and the change gears too.)



There is an option in RideTheGearTrain to produce a long list of conversion gears that could be used to convert between metric and imperial units. It is actually separate from the main 'Ride The Gear Train' program and does not use the data you have entered elsewhere. The program displays some of these notes about imperial/metric conversion:

This program creates a list of various compound gears. These are pairs of gears connected together by a key or rivet. For conversion from imperial to metric the larger of the pair of gears is driven by the stud gear and the smaller gear drives the lead-screw gear. These special compound gears are sometimes referred to as Transposing gears. For conversion we may want a gear ratio of 2.54 or 1.27 and that is how this program is intended to be used. Enter either of these ratios and it will display all possible pairs of gears that give a good approximation to the ratio you requested.

But various multiples of these ratios can also be used when other gears are added to compensate for this multiple. The program requests the gear ratio, and it can be used to find compound gears to produce any gear ratio you may need. This may include other special applications, such as compound gears that approximate pi.

Conversion gears such as 127/100 can be used to convert from imperial to metric, if the gear is flipped over it can be used to convert metric to imperial. In this case the stud gear drives the smaller gear, that is connected to the larger gear, which drives the lead-screw gear. This is possible because the gear ratio required for the first conversion is the inverse (1/x) of the second conversion and vice versa.

One inch = 2.54 cm is an exact conversion defined by the International Bureau of Weights and Measures. But instead of using 2.54 as the conversion factor, it is more common to divide it by two and use 1.27. This is 'corrected' by introducing a factor of two in the gearbox settings, or altering the stud and lead-screw gears by a factor of two. So, one commonly used pair of compound gears is a 127 tooth gear connected to a 100 tooth gear. It should be possible to use this conversion on any lathe. Exact conversions can also be achieved using the 127 tooth gear with another gear such as 120 or 135 etc. Several variations commonly in use are discussed below. Again the 127/100 gear is particularly interesting.

The 127/100 conversion gear:

The most important gear is the one with 127 teeth. But is it compound gear #1 or #2 in the pair? In RideTheGearTrain the gears are numbered in the order that power is transmitted through the gear train. Keep in mind the stud gear drives the first compound gear, so compound gear (#1) is driven and appears on the bottom line. It is connected by a key to compound gear #2 which is a driver. It can either drive the leadscrew gear, or another compound pair, and appears on the top line. Thus the gear ratio driver / driven is compound #2 / compound #1.

Lets forget about TPI and work in pitch measured in inches to make it simpler. This logic is confusing enough without having to invert everything! In that case
threadPitch(inches) = GTR x lead-screwPitch(inches).
If GTR increases the thread pitch increases. (If we include a gearbox it has to be multiplied be the gear ratio of the gearbox.)

Let's say we want a metric thread with pitch 2.5mm. But since the lead-screw is measured in inches we multiply 2.5 x 25.4 = 0.098425196850394 inches pitch. (Note the inverse of this is exactly 10.16 TPI but that is a red herring.) But we know our lead-screw has a pitch of 1/8"=0.125 inches. So we need the gear train to decrease the pitch from 0.125 to 0.0984.
0.0984 / 0.125 = 1 / 1.27 = 100/127
127 is on the bottom line and must be a driven gear.
So the gear train recommended by the program is:
stud=56
compound #1 = 127 (it is a driven gear on the bottom line of GTR)
compound #2 = 100 (it is a driver and appears on the top line of GTR)
LSG =56
GTR = 56 / 127 x 100 / 56
The 56 cancels out so
GTR = 100/127 = 1 / 1.27.

Now if we want a different metric pitch we can adjust the stud and LSG. eg if we want a pitch of 1.25 we have to slow it down by a factor of 2. This could be done by replacing the stud gear with a 30T gear, and the LSG by a 60T gear. Now
GTR=100/127 x 30/60
and ThreadPitch = 1/8 x 100/127 x 30/60 inches x 25.4 = 1.25 mm
Notice that the top line includes 25.4 and the bottom line includes 127 which is 1/5. So this can be reduced to
ThreadPitch = 1/8 x 100 x 30/60 x 1/5 inches = 1.25 mm
Or if we start with the knowledge that this is like a lathe with a leadscrew pitch 2.5mm, we just reduce it by 30/60.
ThreadPitch = 2.5 x 30/60 inches = 1.25 mm
which is the same equation as you would use for a metric lathe with a 2.5mm lead-screw. ie
ThreadPitch = lead-screwPitch x GTR
while ignoring the fact that we have included the conversion gears. Lets look at another example, a 1mm pitch thread would require the 2.5 mm leadscrew pitch multiplied by 1/2.5. This could be provided by a stud gear with 100 teet and a leadscrew gear with 25 teeth, as well as other possibilities.

There are many other pairs of gears that give a good approximation to the ratio of 1.27 and the first list shown below may allow a user to find gears in their collection that will work.

It is even possible to make an adapter to allow you to use change gears as compound gears. In that case you can use 'Automatic Compound Gears' to create a compound pair from any two gears in the list of change gears. So you do not need the list of compound gears in this case.

The user can check the results using RideTheGearTrain software. It tries all possible combinations of gears and may come up with unexpected ratios that actually work for the thread pitch requested, without using one of the standard conversion compound gears.

How to try out a particular pair of compound gears for conversion between metric and imperial: You can choose a particular compound gear for general conversion eg one of those on the list, and enter that pair into the list of compound gears in RideTheGearTrain on its own. Delete all the other compound gears, but keep your own list of change gears. You could enter a particular thread pitch or TPI you want, but instead it may be more useful to enter a range of thread pitches. Using this method you can decide which sets of compound gears and change gears suits you best.

Now it seems ideal converting the leadscrew to a known metric pitch such as 2.5mm. But, imagine building a similar lathe with a gearbox. You would have a metric leadscrew, but still have an imperial gearbox. Would the spacing of the gear ratios in the gearbox give you a full set of metric threads? Not necessarily. This conversion gear probably gives you a pretty good selection of approximations to metric gears. But if it is a particular metric thread you want to produce with high accuracy there may be other, better solutions. And that is where this program could give more precise results.

The 135/127 conversion gear: This program was originally written with Boxford and other South Bend Lathes in mind. These lathes are standardized with 3mm pitch lead-screws on metric lathes and 8 threads per inch on imperial lathes. Conversions may be preferred where the metric lathe with its 3mm pitch behaves like an imperial lathe with 1/8 inch (0.3175mm) pitch and this requires a gear ratio of 3/3.175 = 0.94488 . Similarly the imperial lathe with 1/8 inch pitch can be made to look like a metric lathe with 3 mm pitch using a ratio of 1/0.94488 = 1.058333.
Inverting the ratio like this can be done simply by flipping the pair of gears over so that the driven gear becomes the driving gear and vice versa.

The following explains how these ratios were calculated: Converting the 3mm metric pitch to inches 3mm / 25.4 = 0.11811 inches pitch. We want to convert this to 1/8 inch pitch =0.125 inches. To convert 0.11811 inches to 0.125 inches we have to multiply by 0.125 / 0.11811 = 1.058333. The gear ratio required is 1.058333, and the inverse is 0.94489, as we found earlier.

The following suggest that the 135/127 compound gear provides only an approximation for the conversion. But there is a solution described in the following paragraph which is 100% accurate using this gear.

Lets calculate what larger gear should be paired with a 127 tooth gear: 127 x 1.058333 = 134.4 which must be rounded to the nearest integer 134 or 135. Thus a 127 tooth gear connected to a 135 tooth gear will do the conversion with a small error. (According to this calculation a 127/134 compound pair will also work with a very slightly smaller error.) The gears have to increase the pitch slightly (from 3mm to 3.175mm which is 1/8 inch), which requires the lead-screw to rotate faster, and this requires that the smaller gear of a compound pair drives the larger gear (increasing the number of teeth per turn). So the stud gear drives the smaller of the compound gears which is connected to a larger gear which drives the lead-screw. With this setup the smaller gear is considered the driven gear (explained elsewhere) and the larger is the driver giving a gear ratio of 135/127. The larger gear is driving the LSG. Checking again, 3mm x 135/127 = 3.18898 mm. This seems appropriate since conversion from metric to imperial you would divide by 25.4 so you want 1.27 (1.27 x 20 =25.4) on the bottom line. Divide 3.18898 mm by 25.4 gives 0.12555 inches approximating a lead-screw pitch of 0.125 or 1/8 inch with 0.44% error. However you will find below that this compound gear can give 0% error.

What if you flip the compound gear over?
Flipping the gear gives a ratio of 127/135 instead of 135/127? (In this case the stud gear drives 135T and is connected to 127T which meshes with the lead-screw gear.) On the Boxford Users Group Richard K. pointed out that this compound gear with a 3mm lead-screw gives
3 * 127 / 135 = 2.822mm or 1/9" of carriage travel EXACTLY,
so the 127/135 compound effectively converts a metric 3mm lead-screw to a 9 tpi imperial lead-screw. This seems weird but can easily be changed to a 1/8 inch lead-screw pitch by using a stud gear of 40 and a lead-screw gear of 45. The result is
3 * 127 / 135 * 40/45 = 3.175mm pitch.
Dividing by 25.4 gives 0.125 inches or 1/8 inch lead-screw EXACTLY.
So you are better off flipping this gear over! In fact that is the standard setup for metric conversion Welcome to the weird and wonderful world of compound gears! The conversion is exact because 127 is on the top line and 25.4 on the bottom line giving an integer factor of exactly 5.

Why do we see the RideTheGearTrain Flipping compound gears? This was something that puzzled me for some time, but the above example with the 135/127 gears appears to provide the answer. Logic would suggest that the gears should be used to provide a gear ratio of 135/127 to convert the leadscrew pitch from a metric pitch to a desirable imperial pitch. However, if we flip the gears to give a ratio of 127/135 we now have 127 on the top line. When we divide by 25.4 to convert mm to inches it gives the ratio 127/25.4 = 5.0 exactly. We can easily compensate for 5.0 using standard gears in the gear train or gearbox, eg 100, and 20 teeth. These two alternative methods of conversion appear to explain why the program produces roughly equal numbers of solutions with inverted and non-inverted compound pairs. Another reason is that 127/100 is close to 1.25 which can be a useful factor.

The 76/65 conversion gear: This conversion gear is used on metric Boxford lathes with a gearbox (3mmm leadscrew pitch) to produce imperial threads.
76/65 = 1.16923. 3mm pitch x 65/76 = 2.5658 mm. If we divide 2.5658/25.4 = 0.1010" pitch or 9.9 TPI so this conversion makes the metric lathe behave like one with a lead-screw with almost 10 TPI with an error of 1%. If we flip this compound pair 3mm x 76/65 = 3.5077 mm 0.138 inches. It is used in conjuntion with various stud, LSG and gearbox values. eg 32 TPI uses stud 33, LSG 44 gearbox A1. 33/44.

One size that is used is 51/48 with 0.40% error. If we consider a conversion gear of 134/126 instead of 135/127, the error is 0.48% and the advantage is that both of these numbers can be divided by 2 to give 67/63 as another possible alternative. These gears can be 3D printed in polylactic acid at reasonable cost and there are companies selling various kinds of platic gears which appear to be quite satisfactory..

Will the gears fit? Another reason that this particular compound pair (135/127) is used may be that it fits onto the standard stud gear and lead-screw gear etc. The transposing gears 127/120 used on some lathes has the same advantage. The two gears are almost the same diameter. The difference between the radius of the large gear and the radius of the smaller gear must be sufficient to allow the stud gear and lead-screw gear to mesh with it. It may seem obvious to use a compound gear ratio of 2.54 rather than the usual 1.27. However this would result in a compound gear with 127 teeth driving a 50 tooth gear. The difference in sizes of these gears would make it difficult to mesh with a small stud or lead-screw gear. The 127/100 pair has gear sizes that are closer together, and 135/127 even better. The closer the gear ratio is to 1.0, the closer the two gears are to being the same size. (It is sometimes convenient to consider how much the GTR is changed by a particular compound gear. We have to keep in mind that the 'first gear' is driven and the 'second gear' in the sequence is the 'driver' and the gear ratio is driver/driven.)

This program performs the calculations as follows: Choose an integer for the smaller gear and calculating the size of the larger gear. If we choose an integer for the larger gear and calculating the smaller gear. The results may be slightly different due to rounding numbers to create integers. However, the differences are so small that there is really no need to do both.

The following photo is a compound gear for metric conversion with a 80 tooth gear firmly rivetted to a 63 tooth gear.

Photo of two gears connected together for
     cutting metric threads on the imperial Boxford Lathe



This has also been discussed in detail in the paragraphs above. One inch is now officially defined as 25.4 mm by the International Bureau of Weights and Measures. That will be used with the standard imperial lead-screw with 8 threads per inch pitch and the metric lead-screw on the South Bend clones and similar lathes with 3mm pitch.

Similar to the above explanation of conversion from imperial to metric
we can use the same approach to convert from metric to imperial using a conversion compound gear with a 127 tooth gear.

We found that for converting an imperial lathe to cut a metric thread we needed a conversion gear with
compound gear #1 = 127 teeth
compound gear #2 = 100 teeth


We would expect that simply inverting this gear would allow us to convert back from metric to imperial.
compound gear #1 = 100 teeth
compound gear #2 = 127 teeth


In metric Boxford lathes they use a 135 tooth gear in place of the 100 tooth gear:
compound gear #1 = 135 teeth
compound gear #2 = 127 teeth


This would require other gears to compensate for the substitution. But let's take a different approach. Let's see what happens when the stud gear and lead-screw gear are the same, eg 60. With just the conversion gear and neutral stud/LSG gears, the pitch in mm is
PitchMetric = 127/135 x 3mm
Divide by 25.4 to get the pitch in inches
PitchInches = 127/135 x 3mm /25.4 = 0.111111...
PitchInches = 1/9 inch exactly
So this is equivalent to an imperial lead-screw with exactly 9 TPI. There is no error.
Well that doesn't seem that great, until we introduce special stud and lead-screw gears to compensate. If we multiply 1/9" pitch by 45/40 we get 1/8" pitch or 8 TPI which is the standard imperial lead-screw, again with no error.

When we check this it does work out to 1/8" pitch:
stud = 45
compound #1 = 135
compound #2 = 127
LSG = 40
GTR = 45/135 x 127 /40 x 1/25.4
ThreadPitch = GTR x lead-screwPitch
Lead-screwPitch = 3mm and after conversion
ThreadPitch = 45/135 x 127 /40 x 1/25.4 x 3 = 0.125" = 1/8"

These gears can be 3D printed in polylactic acid at reasonable cost.

So once you have fitted this conversion gear it is the same as having an imperial lathe with an 8 TPI lead-screw which is actually the standard for imperial South Bend 9" clone lathes. (the 13" SB has a lead-screw with 6 TPI.) Others use 4mm.

If you enter it into the program as an imperial lathe it will work if you do not have a gearbox and you do not tell the program about the conversion gear you have installed. Just keep mum. If the program recommends a compound gear it would have to be included along with the compound conversion gear. However it is best to be honest and tell the computer you are using a metric lathe, and include the conversion gear in the list of compound gears. That way the program will try a lot of combinations you might not expect. Unfortunately if you are using Automatic Compound gears there is at present no way to enter a compound conversion pair in the list of change gears. In that case you could make a case for telling a fib and treating it as an imperial lathe and not including the conversion gear in the lists. This will only work if you do not have a gearbox.

Because the gearbox on a metric lathes is different to the imperial gearbox we cannot trick the computer into thinking that we actually have an imperial lathe. Anyway, the program will come up with novel gear combinations that do not even require the imperial conversion gear.



Although this software was developed originally for clones of the South Bend 9" lathe with the Norton style gearbox, such as Boxford lathes, it can be adapted for use with other gearboxes if the necessary details are sent to me. There is also the option of entering custom gearbox data using the thread table which is usually attached to the lathe. See below.



If your lathe has a lead-screw gearbox, and it is not already included with the software, it can be added if you send the following information to me by email. The program also contains an option to create a Custom Gearbox and lathe using the same data. If successful you can send me the URL after entering the data and I will be able to add it to the software permanently. In the meantime you can include your lathe using the temporary data stored in the URL. If you would like to be mentioned as the owner of the lathe send your name. It is interesting to include your location eg state/country and what the lathe is being used for. You will find "Custom Gearbox" near the bottom of the list of lathes.

Required information should include the following:

  • Make and model (To add the lathe to the list.)
  • A copy of the label on the gearbox showing what settings are used for various pitch or TPI
  • Any other useful labels, tables diagrams or photos.
  • The standard gears in the gear train that are required for the gearbox to give correct results
  • What change gears are typically available
  • The pitch or TPI of the lead-screw
  • Whether a fudge factor is required (This is unlikely. See Optional Entries ).




  • The famous Norton gearbox was developed by W.P Norton about 1886. Some other gearboxes are not identical, but similar in concept and can be built into this program. On standard Norton gearbox has two levers. On imperial lathes the lever on the left has 5 positions marked with letters. The right lever has 8 numbered positions giving a total of 40 possible gear ratios. The metric version has the numbered lever on the left and letter lever on the right giving 32 gear ratios.

    One way to check that it is a Norton imperial gearbox, the same as those used on Boxford and other clones, is to compare the gearbox label with the table generated by this program. Otherwise look at row B on the table which should show this sequence: 8,9,10,11, 11.5 ,12,13,14. Note that 11.5 is the odd one out. Double 11.5 gives 23 TPI. Also check that the standard gear train has a stud gear with 20 teeth and a lead-screw gear with 56 teeth.

    The standard set-up for the imperial Boxford lathe with a gearbox is:

    Stud=20,
    Idler=Any,
    Lead-screw=56 teeth.

    This paragraph gets down to the nitty gritty of the gearbox. The gear ratio of the gear train with this 'standard' setup when there are no compound gears included is 20/56 = 1/2.8. When the gearbox is in the A1 position ie with the numbered lever is set on '1' and the letter lever is set on 'A' the table says it will produce a thread with 8 threads per inch, which is the same pitch as the leadscrew. In this case the overall gear ratio must be 1. Since the gear train ratio is 1/2.8, the gearbox must have a ratio of 2.8, thus giving an overall ratio of 1. This can be confirmed by examining the gears in the Norton gearbox if you are really keen! The gear design can be found in the parts manual (or 'Know Your Lathe'). In the letter section of the gearbox 'A' position does not affect the gear ratio. It has a 32T gear driving a 32T gear with an idler between (higher letters of the alphabet increase the ratio by 2 each step ie 1,2,4,8,16.) The number section in position '1' has a 32 tooth gear driving a 16T gear which is on the same shaft as a 28T gear driving a 20T gear mounted on the end of the leadscrew. This gives a ratio of 32/16 x 28/20 = 28/10 = 2.8 as predicted! The other numbered positions '1' to'8' connect with a cone of gears in the following order: 16,18,20,22,23,24,26,28T. In position '8' the 28T gear acts as an idler connecting the 32T gear directly to the 20T gear giving a ratio 32/20 = 1.6 in position 8. Multiplying by the gear train ratio of 1/2.8 givers the overall ratio. Because TPI is not proportional to the gear ratio, but inversely proportional you have to divide the leadscrew 8TPI by gear train ratio: 8 x 1/(1.6 x 1/2.8) = 8 x 1.75 = 14 TPI which is what it says on the thread label for A8.

    Next, what effect does it have when the idler wheel is replaced by a compound gear? The standard gear train for imperial threads can use ANY gear wheel in the idler position ie between the stud gear and the lead-screw gear (which is on the back of the gearbox connecting through to the lead-screw). However, the idler may be replaced by a pair of different compound gears connected together by a key or rivet like the one in the photo.
    I label the gears in the order that power is transmitted through them. Compound 1 is driven by the stud gear
    Compound 2 is a driver gear driving the next gear in the train, usually the LSG.

    Note that the contribution of this compound gear to the overall gear ratio is defined as driver/driven ie Compound 2/ Compound 1. Actually the gear ratios are usually calculated at the point where one gear meshes with the next and are always diver/driven. Idler wheels are ignored as explained in the above link.

    Although the change gears have a central hole bored to 7/16" (on the Boxfords) the compound gears have a larger hole drilled in the center (9/16" usually), so that they can be mounted on a sleeve and rotate freely. But they cannot be used as change-gears without modification and they are considered a separate set of gears in the computer program. An adapter can be made to allow you to use any change gears to create pairs of compound gears.


    Label showing gears to use for cutting metric threads on the imperial Boxford Lathe

    Photo showing gears to use for metric screws on an imperial Boxford Lathe

    Edge view showing gears to use for cutting metric threads on the imperial Boxford Lathe

    This plaque from the side of my ex high-school lathe shows how easy it can be to select gears for metric threads on an imperial lathe once the compound conversion gear wheels have been installed. I leave the conversion wheel installed all the time, as I rarely need to cut imperial/English threads.

    A table showing what gears to use for metric conversion

    Similarly there are compound gears available for cutting imperial threads on a metric lathe (135/127). See these links:
    Converting Imperial lathes to cut metric threads
    Cannot use a thread dial indicator for metric/imperial threads
    Converting Metric lathes to cut imperial threads
    Converting Imperial Lathes to cut metric threads
    How does conversion from imperial to metric work?
    How to make a compound gear adapter.




    This non-standard after-market gearbox was found on a Boxford C lathe in UK. The Model C was sold originally without a gearbox and without power cross-feed or power longitudinal-feed. Although it has a reduced set of gears with only 24 gear ratios to choose from, it is a useful addition covering most of the medium to course threads ranging from 60 to 8 TPI when using the standard gear train consisting of a 20 tooth stud gear and 72 tooth leadscrew gear. Using RideTheGearTrain with a reasonable set of change gears it should cover most threads. The main selection that is missing from the gear label is 11.5, 23, 46 TPI. (11.5 is used for garden hose threads.) The label itself is the original Boxford label with the 11.5 TPI column erased and an eighth column added at the end for 15, 30 or 60 TPI. Rows D and E should also be erased as it only has A,B,C position.

    The A,B,C lever has a fourth position for power feed using the leadscrew with a label saying 7.2/C. I presume this suggests taking the TPI from row C, inverting it to convert TPI (turns per inch) to inches per turn, and then multiplying by 7.2. This results in quite course longitudinal feed rates, and I suspect they wanted us to divide by 7.2 rather than multiply by 7.2, so the feed rate would be much finer:
    1/(7.2 x C). Time will tell.

    Label showing gears to use for cutting metric threads on the imperial non-standard Boxford Lathe



    Before I describe the different Boxford models I should mention how to find the serial number for your Boxford. It is stamped on the topside of the bed near the end, usually hidden by the tail-stock. You can go to Lathes.co.uk to find a list of dates they were manufactured. The list of serial numbers is also available in the Boxford Users Group files section. Apparently the number sequence included everything that Boxford produced including non-lathe items. So the serial number does not tell you how many lathes were sold. The letter included with the number may not have anything to do with the model you have. Mine has a B in front, but it is a model A. Some later model lathes did include the model code such as AUD with the serial number. From the serial number at the beginning and end of 1955 I found mine was in the last 28 numbers and would have been sold about mid-December 1955. This is about the time my father was setting up the Te Puke High School engineering workshop - when I was 5 years old. He was head of the technical department. Ten years later I was a student in his class learning technical drawing, engineering theory, and practice using this same lathe for 4 years.

    Boxford Model A had the thread cutting gearbox, usually referred to as a Norton gearbox as described above. The Boxford Models A and B also have power feed on the cross-slide and carriage. The Model B had no gearbox but retained power feed. Model C had neither gearbox nor power feed. Other derivatives were produced for the education market including the model CSB (a variant of model C) and technical training models T and TUD which originally came without back gear, power feeds or gearbox.

    Originally they were designed as bench-top machines but the countershaft with pulleys on the back of the head took up a lot of bench space and the "under-drive" models AUD, BUD, and CUD were introduced. These models had the motor mounted in a cabinet underneath the lathe instead of mounting behind the head.

    All these models were upgraded to the Mark 2 model with a single back gear lever mounted on the top of the headstock instead of two levers on the left and front of the headstock.

    The lead-screw of model C lathes could be used for longitudinal power feed by adjusting gears in the gear train, but did not benefit from the speed reduction included in the aprons of Model A and Model B versions. In that case the carriage feed was the same as pitch. The other models had a keyway in the lead-screw which was used to drive gears in the apron. This meant that the lead-screw was not getting worn out by being used for power feed.

    These models were available in imperial versions with a lead-screw having 8 threads per inch, or metric with 3mm pitch. The thread cutting quick change gearboxes found in the A models were also different. The imperial version had a lever marked with letters on the left and another marked with numbers on the right. The metric gearboxes were similar but had the numbers on the left and letters on the right.

    Later a continuously variable speed lathe, VSL, was developed. This used cone shaped pulleys or sheaves with a belt that varied its position to change the RPM of the chuck. The ME10 was introduced in 1976, in the same lines as models A, B, and C and later came with a different gearbox. The current software may not work for this particular extended range gearbox unless someone can provide the author with the necessary data.

    The variable speed lathe VSL was first introduced with a larger hole bored though the center of the spindle and an American style L00 chuck mount. Initially it had a different gearbox, but it wasn't long before they changed back to the standard Norton gearbox. A member of the Boxford Users Group in America (Lawrence) has a VSL500 manufactured in 1977 with serial number V.S.L. 71861-L00) with the standard Norton gearbox.

    The X10 STS10.20 and 280 were also newer models which had different gearboxes but the gearbox for X10 is now included with the software thanks to data provided by Ross Jennings. Details are provided below in a section on X10.

    Between about 1977 and the end of production about the year 2000, newer models of Boxford were sold, including the X10, '280' and others. These used a new gearbox system and this is included in 'version 2-9' of this program.


    If you click Choose Lathe in the main menu you will see a list of all the lathes that have been entered into the program. For lathes without a gearbox it is not necessary to list the brand. But gearboxes vary between brands and have to be entered separately. If you have a lathe with a gearbox that is not listed, click Custom Gearbox in the main menu to see how you can enter data for your lathe using the table provided with your gearbox.



    The Norton gearbox was developed by W.P Norton about 1886. Many lathe manufacturers use this design or one similar to it. The South Bend 9" clones such as Boxford used exactly the same design and can use this program. RideTheGearTrain was originally written for Boxford lathes and should be valid for Boxford lathes made between 1948 and 1988 approximately (The original South Bend 9" was introduced in 1933). The Boxford model A was made at least until 1977. As Tony Griffiths of Lathes.co.uk says "Boxford and the original South Bend "9-inch" screwcutting gearboxes were mechanically identical". There is a possible catch. The gearbox on imperial Boxford lathes requires a 'standard' gear train including a 20 tooth stud gear (for some threads 40 may be substituted), and a 56 tooth leadscrew gear (LSG). An idler gear with any number of teeth is usually placed between them. For metric Boxford lathes the 'standard gear train' has a 50 tooth stud gear and 45 tooth LSG. If you have an lathe which requires a different 'standard' gear train, it will be necessary to change the primaryRatio in Optional Entries in the menu. It would be best to contact me to make the adjustment and add your lathe to the list.

    Tony mentioned that at least 22 companies produced South Bend 9" clones. These include: Ace,
    Asbrinks,
    Blomqvist,
    Boffelli & Finazzi,
    Boxford,
    David,
    Demco,
    Harrison,
    Harmal,
    Hercus,
    Fragram,
    Grizzly,
    Joinville,
    Lin Huan(Select),
    Moody,
    NSTC,
    Parkanson,
    Purcell,
    Sanches,
    Blanes,
    Sheraton,
    Smart and Brown,
    Storebro,
    TOS,
    UFP
    (list courtesy of Lathes.co.uk)

    It should be possible to use the software for any of these lathes without resorting to the optional inputs for fudge factors or altered lead-screws. However, if you find that the stud and lead-screw gear used as the standard setup for the gearbox chart are different to the standard Boxford (20 and 56 for imperial or 40 and 45 for metric) then you will probably need to use a fudge factor or contact the author of the program to have your lathe added to the list.


    VSL: The following is a message I received through the Boxford Users Group regarding the changes in gearboxes on the VSL series of lathes:

    Lawrence Sciortino Jan 6 #2481

    Hi Evan,

    The gear box differences question came up several years ago, especially the incorrect reference in the Boxford "Know Your Lathe" owner's manual, page 76. I wrote to Tony at www.lathes.co.uk, questioning him on that anomaly, and informing him that my VSL-500 with L00 spindle nose gear box and change gears are identical to my ME-10, and both require the 127/100 transposing compound gear for cutting metric threads. He added the information to the Boxford VSL information in his website, (which is one of the best machine resources on the internet, in my opinion). Quoted below is his commentary, and the serial number of the VSL he mentions is that of my lathe:

    Fitted to a distinctly different stand, and with a 5-inch centre height, the final version of the VSL was known as the Model "500 VSL" and, unlike most Boxford lathes, the model type was clearly identified by a large badge on the headstock. An interesting point concerns VSL models fitted with the L00 headstock spindle: on these lathes a screwcutting gearbox was standard - but some had different internal ratios and the English/metric and metric/English conversions gears arranged to be more compact with pairs of 64/54t and 76/65t respectively instead of the usual 127/100t (inch to metric) and 135/127t (metric to inch) gears. At one time it was believed that all gearboxes on the L00 VSL lathes had the altered internal ratios, but several examples have been found in the USA (one being a VSL500 manufactured in 1977 with serial number V.S.L. 71861-L00) where this is not the case, the gearboxes being of the earlier, ordinary (Norton) type. It is suspected that, while Boxford fitted a different gearbox to the earlier VSL models with the L00 spindle nose, this practice was discontinued and later editions of the manual not updated to reflect the change. If you buy a gearbox-equipped lathe that appears not to generate the pitches shown on the screwcutting plate check the special manual produced by lathes.co.uk. It shows the ex-factory arrangement of the changewheels.

    So, later VSL's like mine, have the same gear box as the rest of the lathe models produced, and the necessary transposing gears to produce metric threads on the english gearbox/lead-screw is the 127/100 compound gear.

    Keep up your good efforts on all things Boxford, and Happy New Year,

    Lawrence



    Newer Boxford Lathes (about 1977-2000) include X10, 280, STS-10-20 and several other model numbers designated for education or precision engineering. The gearbox ratios used for the X10 are included in RideTheGearTrain and are probably the same as the other later Boxford models. The X10 STS10.20 and 280 were also newer models which had different gearboxes but the gearbox for X10 is now included with the software thanks to data provided by Ross Jennings in New Zealand. His model is an STS 10.20 ie 10 inch throw (diameter) and 20 inches between centers. He was surprised to find that it is labelled 'Gamet Micron Spindle Bearings' as he thought these were reserved for 'Tool Room' lathes with 'TR' designation. It has a 3-phase motor and he plans to fit VFD speed control. (VFD: A variable frequency device. The motor speed locks into the frequency provided by the VFD circuit.)



    Alan Moore provided the following history: "Myford was producing small lathes from 1934, the Myfords 1 ,2, 3 and 4. It was the ML7, which was first produced in '46, that won the hearts of amateurs."

    Although Myford began manufacturing the ML7 right after WW2, the first Myford to include the Norton-style gearbox was released about 1953 with models ML7B and Super 7B. This gearbox differs from the traditional South Bend Norton gearbox by excluding 11.5 TPI and replacing it with 9.5 TPI.

    This early model gearbox used a 12 tooth "tumbler stud" gear. When the "new" version of the gearbox came out in 1956 it had a 24 tooth stud gear and all the gear ratios in the gearbox were reduced by a factor of two to compensate. As a result of this change the gear ratio of the standard gear train is 1.0. These two versions are listed as separate lathes in RideTheGearTrain.

    Before discussing Myford gearboxes, I should mention that the Myford uses a special gear train described below in relation to power feed rates. This includes two compound gears (57/19) in series. When setup for cutting threads with a 24 tooth stud/mandrel gear, the gear train ratio (GTR) is one. This novel and convenient setup is shown in a diagram below.

    But this program assumes that you will be using the gear train like any other lathe. It assumes that you are planning to remove both of the standard compound gears and replace them with any combination of gears that the program suggests. Generally this is necessary when you are cutting metric threads on this imperial lathe. In fact the gear trains that Myford recommends for metric threads requires you to remove the standard compound gears. These arrangements may be seen on a black label on the gear train cover of some models shown in a photo below. However the program can recommend many more possible combinations of gears and sometimes they are simpler and specifically use the set of gears you have available.


    Metric thread cutting chart for the early gearbox with a 12T stud/mandrel gear.


    The older model Myford gearbox referred to in this computer program refers to "Quick Change Gearboxes" with serial numbers prior to QC2500 when the new gearbox was released in 1956. (Another reference said the new gearbox was introduced 1954 for the ML7 model after serial number K1087186 and the Super 7 model after SK115830. The QC numbers probably refer to serial numbers on the quick change gearbox.)

    The first version of the gearbox used a 12 tooth "stud gear" (mandrel gear or tumbler stud gear) in the standard gear train as seen in the photo below. The spindle shaft (which has the chuck on the other end) has gear teeth machined into the shaft.

    The tumbler stud gear actually consists of two gears. The gear closest to the head casting has to have the same number of teeth as the gear machined into the spindle. This ensures that the tumber stud turns at the same speed as the spindle. That is why we can ignore all the gears above the tumbler stud gear when calculating gear ratios. The reversing gears act as idler gears and can also be ignored. The ML7 has 30 teeth on the spindle and 30 at the base of the tumbler stud gear, but apparently early lathes may have used fewer teeth. The reason for a change may be to allow for a larger spindle diameter and larger hole bored through the spindle.

    When we refer to the tumbler stud gear (or stud gear) we are usually referring to the gear that is furthest from the head casting. This is the gear that is frequently changed to produce special threads of feed rates.

    Apparently, the 12 tooth tumbler stud gear is so small that it could not accommodate a key-way, so it was machined as a single piece combined with the gear closest to the head (usually having 30 teeth).

    The second ("new") ML7 gearbox version used a 24 tooth stud gear with a key-way so that it could be changed more easily. To compensate for increasing the gear train ratio by two-fold, the gearbox was slowed down by a factor of 2.

    That is why these two lathes and gearboxes are listed separately in this program.

    These can be identified by the 12 tooth or 24 tooth tumbler stud/mandrel gear.


    This photo shows the Myford gear train with a 12 tooth stud/mandrel gear which identifies this gearbox as being produced between 1953 and 1956. Alan Moore of Leeds, UK says: "The photo shown above is not an S7. The S7 Mark one had a tapered bronze bearing in the front and an angular ball bearing to the rear. Oiling was through a cast-in drip-feed reservoir at the front and oil-nipple to the rear. The split bearing and drip-feed oilers in the photo, and the mandrel gear [spindle gear] right at the end of the spindle, are characteristic of the ML7, though the belt guard is very unusual."

    At this time the standard 'tumbler stud gear' was changed from 12 to 24 teeth and this required the primary ratio of the gearbox to be increased by a factor of two. Otherwise, it appears that the gearbox is the same. Western lathes generally have a changeable stud gear mounted on a special shaft (stud or mandrel or tumbler stud) spinning at the same speed as the chuck spindle. The stud gear meshes with the tumbler reversing gears and Myford call this the "tumbler stud gear" to distinguish it from stud#1 and stud#2 on the banjo. There were no metric versions of the Myford lathes as far as I know.

    The gearbox has a lever that can be moved to 3 positions. Lever position A is all the way to the left, B in the middle and C to the right (shown in the photo below).


    Myford Super 7 Imperial Thread chart and gearbox lever


    It is modelled on the Norton gearbox (above) except that 11.5 TPI in the Norton version is replaced by 9.5 and its multiples by Myford as well as some other lathe manufacturers. In the 1940s it was possible to buy Sparey after-market kitset gearboxes using Myford gear wheels. They eliminated both 9.5 and 11.5 from the list in those models (see lathes.co.uk). Another Myford version was released in the American market with the 19 (9.5 x2) tooth gear replaced by a 23 tooth gear (11.5 x2) to allow for pipe thread pitches but details are not available at this time. Garden hose connectors with 11.5 TPI can still found in the USA today.

    Some terminology needs explanation: As a general rule gears are named according to the power being driven through the whole gear train and gear ratios are normally calculated at the points where the teeth of two gears mesh. They may be labelled A,B,C in Myford documentation and these labels are included in the results table. The first of the compound gears (which I call compound_1) is driven by the stud gear which may be referred to as the 'Tumbler Stud Gear' or 'Mandrel Gear' in Myford terminology. It is a "driven gear" and is connected by rivets or a key to the second compound gear (compound_2), which is a "driver" gear because it drives the next gear in the train. The contribution of this compound pair to the gear train ratio can be calculated by driver/driven or compound_2/compound_1 and combined with the gear ratio provided by stud/LSG ie driver/driven and these two or three ratios can be multiplied together to get the overall gear ratio of the gear train (GTR). But remember this is not the standard method for calculating gear ratios, which shoud use the ratios at the points where teeth mesh. This is also explained in the section
  • How to calculate the gear train ratio GTR
  • .

    The gear that I call the "stud gear" is known in Myford circles as the "Tumbler stud gear" as they refer to other studs on the banjo as number one and two studs, but Myford themselves call the tumbler stud gear the "mandrel gear". The Tumbler Stud is (as usual) a compound gear with the gear nearest the lathe head having the same number of teeth as the gear on the spindle shaft so the stud turns at the same speed as the spindle. This 30 tooth gear and everything before it can be ignored (the tumbler gears themselves are just idler wheels that do not alter the gear ratio.) and the stud gear acts as a substitute for the spindle gear.

    The "new" Myford lathes (after 1956) have a 24 tooth gear attached to the 30 tooth, and this 24 tooth gear is the actual stud gear that drives the rest of the gear train. It is generally a gear that can be easily changed. Old models of the gearbox required a 12 tooth gear in this position instead of the 24 tooth. The lead-screw gear is an extra wide 72 tooth gear connected directly to the lead-screw or to the gearbox. I call the last gear in the train the lead-screw gear or LSG and others use the label 'L'. But because this gear provides power to the leadscrew or leadscrew gearbox, Myford may refer to this as the 'INPUT gear'. The standard Myford input gear is the wide 72 tooth gear.

    The gearbox label indicates that the power feed is 0.1111 = 1/9 times the pitch of the thread. This is the result of an ingenious gear change mechanism in the gear train illustrated in the diagram below. Normally the "new" version has a stud or mandrel gear with 24 teeth, and a wide lead-screw gear with 72 teeth. The contribution of these two gears to the gear train ratio is 24/72=1/3. But mounted between them are two compound gears, each having a 19 tooth gear connected permanently to a 57 tooth gear. Now 57/19 =3. When the bottom compound gear, shown in blue, is slid towards the right in the illustration (towards the head of the lathe casting) it introduces its factor of 3 conveniently resulting in an overall gear train ratio of GTR= 1/3 x 3 = 1. In this position the top compound gear is not set up to operate as a compound gear, but simply acts as an idler gear which does not contribute to the GTR. This setup is used for cutting threads.



    Now if the bottom compound gear (which is blue in the illustration) is moved away from the head of the lathe, as shown in the left illustration, it becomes an idler and the top gear now acts as a compound gear, but although its two gears have 19 and 57 teeth, they are the opposite way around, and its contribution to the GTR is now 19/57=1/3. So this 1/3 combined with 24/72=1/3, produced by the stud and leadscrew gears, gives an overall gear ratio of 1/3 x 1/3 = 1/9 = 0.1111. This gear position is used to give very slow 'carriage power feed rates' to produce a nice smooth finish when turning a cylindrical surface. This gear ratio for the power feed rate is included in the specifications for the Myford lathe, but it can be changed by clicking the "Optional Entries" button in the menu. If these two special compound gears (19/57) are removed to set up some other gear train, this ratio of 0.1111 no longer applies and should be changed to 1.0 if you want to calculate feed rates. Although RideTheGearTrain mentions both carriage power feed rate and cross-slide power feed rate, these lathes do not provide cross-slide power feed.

    Now lets slide the blue compound gear back to the right side for standard single point thread cutting. In this position the gear train ratio is 1. If we want to make a thread with 8 TPI, which is the same pitch as the lead-screw we need an overall gear ratio of 1 so that the lead-screw turns at the same speed as the spindle and chuck. In this case we would be making an exact copy of the pitch on the lead-screw. (Many years ago you actually had to change the leadscrew to make a different thread.)

    So how does the gearbox contribute to this. The table on the gearbox says that lever position A1 is used for 8TPI. In this position the gear ratio of the gearbox itself must be 1 so that when it is combined with the GTR of 1, the overall ratio remains 1. Armed with this knowledge we can work out the gear ratios of all the other lever positions. For example a thread with 20 TPI is produced by lever position B4. This must have a gearbox gear ratio of 8/20. Looking down the number 1 column of the table we see TPI 8, 16, 32 so clearly moving the 3-position lever gives gear ratios of 8/8, 8/16, 8/32 or 1, 1/2, 1/4. Most lathes have a lever that changes in powers of two like this (eg 1,2,4,8,16). This is how RideTheGearTrain knows what gear ratios are available. Here are some links that may be useful:

    Please notify me if I have anything wrong.

    See A Model Engineer forum about Myford Lathes

    and Myford Manuals on DropBox

    and Lathes.co.uk




    These specifications are for the Warco WM180 Chinese mini-lathes but will work for any mini-lathe with no gearbox and a leadscrew with a pitch of 2mm. This defines it as a metric lathe. If necessary specifications can be changed in OPTIONAL ENTRIES in the menu. For further details see the Warco WM180 Chinese mini-lathes below.


    These specifications are copied from the Warco WM180 Chinese mini-lathes but will work for any mini-lathe with no gearbox and a leadscrew with a pitch of 1.5mm. This defines it as a metric lathe. If necessary specifications can be changed in OPTIONAL ENTRIES in the menu. For further details see the Warco WM180 Chinese mini-lathes below.



    These specifications are copied from the Warco WM180 Chinese mini-lathes but will work for any mini-lathe with no gearbox and a 16 TPI leadscrew. This defines it as an imperial lathe. This is the same as the lathe in the video shown below: Emco Maximat imperial lathe with no gearbox. Interestingly this lathe was made in Austria and uses the Z labelling system which I thought was Chinese! If necessary specifications can be changed in OPTIONAL ENTRIES in the menu. For further details see the Warco WM180 Chinese mini-lathes below.



    Please read the general section about the methods used to label gears for mini-lathes, which uses the Warco as an example: Chinese mini-lathes and how gears are labelled

    Now let's look more closely at the Warco lathe. This lathe does not have a thread cutting gearbox on the lead-screw. (Other Chinese lathes have rudimentary gearboxes with only 3 gears.) Lets start at the beginning by remembering that the spindle gear (referred to as the stud gear in this program) is not assigned a letter label because it cannot be changed and is not even mentioned on the charts (even though it is required to calculate the gear train ratio.) The Warco WM180 uses a 40 tooth stud/spindle gear. In RideTheGearTrain this can be set up in Optional Entries in the menu. But I will add this lathe to the list in the program and these optional entries will be set up automatically for this lathe.

    Another number that is required by the program is the pitch of the lead-screw. (If you have an imperial version of this lathe you will need to set it up with the TPI of your lead-screw.) In the Ade's Workshop video he demonstrated a gear train for a 2mm thread. It had the 40 tooth stud/spindle gear and a 40 tooth lead-screw gear, and the two gears between were idler gears that do not affect the gear train ratio (GTR).
    So GTR = 1.0.
    This tells us that the lead-screw has a pitch of 2mm rather than 3mm, and this can also be set up in OPTIONAL ENTRIES in the menu but will be set up automatically for this lathe.
    Feed Rates: This lathe uses the lead-screw for carriage feed along the bed, so the feed rate is the same as a pitch for a thread. There is no other gearing to reduce the speed, so the gear ratios for feedrates are set to 1. As far as I know there is no power feed on the cross-slide.
    Once all this is set up you can use RideTheGearTrain to set up the gear train for any thread whether it is metric, imperial, or Martian.




    If you find that an extra gear will expand the number of threads you can produce you may need to know the specifications for the gear design. Some users have found that a gears with 32 teeth can be helpful, and if you don't have a 21, 39, 63 or 127 tooth gear, one of these would help with converting between metric and imperial threads. The bigger gears give greater accuracy in general, but may not fit on your gear train banjo. The specifications for gears used on the Mini-lathe are: 12mm bore hole, 8mm face width, and the keyway is 3mm wide by 1.4mm deep. The gear tooth profile is defined by module 1, 20° pressure angle. There is a section "All about Diametral Pitch (DP) and Modulus" elsewhere in this help file and this gives a link to a PDF with details about many lathe gears.

    The following discussion of labelling methods is relevant to both metric and imperial mini-lathes, with or without gearboxes. (Labelled is the British spelling. American spelling is labeled and I use a mixture!)

    It is suggested that if you are using RideTheGearTrain to set up your Chinese lathe, you use my method of labelling as shown in the scale drawings because attempting to convert into the Chinese method of labelling may be too confusing. However, it does mean that you have to decide how to mount the gears on the shafts (or banjo studs).

    The labelling method used in RideTheGearTrain is in the order that power is transmitted through the gear train. Consequently they are in the same order that you would use to calculate the gear train gear ratio, GTR. Specifically, using a gear train with one compound pair as an example the power is transmitted through the gears in this order, with ratios based on the point where one gear meshes with the next, using driver/driven. The words below represent the number of teeth on each gear:
    stud > comp_1 > comp_2 > Lead-screw Gear (or LSG)
    And GTR is calculated using:
    GTR = stud/comp_1 x comp_2/LSG


    The method used to arrange the gears in the gear trains of Chinese lathes differs from the method used in RideTheGearTrain.
    Mechanically the lathes all work the same way, but the way the gears are labelled on the charts printed on the outside of the lathe are different, as explained below.

    The Chinese lathes imported by Warco, UK are described very well in Ades Workshop



    Chinese mini-lathes are designed to take two compound gears in series, and in RideTheGearTrain the number of compound gears can be selected as zero, one or two. But nearly all the solutions in the tables printed on the lathe actually only use one compound gear and the others are idler gears which do not affect the GTR. The exception is the gear train recommended for slow power-feed rates, which do use two compound gears. Because there are so many possible solutions with two compound gears (plus varying the lead-screw gear, and possibly a 3-speed gearbox as well) the method of displaying the results looks more complicated than the display used for zero or one compound gears, but the system is fairly easy to use with buttons labelled SOLVE and DRAW leading you to a scale drawing of the gear train.

    THE CHINESE ABC LABELLING METHOD
    The stud or spindle gear is not labelled because it cannot be changed, although it is important for calculating GTR. It always meshes with gear 'A' at the start of the gear train. The other gears are labelled according to the way they are arranged on their shafts, and this bears no relationship to the way power is transmitted through them. On the Warco lathes the top 2 gears are labelled A and B with A being furthest from the headstock casting, and B being closest to the head. On the next shaft down the chain, C is furthest from the head and D is closest to the head. F is the lead-screw gear and H is a spacer. Again this is not the same order that power is transmitted through train and the order may be different for each thread on the table.

    THE Z_LABELLING METHOD
    However, other more common Chinese imports, such as the Precision-Mathews model in the next section, use a slightly different system again using the letter Z, ie Z1, Z2 etc. It is still based on the positions of the gears on their shafts, rather than the order they mesh together.

    The first two gears are labelled Z2 then Z1, but the second pair are labelled Z3 then Z4. I have no idea why the first two are not Z1 and Z2. Again, the stud/spindle gear is not labelled. It always meshes with gear Z2 (not Z1 as you might expect). The first pair on a common shaft are labelled with Z2 furthest from the head and Z1 closest to it. The next pair sharing a shaft are Z3 furthest from the head and Z4 closest to it. Finally L is the lead-screw gear. Again H represents a spacer (H looks a bit like a spacer). There are images in the next 3 sections showing these arrangements.

    I thought this was a Chinese invention but I have included a video below about the Emco Maximat lathe and it uses the same Z-labelling system. It appears to be an older lathe and it was made in Austria! So it is likely that the Z-labelling was copied from lathes made in Austria and it may be a German method.



    Precision Mathews Chinese imperial mini-lathe with extensive discussion of Chinese mini-lathes and Z-labels.

    Chinese metric mini-lathe model WM180, Warco UK,

    Emco mini-lathes with no gearbox are discussed





    This lathe is exactly the same as the Precision Mathews lathe described in the next section, except that it is metric having a leadscrew pitch of 2mm. I need feedback from a user who has a lathe like this to confirm whether these specifications are correct. Check the details in Optional entries to confirm that they match your lathe.





    I would like to thank Quinn Dunki for allowing me to use her lathe as an example with snapshots taken from her 'Blondihacks' video on screw cutting. With model number 10x22 this lathe has a large 10 inch (254mm) diameter swing and is a bit bigger than the average Chinese mini-lathe but is very similar, if not identical in operation to many other lathes such as 7x12, 7x14, 7x16 etc.". It does have a 3 speed gearbox. but this may be common in Chinese mini-lathes, but this does not give the range of threads you would have with a 40 speed Norton gearbox found on British and American lathes. It does not have tumbler gears so the stud/spindle gear cannot be changed. This further restricts thread pitch options but they get around this by providing a lot of change gears and frequently use one or two compound gears in the gear train. It is imperial with a 16 TPI leadcsrew.

    If you find the 'Z' labels on the gears in the gear train confusing (as I did) you might like to read the previous section which uses the Warco Chinese lathe and this lathe as examples to describe the labelling systems. These systems bear no relationship to the equations for calculating gear train ratios. For that reason RideTheGearTrain uses its own systen to label the gears and I suggest that you forget about the Z-system when using RideTheGearTrain. I had thought that the Z-labelling system was Chinese but I found it on the Emco Maximat which is an older lathe made in Austria. See: Chinese mini-lathes and how gears are labelled

    The gearbox generally used in Chinese mini-lathes is limited to 3 gear ratios which increase in powers of two, like most lathes: 1,2,4.

    A good example of this type of lathe is the one used by Quinn in her excellent BlondiHacks series on YouTube. Hers' is a "Precision Mathews PM 1022" model. PM is not the manufacturer but the importer/retailer. Several importers have the lathes built to their own specifications.

    The embedded YouTube videos below include Quinn's excellent "Import Lathe Buying Guide". This is a good introductory video. But the second video is more relevant to the current discussion because she demonstrates how to cut a 16 TPI thread and I have used the gears that she describes to set up her lathe on RideTheGearTrain.





    There are some special characteristics of these lathes that are different from the older English/American style lathes, and it is important that the user reads these instructions. If you choose a mini-lathe in Step 1 all of these setting will have been entered for you, but if your lathe has settings that are different, you may have to adjust them.

    Like other Chinese lathes the gear that I call the stud gear is machined as part of the spindle shaft. People have various names for this gear: stud gear; tumbler-stud; spindle gear; mandrel gear; first gear; top gear; etc. It cannot be changed in this lathe. It generally has 40 teeth. This feature is set up in the program menu called "Optional Entries" which asks whether the stud gear can be changed. Answer NO and enter the number of teeth it has (40 probably). You can also check that the pitch of the lead-screw is correct here (usually 1.5mm or 2mm for small metric machines and 3mm for medium sized lathes or 6-12mm for very large machines. For imperial lead-screws 16 TPI is normal for mini-lathes, 8 TPI for medium sized lathes, and 4 or even 2 TPI for huge lathes.)

    Many larger lathes have a screw cutting gearbox with 32 to 64 gears. But because mini-lathes usually only have a 3-speed gearbox most threads require the user to manually alter the gears. We call these "change gears" or "change wheels". Since you cannot change the "stud gear", you generally have to use one or two compound gears to provide virtually every thread you can imagine. On this lathe you do not use a set of special "compound gears" because all the gears can be made up into compound pairs as needed. These compound pairs are physically connected together with a key in a keyway slot. RideTheGearTrain can automatically put together every possible pair of gears to make sets of compound gears. This will be set to Automatic when you choose this lathe.

    When you click "2 Gear Selection" use the radio buttons to select one or two compound gears. Set the program for "Automatic Compound Gears" and it will work out all possible gear combinations for you. You will see a typical list of gears for this lathe, but if your set is different you can edit this list. You do NOT need to type anything into the list of "compound gears". Any numbers in that box will be ignored in automatic mode.

    Because these lathes often use two compound pairs with a long list of change gears the program can produce huge numbers of results, and a lot of combinations can produce the same gear ratio. For that reason, when you choose two compound gears the program produces a list of gears that you can put together in various ways but resulting in the same gear train ratio (GTR). The program used to ask the user to do this, but now each result has a button marked SOLVE. Click that and it shows you 12 to 36 different ways you can put the gears together to give the same gear ratio.

    They are marked with symbols like ##** to indicate which are the best options. Beside each result there is a button saying DRAW. Click that and it will show you a scale drawing of the gear train so that it suddenly becomes easy to set it up. It all sounds complicated, but if you just click through the steps you will quickly get the hang of it!

    In the first screen of results from the program when you have two compound gears you will see two columns labelled 'Top Line of GTR' and 'Bottom Line of GTR' and SOLVE. The concept of driver and driven gears is described in more detail below but gear ratios are always calculated as driver/driven. The top line is all the drivers and the bottom line is all the driven gears. If you multiply the top line together and divide it by all the items in the bottom line multiplied together, you get the gear train ratio (GTR). But the program does this for you.

    The reason it is done this way is that there will be 5 gears altogether for the mini-lathe. (There would be six for lathes where the stud gear can be changed such as Emco.) The two numbers in the top line can be switched and the three numbers in the bottom line can be shuffled 6 ways giving a total of 12 possible combinations all with the same GTR. The thread these various combinations produce are all the same, with the same % error. Doing it this way reduces the number of results in the main table by a factor of 12. A typical result may have 100 solutions on the first table, but it would be 100 x 12 = 1200 if we displayed them all.

    Why bother with the 12 different combinations? Some of the combinations fit together better than others. The program tries to find the ones that do not clash and marks them with **. The ones with low errors are marked with ##. Some may have an error of zero and they are marked ###.

    Finally, when you click 'DRAW' the program produces the scale drawing and just glancing at this can tell you whether a gear is likely to hit the shaft of the next pair of gears. So take your pick!

    For metric threads the pitch is proportional to GTR.
    eg if there is no gearbox,

    threadPitch = leadscrewPitch x GTR

    But for an imperial thread, TPI is proportional to 1/GTR eg if there is no gearbox

    TPI = leadscrewTPI /GTR

    That is why you see the gear train ratio listed on tables for imperial lathes as 1/GTR. If there is a gearbox you can check the calculations by multiplying 1/GTR by the gearbox ratio to get the thread pitch or TPI. They are both displayed with FYI to indicate that you don't really need them.

    THREAD TABLES ON MINI-LATHES:
    Chinese Minilathes have a peculiar way of labelling their gears as described above. They are labelled according to the way they are mounted on their stud shafts.

    A drawing of the gears in the Mini Lathe gear train

    A photo of the gears in the gear train

    The following table shows the gear train setup needed to produce various feed rates. The top section shows the layout of gears (described later). The icon in the middle section shows power feed moving the carriage along in an operation sometimes called 'sliding'. The direction of movement is 'longitudinal'. The bottom section of the table has an icon that is supposed to illustrate the 'facing' operation with power feed applied to the cross-slide for lateral movement. Feed rates are in inches per turn of the chuck.

    We can calculate from these tables that the carriage feed rate is 0.300 times the lead-screw speed. This is because there are gears in the carriage that slow it down. There are further gears that slow down the cross feed rate and we can see from the table that it is 0.28 times the carriage feed rate. The cross feed rate relative to the screw cutting feed rate is 0.30 x 0.28=0.084. These ratios are typical of most lathes and are included in the specifications for this mini-lathe in the program and can be adjusted in Optional Entries. They are used if you request a feed rate instead of a thread in step 3.

    Of course C, A, B refer to the position of the gearbox knob. Notice that they are not in the usual order A,B,C. From various tables I was able to determine that the gear ratios of the gearbox are in the following proportions"

    C=4
    A=2
    B=1

    These values can be used to calculate pitch or feed rates. Pitch is proportional to the gear ratios provided by the gearbox and gear train (GTR). High gear ratios cause the leadscrew to turn faster resulting in a long pitch or fast feed rate. Nice and tidy and the equation is relatively simple:

    Pitch = gearboxRatio x leadscrewPitch x GTR

    and in this case the gearboxRatios given above for knob positions C, A, B. This is the equation we use for metric lathes. It is correct for calculating pitch or feed rates eg (inches/turn), but threads per inch (turns/inch) are the inverse of pitch or feed rates. When the program calculates threads per inch (TPI) it uses this equation:

    TPI = factorF x leadscrewTPI / GTR

    In this case factorF is a number representing the gearbox position, but it is inverted because it must be proportional to TPI (not pitch). All very confusing! The gearbox factor (which we call factorF) is taken from the numbers on the manufacturers table which is usually printed on the lathe, and they are TPI values. So the table of factorF values for TPI is inverted compared with a table used for pitch or feed rate. This explains why the factorF values are 1/gearRatios. It might have been tidier if we kept the gearboxRatio on the bottom line with GTR, but then we could not use the manufacturers tables directly. The program was initially written for an imperial lathe and this is the way it has been done! The resulting table of factorF values for imperial calculations is the inverse of gear ratios:

    C=1
    A=0.5
    B=0.25

    A table of gears used to produce various feed rates


    On the following diagram I have drawn lines representing the transfer of power through the gears. Although the stud gear is unlabelled on the mini-lathe diagram, it's size is important in determining the overall gear train ratio (GTR), so it has been included in the display output. Most mini-lathes have 40 teeth machined into the spindle shaft, but occasionally lathes are made with a larger spindle so that a larger hole can be bored through the center to accommodate bigger rods. These may have 55 teeth. This can be changed in Optional Entries.

    The red lines in the illustration show gears meshing e.g. the stud gear meshes with the 63 tooth gear. The blue lines indicate that power is transferred through the key into the next gear ie compound gears. So the 63 tooth gear is keyed to the 30 tooth gear. It then meshes with an 80 tooth gear which is keyed to a 40 tooth gear. That finally meshes with the 75 tooth lead-screw gear. The letter H in the diagram indicates that you use a spacer to hold the lead-screw gear in place. Notice that the diagram shows the gears arranged in two planes.

    What is the gear train ratio of this setup? The program calculates it for you but FYI: The convention is that the gears are considered as 'driver' or 'driven' in this sequence:
    driver-driven-driver-driven-driver-driven.

    The gear ratios are always calculated as driver/driven. It may seem counterintuitive, but because a compound gear is in the middle of a chain, the first gear in a compound pair is 'driven' by the gear before it, while the second gear keyed to it is a 'driver' for the next gear and therefore its contribution to the GTR is driver/driven = second-gear/first-gear. Because of this it is usual to calculate ratios at the points where two gears mesh rather than looking at each compound pair separately. But since compound gears are added extras, I often think about the gear ratio they are contributing to the gear train.

    For the gears in the drawing, starting with a stud gear of 40 and calculating ratios where the gears mesh:
    GTR= 40/63 x 30/80 x 40/75 = 0.127
    Note that the program would have reported:
    Top line of GTR = 55 x 30 x 40
    Bottom Line of GTR = 63 x 80 x 75

    Since we are calculating a feed-rate, which is like a pitch, we use the pitch equation above. So we multiply by the pitch of lead-screw in inches: 1/16 inch
    0.127 x 1/16 = 0.00793
    Multiply by the gear ratio of position B on the gearbox
    ie 1.0 giving 0.00793
    Applying the power feed gear ratios in the carriage mentioned above, the carriage feed is 0.3x the lead-screw feed rate:
    0.00793 x 0.3 = 0.0024
    and the table says 0.0025 which is close enough. Eureka!


    A drawing of the gears in the gear train

    Now we can apply what we have learned to the metric thread table:

    A drawing of the gears in the gear train

    CALCULATING THREADS FROM MINI-LATHE TABLES

    This is essentially the same as the above example for calculating feed rates, but there are a couple of different gear layouts used. Looking at the table for a metric thread with a pitch of 0.7mm we we see a layout with two compound pairs of gears being used the same way as the feed rates table.

    But for a pitch of 1.5mm they use only one compound pair (joined by a key). Remember that in all these diagrams the stud/spindle gear is not shown but it has to be used in the calculations. Furthermore, the first gear shown in the case of a 1.5mm pitch is 63, but it is just an idler gear used to fill the gap and is completely ignored in the calculations. idler gears have no effect on gear ratios. It is as though the 40 tooth stud/spindle gear is meshing directly with the 55 tooth gear. So, the gear train ratio GTR is:
    GTR = 40/55 x 39/60 = 0.47272
    Now we have to multiply by the pitch of the lead-screw in metric units:
    lead-screw pitch = 25.4 * 1/16 = 1.5875 mm
    Screw pitch = 0.47272 x 1.5875 mm = 0.750
    This matches the table for gearbox position C=1
    For position A: 0.750 x 2 = 1.50 mm pitch.
    And position C: 0.750 x 4 = 3 mm pitch.
    The table says to use gear position A for a pitch of 1.5mm, so this is correct. These calculations were used to check that the program is producing the correct results, and it is. Remember, if we run through the same process for TPI we have to use the TPI equation with the table of gearbox factorF values which are inverted!


    This is the designation assigned to the Emco Maximat 7 lathe in line with the other mini-lathes. It has no screw-cutting gearbox. The lead-screw is imperial with 16 TPI. This Austrian lathe differs from the Chinese Mini-Lathes because it has the old style tumbler gears for reversing the direction of rotation of the lead-screw. This has the advantage that the stud gear (which they label gear W) CAN be changed, whereas this gear cannot be changed on most Chinese mini-lathes. That is why it is listed separately. This lathe is also listed in the next section as the Emco Maximat 7. The information was found on John Socha-Leialoha's Youtube Channel where he is known as JohnSL. His YouTube video about the gear train on this lathe is embedded below. It is interesting that the method used to label the gears is similar to that used by Chinese lathes and this may be their forerunner. It is recommended that you use the same system to label gears as that used by RideTheGearTrain, because the Chinese methods will not work for calculating gear train ratios and it is difficult to translate between the two systems.
    Click the yellow help button (?) to learn about the labelling systems used by mini-lathes.


    Thanks to John SL for allowing me to use material from his YouTube channel. Rather than being listed in the lathe list under the Emco brand this lathe is labelled along with other mini-lathes as "Mini_Lathe_Tumbler_No_Gearbox_Leadscrew_16TPI" and is described in the section above. Please also see Chinese mini-lathes and how gears are labelled This lathe has an imperial lead-screw with 16TPI. It was made in Austria.

    We can easily get bogged down working out how gears are labelled. If you use RideTheGearTrain it is simplest to use the gear labels provided by the program. But a brief overview may help make the terminology clear. What I call the stud gear, Emco call gear W. What I call the lead-screw gear (or LSG) they call gear L. The gears in between could be none, one, or two compound gears which can be specified in RideTheGearTrain. The lathe may have a table showing gear trains for various threads, and they label their compound gears with the letter 'Z' in a similar fashion to Chinese lathes. The problem is that the gears are not listed in the order required to calculate the gear ratio of the gear train. It is based on the way gears are positioned on their shafts. The outside gears are shown in the left column, and inside gears (closest the the lathe head) are in the right column with H as a spacer when no gear is required in that position. Since this lathe was made in Austria it is likely that this method originated in Austria or Germany. This lathe comes with an adapter which allows you to use any gears in your set to make up compound gears. This means that you can use automatic mode to calculate the ways these gears can be combined into compound pairs and automatic mode is selected for you when you choose this lathe.

    In the setup John SL demonstrated in his video, for a 1mm pitch, the stud gear has 40 teeth, then the gear with 50 teeth is an idler which does not contribute to the overall gear ratio and you can ignore it. It basically fills the space and reverses the direction of rotation. Then there is a compound pair. They are the two gears connected together with the black adapter with a key. (This adapter is the same as the one described for Myford and Boxford lathes.) The compound pair consists of a driven gear with 55 teeth connected to a driving gear with 65. They alter the gear ratio by a factor of 65/55. Then finally the 65 gear is connected to the lead-screw gear with 75 teeth. The stud gear and lead-screw gear contribute a gear ratio of 40/75 and this is modified by the insertion of the compound gear. So the overall gear train ratio (GTR) is 40/75 x 65/55. Most people prefer to write this in order: 40/55 x 65/75 but the result is the same. We multiply this gear train ratio (GTR) by the pitch (or TPI) of the lead-screw itself. Since we know this produces a metric thread with 1mm pitch I calculated that it has an imperial lead-screw with 16 threads per inch.

    Once the pitch of the leadscrew is known and there is no gearbox, and a list of gears has been entered, the program has all the information it needs to calculate gear trains.


    Find Compound Conversion Gears to
    convert an imperial lathe to cut metric threads or
    convert a metric lathe to cut imperial threads .

    The 'RideTheGearTrain' program can create a list of various compound gears. These are pairs of gears connected together by a key or rivet. For conversion from imperial to metric the larger of the pair of gears is driven by the stud gear and the smaller gear drives the lead-screw gear. These special compound gears are often called 'transposing gears'.

    Some lathes do not provide a way to use any two change gears to make up a compound gear. That is the case with Boxford lathes, but an adapter can be made to solve this problem and then RideTheGearTrain can be used in 'Automatic' mode to mix and match gears, so click the link.

    In case you had the preferences for instructions turned off I think it is worth repeating the instructions here (in italics).

    Enter the gear ratio you require in the box.

    The default is 1.27 for converting between imperial and metric. This is used because 1.27 * 2 = 2.54 which is the conversion factor. The ratio 1.27 is used to convert imperial to metric. The inverse ratios are used to convert metric to imperial and this can be achieved simply by flipping the compound gear over e.g. 100/127.

    Other ratios can be used for the conversion, as explained in the help file. The ideal conversion gear for converting an imperial lathe to metric is a compound gear with 127/100 teeth, but actually you can use any gear combined with the 127 tooth gear to give conversions without any error.

    eg 127/80, 127/100, 127/120, 127/130, 127/135 etc.

    For metric to imperial you could use any ratio with 127 on the bottom line:
    eg 80/127, 100/127, 120/127, 130/127, 135/127 etc.
    You need to be able to compensate for these deviations from the 100 gear. eg if you use 127/80 instead of 127/100 you can compensate with stud and leadscrew gear(LSG) eg stud=100, LSG=80 or stud=50 and LSG=40 or using gearbox settings.

    The program allows you to enter the ratio e.g. 1.27 or any fraction containing a "/" as in 127/120. The display tells you other gear combinations that give approximately the same ratio is you selected, and shows the percentage error with these combinations. Any gear combination you choose can be tested in the geartrain program (see Help).

    A close approximation is 80/63 and 63 can be used in place of 127. But if you enter 80/63 which is 1.2698, which has -0.01574% error, the program calculates errors relative to 1.2698, not relative to 1.27, so we have to add % errors together. They could cancel if one is positive and the other negative.

    Other uses for compound gears include the ratio Pi=3.14159 for modulus and diametric pitch.

    This function does not use any of the lathe data you entered above for gear train calculations!

    HOW TO TEST THE CONVERSION GEARS YOU SELECTED

    Ride the gear train can help you do this.
    Of course just running the program in the usual way will test it. But if you want to force it to use your new compound gears with specific stud and LSG gears, this is how you can do it.

    Select the lathe as 'Imperial with no gearbox' or 'Metric with no gearbox'.
    Go to 'Optional Entries' in the main menu.
    Scoll down to 'Changeable Stud Gear or Spindle Gear?'.
    Say no, and enter the number of teeth on the stud gear.
    Scoll down to 'Changeable gear on the leadscrew or gearbox?'
    Again enter NO and enter the number of teeth on the LSG.
    Scroll down and check that the leadscrew pitch is correct.
    Go to Step 2 'Gear Selection' and choose 'One Compound Pair'.
    Scroll down and select 'No Automatic Compound Gears'.
    Scroll down and enter your new compound gear in the compound gear list.
    Delete any compound gear that was there previously.
    Now you can run the program to see what threads it can produce.
    You might like to use Step 5B to enter a range of threads to test all in one run.

    FURTHER DISCUSSION OF CONVERSION GEARS

    For conversion from metric to imperial exactly the same gear pair can be used but the pair is flipped over so that the stud gear drives the smaller gear, that is connected to the larger gear, which drives the lead-screw gear.

    This is possible because the gear ratio required for the first conversion is the inverse (1/x) of the second conversion and vice versa.

    Although one ratio, and its inverse, will work for both conversions there are many other ratios that could be used by applying 'corrections' with the gearbox or other change gears. This program allows you to enter a ratio and will produce a list of all the gear combinations that produce this ratio.

    However, multiples of 127/100 are not the only compound gears that could be used. These 'transposing' gear ratios have the advantage of working to produce any metric thread.
    (RideTheGearTrain may find other combinations that work for the specific thread you have requested by combining them with other gear combinations, but may not be useful for all metric threads.) However, I have devised a procedure for finding many compound gears that can work the same way as 127/100 if small errors are acceptable.

    The gear ratio of 1.058333 makes a metric 3mm leadscrew behave like an 8TPI imperial leadscrew. The compound gear can be flipped over to get the inverse ratio 0.94488. to make an 8TPI imperial leadscrew behave like a metric 3mm leadscrew. These gears can be used to convert between imperial and metric on any lathe with lead screw pitch of 3mm or 8TPI or multiples of these e.g. 2, 4, 8, 16 TPI and 1.5, 3, 6 mm pitch leadscrews.

    Similarly 1.5875 can be used to convert a 2mm pitch into 8TPI. which would work for leadscrews with pitches of 1, 2, 4, 6, 8 mm. This is calculated from 1/8 * 25.4 / 2. Also these ratios can be altered by any other gears in the gear train and/or gearbox and the possibilities seem endless.

    This leads us to the question of what metric leadscrews do we want to imitate by applying gear ratios to an imperial leadscrew with 8 TPI? Given that one compound pair can be combined with various stud, and leadcsrew combinations we could look at imitating metric leadscrews with primary numbers: 1,2,3,5,7 mm pitch.

    Let's look at the general equation for calculating these ratios:

    Let Rim represent the ratio for converting imperial to metric.
    Let Lsi represent the imperial leadscrew TPI (eg 8) and
    Let Lsm represent the pitch of a metric leadscrew in mm.

    Rim = 1/Lsi * 25,4 / Lsm

    Notice that if Lsi * Lsm = 20 then Rim = 1.27
    eg when Lsi=8 TPI imitating Lsm=2.5mm pitch.
    or when Lsi=4 TPI imitating Lsm=5mm pitch.
    or when Lsi=2 TPI imitating Lsm=10mm pitch.

    Let's apply this where Lsi=8 then

    Rim = 3.175 / Lsm

    Lsi=8 and Lsm=7 gives Rim = 0.453571428
    Lsi=8 and Lsm=6 gives Rim = 0.5291666
    Lsi=8 and Lsm=5 gives Rim = 0.635
    Lsi=8 and Lsm=4 gives Rim = 0.79375
    Lsi=8 and Lsm=3 gives Rim = 1.058333
    Lsi=8 and Lsm=2 gives Rim = 1.5875
    Lsi=8 and Lsm=1 gives Rim = 3.175

    But then we have the question, which one of these should we use? That depends on what other gears it is being modified by (stud, leadscrew gear and gearbox). The answer is probably any of them. In the above table Lsm=6 gives 0.5291666 but if we combine it with stud gear=40 and leadscrew gear 20, giving a ratio of 2.0 we can multiply 0.5291666 by 2 to produce 1.0583332. This is the same ratio that we had previously.

    In the case of Boxford lathes, they made imperial lathes with 8 TPI and metric lathes with 3mm pitch and I noticed that they used the same gear ratios in their gearboxes. The ratio Rim for 3mm is closest to one because 1/8 inch is 3.175mm which is quite close to 3. So I think the rule should be to choose the ratio closest to 1. i.e. 1.058333.

    Now let's look at an imperial leadscrew in multiples of two eg 4 TPI.
    Now the equation is

    Rim = 6.35 / Lsm

    Lsi=4 and Lsm=7 gives Rim = 0.90714285
    Lsi=4 and Lsm=6 gives Rim = 1.058333
    Lsi=4 and Lsm=5 gives Rim = 1.27
    Lsi=4 and Lsm=4 gives Rim = 1.5875
    Lsi=4 and Lsm=3 gives Rim = 2.11666
    Lsi=4 and Lsm=2 gives Rim = 3.175
    Lsi=4 and Lsm=1 gives Rim = 6.35

    The program chooses an integer for the smaller gear and calculates the larger gear. Try using a gear ratio of Pi = 3.1415826. The resulting compound gears can be used to cut worm gears instead of threads using Diametral Pitch (DP) in imperial units or Modulus in metric.

    One inch = 2.54 cm is an exact conversion defined by the International Bureau of Weights and Measures. But instead of using 2.54 as the conversion factor, it is more common to divide it by two and use 1.27. This is 'corrected' by introducing a factor of two in the gearbox settings, or altering the stud and lead-screw gears by a factor of two. So, one commonly used pair of compound gears is a 127 tooth gear connected to a 100 tooth gear. It should be possible to use this conversion on any lathe. Another common variation is 127/120 and again using 120 can be compensated by other gears in the system. An advantage of this compound gear is that the 127 and 120 tooth gears are almost the same size, and this makes it easier to mesh with other small gears without using an idler gear.

    There are many other pairs of gears that give a good approximation to the ratio of 1.27 and the list shown for this ratio may allow a user to find gears in their collection that will work.

    Some lathes allow you to combine any two gears to make a compound pair. But other older lathes require two different sets of gears because the compound gears have a different sized hole in the center. However, some lathes like Myford provide an adapter allowing you to combine any gears, while nother manufacturers don't bother. In that case you can make your own adapter. Elsewhere in this file there is a photograph of an adapter for Boxford lathes.

    The user can check the results using RideTheGearTrain software on this site. RideTheGearTrain tries all possible combinations of gears and may come up with unexpected ratios that actually work for the thread pitch requested, without using one of the standard conversion compound gears. If you can use any gears to make compound pairs, use the 'Automatic Compound Pairs' feature in step 2 of RideTheGearTrain.

    How to try out a particular pair of compound gears for conversion between metric and imperial: You can choose a particular compound gear for general conversion eg one of those on the list, and enter that pair into the list of compound gears in RideTheGearTrain on its own. Delete all the other compound gears, but keep your own list of change gears. You could enter a particular thread pitch or TPI you want, but instead it may be more useful to enter a range of thread pitches. This would allow you to list all the more common types of threads, showing what change gears (and/or gearbox settings) you require and the % error for each. Using this method you can decide which sets of compound gears and change gears suits you best.

    The 127/100 conversion gear: Using the 127/100 conversion gear with the larger gear transfering power to the smaller gear slows down the lead-screw by 100/127. Note that to calculate the contribution of a compound gear to the overall gear train ratio, you have to invert the numbers. The imperial (English) lathe has a lead-screw pitch of 1/8 inch=0.125 inches. Now 0.125 x 100/127 = 0.09842 inches.Multiply by 25.4 gives 2.5000 mm pitch exactly. This calculation is exact because 127 on the bottom line ends up being multiplied by 25.5. Now 25.4/127 = 1/5 exactly. This can be adjusted by any pair of gears to multiply the result by 5, giving an exact integer solution. This compound This gear makes the imperial lathe behave as though it has a lead-screw with a pitch of 2.5 mm. Varying the other gears in the gear train and gearbox can produce a wide range of multiples of 2.5mm such as 1.25mm or 5mm. What happens if we flip this compound gear over, and the gear ratio becomes 127/100 instead of 100/127? Our 1/8 inch pitch leadscrew becomes 0.125 x 127/100 = 0.15875 inches. Now multipling by 25.4 gives 4.03225 mm pitch which is only 0.8 % more than a 4mm leadscrew pitch and this could be used to produce metric threads with acceptable accuracy. When we convert from metric pitch to imperial we divide by 25.4. Here the top line includes 127 and 127/25.4 =5 exactly, and that is why we get an exact integer measurement in imperial.

    The 135/127 conversion gear: This program was originally written with Boxford and other South Bend Lathes in mind. These lathes are standardized with 3mm pitch lead-screws on metric lathes and 8 threads per inch on imperial lathes. Conversions may be preferred where the metric lathe with its 3mm pitch behaves like an imperial lathe with 1/8 inch pitch and this requires a gear ratio of 0.94488 . Similarly the imperial lathe with 1/8 inch pitch can be made to look like a metric lathe with 3 mm pitch using a ratio of 1/0.94488 = 1.058333.
    Inverting the ratio like this can be done simply by flipping the pair of gears over so that the driven gear becomes the driving gear and vice versa. (By the way, some lathes use compound conversion gears 91/86 = 1.05814 giving a pretty good approximation of this ratio.)

    The following explains how these ratios were calculated: Converting the 3mm metric pitch to inches 3mm / 25.4 = 0.11811 inches pitch. We want to convert this to 1/8 inch pitch =0.125 inches. To convert 0.11811 inches to 0.125 inches we have to multiply by 0.125 / 0.11811 = 1.058333. The gear ratio required, 1.058333, is the inverse of 0.94489 we found earlier.

    Lets calculate what larger gear should be paired with a 127 tooth gear: 127 x 1.058333 = 134.4 which must be rounded to the nearest integer 134 or 135. Thus a 127 tooth gear connected to a 135 tooth gear will do the conversion with a small error. (According to this calculation a 127/134 compound pair will also work with a very slightly smaller error.) The gears have to increase the pitch slightly (from 3mm to 3.175mm which is 1/8 inch), which requires the lead-screw to rotate faster, and this requires that the smaller gear of a compound pair drives the larger gear (increasing the number of teeth per turn). So the stud gear drives the smaller of the compound gears which is connected to a larger gear which drives the lead-screw. This gives a gear ratio of 135/127. Checking again, 3mm x 135/127 = 3.18898 mm. Divide by 25.4 gives 0.12555 inches aproximating a lead-screw pitch of 0.125 or 1/8 inch with 0.44% error. However you will find below that this compound gear can give 0% error.

    What if you flip the compound gear over to give a ratio of 127/135 instead of 135/127? On the Boxford Users Group Richard K. pointed out that this compound gear with a 3mm lead-screw gives 3 * 127 / 135 = 2.822mm or 1/9" of carriage travel, so the 127/135 compound effectively converts a metric 3mm lead-screw to a 9 tpi imperial lead-screw. This seems weird but can easily be changed to a 1/8 inch lead-screw pitch by using a stud gear of 40 and a lead-screw gear of 45 so 3 * 127 / 135 * 40/45 = 3.175mm. Dividing by 25.4 gives 0.125 inches or 1/8 inch lead-screw exactly. So you are better off flipping this gear over and using these stud and lead-screw gears! Welcome to the weird and wonderful world of compound gears! When we convert from metric pitch to imperial we divide by 25.4. Here the top line includes 127 and 127/25.4 =5 exactly, and that is why we get an exact integer measurement in imperial.

    The 76/65 conversion gear: Another conversion gear I have come across is 76/65 = 1.16923. When used on a metric lathe with a pitch of 3mm we get 3 x 65/76 = 2.5658 mm. If we divide 2.5658/25.4 = 10.101 so this conversion makes the metric lathe behave like one with a lead-screw with 10 TPI with an error of 1%.

    Will the gears fit? Another reason that this particular compound pair (135/127) is used may be that it fits onto the standard stud gear and lead-screw gear etc. The difference between the radius of the large gear and the radius of the smaller gear must be sufficient to allow the stud gear and lead-screw gear to mesh with it. It may seem obvious to use a compound gear ratio of 2.54 rather than the usual 1.27. However this results in a compound gear with 127 teeth driving a 50 tooth gear. The difference in sizes of these gears would make it difficult to mesh with a small stud or lead-screw gear. The 127/100 pair has gear sizes that are closer together, and 127/120 or 135/127 are even better. The closer the gear ratio is to 1.0, the closer the two gears are to being the same size. Keep this in mind when you enter the ratio in this program.

    Actually, the gear sizes can be calculated from the diametral pitch DP, of the gear teeth which for Boxford lathes is 18. This is the number of teeth on the gear divided by the pitch circle diameter ie the diameter in inches of the gear at the point where the teeth make contact (about half way between the root and crest of the teeth). This is analogous to threads per inch and is used in the imperial system. The 'modulus' is used in the metric system: pitch circle diameter in mm divided by the number of teeth, which is similar to a metric thread pitch in mm. However the diameter and radius of a gear is proportional to the number of teeth. In determining whether a compound gear can mesh with another gear we only need to use number of teeth as a substitute for the actual radius.

    In the computer program for finding compound gears that approximate a particular gear ratio, it loops through all reasonable gear sizes one at a time. Of course the number of teeth must be an integer. Then we multiply by the required gear ratio to calculate the size of the second gear. The results may be slightly different due to rounding numbers to create integers.



    A user of the program need not be concerned with the equations and methods used to calculate TPI or pitch, but it may be of interest that I devised simple methods for determining the TPI produced by any gearbox setting on the imperial Boxford lathe. Similar methods are used for the Boxford metric lathe (below) and many other lathes listed in the program. Nearly all lathes have one of the levers or knobs with gear ratios increasing in powers of 2 eg 1,2,4,8,16. Numerical values are assigned to each of the gearbox lever positions in proportion to the gear ratios. One set corresponds to a column in the table normally attached to the screw cutting gearbox. The other set corresponds to a row. These tables are usually designed to be used with a standard set of gears in the gear train. (However Chinese lathes generally use a more complicated system with 4 knobs and also varying gears in the gear train.)

    FOR THE LEVER MARKED WITH LETTERS ON THE IMPERIAL NORTON STYLE GEARBOX
    A-1
    B-2
    C-4
    D-8
    E-16
    (all in powers of 2, from 1 up to 2 to the power of 4)

    FOR THE NUMBERED LEVER
    1-8
    2-9
    3-10
    4-11
    5-11.5
    6-12
    7-13
    8-14

    Drawings of the gears inside the Boxford 'Norton' gearbox show a bank of output gears with 16, 18, 20, 22, 23, 24, 26, 28 and they mesh with a 20 tooth gear. If you divide these by two you see where the values assigned to the numbered positions come from.


    Multiplying the letter value by the number value we get a value I call Ffactor. This must be multiplied by a constant which I call the 'primaryRatio' to get threads per inch or pitch. (The program displays the equations used.)

    TPI = primaryRatio x Ffactor x leadscrewTPI / GTR

    For lathes without a gearbox, primaryRatio=1 and Ffactor=1 so

    TPI = leadscrewTPI / GTR

    To make a thread with the same TPI as the lead-screw (eg 8 TPI), GTR must be one. This generally requires two gears with the same number of teeth if you do not have a gearbox.

    The first three factors are related to the gearbox and lead-screw and in the program they are lumped together and called the gearbox ratio:

    TPI = gearboxRatio / GTR

    where
    gearboxRatio = primaryRatio x Ffactor x leadscrewTPI

    For the imperial Boxford Model A lathes with a gearbox, the standard gears are stud 20 and lead-screw 56 giving a ratio of 1/2.8. Now by rearranging the above equation we can calculate the constant I call the primary ratio:

    primaryRatio = TPI x GTR / (Ffactor x leadscrewTPI)

    This can be calculated from any valid thread on the table. To calculate primaryRatio for a particular gearbox I like to use the settings where TPI is the same as the leadscrewTPI. Then they cancel out and the equation becomes:

    primaryRatio = GTR / Ffactor

    For the Boxford
    primaryRatio = 1 / (2.8 x Ffactor)

    Where Ffactor corresponds with the gearbox lever positions used to cut a thread the same as the lead-screw. In this case the Boxford A imperial lead-screw has 8 TPI and the Ffactor for 8 TPI is actually 8, so

    primaryRatio = 1 / (2.8 x 8) = 1/22.4 = 0.04464.

    This constant can now be included in the first equation for TPI and used with any gear train ratio. It can be considered a kind of calibration and compensates for any constants introduced when numbers were assigned to the levers.

    In imperial lathes the equation includes division by GTR. The program displays 1/GTR as well as the overall gear ratio of the gearbox (shown above) so that these two numbers can be multiplied together to calculate TPI and the user can check the calculations.

    In the standard setup the idler gear has no effect and can have any number of teeth. However, the idler can be replaced by a pair of two compound gears providing exotic threads such as metric threads or odd numbers. This provides an additional gear ratio that has to be included in GTR.

    The full set of equations used in the computer program is for a gear train with up to 6 gears in sequence. When combined with a long list of gears to choose from this can produce millions of possible combinations.

    Lets review the actual sequence of operations in the program. We have an outer loop which calculates every possible combination of gears in the gear train. For each combination we try out every possible combination of lever positions and look up the Ffactor for each one. Then we can calculate the overall gearbox ratio described above. We can then use the above equation to calculate the TPI for this "random" setup. We compare this with the required TPI and calculate the percentage error it would produce.
    error = 100 * (TPI - requiredTPI) / requiredTPI

    Only the combinations of gears that produce the acceptable error, or better, are diplayed and sorted with smallest errors listed first. Sometimes a metric equivalent is required and the TPI is simply converted into pitch as follows:

    pitch(mm) = 25.4 / TPI

    This method was derived by studying the gear train, lead-screw and the labels for the screw cutting gearboxes on different lathes (like the one below from my imperial or English Boxford A), and this is what I would need to analyze other lathes.

    Label showing gears to use for screw cutting on the Boxford Lathe



    I have given the solution for the primary ratio above. We know that the imperial lead-screw is 8 TPI. Position A1 on the gearbox produces 8 TPI with the standard setup. In this case the overall gear ratio from spindle to lead-screw must be 1:1 to give 8 TPI. We can therefore calculate the constant that is required to give an overall ratio of 1:1. This takes into account all of the variables in the system. Evaluating setting A1 on the gearbox we find the value assigned to lever position 1 is 8, and value assigned to lever position A is 1. Multiplying these together gives an Ffactor of 8. So Ffactor=8 corresponds to a thread with 8 TPI. This is with the standard gear train setup with stud gear 20 and lead-screw 56, so clearly the gear ratio of the gearbox at this setting is not 1 as you might have expected for 8 TPI. The gear ratio of the standard gear train is 20/56=1/2.8 so the fundamental gearbox ratio must be 2.8 to compensate. The constant 'Primary Ratio' is multiplied by the leadscrewTPI and factor F so these have to be taken into account as well using the equation given above.

    If we now look at lathes without a gearbox the situation is simpler but interesting. Obviously with an 8TPI lead-screw to cut a thread with 8 TPI you need 1:1 gear ratio ie the gear train ratio=1. We calculate the TPI from the formula

    TPI = primaryRatio * factorF * leadscrewTPI / GTR

    The primaryRatio can be calculated from any thread data where the gearbox ratio (factorF) and GTR are known for a given thread (TPI):

    primaryRatio = TPI * GTR /( factorF * leadscrewTPI )

    In the absence of a gearbox we assign the gearbox ratio to 1.0 ie factorF=1 and primaryRatio is 1.0 so

    TPI = leadscrewTPI / GTR

    Again, to cut a thread the same as the lead-screw requires GTR=1.



    The primaryRatio for metric lathes can be calculated in a similar fashion to imperial lathes. In this case the equation for pitch is

    pitch = GTR * leadscrewPitch * primaryRatio * Ffactor

    Rearranging this equation we can get the primaryRatio:

    primaryRatio = pitch / ( GTR * leadscrewPitch * Ffactor )

    The lead-screw has a pitch of 3mm and the gearbox setting for 3 mm is D1 and D1 corresponds with factorF=8x15=120 derived from the numbers assigned to the letter lever and numbered lever described in detail below. The standard setup for metric lathes uses a stud gear with 20 teeth driving a lead-screw gear with 45 teeth, (and any gear as an idler in between. Again the idler wheel does not affect the gear train ratio.). A small gear driving a larger gear slows down rotation so the gear ratio produced by these stud and lead-screw gears should be smaller than one i.e. the gear train ratio is GTR=20/45. Using the above equation:

    primaryRatio = 3 /( 20/45 * 3 * 120 ) = 3 / 160

    primaryRatio = 0.01875 exactly

    This is the primaryRatio I actually use. It incorporates all the variables involved including the fundamental gear ratio of the gearbox and a constant (8) that was included to produce convenient integer values for the letter lever and numbered lever on the gearbox.

    It can also be helpful to look at other charts such as English-metric conversions on the aluminium label shown above to check the accuracy.



    Since we have an equation to calulate TPI or pitch from gearbox factor F, we can reverse the equation to calculate factor F from the required TPI. This means that we may not have to loop through all 40 gearbox settings trying every F value. Instead we can calculate it in a single step. If it does not correspond exactly with one of the Ffactor values in the tables, we can choose one smaller and one bigger to calculate the thread pitch or TPI and the error relative to the required value. This should make the program run about 20 times faster. However, if there are too many steps in the calculations, it can actually take the computer longer.

    For imperial lathes:
    TPI = primaryRatio * Ffactor * leadscrewTPI / GTR

    Ffactor = TPI * GTR / (primaryRatio * leadscrew)

    For Metric lathes:

    pitch = GTR * primaryRatio * Ffactor * leadscrewPitch

    Ffactor = pitch / (GTR * primaryRatio * leadscrewPitch)

    Also if the gears were sorted into order, smallest to largest, we could work out when the F value exceeds the range available in the gearbox, and then stop that loop early as there would be no advantage to continue trying bigger gears. However this became more complicated when fixed pairs of compound gears were introduced as these pairs can be flipped over. Also the calculation of (GTR * primaryRatio * leadscrewPitch) has been moved out of the inner loops of the program as they remain constant and do not have to be recalculated every time.



    I devised methods similar to the imperial method for determining the pitch produced by any gearbox setting on the metric Boxford lathe. The method was derived from this metric Boxford lathe screw-cutting gearbox label thanks to Andy P. on the Boxford Users Group.

    Label showing gears to use for screw cutting on the metric Boxford Lathe

    The label below is useful for checking the accuracy of calculations of imperial threads on a metric Boxford lathe, and was also used to find out what change wheel and compound gears may be available on these lathes. There are a lot on this chart! :

    Label showing gears to use for screw cutting imperial threads on the metric Boxford Lathe


    Numerical values are assigned to each of the gearbox lever positions as follows:

    FOR THE NUMBERED LEVER (on the left)
    1-15
    2-14
    3-13
    4-12
    5-11
    6-10
    7-9
    8-8

    (Actually you could use 16 minus the lever number to get its value.)

    In order to get integer numbers for the letter table below, I multiplied all the letter values by 8. This resulted in a table which looks remarkably similar to the imperial lathe table! (When the "primaryRatio" is calculated it automatically includes this value, 8.)

    VALUES ASSIGNED TO THE LETTER LEVER (the lever on the right side of metric lathes)

    A-1
    B-2
    C-4
    D-8

    Actually these are powers of 2 like the imperial lathe and most other lathes as well.

    To calculate the pitch we start by multiplying the letter value by the number value to give factor F. Multiply F by the gear ratio of the gear train on the back of the headstock and multiply by the 'primaryRatio' (calculated above) to get the pitch. The primaryRatio takes into account the fundamental gear ratio of the gearbox, and dividing by 8 to compensate for the letter code I used.

    If you do not include these standard gears in your change wheel set, you may be surprised that there are certain threads you cannot cut. The thread that causes the most problems is one equal to the lead-screw thread. Without a gearbox you need a 1:1 gear ratio for the gear train, and this often requires you to have two identical gears in your list. With a gearbox it is less obvious because the gearbox does not have a 1:1 gear ratio on any of its settings. Instead it requires you to use the standard gears: Stud=20 and lead-screw-45 for metric lathes and Stud=20 with lead-screw=56 for imperial lathes.

    In the standard setup the idler gear has no effect and can have any number of teeth. It is placed between the stud gear and lead-screw gear, just to fill the space. It should be noted however that it reverses the direction of rotation. Although this can be corrected using the reversing tumblers it can be confusing and lead to mistakes.

    The idler can be replaced by a pair of compound gears providing exotic threads such as English threads or odd numbers. The pair of gear wheels joined together to make a compound pair are referred to as Comp-1 and Comp-2 in the results table.

    For convenience in programming the idler gear is considered to be a pair of compound gears with the same number of teeth. So again this has no effect on the gear train ratio and they can have any number of teeth. But if the two compound wheels (comp-1 and comp-2) have different numbers of teeth they do have an effect on the gear ratio and this is an additional gear ratio that has to be included in the equations.



    Gear ratios are always calculated as driver gear over driven gear and it is important to understand how diver and driven are assigned. Since idler gears have no effect of the gear ratios they are ignored in this process. As noted previously we can ignore any gears prior to the stud gear. The first gear that affects the gear train ratio is the stud gear and it drives all the other gears, so it is logically a driver. If there is only an idler wheel between the stud gear and lead-screw gear (which is the last gear in the train) then the lead-screw gear is 'driven' by the stud gear (ignoring the idler). Thus the gear ratio is driver/driven and the number of teeth on the stud gear is divided by the number of teeth on the lead-screw gear. This is the gear train ratio (GTR) when there is no compound gear.

    Now if we replace the idler with a compound pair of gears the stud gear drives the first of the compound gears (comp-1) which is considered a driven gear. It is connected to the second gear (comp-2) and it drives the lead-screw gear. So comp-2 is a driver and the lead-screw gear remains a driven gear. I prefer to calculate the contribution of the compound pair as comp-2/comp-1 and multiply that by stud / lead-screw to get the GTR.



    The gearbox makes setting up a lathe for gear cutting much simpler. Although the Boxford Model A does have a gearbox, Models B & C and their derivatives BUD and CUD, do not. But for the hobbyist who has more time to fiddle with gears it may not be such a big issue. It can get complicated with several different kinds of gear arrangements shown in this label from a Boxford lathe (see Know Your Lathe and Lathes.co.uk).

    Label showing gears to use for screw cutting on the Boxford Lathe without a gearbox

    The computer program may be especially helpful when using these lathes. The same equations are used except that the gearbox is considered to have only one gear with a gear ratio of one. The conversion factor that I call the primaryRatio is 1, and is multiplied by the number of threads per inch on the lead-screw on imperial lathes. It is also equal to the pitch of the lead-screw in metric lathes. Actually the analysis of these lathes is simpler without a gearbox.

    Fig.1 in the black label above includes two compound gears, but the first is simply for converting from imperial to metric and will not be varied. You can tell the computer program that this is not am imperial lathe but a metric lathe with a lead-screw pitch of 2.5mm as explained earlier but you don't have to do it that way. There appears to be a second compound gear consisting of a 72 tooth gear and an 18 tooth gear. But on closer inspection this is misleading. The 18 tooth gear is not connected to anything and is simply used to keep the 72 tooth gear in the correct position. The 72 tooth gear is being used as an idler gear and has no effect on the gear ratios. Consequently this 72/18 gear can be completely ignored!
    Fig.2 is functionally exactly the same as Figure 1. The only difference is that as the lead-screw gear is increased in size it will mesh more easily with other gears and there is no longer any need for an idler gear.
    Fig.3 in the black label above shows two pairs of compound gears making a total of 6 gears in sequence! If they could all be varied there would be millions of combinations. However, that is not the intention of these diagrams. They are not varying these compound gears. The first in the series is the standard gear for allowing metric threads to be cut on an imperial lathe (127/100) and this has the effect of making the lathe behave like a metric lathe with a lead-screw pitch of 2.5mm (as discussed earlier). This can be entered into the computer as a metric lathe without a gearbox and change the lead-screw pitch to 2.5 in the Optional Entries section of the menu. But you do not have to do it that way. You can leave it as an imperial lathe and ask it to produce metric threads. No problem. Often you can get the results you want without even using a special imperial to metric conversion gear. If not you can use the special conversion gear 127/100 teeth, or some other ratio approximating 2.54:1. You can even use the program to list all possible imperial to metric conversions gear combinations. See List all compound gears for converting between metric and imperial.

    The second gear is a 72 tooth gear driving an 18 tooth gear (keyed together). This slows the rate of rotation by 18/72 = 1/4. Since this is not going to be varied it can be accounted for in the fudge factor. A lead-screw turning 4 times slower will produce a metric thread with a shorter pitch, so the fudge factor should be 1/4 = 0 .25. (If this had been an imperial thread with a lead-screw turning 4 times slower it would increase the threads per inch by a factor of 4, so the fudge factor would be 4.). Otherwise you could just include a fixed 72/18 compound gear in your list of compound gears. It will include that in your gear train if necessary, but will also try flipping it over. It is quite likely that the program will come up with solutions that do not even require such a complex gear train.

    In summary Figure 3 can be represented by entering data for a metric lathe with lead-screw pitch of 2.5 mm and fudge factor of 0.25. A second compound gear probably isn't necessary. Now the program will vary the stud gear and the lead-screw gear to find the thread you want. So a situation that looked complicated turns out to be quite simple when it comes to entering the data into the computer program. (There is a similar situation with the Logan 200 lathe described elsewhere in this document.)

    I have checked the pitches that require Figure 3 setup on this machine label and found that they can be solved with a single compound pair if you are able to make up unusual compound pairs such as an 18 tooth gear driving a 63 tooth gear giving 0.0125% error for pitches of 20,25,30,35mm. Let me know if you have any problems with this.



    I have now found the link to software used on PCs and again it is at Lathes.co.uk. I had seen it mentioned previously in a discussion thread on the Boxford Users Group called "Changing Boxford changewheels" but forgot where I had seen it. I received a very nice comment on the instruction video from the author of that program, Barney C. and I appreciate that! I have now read the instructions that come with the software. Like my program it goes through all the possible combinations and permutations of gear wheels to find which ones give the greatest accuracy. It is designed for use on any model of lathe, but it appears to be more complicated to use. The gear ratios of the screw-cutting gearbox have to be entered but they can be saved on your own computer. Unlike this program it will run with your laptop in a workshop with no internet access, but it will not run on phones or tablets or Apple products. I have also found a couple of other internet based programs and thread tables. There is a program at The Little Machine Shop web site. I discovered another internet based program online by Duncan who is a member of the Model-Engineers users group. An advatage is that it is easy to use, but with less flexibility and fewer features than RideTheGearGTrain.



    This is a list compiled by Tony Griffith (of Lathes.co.uk) who mentioned that there may have been 22 manufacturers of these clones. Many of them may have the same gearbox ratios as the Boxford in which case this program could be used directly.
    Boxford lathe,
    Harrisons lathe
    Hercus lathe,
    Purcell lathe,
    Joinville lathe,
    Ace lathe,
    Sanches Blanes Lathe,
    Sheraton lathe,
    Smart & Brown lathe,
    Storebro lathe,
    UFP lathe,
    Boffelli and Finazzi lathe,
    Demco lathe,
    NTSC lathe,
    Select lathe,
    Parkanson lathe,
    Lin Huan lathe
    Mathew and Moody lathes,
    Blomqvist
    Asbrinks,
    David 600,
    Fragham LHB,
    UFP lathe,
    Selson lathe,



    Certain models of Logan lathes in the '200' range apparently have no lead-screw gearbox and that makes the programming simpler. This software can be used with ANY lathe without a gearbox. The imperial Logan lathe has a lead-screw with 8 TPI. As explained above under the heading 'Converting Imperial lathes to cut metric threads', metric conversion gears can be used and then the software can be used as though it is a metric lathe with a non-standard lead-screw pitch of 2.5mm.

    It is interesting to analyze the complicated looking diagrams of gear train setups that are recommended for the Logan lathe. But in real life I would ignore all that and let RideTheGearTrain tell me what gear train is required.

    It is interesting to review the white chart below for metric pitches. The fact that it says a 2.5mm pitch requires a gear train ratio of 1.0 when there is no gearbox confirms the conclusion that it behaves like a metric lathe with a lead-screw pitch of 2.5mm. On the same line of the table the stud and lead-screw gears both have 60 teeth, so again this is a gear ratio of 1.0. This is used with a gearbox setting of 16 and at that setting the gearbox ratio must also be 1.0 so that the overall gear ratio of the gear train and gearbox combined is 1 (ignoring the conversion gear). That way a thread with a pitch that is equal to the effective lead-screw pitch of 2.5mm is produced. (This is different to the Boxford lathe which does not have a 1.0 gearbox ratio available.)

    The bottom drawing of a gear train shows the addition of a second compound gear but it is not actually functioning as a compound gear at all. It is simply used as an idler wheel that does not affect the gear ratios at all. It is used to fill the space and transfer the drive from the real compound metric conversion gear to the lead-screw gear. As smaller lead-screw gears are used for courser threads they cannot mesh directly with the metric conversion gear. So why use a compound gear marked clearly as a 72 tooth gear connected to an 18 tooth gear? The smaller gear is used as a spacer to get the larger 72 tooth gear on the same plane as the 100 tooth compound gear. It happens to be one of the standard compound gears.

    The black plate from a logan lathe shows some gear train diagrams that look very complicated. It would have looked simpler if they left out the reversing tumbler gears that have no effect on the gear ratio. There are also idler wheels in figures 1 and 2 and they can be ignored. These are actually pretty standard gear trains.

    Figure I has the stud gear driving an idler driving the lead-screw gear. The gear ratio for the whole gear train is simply 'teeth on the stud gear' divided by 'teeth on the lead-screw gear'.

    Figure II does insert a compound wheel with the stud gear driving the 54 tooth gear which is connected to an 18 tooth gear which connects to the lead-screw gear, via an idler that has no effect. The big gear of the pair driving a smaller wheel means that it slows down the output to the lead-screw gear. So we want a ratio smaller than one and we multiply the whole gear ratio (originally stud/lead-screw) by the small compound gear over the large compound gear ie 18/54 = 1/3. But this is an imperial lathe so a lead-screw gear turning at 1/6 speed will produce threads with the TPI increased 6 fold, so the fudge factor will be 6. If a similar gear train had been used on a metric lathe the fudge factor would be 1/6, because slower rotation of the lead-screw produces a shorter pitch.

    Figure III is the really complicated one, but actually analyzed easily. It is recommended for turning threads finer than 64 TPI or very fine tool feed rates. This time there are 6 gears in the chain and if you could vary them all you would have tens of millions of possible gear ratios. However the interesting thing is that they have no intention of varying them. You are expected to use the two compound gears they have shown, and no others. Once that is set up you only need to vary the stud and lead-screw gears as usual. I have blown up Figure III and you can see that the stud gear drives the larger wheel with 48 teeth connected to a smaller gear with 24 teeth. This will cut the gear ratio exactly in half since 24/48=1/2. Now the output from this compound pair is sent to the second compound pair. The smaller wheel provides the output to the larger wheel (with 54 teeth) of the second compound gear and that is connected to the smaller 18 tooth gear, so this pair will again slow down the chain by a factor of 18/54 = 1/3. This smaller wheel drives a fairly large and variable wheel on the lead-screw. The overall gear ratio was initially stud/lead-screw but now that is multiplied by 24/48 (ie 1/2) for the first compound gear, and the result is multiplied by 18/54=1/3 for the second compound gear. The overall effect of the two compund gears is 24/48 * 18/54 = 0.1666 = 1/6. So the lead-screw runs at 1/6th of the speed that it would without these two compound gears. (Perhaps it could have been done with a 20 tooth gear driving a 120 tooth gear or 18 driving a 108 tooth gear ie only one compound gear instead of two).

    The computer program is most commonly used with one compound gear where both wheels are variable. However these diagrams can easily be accommodated by entering a fudge factor. The primaryRatio is multiplied by the fudge factor you enter. On imperial lathes the TPI is proportional to the modified primary ratio. If the lead-screw is turning at 1/6th speed the TPI will be increased by a factor of 6.

    We would not need a fudge factor for Figure I, but for Figure II we could use a fudge factor of 3 or and for Figure III the fudge factor is 6. Then you could use it with or without adding a third compound gear! Simplest without. The program will tell you what stud and lead-screw gears to use for a particular thread with these three setups.

    If it was a metric lathe the pitch is proportional to the primary ratio and again the primary ratio is multiplied by the fudge factor. But this time, slowing the lead-screw by 6 decreases the pitch so a fudge factor of 1/6 is required for metric lathes.

    Any of the gear trains for this lathe could be combined with imperial to metric conversion compound gears. Then you could tell the program that you have a metric lathe with a lead-screw having an effective pitch of 2.5mm. That could even be combined with any of the three gear trains in Fig.III by including the fudge factors of 1, 1/3 or 1/6 as explained above. The black table also shows feed rates. These are 0.1 * pitch but it doesn't say whether this is longitudinal or cross feed rate. Generally they document longitudinal feed and some lathes do not have power cross-slide feed.

    Drawings on a label showing gears to use for screw cutting
                 metric threads on the imperial Logan Lathe


    Label showing gears to use for screw cutting metric
                 threads on the imperial Logan Lathe


    Label showing gears to use for screw cutting metric threads on the imperial Logan Lathe


    Label showing gears to use for screw cutting imperial
                 threads on the imperial Logan Lathe



    A large lathe with a gearbox with a rotary dial and numbered lever. The rotary dial lever has 10 positions, but 5 are disengaged and marked 'OUT'. The other 5 positions have labels for the lead-screw including EQUAL meaning 1:1 ratio:
    1:1 at the 7 O'Clock position on the dial (also marked 13)
    2:1 at the 12 O'Clock position (26/13) and
    4:1 at the 5 O'Clock position (52/13).
    38/13 = 2.92:1 at the 2 O'Clock position.
    18/13 = 1.38:1 at the 10 O'Clock position.

    The 5 positions can also be used for Carriage feed rate and turret or capstan drive:
    Numbers for carriage feed are 38/152 = 1/4 of thread cutting speed.
    Numbers for the turret are 38/193 = 1/5 (approximately) times thread cutting speed.
    The metric conversion chart suggests they use 127/150 compound gear or equivalent.



    This Raglan lathe was in Nottingham, UK in 1954. It was owned by "Winky's Workshop" who has a famous YouTube channel. Thanks to Winky for providing the information and for his great videos and electrifying projects!

    This lathe has a Norton style gearbox and 8 TPI lead-screw like the Boxford and South Bend clones. Although they call it a "Norton Gearbox" it is missing the 11.5 TPI found on South Bend clones and the 9.5 TPI found on Myfords. It has a lever with three positions labelled A,B,C to add gear ratios of 0.5, 1, and 2 instead of the usual "lettered lever" with ratios of 1,2,4,8.

    Terminology was not standardized and can be confusing. Most people call the pair of reversing gears tumblers but Raglan calls their letter lever a tumbler. What I call the "numbered lever" they call the "sector lever". What we call simply "The Stud Gear", they call "Stud E" and the "lead-screw gear" they call "Stud D". The compound or idler wheel is on "Stud F" on the banjo or quadrant. If a compound gear is placed on "Stud F" between the stud and lead-screw gears, they label the gear driven by the "Stud E" as "gear A". It is connected to "gear B" which is driving the lead-screw gear or "Stud D". The gear ratio which is provided by this compound pair is "gear B"/"gear A".

    The ratios they assign to the letter lever are arranged so that they are proportional to TPI, but TPI is proportional to 1/GTR. I have to invert their ratios to calculate the true GTR. This reverses the labels on the letter lever to C,B,A instead of A,B,C.

    They use a constant of 2/5 in calculating TPI. I use a similar constant and named it the "Primary Ratio" because all the gearbox ratios have to be multiplied by this constant. This varies according to the values assigned to the gearbox levers and standard gear train.

    The lead-screw is the "standard imperial" 8 TPI. The standard change gears have diametric pitch of DP=14 when a gearbox is fitted.

    The standard "British" gear train they recommend for 8 TPI is : stud=40 leadscrewGear=50 idler=39 gearbox B1 which is marked 16TPI. From these I calculated the primary ratio of 1/20=0.05. Using this value the results of this program match their tables. The compound gear used for metric conversion is 39/33 but any other conversion can be substituted.




    The Norton gearbox was developed by W.P Norton about 1886. Some other gearboxes are not identical but similar in concept and can be easily built into this program. On imperial lathes the standard Norton gearbox has two levers. The lever on the left has 5 positions marked with letters. The right lever has 8 numbered positions giving a total of 40 possible gear ratios. The metric version has the numbered lever on the left and letter lever on the right giving 32 gear ratios. One way to check that it is a Norton imperial gearbox is to compare the gearbox label with the table generated by this program. Otherwise look at row B on the table which should show this sequence: 8,9,10,11, 11.5 ,12,13,14. Also check that the standard gear train has a stud gear with either 20 or 40 teeth and a lead-screw gear with 56 teeth. With the 20 tooth stud gear, the gear train gear ratio is 1/2.8. To compensate for this standard gear train, all the gearbox ratios must be 2.8 times bigger than expected.



    A medium sized lathe with a numbered gearbox (no letter lever)



    A large British lathe with number and letter gearbox levers. It has a flat overhead belt drive and is fitted with a taper turning attachment.



    Grizzly_G0752_G0602_imperial. The Grizzly lathes are manufactured in China for an American company. They are popular with gunsmiths, especially the models with long beds.

    Grizzly_G0750G is also included here. It has a 36 inch long bed. This model uses an unusually complex, but somewhat limited, gearbox necessitating the use of change wheels (gears). Matthew Helton and Micheal Kennedy did a detailed analysis of the lathe and produced a spreadsheet of all the gear ratios. I appreciate them sending it to me so that I could include this lathe.



    A solid Chinese lathe 640mm swing x 1000mm bed. This model, made in 1992 and owned by Michael Evans in Perth, Australia, has an unusually complex gearbox which actually functions like three lathes, one for cutting metric threads, another for imperial and a third for power feeds. It is designed so that you cannot mix and match gear ratios from each set. A number wheel marked 1-10 has the usual gear ratios in metric, but when in imperial mode the ratios are inverted. I think they must switch the input and output gears. Imperial lathes use TPI which is the inverse of pitch. I have created gear ratio tables for metric and then converted the imperial tables to metric and added those as well.



    Owned by Dirk Van der Walt in South Africa. Apparently the Chinese lathe with CO codes probably come from the Seig factory. This is fitted with a full thread-cutting and feed gearbox which has 4 knobs. This produces 64 possible gear combinations. However, 16 of them have the same gear ratios. So gearbox codes may include V4*, S2*, T3*, or R1*, but these 4 codes give the same ratios and the codes can be switched around. The least confusing solution is to include them all. I placed a * beside them so that you realize they are all the same ie redundant codes.

    This is a medium sized lathe with a 360mm swing diameter increasing to 502mm swing over the gap in the bed. The length is 1000mm between centers. The spindle bore is quite large at 52mm. There is no manufacturer's name but the title of the file containing the pdf manual is THMT, suggesting that it was supplied by TH Machine Tools in South Africa. That has been confirmed by the owner.




    The Himount Imperial Lathe is a Taiwanese lathe built in 1983. The gearbox is not quite the same as Norton gearbox. It does not have 9.5 or 11.5 TPI like most other lathes. This lathe is being used by Thames Auto Electrical, New Zealand. There is no information about a metric version of this lathe.




    This Craftsman lathe was manufactured by Atlas Lathes and sold by Sears and Roebuck in USA. This one is owned by a friend in Texas who sent the specifications.
    His Model Number is 101.28940, with Serial Number 004894.

    This lathe has a special gear lever marked 'E' to control feed rates, but this lever is not used for cutting threads. The table has the following carriage feed rates in inches per revolution:

    Eout 0.0078 0.0069 0.0063 0.0057 0.0055 0.0052 0.0048 0.0044 0.0042

    If these values are inverted (1/x) you get TPI. I found that Eout can be added to the thread chart, which allows the program to use it for calculating feed rates. I changed its label to EoutFEED. If you are requesting a thread and you see solutions using EoutFEED you have to ignore them because this gear setting can only be used for Feed Rates. Conversely, if you request a feed rate and you see other gear settings, they can only be used by engaging the half-nuts as though you are cutting a thread and it probably won't work for the cross feed.




    Colchester_Master_imperial is an old medium sized lathe listed by lathes.co.uk.




    This lathe is owned by Gary Ferrer in Vancouver. The Dominion lathes were made for export from their factory in Colchester, UK. It has a swing of 13 inches diameter. Date of manufacture is thought to be about 1961-62.



    The Chester Crusader is a metric lathe owned by Barry Dewett in UK.



    'A large imperial lathe 44" swing x 196" between centers. Manufactured in USA by "Niles & Erfurt", this imperial lathe has a gearbox. It is located in Nova Scotia Canada. Blair Mullen provided the details about this lathe.


    This is a very large lathe, 16 feet in length. Blair Mullen kindly provided the information required to include this lathe. He works on reconditioning hydraulic rams for large diggers used in open cast mining. He says it was made in USA as an "oilfield lathe" but is currently located in Nova Scotia, Canada.


    This imperial lathe was built in 1937 and is located in UK. The first gear in the train, which we refer to as the "Stud Gear", they call "Reversing Frame Gear". The gear we refer to as the leadscrew gear is called the "The Wheel on the Guide Screw" Both gears can be changed with a selection of change gears. Compound gears can be added in between and they can be made up from pairs of change gears. This means that the software can use Automatic mode. There is a gearbox lever with three positions marked A,B,C. But B is only used to provide slow carriage feed rates and does not feature on the thread cutting chart. Their chart does include a range of feed rates and metric threads, as well as the list of standard change gears. Thanks Roger for sending the data.

    The gear lever on the Denham lathe
    The gear train on the Denham lathe
    The table of gears to use on the Denham lathe for cutting threads


    Choose a standard thread from reference tables using the drop-down menus. There is a set of imperial standards and a set for metric, but they are all presented on the same page. The program displays a lot of specifications and information about the thread you chose. There is an explanation of why the percent thread depth is used.

    The idea behind the program is that most drill tables will tell you one drill size to use, but you may not have that size, especially if you are a hobbyist. The program produces tables of common drill sizes and the percentage thread depth. From that you can choose a drill that you DO have in your collection and see what percentage thread depth will be achieved. The standard recommended depth is 75%. But if your nearest drill is 60% or 80% you may be perfectly happy with that. If it is 30% you probably realize that you need to go and buy the right drill.

    Two or three tables are displayed. These list common drill sizes for metric, imperial and number/letter drills. The number/letter drills are based on old wire gauges and are obsolete in most counties, but still use in USA. For each percentage thread depth ranging from 30 to 100, the table shows the percentage then the nearest drill that will get close to that percentage. Since it is not a perfect match, the actual percentage is calculated and displayed.

    Percentage thread Depth: Why is the recommended depth only 75%? The main reason is that the amount of torque you have to apply increases exponentially as the percentage increases, but the strength of the resulting thread levels off at about 75%. At high percentages there is substantially increased risk of breaking a tap.

    A second reason is that the commonly used two fluted taps have a 'forming effect' as well as 'cutting' the thread. That means that the pressure applied forces metal up from the root of the thread into the crest. This can produce close to 100% thread, even though a 75% drill was used. Obviously this is likely to be more effective with softer materials like aluminium than it is with stainless steel.

    The recommended percentage was mentioned in an old book "Workshop calculations tables and formula" by FJ Camm (1959) based on standards from about 1951 for tapping drill sizes expressed as percentage of thread depth:
    Class A 95% hand tapping
    Class B 87% hand tapping
    class C 75% for power tapping

    Clearance drills
    Class A 1% over major diameter
    Class B 2.5%
    Class C 5%


    This stand-alone program works out how much offset to use when you plan to turn a shallow taper by the tailstock offset method (also called the 'setover method'). The result depends on the length of the bar you place between centers as well as the length of the machined taper or angle.

    Before you change the alignment of your tailstock, check it first, and then check it the same way afterwards. Place a center in the tailstock. Remove the chuck and place another center in the spindle. This might require a morse taper adapter eg M3 to M2. Slide the tailstock up to the spindle center. They should line up perfectly. If they do not line up before you turn the taper you will at least know that you did not cause the problem.

    Data entry for this program is divided into three sets on separate web pages. The first set of three numbers are the dimensions of the taper and these should all be in the same units eg all inches or all mm. You do not need to enter any units such as mm or inches because the program uses ratios and angles. Angles are all in degrees.

    (You do not need to enter any of the lathe data used by the gear train calculator in the main menu.) Full instructions follow, but there is a relatively simple example to follow after that. It's a good place to start your first run.

    INSTRUCTIONS

    • The program attempts to calculate any numbers that are left blank.

    • The First Set of entries consists of 3 dimensions as seen in the diagram including two diameters and the machined length of taper: D1, D2, Lm. These are generally obtained from an engineering drawing where Lm is measured parallel to the axis of the object. (see discussion of sin and tan functions below.)

    • The First Set can be skipped and left completely blank if you do not need these dimensions and do not want to use a standard taper from the drop-down menus. In this case enter one of the numbers in the Second Set (angle or taper). You do NOT need to enter all six numbers on this page. Enter any one of them and the program will calculate the other five. They are provided for your general information, but they also allow you to choose which one to enter.

    • You can use the drop-down menus to select a standard taper (eg Morse Taper). Selecting one of these automatically provides all three dimensions for the First Set and the manual inputs can be left blank or filled with numbers from a previous calculation. They are ignored in this case.

    • Alternatively you can enter all 3 dimensions in the First Set manually, using the input boxes below the drop-down menus. Make sure the drop-down menus have not been selected if you want manual input.

    • Once the first three numbers have been entered the program will calculate the taper and skip the Second Set of data entry.

    • If the First Set only has two numbers assigned, the program can calculate the third item later, but it will require the angle. In this case you need to provide ONE number in the Second Set:

    • The Second Set is for entering the taper, angle or half-angle. Six different ways of specifying the taper are provided, but you only need to enter ONE of them. The program will calculate the other five.

    • The Third Set is usually used for calculating the offset from the taper. If you enter the length between center (Lcc) and leave the offset (S) blank, it will calculate the offset from the half-angle.

    • Alternatively in the Third Set you can enter the offset (S) and leave the length between centers (Lcc) blank. Then the program will calculate Lcc, the length of barstock required.

    • If you get to the Third Set of data input, and the taper half-angle is still unknown, it can be calculated if you can provide both the length between centers (Lcc) and the offset (S).

    • To get started go to the main menu and find the orange button for Taper Turning.



    Menu Snapshot of Taper turning button

    This illustration is displayed:

    A drawing showing the bar mounted between centers with dimensions labeled.

    EXAMPLE
    It is a good idea to use this simple example first as it will show you what the results mean. Choose a standard Morse Taper MT3 taper from the drop-down menu marked 'MORSE'.

    Choose Morse taper 3

    Skip all other entries in the 'First Set' and 'Second Set' because they are provided by the standard.

    Go to the 'Third Set' of input data and enter the length between centers (Lcc). eg 300 mm. Click calculate. If you use mm the offset will be in mm. If you use 12 inches instead the offset will be in inches.


    Enter the length of the bar Lcc

    and it will produce the offset (S) and all the taper angles.

    THE RESULTS: (the diagram above helps you interpret the results:


    the results

    Note that you can use inches or mm. In this case the MT3 spec is in inches, but I entered the length of the bar stock as 300 mm. It applied the half-angle to calculate the offset in mm.

    There are many different ways you can enter data.

    In the First Set of data entry points, the program provides drop-down menus for some standard tapers. This allows you to choose a standard taper such as Morse Taper MT3. The main thing the program needs is the angle of the taper. These standards use a taper definition consisting of the length of the machined taper, and its diameter at the smallest and largest ends of the taper.

    The user also has the option of entering the three dimensions manually. The program can calculate the taper from these dimensions. In that case the user does not need to enter the taper in the Second Set of data entry points.

    However, if the user does not want to use the drop-down menus and doesn't have these dimensions available, the Second Set of data entries can be used instead. There are 6 different ways the taper can be expressed but you only need to use one of these options. If you enter one, the program can calculate the other five. But keep in mind that if you used a standard taper or manually entered the 3 dimensions in the First Set, then you do not need to enter any taper data in the Second Set.

    Third Set: If you enter the distance between centers (Lcc), the program will calculate the tailstock offset (S) from the taper angle. Note that the length of the bar stock you plan to turn will be the same as the distance between centers. If you drill the center holes too deep it may alter the distance between centers slightly.

    There are two other, rather unusual ways the Third Set can be used. If you enter the offset (S) it will calculate the distance between centers (Lcc) from the angle of the taper.

    Alternatively, if the taper has not been calculated already and you enter both the length between centers (Lcc) and the offset (S) it will calculate the angle of the taper for you.

    Notes:The angle of the taper you can achieve is limited by how much offset you can set on the tailstock. Tapers made using this method are limited by this factor, but you can achieve steeper tapers by using shorter bar stock (Lcc) if your design allows it.

    These YouTube videos about this method may help to explain it better.



    Reference tables are provided so that you can look up standard tapers such as Morse tapers, Jacobs tapers and many others. Choose one of these standards and open the drop down list to select the size you need, eg Morse Taper #3.

    In this case you do not need to enter the taper angle in Step 2, and it takes you straight to the final stage, Step 3. In step three you simply enter the length of the shaft between centers (Lcc). Leave the offset (S) blank and it will calculate the tailstock offset.

    These tables contain information which allows the program to calculate the taper and its angle from the diameter at each end, and the length of the standard taper. You can see these numbers inserted into the program, as well as the angle and taper.


    The following YouTube video shows my method of turning a Morse taper by measuring the tailstock offset directly, using these calculations. You could use a dial gauge to set the offset with a single reading at the tailstock end of the bar using the calculations from this program. However, Quinn in her Blondihacks YouTube series shows an alternative method using two dial gauges (clock indicators).



    Quinn Dunkie's methods for taper turning.
    She demonstrates a very nice tailstock offset method in the second half.


    Engineers are generally aware of the fact that a taper can be calculated from the TAN of the half-angle. This is correct. So why did I use the SIN function to calculate the tailstock offset?

    Engineering drawings measure the length of the taper (Lm) along the axis of the turned object and define the taper as the change in radius per unit length. This is exactly equal to the TAN of the half angle shown in my drawings.

    But the situation changes when you put the barstock in a lathe and offset the tailstock. In this case we should use the SIN function. We can no longer use the taper ratio either because it is equal to the TAN function. The mathematical proof is shown below, but first I will try to describe the situation.

    TRIGONOMETRY REVIEW
    Lets take a step back and quickly review some basic trigonometry. Recall that trigonometry functions are based on right triangles with the hypotenuse opposite the right angle corner. In this case we are interested in the shallow "half angle" and the length of the taper forms the side adjacent to the half angle. The side opposite the half angle is the radius at the end of the tapered shaft, which is always measured at right angles to the axis. The TAN function is defined as opposite over adjacent and this is exactly the ratio that engineers use to describe a taper ratio ie change in radius with distance along the shaft is equal to the TAN of the half angle. This is correct. In contrast, the SIN function is the length of the opposite side divided by the length of the hypotenuse and the COS function is the length of the adjacent side over the length of the hypotenuse.

    DESCRIPTION OF THE PROBLEM WITH THE TAN FUNCTION
    We will use the half-angle provided by the engineering drawings and TAN of this angle gives the taper ratio. But once we put the object in the lathe with an offset tailstock the situation is different. In this case the length of the bar stock is positioned with its axis along the hypotenuse of the triangle. The right angle remains on the axis of the lathe and the hypotenuse is opposite this right angle. The length of the bar stock is the one measurement that is known with some accuracy and it corresponds with the distance between centers (assuming the center holes have not been drilled too deeply). So we should use an equation that is based on the hypotenuse of the triangle and the offset which is the side opposite the half angle. The function that tells us the relationship between the opposite side and the hypotenuse is the SIN function. We simply re-arrange this equation to calculate the offset from the half angle and the length of the hypotenuse (Lcc).

    But we need to look into this more closely. Lets think about what happens when we adjust the tailstock offset. The offset is generally provided by adjusting grub screws in the base of the tailstock, which cause the tailstock to move through a dovetail slot. This makes it clear that the tailstock movement we are trying to calculate IS a straight line at right angles to the bed.

    As we move the tailstock the bar rotates around an arc. The tailstock has to be moved, not only at right angles to the bed, but also moves slightly closer to the head of the lathe. These two movements could be considered using two vectors, one movement at right angles to the lathe bed, and the other movement parallel to the axis of the lathe. In calculating the offset all we want is the vector at right angles to lathe axis. If we use the SIN function we do not need to know the distance along the axis of the lathe. We use the hypotenuse Lcc instead. In that case we can ignore the change in the length along the adjacent side. It is not relevant. This means we ignore the vector along the axis of the lathe.

    MATHEMATICAL PROOF
    If we used the TAN function we would divide the offset by the adjacent side. The adjacent side is the slightly shortened distance along the lathe bed. Let's call this adjacent distance A, and call the half angle h, while S is the offset or "setover" distance and Lcc the length of the barstock.

    TAN(h) = Opposite side / Adjacent side

    TAN(h) = S / A

    Rearranging this equation

    S = A . TAN(h)

    This is the equation commonly used to calculate the offset assuming that A is equal to the distance between centers. Now TAN(h) exactly equals the "taper" ratio defined by the engineering drawings (T), so

    S= A. T

    But both of these equations are incorrect if we assume that A is the same as the length of the hypotenuse Lcc. This introduces an error because the adjacent side has been shortened slightly by the movement along an arc. We can calculate how much the adjacent side is shortened relative to the length of the barstock (Lcc). This adjustment is given by the COS function which tells us the ratio of the adjacent side divided by the length of the hypotenuse (Lcc).

    COS(h) = Adjacent side / Hypotenuse

    COS(h) = A / Lcc

    A = Lcc . COS(h)

    Now we can apply this correction to the equation using TAN:

    S = A. TAN(h)

    S = Lcc . COS(h) . TAN(h)

    But we know from trigonometry that

    TAN(h) = SIN(h) / COS(h)

    Now

    S = Lcc . COS(h) . SIN(h) / COS(h)

    The COS functions cancel, so

    S = Lcc . SIN(h)

    This is definitive proof that we should use the SIN function to calculate the offset S.

    Since TAN(h) is exactly equal to the taper ratio defined by the engineering drawing, it also means that this taper ratio cannot be used to calculate the offset accurately. It would need to be corrected by the COS function.

    METHODS OF MEASUREMENT
    This means that using a dial gauge or DRO to measure the travel of the carriage is also using the adjacent side and should ideally be adjusted by multiplying by the COS of the half angle. If the measurement was made along the axis of the bar stock it would be precise.

    e.g. A Morse Taper MT2 has a taper defined as 0.050" per inch along the axis of the taper. So if we measure 2 inches along the shaft and mark it we could use a dial gauge to measure the radius at that point, and adjust the radius at the end of the taper until the difference is 0.100" As the tailstock is moved, both radii would change and the process would have to be repeated unless the bar stock was exactly 2 inches long to begin with.

    EQUATIONS USED IN THE PROGRAM
    I use the inverse TAN function to work out the half angle (h) from the taper (T) given in engineering drawings:

    ARCTAN can also be written as
    ATAN or TAN-1.
    Read ATAN(Taper) as "give me the angle whose TAN is equal to the taper."

    If D1 and D2 are the diameters at each end of the taper and Lm is the length of the taper
    T = (D2 - D1 ) / ( 2 . Lm )

    Since

    T = TAN(h)

    h = ATAN( T )

    The full included angle is 2h degrees.

    Then to calculate the offset the program calculates

    S = Lcc . SIN(h)



    ESTIMATING THE ERROR
    How much difference does it really make if we use the TAN function as an approximation. For small angles the TAN and SIN functions produce almost the same results and this issue may not be important. However, the precision quoted for machine tapers is generally 0.0002 inches or 0.005 mm. Morse tapers have a half-angle of about 1.5 degrees and the difference between SIN and TAN is tiny 0.034% or 0.00034 inches on a 1 inch diameter. But it may still be enough to affect this level of precision (assuming that can be achieved with your lathe!).

    Lets take the most extreme tapers with half-angle of 8 degrees used in milling machines and ER-32 collets. For an 8 degree half-angle taper, using TAN instead of SIN causes 1% error. This works out to about 1mm difference in the offset for a 100mm long bar or in imperial units about 0.1 inch difference in the offset for a bar 10 inches long. That sounds significant, in practice you would probably use the compound slide method for a taper with a half-angle of 8 degrees, rather than the tailstock offset method.

    What is the most extreme angle that could be turned by the tailstock offset method? Of course it depends on the lathe. Lets say the maximum offset is 15mm and the shortest barstock you might turn is say 50mm, the taper would be 15/50=0.3 giving a half-angle of 16 degrees and in that case the difference between using a TAN function and a SIN function would be significant at 4.2%.


    SUMMARY
    In summary, the first three dimensions from an engineering drawing (in the First Set of data input) are used to calculate the half-angle using TAN. Once the angle has been obtained we use the SIN of the half-angle to calculate the offset.
    Offset = Lcc x sin(half-angle)

    (In the PHP programming language we also have to switch between degrees and radians.)



    Choosing this selection displays a few tables of the cutting speeds recommended for various metals of different hardness and different cutting tools. Scroll down for related topics.


    This is a simple calculator for calculating cutting speeds. It has three boxes where you can enter data:
    Cutting speed,
    Diameter
    RPM

    You can enter any two and leave the third item blank. When you click calculate, it fills in the blank entry. e.g. If you enter the cutting speed you want to use and the diameter, it will calculate the required RPM. For a lathe the diameter refers to the diameter of the material spinning in the lathe. For a milling machine or drill it is the diameter of the cutting tool. Before ariving at the calculator you specify whether you want metric or imperial (inch) measurements. In metric the diameter is in mm and cutting speed is converted to meters per minute. In imperial the units are inches and surface feet per minute sfm.


    The calculator mentioned above calculates the relationship between 3 variables:
    Cutting speed,
    Diameter
    RPM

    The same equations can be used to make a table to tell you what RPM is required for any diameter and cutting speed. The program allows you to design your own tables.
    You can enter the range of values to be shown in the rows and columns of the table.
    You can say whether you want the diameter in the rows or in the columns.
    You can say which number you want displayed in the middle of the table (called the body). Usually this will be RPM because that is what people want to know, but you could put cutting speed or diameter in the body of the table.
    You can specify the numbers that go in the rows and columns by setting starting value, ending value and step size. Step size is the increment, eg the amount the value increases in each column.
    You do not have to set these values for the body of the table.
    You can choose metric or imperial units


    You should be able to make your computer print the table shown on the screen, or share it and print later, or copy and paste, take a screen shot etc.

    In metric the diameter is in mm and cutting speed is in meters per minute.
    In imperial the units are inches and surface feet per minute sfm.



    The recommended cutting speeds described in the previous sections are mainly dependent of the hardness of the metal being turned in a lathe. Additional tables show the color of steel when it is heated prior to quenching during the hardening process. Another table shows the color of the oxidised surface of steel during the tempering process.

    Some tables show both hardness and cutting speeds. This allowed me to derive an equation relating the two. Due to scatter in the data it is not highly accurate, but probably suitable for most purposes when the hardness of a material is known, and we need to estimate the recommended cutting speed.

    Once the cutting speed is known we can use the cutting speed program provided here to calculate the required RPM. A table can also be produced for future reference.



    You can enter your own custom gearbox data and use it immediately. Instructions for using the program to enter Custom Gearbox data is in the next few sections. You will find the Custom Gearbox button at the bottom of the list of lathes in Step 1 and it now has its own button in the main menu. You can send me the necessary information and I can add your lathe as a permanent addition to the program. If you can't handle entering the data described below, you can just send it to me by email.

    After entering your custom data below, and selecting RUN, the URL will contain all the data I need. Then you can either send an email with the URL. You save the URL by selecting and copying the address bar and pasting it into a text document, or saving it as a bookmark or favourite or paste it into an email. Then you can go back to your custom data by clicking the saved URL at any time.

    The information you need is listed here.
    If you prefer you could send the following information to me by eMail.
    (1) Photo or drawing of the thread cutting gearbox table,
    (2) standard gear train to cut a thread the same as the lead-screw pitch,
    (3) lead-screw TPI or pitch
    (4) brand, model and year if possible, just to identify the lathe.
    (5) your name and/or email if you would like to be recognized.
    Contact me: a link to my email address is in the program heading or you can use AEDLewis at gmail dot com.


    The following sections describe each step of the process of entering teh data directly into this program. Once the data has been entered it is stored in the URL, and if you send it to me by email I can add your lathe to the permanent list.

    Label showing gears to use for screw cutting on the Boxford Lathe

    This copper plaque is the original thread table attached to the leadscrew gearbox on my Boxford A imperial lathe. Unfortunately they did not include the top row which should show the position of the numbered lever for each column ie 1, 2, 3, 4, 5, 6, 7, 8. Instead, the lever was right beside the chart, so you could move the lever to the appropriate column. Arrows pointing downwards point to the lever positions. The large numbers in the body of the table are threads per inch. The small numbers are carriage feed rates.

    If your table has extra rows which require a different stud gear or leadscrew gear, please ignore these rows in your table. All entries in the table must have the same gear train. The copper plate is a good example with one row requiring a stud gear with 40 teeth and all the others are 20 teeth.

    Cross slide feed rates are 0.3 times the carriage feeds.

    The examples and default values shown in the program define my Boxford Model A lathe. If you want to see how the program operates, just use these default values and compare them with the numbers on the copper plate. Enter "imperial" lathe with leadscrew 8 TPI.

    In all cases enter numbers without units eg 8 instead of 8TPI or 3 instead of 3mm.



    Find a suitable row in your thread cutting chart and copy it into the first input box in increasing order. Use numbers separated by commas like this
    . eg 8,9,10,11, 11.5, 12,13,14
    These represent pitch or TPI on the table and the program asks for these first. They are required to calculate the gear ratios.


    I usually choose the row and column containing the pitch (or TPI) of the leadscrew so that this number appears in both the row and column. In this example it would be 8 TPI. However, some lathes do not list the leadscrew pitch in the table.


    Each lever position requires two entries. We have talked about the first string of numbers. The second string required by the program merely contains symbols used to identify the position of the lever. For every number in the first string, there should be a symbol representing the position of the lever that produces that thread. So the number of items in each of these strings should be the same.

    You can use any symbols, and in any order. For the numbered lever on the Boxford the symbols are
    1, 2, 3, 4, 5, 6, 7, 8 and that is the default shown for the second input box. But you could substitute
    s,t,u,v,w,x,y,z or
    z,y,x,w,v,u,t,s if that is how your gear lever is labelled.


    Now we move on to the second gear lever which is commonly labelled with letters instead of numbers. It is defined by the next two input boxes, but the method is much the same as the first two input boxes. First we choose a column to copy. Ideally this is the column that contains the same number as the leadscrew. Since the leadscrew on the Boxford Imperial lathe has 8 threads per inch, we look for a column that contains 8 TPI. The row we chose earlier should also contain the same number.

    When you enter these numerical values they should be in increasing order. The threads shown in the columns usually increase in multiples of two as shown on the copper plate for the Boxford and this is the default list for the third entry box: 4,8,16,32,64,128.


    This is the fourth, and last, input box defining gear levers. It assigns a different symbol to each position of the second lever. Usually the positions of the lever are marked with letters or other "symbols". They are usually listed in the first column of the table as on the copper plate. The default values are A,B,C,D,E,F for the Boxford and these appear in the fourth input box in the program. Again, if your lathe uses other symbols for these gear positions you can simply substitute.


    Does Your Lathe Have Three or Four Gear Levers?
    If your lathe doesn't fit this exact pattern you can usually make up a similar system that works for you. eg if your lathe has 3 levers you can assign one lever with positions A, B, C and the second lever D, E, F and then combine the settings of two levers eg AE BF etc used in place of single letter symbols. Often these combined symbols are seen on the thread tables. This can be seen in the Boxford X10 lathe which has been listed already. This can get complicated because you may have to work out the gear ratios for each letter combination eg AE and BF. The same method can be used for four levers or more. If you contact me by email I can work it out for you.

    Does Your Lathe Have Only One Gear Lever?
    What if your lathe does not have a numbered lever? If it has a lever with letters instead of numbers you can simply replace the list of number symbols with a list of letters. If your lathe has a simple gearbox with only one lever you can eliminate the number lever by pretending that it has a second lever with only one position and a value of 1. Its symbol can be left as a blank space. Similarly you can eliminate the letter lever if necessary. Some lathes have a number lever and no letter lever.

    This lathe had a dial instead of a lever?
    There is a lot of flexibility in this system to accommodate any lever arrangement. Even dials can be accomodated and an example can be seen in the WARD lathe found in the 'Choose Lathe' list. In that case the symbols for positions were defined as 3 O'Clock, 6 O'Clock etc. If you need help, contact the author of the program. Contact details are shown just below the gold logo on the main menu.




    Studying the gear train in isolation can be useful for applying to other machines such as milling machines. The program will find gear trains with the GTR you require with the level of error you are willing to accept.

    (The 'GTR calculator' works by creating an imaginary metric machine with no gearbox and a lead-screw with a pitch of 1mm. It does the calculations for a metric thread with a pitch equal to the required GTR. Metric is used because pitch = GTR x leadscrewPitch, and lead-screw pitch is one, whereas imperial TPI is proportional to 1/GTR.)

    INSTRUCTIONS
    In Step 1 'Choose a lathe' you will find at the very end of the list of lathes 'GTR Calculator'. Select that.
    In Step 2 set up the gears any way you want, with 0,1 or 2 compound gears. You probably want automatic compound gears, and a good selection of change gears.
    Skip Step 3 which is automatically set to a metric thread.
    In Step 4 you choose 'acceptable error' which can be zero for an exact GTR or whatever you prefer.
    Use Step 5A enter the required GTR (gear train ratio) as a single number instead of the pitch.
    Skip 5B and 5C and go to Step 6 RUN.

    The display of results will show various possible gear trains. The minimum and maximum values of GTR that can be acheived with your gears is provided after the results, in a box with rounded corners and the heading LATHE SETUP.

    If your gear train does actually drive a lead-screw like a cross-slide, you can enter the lead-screw pitch in "OPTIONAL ENTRIES".

    If the gears in your change gears list can be used anywhere in the gear train, use the 'auto compound' button. This does not use the gears listed as compound gears, but will mix and match all possible combinations from one set of gears.

    USING THE GEAR TRAIN FOR INDEXING Jim in our Boxford users group asked about using the gear train as an indexing system to move the chuck a specified number of degrees. To do this we asked RideTheGearTrain for GTR=25 to give a 25:1 ratio where one turn of the LSG resulted in 1/25 turn of the stud, spindle and chuck. The amount of backlash in the gear train is likely to be significant and you would need to keep a constant load on it. It can be done but requires a rather complicated gear train and I think it would be better to use a circular saw blade attached to the spindle as I demonstrated in one of my YouTube videos on even-e-cent channel.

    I have seen a cat without a smile, but I have never seen a smile without a cat! (Alice in Wonderland by Lewis Carole.)



    The following images show my father's lathe before and after a clean-up, overhaul and paint job. And one of my favourite photos of my father at age 84, in his own garage, teaching my son, age 14, how to use his lathe. Three generations.

    A photo of my Boxford A Lathe before overhaul

    A photo of my Boxford A Lathe after overhaul


    My father teaching my son (age 14) how to use his lathe.