What change gears are needed to cut metric threads on an imperial lathe or imperial threads on a metric lathe.

evan-e-cent

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What change gears are needed to cut metric threads on an imperial lathe or imperial threads on a metric lathe.

This is probably the most common question involving the gear train. I have just completed a major update of RideTheGearTrain.com to help address this question. The only change that a user will see is a new option in Step 5B where you can run the program with more than one pitch or TPI. (try clicking the blue links.) The older method was to ask the user to enter a range of values from a low value, to a high value at fixed intervals. The problem with that is that the pitches in the M-metric series or BA etc are not equally spaced. So the new option is for the user to enter a LIST of pitches or TPI.

Efficiency Improvement:
Originally, if the user requested 25 values (eg the M-series of metric pitches), the program would run 25 times. Going through every possible gear train setup (and gearbox settings) requiring huge numbers of calculations and the program would take so much time that the server would kill it (time-out error). SO, the new version only goes through all the gear and gearbox settings once. With each setup it calculates the thread produced and then compares it with the list of required pitch or TPI values to see whether any of them are within the acceptable error. If so they are added to a results array. At the end the array is sorted and displayed. That required some major changes, but it is very useful.

How to enter a list of pitches or TPI:
Very simple really. Go through steps 1-4 to set up your lathe. In step 3 choose either imperial thread with TPI or metric thread with mm pitch. Choose Step 5B and click the radio button marked LIST. Type in a list of pitches or TPI you want to run. Then return to menu and RUN (step 6). However, instead of typing all the numbers yourself, the instructions display lists for standard threads: UNC/UNF/BSW, another for BA, and for the metric M-series etc. You can copy and paste these lists into the INPUT box to save you typing. You may choose a smaller set by just using part of the list.

HELP:
The help file now contains over 11,000 lines of text, photos and video links. There is a HELP button in the main menu. If you click that you can search the help file. Also each page of the program has several help buttons to take you directly to relevant chapters in the help file, so you don't have to read the whole lot! I will include some links to useful chapters below:

METRIC IMPERIAL TRANSPOSING GEARS
These are the compound gears that can be used to convert between metric and imperial. Keep in mind however, that you can often produce certain metric threads without using these special gears. Run RideTheGearTrain with a single pitch or TPI in Step 5A to find out whether you can produce the required thread.

The standard gear for conversion has 127 teeth and this is used because 2 x 127 =254 and the required conversion factor is 25.4 so this can give perfect conversions with 0% error. It can be combined with any other gear eg 100 to make 127/100, 127/120, 120/135 provided that you have other gears to compensate for these changes.

However if you are willing to accept small errors you can use other gear combinations. There it a special item on the menu called Metric-Imperial Conversion Gears. This does not require specific information about your lathe. You simply enter the gear ratio you require (in this case 1.27) and it lists the pairs of gears that will produce this ratio. It is quite surprising how many options are available. Click the blue help button under the heading. It is called Conversion Gears.

ADAPTER:
You may be able to use gears that you already have to make the conversion. More modern lathes allow you to use the change gears to make up compound pairs without connecting them permanently. Older lathes such as Boxford lathes which are South Bend clones, require an adapter to do this. Photos and drawings of the adapter are shown here in the help file and there are yellow HELP buttons in the program.

With this feature you can select Automatic Compound Gears when designing the gear train in Step 2A. If you select a gear train with one compound pair (2 gears joined together), combined with a stud gear and leadscrew gear that can be changed, you have 4 gears in the train. If you have 6 gear wheels to choose from the number of combinations the computer program tries automatically is 6 x 5 x 4 x 3 =360 and if you have a gearbox with 40 lever position you multiply that by 40 giving 14,400 combinations. If you had 10 gears to choose from there would be 10 x 9 x 8 x 7 = 5040 combinations x40 with a gearbox gives 201,600 possibilities. So there are a lot of possibilities. If you are really keen you can add a second pair of compound gears (which may require a second adapter) with 6 gears in the train and if you have 10 gears to choose from the number of calculations increases to 10 x 9 x 8 x 7 x 6 x 5 = 151,200 and with a gearbox x40 gives 6 million combinations. It is quite likely that you don't need a special metric conversion set.

ADJUSTING THE NUMBER OF RESULTS YOU GET
You may find that you get either too many or too few results. In that case you can make alterations and run the program again.

Increasing the acceptable error in Step 4 increases the number of results, and decreasing the error reduces the number of results.

Altering the geartrain design in Step 2A makes a big difference, as illustrated by the calculations above. It may be best to start with "No Compound Gears" with say 2% error, because this is the simplest to set up, but produces the fewest possible combinations. If this does not provide your answer try "One Compound Gear" without Automatic compound gears turned on. If you have an adapter or have a more modern lathe that does not require an adaper turn on Automatic Compound gears. This gives a lot more possibilities. Finally, you could try "Two Compound Gears" but this is much more complex to set up.

EXPERIMENTING WITH NEW GEARS
If you are unable to produce the threads you want, you can start experimenting by adding extra gears to your set of change gears. That way you can decide what new gear you might need to make or buy. Keep in mind that 3D printed plastic and composite gears are now readily available (as mentioned in previous posts).

One thing you might consider is a 127 tooth gear or an approximation such as the common 63/80 conversion set. But notice that 63 divided by 3 is 21, so a 21 tooth gears combined with other gears that can multiply by 3 may solve your problem, and another gear you could try is 21 x 2 = 42 teeth. So just try everything!

I have made video tutorials about how to use the program and they are shown at the bottom of the menu. But it is easy enough just to follow the Quick Start guide at the top of the menu. The process has been divided into several steps to make it easier to make changes after you have completed the first run. If you need more help or want your lathe added to the list, please don't hesitate to contact me.

Evan
 
A MAGIC number for conversion between metric and imperial:

With a bit more work I have derived an equation for calculating the gear ratio needed to make a general purpose metric-imperial conversion compound gear or 'transposing gear': It is independent of the kind of gearbox you have.The ratio to convert to metric can be inverted (1/x) to convert from imperial to metric. It can be inverted simply by taking the same pair of gears and flipping it over. So the same pair can be used for conversion either way.

For example, the general idea is to make a metric lathe with say 3mm pitch behave like an imperial lathe with 8 TPI leadscrew or conversely to make an imperial lathe with an 8TPI leadscrew behave like a metric lathe with say 3mm pitch.
In general terms we can
let the metric leadscrew pitch be Lm mm and
the desired imperial TPI be Li.

The equation for the gear ratio for the conversion is


R = 25.4 / ( Li * Lm )

You can see why the answer is the same for coversion either way. Also there are no gearbox numbers required.

eg to convert a 2.5mm pitch to 8 TPI

R = 25.4 / ( 2.5 * 8 ) = 25.4 / 20 = 1.27
This is very familiar and can be acheived with 127/100 gear combination.

Another example to convert from 3mm pitch to 8TPI

R = 25.4 / (3 x 8) = 25.4 /24 = 1.058333

If you want to use a gear with 127 teeth, multiply this ratio by 127 and you get approximately 135
hence the comon conversion gear 127/135.

To convert the other way you can invert this ratio (1/x) to give 0.94488.
This requires exactly the same pair of gears, just flipped over. (RideTheGearTrain automatically flips compound gears.)

Now to find what pairs of gears produce this ratio you run RideTheGearTrain and select the

metric-imperial compound gears button. Enter this ratio R= 1.058333 and it will show a long list of gears that approximate this ratio.
Choose one of these and enter it as a compound pair with a slash between them eg 127/135, in step 5B with your own lathe specifications.


This will give you a lot of possibilities, but to be complete I must mention that it is still possible to think up more options by multiplying the ratio by some constant that can be achieved by using various combination of stud gear and leadscrew gears, or even gearbox setting with a conversion gear. But that is making things more complicated. The only advantage is that it may be possible to reduce the errors in approximating R caused by the fact that the number of teeth on a gear wheel has to be an integer. But errors are small to begin with.

Examples from the list from RideTheGearTrain:

eg 1.058333 x 36 gives 38.3 so the program suggested 38/36 conversion gear:

38/36 = 1.05555555555555 where 1.058333333333333 is the perfect ratio

1.058333333333333 / 1.0555555555555

= 1.00263 or 0.263 % error

For converting between 8 TPI and 2.5mm pitch which is also quite common

R = 25.4 / (8 * 2.5) = 1.27 eg using the compound pair 127/100

For converting between 16 TPI and 2.5mm pitch

R = 25.4 / (16 * 2.5) = 0.635

For converting between 16 TPI and 1.25 mm pitch

R = 25.4 / (16 * 1.25) = 1.27 eg using the compound pair 127/100

PROOF OF THE ABOVE EQUATION:


Expressing the imperial leadscrew in metric units so that it is compatible with the proposed metric leadscrew:

Li TPI has pitch 1/Li inches.
Multiply this pitch in inches by 25.4 to get pitch in mm (of the imperial leadscrew):

Li (mm) = 25.4 * 1/Li

Li(mm)= 25.4 /Li

What is the ratio R to convert Li(mm) to Lm(mm)

Li(mm) = R * Lm(mm)

25.4 / Li = R * Lm

R = 25.4 / ( Li * Lm )


CONVERSION WITHOUT SPECIAL GEARS:

Don't forget that you can do a lot without even using a conversion gear. I found that the Boxford with its standard list of change gears, which can be used to make up compound pairs, produced ALL the standard metric pitches to within 0.25% error, without even obtaining special metric-imperial compound gears! Run RideTheGearTrain and select option 5B to request ALL metric pitches to create a table of ALL imperial TPIs.

Please don't hesitate to contact me for help.
 
A MAGIC number for conversion between metric and imperial:

The equation for the gear ratio for the conversion is

R = 25.4 / ( Li * Lm )

I have now included a table in RideTheGearTrain.com which is displayed if yoiu click the 'Metric-Imperial Conversion' button in the menu. It saves you from using the above equation. Here it is.

Table of gear ratios for Metric-Imperial Conversion.jpg

Table of Ratios:
If you have an imperial lathe, look across the top row to find the column which matches the TPI of your leadscrew. Look down the left column and decide which leadscrew pitch (in mm) that you would like your lathe to produce. Find the ratio where the row and column meet. Use copy and paste to use this ratio.

If you have a metric lathe, look down the first column to find the mm pitch of your leadscrew. Look across the top row and decide which leadscrew TPI that you would like your lathe to produce. Find the ratio where the row and column meet. Use copy and paste to use this ratio.

Enter this ratio in the INPUT on this page of RideTheGearTrain. It will list all the pairs of gears that approximate this ratio (eg 127/100), and the amount of error that is introduced. This error is caused by the fact that the number of teeth on any gear must be an integer.
 
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