Change gear and gear box math for thread cutting

1. Aluminum
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## Change gear and gear box math for thread cutting

My lathe a TOS S 28 has change gears and a gear box. It also can be thrown from forward to reverse while running. I have tried to do the math for the gearing and compare it to the threading chart. I can not seem to get my math to match the chart. I have attached some photos of what I have to work with. On the chart under #7 it gives the change gears tooth count and order. I am not sure what the 6mm and ¼ stand for but the worm is 4 tpi. I also added a picture of them installed. The gear tooth count for the gear box as well as how it works is not as intuitive. The gear box is on the bottom of the photo. The numbers 1-6 and ABC collate to the chart. I tried to use the gearing setup of the easily read gears to do the math.

Example:
Using the gearing in 15 column 7 under ¼” I get 25/100*120/80= a ratio .375
In the Gear box if I use 4 C, for a thread of 7/32, the gear ratio I think is
28/24*34/17= a ratio of 2.3333333.
Now multiplying both ratios gives .875 now dividing this by the worms 4 tpi gives
.625/4=.21875
This is correct but when I try to do the top of the chart I get an error

Example:
Using the gearing in 9 column 7 under ¼” I get 25/127*120/100= a ratio .23622
In the Gear box if I use 4 C, for a thread of .28, the gear ratio I think is
28/24*34/17= a ratio of 2.3333333.
Now multiplying both ratios gives .55118 now dividing this by the worms 4 tpi gives
.625/4=.137795 a multiple of 2.032 off.

Any suggestions on why this is? I also need to buy a set of gears or make them. Any ideas on prices or where to buy the gears or equipment would also be helpful.
Thanks

2. Cast Iron
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Hi Schwartzer, are you sure you want to do this?? I didn't necessarily follow all the numbers that you have here but I saw a few things that may be significant.

First off, it is called a "lead screw" not a "worm".

Also, any change gear train that has a 127 tooth gear in it has something to do with cutting metric leads/threads with an inch pitch lead screw, which is why it doesn't divide evenly. Which is why you use that "apron controlled reverse to the lead screw" to cut a metric thread.

Hope I didn't confuse you more! Dave

3. Diamond
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you could have bought the lathe with a 4tpi, or a 6mm pitch screw.

the manual covers both arrangements.

you yould order the machine with whiver you would use most. but ofcourse the change gears could adapt to the other system (mostly, you might miss a few usefull pitches)

4. Aluminum
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I believe you are correct with the lead screw being either tpi or metric. Mine is 4 tpi wich does make sense with the 127 tooth gear. As far as the reversing feature there might be something on the apron but that is not what I was referring to. My lathe has a clutch and will spin the spindle in the opposite direction but at a slower RPM. This also moves the apron in the opposite direction. It can also be used as a break. Becksmachine can you explain more on the difference from LEAD to Pitch. Thanks

5. Aluminum
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Hi Schwartzer,

First, when using a software program such as MS Excell, or WP Quatro Pro, column's go up and down and rows go across, or ,left and right.

I too own a TOS lathe but, a little larger an SN55, as well I have operated other Eastern block lathes too.

European's don't count number of threads for a fixed length, they just measure from thread to thread. So in your chart block out anything under the 6mm column, as those gears are only used on a lathe equipped with a metric lead screw having a pitch of 6mm.

For your lathe only the gears under the 1/4" column apply to your lathe, that's the European way of saying "for lathe with a inch pitch lead screw".

Now how you read the gear set up is as follows your first example

25 Tooth stud/spindle gear drives a 100 tooth gear that is on the same keyed stud as the 120 tooth gear, together they are a compound gear set, the 120 tooth gear just mentioned drives the gear on the QC box that has an 80 tooth gear.

You may or may not need a intermediate or idler gear in the gear train, the number of teeth is unimportant as this gear is used to only transmit motion from the 120 tooth gear to the 80 tooth gear on the QC box The idler or intermediate gear is not part of any gear calculation. The addition of each other idler or intermediate gear only changes the rotation of the last gear in the gear train. CW or CCW rotation.

You will need all the gears under the column 1/4" for feeding or threading, and maybe a few idler gears to, do you have a manual for your machine.

Most TOS lathes have all metric module pitch gears, my SN55 does and the size is 1.5 module pitch. I think Browning or Martin carry metric gears. As to pricing I have no answer for you as I make most of my own gears.

Take Care
Doug

PS: I notice your chart doesn't show cutting 11-1/2 TPI, or 13TPI, on my TOS there is a special lever for those two thread pitches.

6. Cast Iron
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Hi Schwartzer, ok, so you were talking about reversing the spindle instead of reversing the lead screw. As far as cutting a thread is concerned, either feature accomplishes the same goal, meaning you can make successive cutting and return passes without ever disengaging the half nuts. This is necessary if you are cutting a thread/pitch that does not lend itself to using the thread dial, or even if you just don't trust yourself to use the thread dial.

However even in the inch system there can be a need to cut a "thread" to a specific lead. These threads aren't used on a nut or bolt but as a worm for a worm drive speed reducer or as a hob to cut gears. that is why your chart lists some "threads" like .375 or .625 which are leads of 3/8" and 5/8" respectively.
Ok, enough for now. Dave

7. Aluminum
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Thanks for all of the replies. My lathe does use metric module pitch 1.5 and 2. I do have a manual but it is written in Czech! The reason for all the math is because the change gears I do have, none of them make up any of the sets in the table. The lathe came with chain and sprockets installed instead of quick change gears. The first example worked using LEAD calculations but for the second calculation did not work for metric. The gear ratio has nothing to do with pitch or tpi until it is multiplied by one or the other. If I multiplied by 4 instead of dividing it would be in tpi, but since I multiplied by ¼ it is in pitch. Correct? Either way it still does not add up for the metric pitch. Doug does your gear set similar to mine? And the lever that gives you 13 and 11 ½ tpi do you know what gear ratio it is using?
Thanks

8. Aluminum
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Hi Schwartzer,
Like I said before, don't waist your time trying to figure out the math, that QC gear box is World Class, very well engineered. Because, you can have either, 6mm pitch or 4TPI lead screw, and the only thing you have to change are 3 or 4 gears at the back end of the QC and it will still cut all the threads shown on the chart.

My thread chart is a little different than yours as I can cut 11-1/2, and 13TPI from the QC, on my thread chart it is 19TPI that requires a little extra work there is a lever that you must shift for the 19TPI, and only the British 3/8"pipe thread uses the 19TPI.

In the first pic is my actual thread chart almost, notice the lever to the left, look close at it's base you will see a pin in the "W" or Whitworth & Inch position, thats to cut inch feeds and pitches, to cut metric the little pin is in the "M" or metric mode position to cut metric threads.

This is a spread sheet of my TOS SN55 thread and feed chart, that I made, the only thing missing is the picture drawings of the gears, and how they are placed on their respective shafts. If you look back at my first pic you can see the gear drawings, lower left. Gears B & C are on a common keyed shaft, they are a compound gear set.

The gears in red are missing above.

Here is a pic of my actual rear end of the QC showing the gears, I keep the spares on another shelf, along with their keys, and spacers.

And this, is the lever for selecting the 19TPI, on your lathe it may say 13TPI

No, I don't know the gear ratio, I just know, if I need to cut 19TPI, I move the lever there, check to see the gears on the back end of the QC, are as in the chart, and it cuts them, I don't disengage the half nuts for this inch pitch thread, the manual doesn't say anything about the19TPI.

You could, seeing that you don't have any gears on the back end, use 16DP gears just make sure all the gears on the back end of the QC are 16DP. They are just a tad bigger, but there is enough room to accommodate them. Where to find 16DP gears, look for 10" or 13" South Bend Lathes. Do you have the gear quadrant (swing arm) or is that missing too.

9. Titanium
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## Clarifying relationship between Lead and Pitch

Originally Posted by becksmachine

<snip>

As for the difference between "lead" and "pitch", mathematically they are the inverse of each other.
<snip>
Dave
Not true ! This notion has gained some traction on the web, please don't be a party to this misconception.

Lead and Pitch are the *same* as each other, for single start threads.

Lead is the amount the screw advances in one turn. (what you set up the gearbox / changewheels to cut)
(what you measure with a thread gauge).

It is TPI which is the inverse of Pitch in inches.
There is no corresponding metric equivalent to TPI

10. Cast Iron
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Hi Troup, sorry, I was using "tpi" interchangeably with "pitch". Dave

11. Aluminum
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Ok I figured out the math problem for the metric it still has to be multiplied by ¼ and multiplied by 25.4 and I match the chart. Since I have not cut any threads on this lathe I did not pay close attention to the chart on the lathe witch is a little different than the one on the manual. It only has the ¼ and it has pictures instead of numbers. It has a few measurements between threads thread to thread. “, Mmm, D.P., and Mod. Now I now the “ stand for inches pitch, Mmm is millimeters pitch, D.P. is diameter pitch, and Mod is Module Pitch. I also have one more that shows a picture of a tool cutting from right to left. I think this is for the compound rest drive. The Gears I do have that are original have a Module pitch of 1.5. I also have the gear quadrant (swing arm). Now finding gears with the right number of teeth and the same DP or Module is difficult. I have not seen any lathe with more than half the correct gearing I need. The cost to get one gear made is around \$500!! So I am heading down the path of cutting my own. I have a horizontal mill I need to get either a dividing head or a rotary table with dividing plates, a gear cutter or a hob. I am not exactly sure witch is better or cheaper. Any opinions on equipment, price, ease of use, and web sites/ books on how to cut gears? Lastly is material for the gears. My gears have no rust on them at all and they are too heavy to be aluminum so I am assuming they are stainless. Is there any place that sells cheap blanks?

12. Titanium
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You may be able to buy the gears you need from one of several gear manufacturers. Do a google for gear companies. You will have to bore it out and cut a key way and maybe machine one side to make it the thickness you need.

Boston Gear is one company.

13. Plastic
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Hello
I also have a TOS or as the earlier versions were known as Andrychow lathes. Mine is a TUG-40 Engine Lathe.
I didn't have the correct gears either when I purchased the lathe. I just purchased standard inch gears and bored them for the metric mounting. This worked out great as the machine only cares about counts and can't tell metric gears from inch. I do have some of the spare metric gears from the changeover. You can email me if you are interested. Just another option as the metric gears are so expensive.
BTW I also have the English manual for this lathe. Paid big bucks for it but willing to some of the information if needed. Mine has the English lead screw. You may need to confirm which one you have to go any further.
Rick in Longview WA

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