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Post By EPAIII

How are diametral pitch / modulus geared on a lathe?
I have seen mention of some lathes that, in addition to tpi and metric threads, cut diametral pitch and modulus "threads." I'd like to learn more about this, so if anyone can answer some questions, I would be most grateful!
1) I am thinking that these would be used to cut a hob  yes? No?
2) If I have done the math right (which is a big if!) then these "threads" would need to include a factor of PI. For example, modulus 1 gears have a circular pitch of PI mm (again, assuming my math is correct ...), so I'm thinking that the hob would need to have threads of 3.1415926 mm pitch. If I'm right about question # 1, then lathes that can cut a modulus 1 "thread" would be cutting 3.1415926 mm threads. Yes? No?
3) If I am right about question # 2, then what sort of gear train is used to generate these "threads"? Since PI is not a rational number, it can only be an approximation. 22/7 gives an approximation with an error of a little over .04% but to get much better than that, it looks like you have to go all the way up to 201/64. Is this the sort of gear ratio that is used, or am I missing some really easy way to get PI into the gear train?
Thanks for any help!
Andy

You are mixing a couple of systems together
Yes, I believe lathes do use the 22/7 gear ratio to achieve the approximation of Pi, although the denominator may be other multiples of 7, because you can switch up or down by multiples in the quickchange gearbox.
So for diametral pitches, you'd be using the Pi gearing with an inch leadscrew, or Pi gearing + metric gearing to cut module threads with that inch leadscrew. For all of them, I think you'd have to reverse the spindle to move the carriage in reverse, because the thread dial won't keep track of where anything is if you disengage the halfnuts.

Originally Posted by HuFlungDung
I believe lathes do use the 22/7 gear ratio to achieve the approximation of Pi, although the denominator may be other multiples of 7, because you can switch up or down by multiples in the quickchange gearbox.
71/113 is a much more accurate approximation of 1/5th Pi.
I wouldn't think 22/7 is accurate enough to cut a gear hob.

My lathe will do diametral & module pitches, by changing one gear in the train. Of course, this is the gear that I don't have. Everything else can be done with the QC box, it has hundreds of threads.
The module & diametrial pitches apparently are used on worms. I'm not certain how to use them to make a hob.

Originally Posted by lazlo
71/113 is a much more accurate approximation of 1/5th Pi.
I wouldn't think 22/7 is accurate enough to cut a gear hob.
Say, that is a good ratio to know But that doesn't mean that a typical lathe has those gears on it. My old Summits use a 22/21 for diametral and module pitches.
I may be mistaken, but the error caused by 22/7 amounts to .0014" in 3.14 inches of travel, does it not? So its not as gross of an error as it sounds. And the change gears force the rotation of the gear blank when a hob is doing its cutting, so the actual pitch accuracy of the hob, how significant is it? A slight tweak to the cut angle setting of the hob when hobbing gears could also cause as much error (or more) or reduce it. What do you think?

For a full discussion on this I would recommend getting a copy of "Screw Cutting In The Lathe" by Martin Cleeve. My copy is in the shop but I believe he devotes at least a chapter to cutting various odd pitches. His technique involves making various compound gears from standard change gears and using them in the gear chain.
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