Optimal change gear ordering?

[RJSakowski]

The bigger the gear diameter the less load each tooth will have on it (Simple lever, the farther away you are from the fulcrum the less the load). So bigger gears closer to the driven shaft should technically be stronger and maybe even wear less. (But I really don't think it matters.)

This would depend on which was the higher rpm drive or driven.

When gearing from high to low rpm, stepping down the gear ratio sooner rather than later will reduce bearing wear. The opposite would hold when stepping up from low rpm to high rpm.

 

[Bill Kahn]

Just a guess, but I would suspect that gear combinations are chosen to minimize the total number of gears required for the machine. Or did I misunderstand the question?

The lathe comes with 16 change gears: 20,30,35,39,40,45,46,50,55,60,63,65,70,75,76,80. They are, jointly, adequate for all the common TPI one needs. The set even gets pretty close to many metric threads too.

I have two related questions. First, if you select 5 gears that produce the TPI you want you can nevertheless mount them in up to 12 different ways (Not always, some of the 12 sometimes don't geometrically fit) but there are (basically) always choices. I am interested in why the designers select one of the 12 over the others.

And, related, there are often multiple sets of 5 gears that will produce the target TPI. Again, why have the designers selected the particular set they have?

I see the principle to get relative primes meshing to get uniform tooth wear. And to gear down sooner in the gear train than later to minimize bearing wear.

-Bill

 

[higgite]

And, related, there are often multiple sets of 5 gears that will produce the target TPI. Again, why have the designers selected the particular set they have?

Ever heard of Hadacol? It was a “vitamin tonic” popular when I was a kid, mostly because it contained alcohol. The question of the day was how did Hadacol get its name? The answer was… they hadacall it something! I suspect whoever chose the gear combos for different threads may have operated under the same principle. They hadapick one.

Tom

 

[RJSakowski]

Considerong that early 20th century didn't have the benefit of modern computers and spreadsheets to calculate all the permutations,KI would expect that once they found a combination that worked, they would stop . Appoximate combinations could be determined by use of a slide rule but exact combinations would require laborious multiplication and long division. There were mechanical calculators that could do this in the 1960's when I was in college. To use a computer, I had to deal with time share on a mainframe and creating a program on a stack of punch cards.Calculating redundant gear combinations would have been a luxurious use of time and resources.

That said, there are families of thread pitches which can be developed quickly without any complicatted mathematics. If a 48 tooth driving gear produces a 12 tpi thread, replacing it with a 52 tooth gear will produce a 13 tpi thread. Similarly, a 40 for 10 tpi, 44 for 11, and 46 for 11-1/2.

Atlas published a threading manual for its 6" lathes which has gear combinations for every integral tpi and some half integral tpi's from 7.5 to 79tpi. http://vintagemachinery.org/pubs/51/19942.pdf

 

[Bill Kahn]

I agree you have to pick one. And for my little Chinese hobby lathe I guess it is perfect likely that they just picked one. But, more generally, gear trains must have been subjected to the most serious mechanical engineering analysis, both theoretical and empirical. There must be a real set of principles to guide such decisions at the professional levels.

Working out the multiple combinations can certainly be done just by generating all 43,680 four gear possibilities and all 524,160 five gear possibilities on a computer, and evaluating each TPI. However, like was mentioned, they way I did it for 27 TPI was just by hand--just factoring the numbers. For example, for the five gear combination the TPI = A*C*E/(5*B*D). (The letters representing number of teeth on each of the five gears). And you can double or half this number with the gear box. Just by factoring the teeth on each available gear you can pretty quickly figure out the options available that work. No real need for a computer and enumeration. The engineers of a hundred years ago were more than plenty smart to do this. My guess is the engineers of 2000 years ago (say the Antikythera designers) were also fully able to factor and work out ratios.

Even for my Chinese hobby lathe, someone decided that I needed 16, and these 16, change gears. There was clearly some combinatoric puzzling there. I wonder if it is possible to drop one of the 16 and still generate all the TPI needed. And if I were to add one more, to get to 17, what value would it be to expand the available TPI as much as possible. Might it be a repeat value? This now does seem to me to require some enumeration. I think it is a version of "The Knapsack Problem" which is a classic, hard, computer science problem.

This hobby machine hobby takes one into some amazing puzzles.

-Bill

 

[Weldingrod1]

I made a spreadsheet when I added metric to my Hardinge ;-) That also added a LOT more threads to my arsenal. Some of which I've actually used!

You just search for gear sets that give an integer inch or metric thread, or perhaps 1/4 fractions too.
Its really amazing how fast the number of possible threads explodes as the number of change gears go up.

As for choosing, you want to be able to hit the threads you want with the minimum number of gears. You have limits on minimum and maximum gear size and usually some limits on what diameters your banjo can handle. Really small gears have tooth strength issues and stress concentration problems at the keyway. That said, you always want your set to have the smallest gear you can physically use in it, probably with an even number of teeth.

Really fine pitch will help the diameters if you need the magic metric ratio. However, these are much more fiddly to get the center to center right.

Since you only cut one direction at a time, backlash isnt a big issue, and you dont have to be super careful setting it.

Sent from my SM-G892A using Tapatalk

 

[Lo-Fi]

We may never know the actual reasoning. I suspect that calculations were made to figure out the combination of change gears to supply giving all the desired pitches with the minimum numbers of gears. Once that had been established it's simply a case of choosing gear trains that physically fit. Or they copied someone elses previous design. I mean, why reinvent the wheel?

I know from experience on my Myford - on which I'm missing the 30 tooth wheel - that I've been able to hit the ratios I've needed by substituting pairs that the chart doesn't show. The 30 tooth seems to have been particularly popular with whoever designed it! I must order one...

 

[Tozguy]

I just realized that the same set of 5 change gears on my lathe (PM1030) can be mounted up to 12 different ways and still get the same TPI. Not all the 12 ways are always geometrically possible, but normally there are, indeed, multiple options.

What is the mechanical engineering or practical machining reason for selecting one of the options from another?

Maybe there is none and all combinations work within sound engineering principles. If a gear tooth gets broken it is nice to have other gear combinations on hand to sustitute.

What does the manual recommend for a given tpi? What can you deduce from the combinations they provide? Maybe they tried to minimize gear changes within the range of common tpi. Maybe some of the possible other combinations are simply accidental.

Good question for all you reverse engineers out there.

 

[higgite]

If I were forced to bet the farm on it, I'd say they probably picked the cheapest combination of the most common gears they could find. Money talks while us engineers sit in the corner changing batteries on our calculators and trying to remember if "e" comes before or after "i".

Tom.