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A question for the gear guys.

There are things people call "standards" but the fact is, they are only conveniences. For example, a gear by itself DOES NOT HAVE A PITCH DIAMETER. All these statements people make "A 100 tooth 10 DP gear has a pitch diameter of 10" ARE NOT TRUE. The only way a gear has a "pitch diameter" is mating it with another gear, measuring the center distance, then dividing by the number of teeth on each part. Then you get the REAL numbers for what is termed "pitch diameter".

Everything about gears is the same way. It's ALL malleable. The so-called 'standards' should be called 'conveniences' because it makes most calculations a lot faster and easier. But all they are is numbers or formulas that people use to make things quick or cheaper (less expensive to make production runs of cutters in accepted sizes than one for each situation).
You can even cut teeth of a different pitch and pressure angle from the cutter you are using, by changing what would be the "normal" cutting relationships.

For anything you can say about gears, someone could come up with an equally true opposite example.

That should be printed out and made the forward of a gear making book. At the very least, a sticky in a forum. That is as accurate and truthful as it gets. 👏👏👏
 
EG, make'm all like this and save the unnecessary material for something important.

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EG, make'm all like this and save the unnecessary material for something important.
Them guys got hit with the ugly stick :) but thanks, illustrates what I was trying to say. In all this explanation I kinda forgot what that was but let's try to wrap it up a little ...

I think the question was, how can you figure out the tooth thickness ? The answer is, there's formulas but what I was trying to express was, conventional terms will trip you up if you don't understand that they are just shorthand. Teeth don't have to be a 'standard' size, shape, or thickness. Even 'standard' teeth, you can scooch them out or you can scrunch them in. They will still work, altho not as well as having them be in the 'normal' middle of the range.

You calculate the tooth thickness by using the pitch diameter with formulas that are in several books - but it has to be the real pitch diameter, the ones that the gears see, not "100 tooth 10 DP has a PD of 10" .... That isn't reality.

All that to get here, sorry, may as well use it for something useful ...

All of sane parallel-axis gearing is based on that idea of two friction disks, which are the pitch diameters of which we speak all the time. (Module teeth are upside-down and backwards, as befits anything invented by the french. We're going to totally ignore that except to say, if you want to retain your sanity, figure everything out in DP then convert).

Imagine you are back in the tenth century or something, you have a grist mill with one three-foot stone friction driving a six foot stone. Basic 2:1 reduction but it doesn't work too good, put any pressure on and it slips. So you get a brainstorm, think "let's stick some prongs into the little one so the big one can't slip !" and if you have prongs in one, then you need holes in the other to accept the prongs. That's a biological concept which they understood even back then.

So you take the small stone, measure the circumference, divide it into even segments, and put 19 pegs in it. (The witch down the street said 19 was a good number, okay ? sheesh). 3' pitch diameter times pi equals 9.425' circumference. Space your pegs at .496' or 5.95" -- 6" is going to be close enough for the tenth century, and since there's no bureau of standards yet and they say the average dick is 6" it's easy to get the village together, measure them all and average it out - - and you now have a 6" circular pitch pinion.

Circular pitch is really popular with gears made out of pegs - "lantern gears" because it's super easy to figure out.

If you made the sticks stick out about a foot (that'd be two dicks long, which is conveniently equal to one horse dick, in the old measurement system) you'd already be using modern practice :). We can call that the addendum because it's added to the pitch diameter, and the holes in the mating part get to be the dedendum because they are deducted from the pitch diameter. {Sorry for the childish extra emphasis but it's a really easy way to remember which part of the tooth is which).

Once again I'l beat you in the head with this but remember the numbers are added to the real friction disk not something the witch said because she didn't understand gearing yet and hadn't written up any tables. It's all from that damn friction disk.

The holes should be deeper than the stickouts, because you don't want the prongs to bottom out and get smushed and dirt needs a place to go and so on, so the dedendum is bigger than the addendum. Now you've got the modern terms pitch diameter, addendum and dedendum all figured out. We're well on our way to nukular submarine turbo-reduction boxes :)

Dead horse but the concept of the friction disks and the point at which they touch is basic to all gear terms and geometry calculations. From this law hangs all the books and tables.

If you understand that then everything down the road makes sense but if you don't, you'll be forever beating yourself in the head with a frying pan because the only thing that will ever work right with book numbers is totally 'standard' sizes and dimensions. Since many or maybe most gears are not 'standard' then you're going to be plenty miserable if you skip that first piece of info.

The next step is improving them pegs by making them shapely and curvaceous but if the audience has evaporated, I can take a nap instead. Us old folks need our naps.
 
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Emmanuel, read much David Hume lately? Tolstoy?
Yeah I know. But we're talking something that's not so simple, altho it really IS simple if you start from the correct basics.

If you look at all the crap people spout about gears, all I'd like to see is if people at least can get the concepts right. I read stuff here that's like totally impossible and it just gives me a headache.

If you can explain it more clearly in less words, I'll hand you the podium like right now :D
 
Dead horse but the concept of the friction disks and the point at which they touch is basic to all gear terms and geometry calculations. From this law hangs all the books and tables.

If you understand that then everything down the road makes sense but if you don't, you'll be forever beating yourself in the head with a frying pan because the only thing that will ever work right with book numbers is totally 'standard' sizes and dimensions. Since many or maybe most gears are not 'standard' then you're going to be plenty miserable if you skip that first piece of info.
What's really ironic about this is that it jives with the basic premise to Alex Kapelevich's assertions about what he named "Direct Gear Design". There are no standards. No rules. Start with the premise that the working envelope and desired ratio dictates everything that follows and "So what" if you can't just pop down to the 7-11 for tooling on the shelf.

And when you do that... boy howdy... does the world give you options! Once you do that, all this talk about DP and Module and Circular Pitch seems really, really dumb. Even Pressure Angle is up for grabs. Heck, especially Pressure Angle.

You've been spittin' fire, lately. Keep it up. Just don't pee fire. That's completely different and not a good thing.
 
OK, now I am getting the idea on how DP/MOD sizing and center distance work together, which is prompting some other questions tomorrow.

Ed.
 
OK guys, I think I am learning a few things and want to check them out.
Lets make an example, 6" center to center,2 30 tooth gears created with a hob. Comes out to an even 5DP?
How do we get clearance between teeth? Cut slightly deeper? Doesn't that change the DP? How is the amount determined?

Same thing except 6.075 center distance. Make both slightly larger? Is this what makes the teeth more pointed?

Back story. I have made several gears over the years using single cutters and a dividing head. Almost all simply made to " the numbers ", OD and the depth stamped on the cutter. Even made couple of helicals on my ancient universal mill.

So the end question is, is it the action of the hob that keeps the tooth shape true to form with the varying changes in diameter? My guess is yes. Bonus question, how large a percentage can you change PD and keep the proper tooth counts?

Thanks, Ed.
 
Thats called 'faking the pitch circle' and is commonly done in lathes to get desired ratios ..........the other well known application was Phil Vincent used 'faked' gears in the gearbox of his bikes to get evenly spaced ratios.
 
Lets make an example, 6" center to center, 2 30 tooth gears created with a hob. Comes out to an even 5DP?
yes

How do we get clearance between teeth? Cut slightly deeper? Doesn't that change the DP? How is the amount determined?
yes, cut slightly deeper. No, why would it change the dp ? You have a 6" diameter divided into 30 teeth, that's 5 teeth per inch, yes ? What changed ? Nothing. Just how fat or skinny the tooth is. Still the same number of teeth per inch of diameter.

Backlash is determined by a few different factors but the biggest ones are runout and center distance tolerances. You always need backlash, solid objects don't like to be crushed into each other. So you need enough backlash so there's still space even at the minimum center distance with the maximum runout. And then a tiny bit extra, just to be safe and in case the part goes to the arctic, where it's cold :)

Same thing except 6.075 center distance. Make both slightly larger? Is this what makes the teeth more pointed?
Yes, because of the way an involute curve changes radius as it gets farther away from the base circle.

I have made several gears over the years using single cutters and a dividing head So the end question is, is it the action of the hob that keeps the tooth shape true to form with the varying changes in diameter?
A hob or shaper cutter does not have a "shape" like a space cutter does. Hobs and other generating process cutters have straight sides. The curve is created by the relative motion between the cutter and the workpiece. Kind of like if you take an angle grinder and grind a radius on an edge - from a straight cutter you get a curved corner.

Gear machines are controlled better than that but that's the idea. So cutter deeper, cutter shallower, it's still going to give you a curve which mates with any other part cut by a tool with the same specs. That's one of the reasosn an involute became the curve of choice. There's another history lesson here which (I hope) can help but it's almost lunchtime, if I'm late all heck breaks loose.


. Bonus question, how large a percentage can you change PD and keep the proper tooth counts?
As a really loose rule of thumb, one tooth off is usually okay. Two would be too much, normally. Don't depend on that but just generally speaking ....
 
How do we get clearance between teeth? Cut slightly deeper? Doesn't that change the DP? How is the amount determined?
My go-to for that calculation is the Van Keuren Precision Measurement handbook. It's inexpensive and lots of copies are available on ebay. It's relatively small compared to most gear books, you don't have to wade through tons of text to get the data you need for backlash. You simply increase the infeed of your cutter to reduce the theoretical pitch circle by a calculated amount to get the backlash you want.

When I read the Fellows The Involute Gear book the light went on for me about how the curves and angles are created. In particular, this presentation that gears can operate like a pair of pulleys with a crossed belt. The involute curve follows a point on that belt as the pulleys turn.
Capture.JPG
From that all the numbers are generated, pitch, pressure angle, pitch diameters, etc. All those numbers are attached to the actual theoretical geometry that exists independent of the math. (Which takes us to the question was math invented or discovered, right?)

Here's an online copy of that book - https://drb-qa.nypl.org/read/4000510
 
You simply increase the infeed of your cutter to reduce the theoretical pitch circle by a calculated amount to get the backlash you want.
See, this is what drives me crazy. There is no "theoretical" pitch circle and driving the cutter in deeper does not do a damn thing to the pitch diameter. All it does is make the teeth thinner. A gear by itself does not have a pitch diameter.
 
Shown in the video is a thirty-tooth gear on a thirty-and-one-half-tooth gear blank. The gear on the right is standard size:

Same as above, but having a complete tooth profile shift:
 
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See, this is what drives me crazy. There is no "theoretical" pitch circle and driving the cutter in deeper does not do a damn thing to the pitch diameter. All it does is make the teeth thinner. A gear by itself does not have a pitch diameter.
In my small sampling of experience, usually people that deal only with the making of gears (or gear trains) don't belabor this point. It's similar to how actual cut depths can vary depending on process used... for the most part, no one really cares... It's when someone has gone past the basic gear making application and into non standard stuff or gear design that PC becomes a less rigid existence and refers specifically to two specific specimen in an actual gear train. Then, it suddenly has not only a meaning, but very much a relationship, that matters. And *that's* when people start getting nit picky about it. I've been on both sides of that fence and "get it". It's one of those things that doesn't really matter until it very much matters. And then, it matters A LOT.
 
EmGo, your treatise in post #50 explained it so that even I can understand, seems adjusting gears and their centers is somewhat of an art. The last paragraph seems to explain an enlarged pinion. Thanks.

Ed.
 
David_M. I appreciate the videos of the rotating gears. You mentioned tooth profile shift. Is this a different way of saying increasing or decreasing the pitch line of the teeth?

Ed/
 
It's when someone has gone past the basic gear making application and into non standard stuff or gear design that PC becomes a less rigid existence and refers specifically to two specific specimen in an actual gear train. Then, it suddenly has not only a meaning, but very much a relationship, that matters.
It's a little bit weird maybe - it's common even for people who know, to use terms and say things that are not true. And you're right, generally people don't belabor the point.

But as soon as you try to understand what's going on, then the misuse of definitions will drive you crazy, because there is a huge conflict between what people say and what actually happens. That's when people start flinging around weirdass terms like "operating pitch diameter" or "theoretical pitch diameter". Those things don't exist. They are just made up to try to cover the conflict between reality and the common "rules".

As soon as you understand that these "rules" are just a convenient shorthand, not reality, then everything suddenly can make sense. There's no more weirdass conflicts between the words and what is happening. Then you don't care anymore when people say "the pitch diameter of a 100 tooth 10 DP gear is 10" because you know it's bullshit and the guy doesn't really know what he's talking about.

[edit: evidence above :D "You mentioned tooth profile shift. Is this a different way of saying increasing or decreasing the pitch line of the teeth?"

NO !! Nothing about pitch diameters changes and wtf is the "pitch line " There is no such thing !! These ideas (I think) come from trying to fit the reality of how it works into incorrect terms wrongly used. You can move the profiles all over the map, the pitch diameters NEVER CHANGE. The pitch diameters are and will always be and ONLY are determined by the ratio of teeth and the center distance. { And there is no "pitch line" whatever that's supposed to be. There is a "line of contact" which starts at the spot where two teeth first touch and goes to where the two teeth finally disengage. The ANGLE of this line with a line between the two centers IS THE PRESSURE ANGLE. Not whatever the hob is, not whatever the tooth gages roll with. Reality }

I guess this is all because an involute curve is kind of weird. The shape of the curve varies according to how far from the base circle it is. This is quite useful for gear teeth but not so useful for easy terminology :) The whole thing with long addendum and so on works because you are just moving the positions of those curves in and out against static pitch diameters. The pitch diameters stay where they are. Probably need some David M graphics to illustrate this.

If you just want to buy a 127 tooth gear out of a catalog for the Logan, doesn't matter. If you want to understand why you can just drive the cutter in a little deeper to get backlash and it doesn't fuck everything up, then you need to know all that stuff you were told is bullshit. That's not how it really works.
 
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