Gearing Puzzle

Find the pitch circle, and then compare addendum and dedendum of each.

No one else around here appears to know anything about the mechanics and terminology of gears. We're supposed to be discussing engineering here, not religion or pseudoscience, where knowledge is absent.

... but your post is hardly helpful is it?

Especially as you don't even have the cojones to put your name to it... twonk

Del

Well I did encourage head scratching but as many of us here know for some members here scratching their ass is as close to their head as they will get.

You too.

Please feel free to furnish some real gear terminology and/or theory.

The ratio (1:1) goes as the number of teeth since they stay meshed. The teeth on the larger gear are a little bit wider, so the circumference of the larger gear moves a little bit faster. The contact point moves along the two meshed teeth as the gears rotate. The limit for this to work would be when the root radius of the larger gear is larger than the tooth radius of the smaller gear.

Is the tooth configuration of the same pitch? Perhaps you have a metric gear and an imperial one?

There is still some "range" to play with teeth undercutting, while you adapt the height.

Hence 2 planetaries can differ in diametric size, depending on the module and/or pitch the teeth received at concept.

This is starting to sound like a strain wave gear set.

...and even that's overpaying...

As they have have the same number of teeth but different circumferences the bigger gear must have bigger teeth, so "meshed together fine" is a relative term, IMHO. If the set-up were used on load I'd expect wear to be a problem, as Del said in #1.

The point of contact moves at the same (linear) velocity, so the bigger gear has a lower RPM.

Proper meshing gears have same size teeth so number of teeth is proportional to PCD, and RPM is inversely proportional to PCD.

If gear teeth meshes perfectly, the gears could nor rotate. The teeth are always narrower than the slots so they can slip in and out. That is why gear-driven systems have 'backlash' when reversing direction, and why gears only need to be 'close enough' to mesh and drive each other.

Here at the Museum of Science and Industry in Chicago, there is a permanent exhibit in the Blue Stairwell about gears, it shows all sorts of unusual gear setups, all transferring power smoothly despite the counterintuitive designs. (I'm sure there's a similar exhibit in all Science Museums worldwide.) One pair is two (mostly) square gears alligned with a 45 degree offset, so the corner of one gear hits its partner midway between corners, and another has two 'nautalus' gears meshing, so the one gear's radous shrinks as the other one grows, and the teeth mesh so well, the flats where the gears 'jump back' to their starting radii never touch. They also have a number of gear arraingments on display that change one type of motion to another, but those aren't relavent to this thread.

I once made a pair of elliptical fears out of Plexiglas, pivoted on their foci so that the ration varied from about 1:2 to 2:1 within one revolution. It was part of a math display on conic sections.

I think MSI has a set of gears like that in the exhibit too, although they rotate them on center of mass. These displays are built into the walls of the staircase, and run pretty much 24/7/365, so they want to keep the strain on the motors to a minimum for greater mean time between failures.

For two gears to 'mesh together fine' they must have the same diametral pitch and pressure angle… assuming spur. If they are involute, their center-to-center distances can vary within a minimal tolerance range, but if they're cycloidal the center-to-center has to be 'exact'.

So, not sure how you can have two gears of differing diameters with the same number of teeth match together correctly, unless you're 'diameter' is not in reference to their pitch diameter and we're talking about an internal gear and an external gear?

Both are external gears and by meshing fine I mean they will roll across each other when held by hand without any high degree of loading.

They may not have perfect tooth meshing geometries but they do mesh with each other with over 50% tooth to tooth interlacing.

Not a perfect match of course but still a bit of a puzzle when looked at mathematically and that's what this thread is about. Reality shows it can work where as standard math says there is a conflict.

You asked "What are their tooth tip speeds/rotational velocity at 100 RPM and how can they be different despite having a mechanically locked 1:1 gear ratio?"

Being mechanically locked means the point of contact moves at the same linear velocity for both. It doesn't mean they rotate at the same RPM.

Huh? If they are 1:1 then they rotate at the same rpm. However, if one has a greater addendum, its tip velocity will be (slightly) greater.

A picture would be worth 20 questions, ;-)

You gave a big clue when you said that the gears did not match perfectly. If you don't match the DP you can do almost anything;