Settle an argument...

[Anton]

Heya, guys.

Help me settle an argument - is a diff ratio a function of the size of the crownwheel versus the size of the pinion?

And can you make the teeth on a pinion smaller without making the pinion smaller *or* increasing the number of teeth on the pinion?

[Rhinoman]

Its the ratio of the number of teeth on each.
You can't change the number of teeth on the pinion without changing the thickness of them or the diameter of the pinion so the crownwheel has to be changed/altered as well.

[Ladaman]

As Rhinoman says the ratio is calculated from the teeth numbers, not diameters. This is true for all gears, not just diff gears (epicyclic gear ratio's are a bit tricky though).

But what do you mean by making the pinion teeth smaller? The diameter of the blank or the size of the teeth?
The size of tooth, or pitch has to be the same as the wheel for them to mesh.
The diameter could be reduced, or increased, but you would need to adjust the wheel to suit. All this would be done at the design stage. It isn't something that can be "adjusted" at a later date.

And bevel, or indeed hypoid gears, as diffs really are, are made in matched sets, and really shouldn't be mixed up.

Have you been on the "pop" Anton to be having discussions like this on a Saturday night?

[Anton]

As Rhinoman says the ratio is calculated from the teeth numbers, not diameters. This is true for all gears, not just diff gears (epicyclic gear ratio's are a bit tricky though).

You're trying to tell me that the diameter of a gear in relation to the diameter of the gear it is mated to has nothing to do with the ratio?

So if a "gear" has no teeth at all, just a rubber surface, and is mated to another "gear" with no teeth (like a fairground ride - truck tyre used to turn a merrygoround, which is basically the same principle as a crownwheel and pinion) then you're saying it has no ratio at all? Or an infinite ratio?

Or is it that the number of teeth on the two gears is always set by the relative sizes of the two gears (how many equal sized teeth you can fit on both gears without using fractions) and therefore the ratio is set by the size of the two gears, but the number of teeth can be used to work out the ratio because how many teeth is *has* to have is mathematically determined from the size of the two gears in relation to one another (and therefore, by the gear ratio)?

But what do you mean by making the pinion teeth smaller? The diameter of the blank or the size of the teeth?
The size of tooth, or pitch has to be the same as the wheel for them to mesh.
The diameter could be reduced, or increased, but you would need to adjust the wheel to suit. All this would be done at the design stage. It isn't something that can be "adjusted" at a later date.

I mean the teeth on the pinion. I've been told that a pinion is always the same size, and that the teeth are simply made smaller without changing the number of teeth when mated to a crownwheel with more (and therefore smaller) teeth.

I argued that it's impossible to make the teeth smaller without either making the pinion smaller, or increasing the number of teeth (to take up the excess surface area created by making the teeth smaller).

And bevel, or indeed hypoid gears, as diffs really are, are made in matched sets, and really shouldn't be mixed up.

Agreed. The person I was arguing with would agree with that too, I believe.

Have you been on the "pop" Anton to be having discussions like this on a Saturday night?

No, just being stubborn, as was the person I was arguing with!

[Edweird]

If there aren't any teeth, then they're not gears. Then you'd use either the diameter or circumference for ratio.

The diameter of a gear is whatever size it is to accommodate the number of teeth it's supposed to have.

[Anton]

Yup, you're right on both of those points, but that doesn't change the fact that the circumference of the gears is what sets the ratios, surley?

Yes, you can use the number of teeth in both as a shortcut to work out what the ratio is, but the ratio of a pair of gears is the radius of one gear divided by the radius of the other.

Right or wrong?

[Edweird]

Yup, you're right on both of those points, but that doesn't change the fact that the circumference of the gears is what sets the ratios, surley?

Yes, you can use the number of teeth in both as a shortcut to work out what the ratio is, but the ratio of a pair of gears is the radius of one gear divided by the radius of the other.

Right or wrong?

Right, I'm going to work my way through it and post my thoughts

Lets suppose that one complete tooth of a set of matching gears is a unit length which we'll call.....

You've got a 12 tooth pinion and a 60 tooth crown so circumference is 12 and 60

Using teeth the ratio would be 60:12 = 5:1, i.e. 5 complete rotations of the pinion for one complete rotation of the output.

Now, the radius of the pinion is going to be 12 /2π = 6 /π
Same goes for the crown 60 /2π = 30 /π

If you do (30 /π) / (6 /π) which would cancel down to 30/6, i.e. 30:6 = 5:1 so I think there is a direct relationship between the teeth, radius and ratio of gears, assuming all of the teeth are equally spaced.

That's assuming the gears are straight cut. With bevel gears, I think you'd have to use the average radius across the thickness of the gear.

[Anton]

Yup, you're right on both of those points, but that doesn't change the fact that the circumference of the gears is what sets the ratios, surley?

Yes, you can use the number of teeth in both as a shortcut to work out what the ratio is, but the ratio of a pair of gears is the radius of one gear divided by the radius of the other.

Right or wrong?

Right, I'm going to work my way through it and post my thoughts

Lets suppose that one complete tooth of a set of matching gears is a unit length which we'll call.....

You've got a 12 tooth pinion and a 60 tooth crown so circumference is 12 and 60

Using teeth the ratio would be 60:12 = 5:1, i.e. 5 complete rotations of the pinion for one complete rotation of the output.

Now, the radius of the pinion is going to be 12 /2π = 6 /π
Same goes for the crown 60 /2π = 30 /π

If you do (30 /π) / (6 /π) which would cancel down to 30/6, i.e. 30:6 = 5:1 so I think there is a direct relationship between the teeth, radius and ratio of gears, assuming all of the teeth are equally spaced.

That's assuming the gears are straight cut. With bevel gears, I think you'd have to use the average radius across the thickness of the gear.

Thanks, Ed. That's the way I was taught it in mathematics and CDT in school, so I'm glad I'm not going mad.

The circumference (measured in teeth (because the teeth of both gears have to have the same dimensions in order to mesh), mm, inches, feet, lightyears, whatever) divided by the circumference of the other.

I believe that's that settled, but now for the one that's really boggling my brain - how someone can believe that you can change the size of the gear teeth without changing the number of teeth, and still maintain the same size pinion/crownwheel.

Now, forgive me for going back to basics, but the circumference of a gear cannot be bigger or smaller than the size of the teeth (from one "low point" whatever that's called to the next) times the number of teeth, right?

I honestly can't see how you could change the size of the teeth without changing the number of the teeth and keep the gear the same size. Or am I being dumb?

[Rhinoman]

I honestly can't see how you could change the size of the teeth without changing the number of the teeth and keep the gear the same size.

You can't.

[Edweird]

Not without having odd teeth spacing, like having the gaps wider than the teeth.

My Step-Grandad builds clocks and I've seen him use gears like this:

blargh.png (1.93 KiB) Viewed 6149 times

Forgive the shoddy diagram but you get the idea.