Naked Science Forum
Non Life Sciences => Technology => Topic started by: Geezer on 09/01/2012 02:36:35
-
Gear teeth come in all sorts of shapes and sizes. Generally, as gear wheels get bigger, the size of the teeth on the gear wheel get bigger too. In other words, the number of teeth on any gearwheel may not be constant, but it tends to fall within a particular range.
Is this range dictated by a fundamental scientific principle, or is it simply a consequence of practical limitations imposed by application and manufacturing (engineering stuff)? After all, when you boil it all down, gears are really just a means of enforcing friction with extreme prejudice.
-
Obviously the proportion of the numbers of teeth would make a big difference in the gear ratio.
But... your question is more... say you have a gear ratio:
Is there any difference between, say:
30:10 and
60:20
with the gears having the same overall diameter.
Hmmm, I just happen to have a ring & pinion set sitting next to my computer, with slanted/curved gears.
Ok...
Here is what I think.
At any one time, you are really only driving your system by 1 or 2 teeth. The slant/curve in the ring&pinion set allows a third tooth to start engaging before the previous teeth release.
Since your teeth typically have a taper where they mesh, any tooth that isn't fully engaged really isn't giving full driving force.
So, what I would expect is the following:
More teeth --> smoother, and perhaps less friction.
Fewer teeth --> stronger, less chance of stripping teeth.
However, if the more teeth does actually make it smoother, then that may offset some of the benefits of fewer, big, strong teeth.
The slanted teeth are modifying this equation slightly, and giving an extra partial tooth engaging, and thus somewhat smoothing the motion of the teeth engaging.
-
I found some data (I have no affiliation with this company btw)
http://martinsprocket.com/2001/SecG.pdf#G25
Everything else being equal, larger teeth do seem to be able to transmit more power, but the difference is not proportional to size.
For example,
a 20 degree DP6 gear with 22 teeth can transmit 28.59 HP at 500 RPM
a 20 degree DP12 gear with 44 teeth can transmit 10.03 HP at 500 RPM
(both gears have the same pitch diameter)
However, the DP6 gear is twice the width of the DP12 gear, so it's more like 29 versus 20, even though the DP6 teeth are twice as large (in cross section) as the DP12 teeth.
-
If you look hard I'm sure you can find all sorts of patents and proprietary gear tooth-shapes, optimised variously for strength, smoothness, quietness, longevity ...
Of course bigger teeth also allow you to get away with less precision in the relative spacing of the gears, so sloppy/worn bearings or bent shafts will be more or less of a problem.
-
Of course bigger teeth also allow you to get away with less precision in the relative spacing of the gears, so sloppy/worn bearings or bent shafts will be more or less of a problem.
Yes, I think that's really what tends to determine the size. In theory, a large number of very fine teeth can transmit just as much force as a small number of large teeth, but the fine teeth would have to be manufactured to much tighter tolerances and be maintained in the correct meshing relationship by very precise bearings, so it's a lot more practical to use larger teeth.
-
Smaller teeth can carry a lot less load, only a few teeth mesh at any time, and smaller teeth have less material per tooth in cross section, so they tend to chip. But you can get better gear ratios in a more compact space.
The other thing is the thickness of the gear along the axis; the thicker the stronger it is, but if it's too thick it's hard to align the gear's axes well enough to make good contact over the whole meshing region particularly if it's very fine pitch; I'm pretty sure it helps to go to fewer teeth with thicker gears.
-
Wouldn't larger teeth increase friction? It must be best to opt for the smallest teeth for the load.
Say's he, with no idea as to what he's talking about, as usual.
-
Smaller teeth can carry a lot less load, only a few teeth mesh at any time, and smaller teeth have less material per tooth in cross section, so they tend to chip. But you can get better gear ratios in a more compact space.
I'm not sure that's strictly true. As the teeth become smaller, more of them are meshed at any point in time, so the load is (in theory) spread across more teeth. However, that only works if the tolerances are very tight, and that rapidly becomes impractical or uneconomic.
If you look at the data I posted earlier you can see that the relationship between size and power capacity is quite interesting. The pitch diameter of the gear seems to be more significant than the size of the teeth, which is hardly surprising.
-
Wouldn't larger teeth increase friction? It must be best to opt for the smallest teeth for the load.
In a way, I think it does. Friction increases as the "sliding speed" increases, and bigger teeth means a bigger distance to slide in a certain amount of time. (You kind of have to visulaze what's happening as the gears move in and out of mesh.)
I don't know how significant this is though. There may be other friction losses than increase as the teeth get smaller, so it maybe its a case of gaining on the swings what you lose on the roundabouts.
-
I think probably some of the 'patent' tooth-designs are made so that the teeth predominantly roll over each other rather than slide, hence reducing frictional losses and wear...
-
I think probably some of the 'patent' tooth-designs are made so that the teeth predominantly roll over each other rather than slide, hence reducing frictional losses and wear...
I think you are correct in saying that, though there always seems to be some amount of sliding friction. I wonder if it is a function of the gear ratio? If so, a 1:1 ratio might be geometrically perfect and have very little friction, although it would not be much good at producing any mechanical advantage :)
-
Have any gears been produced that incorperate rollers into the teeth it would seem to be a way to reduce sliding friction.
-
Have any gears been produced that incorperate rollers into the teeth it would seem to be a way to reduce sliding friction.
Kinda sorta, yes!
That's what roller chain drives (as in bicycle chains) do, and that's why chain drives are very efficient.
-
As well hypoid gears transmit more power, as there is a larger contact surface to transfer energy. Disadvantage is side thrust, which then needs a extra thrust bearing on both sides. That was solved by Andre Citroen, who invented his famous gear design, immortalised in the logo of the car company he founded.
Gear tooth design is a complicated thing, the requirement being to have a constant movement of the contact patch to minimise torque changes as the teeth mesh and unmesh. There is a whole lot of mechanical engineering devoted to these designs, and a lot of research has resulted in the current profiles used. A big improvement is in the lubricants used, as they need to be chosen based on load, temperature, speed and operating conditions. There is no one size fits all here, I have a few gearboxes that each have a different lubricant requirement, from a synthetic that runs like water to a liquid grease.
-
Don't you mean "helical" gears? If so, they actually transmit less power than straight cut spur gears. The advantage of helical gears is their quiet operation.
-
From my reading (cos I didn't have a clue what Sean and Geezer were talking about) the hypoid gear is a sub-category of the spiral bevel gear.
The spur gear (http://en.wikipedia.org/wiki/File:Spur_Gear_12mm,_18t.svg) has teeth on the edge of the disc/cog - ie the point of the teeth are on radius lines - and the line of ridge of the tooth is parallel to the axis of the cog
The helical gear (http://commons.wikimedia.org/wiki/File:Helical_Gears.jpg) also has teeth of the edge of the cog. But the line of the ridge of the tooth is at an angle to the axis of the cog - because this is on the edge a cylinder the ridge describes a helical section
The bevel gear (http://commons.wikimedia.org/wiki/File:Kegelradgetriebe.jpg) has teeth that are at an angle to edge of the cog in on a bevelled surface. The line of the ridge in the same plane as the axis of the cog
The spiral bevel gear (http://en.wikipedia.org/wiki/File:Gear-kegelzahnrad.svg) also has teeth that are at an angle to edge of the cog - but the line of the ridge is not in the same plane as the axis - again they will decribe a helical section
and finally
the hypoid gear (http://en.wikipedia.org/wiki/File:Sprocket35b.jpg) also has teeth that are at an angle to the edge, and also not in the same plane as the axis of the cog. additionally the axes of the two cogs are not coincident - ie a continuation of the driveshaft would not cross
Sorry about that - but I have a bit of an obsession about nomenclature - and I was very confused
There is a comparison of spiral bevel standard gears to hypoid gears here (http://en.wikipedia.org/wiki/Spiral_bevel_gear#Comparison_of_spiral_bevel_gears_to_hypoid_gears)
-
Don't forget the good old worm gear, although it has helical teeth too, so maybe it's a variation of the helical gear, but that's really a matter of a pinion.
-
Don't forget the good old worm gear, although it has helical teeth too, so maybe it's a variation of the helical gear, but that's really a matter of a pinion.
ba dum tish!