Crowned pulley instead of flanged

Pasted from my Thingiverse entry:

Description

Over the last couple of months I've read in the forums about people having difficulty with the belts' teeth rubbing on the pulley flanges or fender washers and causing print quality issues. The other night I remembered that flat belts on a crowned pulley will automatically find the center of the pulley. Flanges or fender washers are completely unnecessary!

I consulted my old copy of Machinery's Handbook, 24th edition, and even though it's from the early 1990's, it has a chapter on flat leather belts, how to splice them, how to design pulleys, etc. The quoted rule of thumb is for 1/8" of crown for every foot of pulley width. That would be imperceptible and probably ineffective on a pulley this size. I suspect that recommendation has to do with the geometry and strength of the leather belts.

I took a guess at a 10mm radius crown for the 6mm wide GT2 belt, and it worked great on the first try. This will concentrate the belt tension in a narrow band instead of spreading it across the whole width of the belt, but I think there is more than enough strength in the belt for that.

The belt doesn't track exactly on center due to the various inevitable misalignments of my printer, but it does return to to its happy spot pretty quickly when disturbed.

Video demo on my MakerGear Prusa with GT2 belts:YouTube

Files in my GitHub fork of the Prusa Mendel: Github

Instructions

Just print and press the bearing in, then mount as usual.

Versions for 608 and 688 bearings are included. My MakerGear Prusa uses 688 bearings, so I haven't tested this with a 608. It should work just fine, but please post in the comments if you find another crown radius works better.

I also haven't tried it on my Y axis because I don't want to disassemble the printer just for this.

Leather belts were ususally run at low tension, low speed, were usually 10 or more feet long and had a lot of slop, so the crown was necessary. That being said, a high tension, high speed nylon belt needs a little bit more of a crown than a leather belt. I usually set the crown height at twice the thickness of the belt and the crown length to be 75% of the belt width. Note this gives you a pulley that is 1.5 times the width of the belt.

Crown pulleys will work, but they cost more to buy and take more material to make than a standard pulley

criswilson10 Wrote:
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...
> Crown pulleys will work, but they cost more to buy
> and take more material to make than a standard
> pulley

Commercial ones, yeah. Printed ones are dirt cheap and won't catch on the belts' teeth.

Do you use crowned pulleys on a regular basis?

I use crowns when I'm prototyping because I can just eyeball the pulley alignments and loosen the lock screws to let the
belt align the pulley. If the prototype moves on to production, then I use "regular" pulleys to save a penny or two.

I haven't tried printing one yet, I usually just screw a regular wide pulley to a drill bit, spin the drill up, and drop
a 120 degree file across the belt area to cut a crown.

So will a crowned pulley work the same on the toothed side of the belt? I'd like to try this on a 624 bearing.

If you use the tooth side against the pulley, you usually have to have a bit more belt tension - or have a gear tooth crowned pulley.
In a pinch, I've use a heated, bent paperclip to burn gear teeth into a crowned plastic pulley.

I'm using my crowned pulley on the toothed side of a GT2 belt. A more coarse pitch like T5 probably needs more tension like Cris said, or possibly a higher crown.

great, thanks. I'll have to give it a try someday soon.

Dale Dunn Wrote:
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> The other night I remembered that flat belts on a
> crowned pulley will automatically find the center
> of the pulley.

To put it right, they dont automatically find the geometric middle. What they do find is the point where the friction is maximal. Or better yet they automatically get "stuck" or get "attracted" in that place with most friction. It could be the middle, but its not necesarily so.

Are you sure? I thought they found the point with the largest diameter.

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[www.hydraraptor.blogspot.com]

Technically, they find the point with the largest diameter, which happens to be the point with the greatest friction for that belt.
Rarely is that in the middle.
[woodgears.ca] explains it pretty well and has pictures.

V drive pulleys are the ones that track to the middle and are move common, these days, in belt drives.

Nice video. It occurs to me that I probably have too much tension on my belt, since it doesn't ever pull itself all the way up onto the crown. I just swapped the new pulley in, and never adjusted the tension. Oops.

Great article and video! Thanks for sharing

Yes the belt finds the point with highest friction and sticks to it because all the other directions frictions are smaller. Diameter works for that, but its not the cause. The shape here is what makes a certain friction happen, but the friction is the force that draws it and make things happen. The diameter is just a plain unit of measure, and it is not a force, hence the diameter cant do anything by itself.

So its a bit the other way around: it finds the point with higher friction, which happends to be on the center. Not the other way around.

Where the guy in that tutorial says "tension" you should read friction. The belt tension by itself also like the diameter, has no meaning. What it does do, it increases the force to which the belt presses against the pulley. Now friction force is [friction coef * perpendicular force].

By increasing the tension in the belt, the belt pushes harder against the bump, and therefore its "weight" increases, and the friction in that point increases even if the friction coef stays the same. Thats the "magic" of attraction. If you think of centimeters diameter, ofc its "magic". Once you think of friction, there is no "magic" anymore.

When we walk friction is the force that vectors to our behind and depends on our weigt * friction coef of our shoes with asphalt. The area of contact has no deal in it. We can have 1 ton of mass on ashpalt and either if it contacts on a 100sqm area or on the top of a needle, the friction force is the exact same regardless.

When you see the belt moving towards center, that is when the highest friction force won the vectorized battle with all the other smaller forces in other direction, including it overcomes the tendency of the bump's higher diameter to throw the belt away.

Because if anything the diameter itself of the bump would throw the belt away, and would never draw it in. To draw it in, it would have to be a groove and not a bump. But the bump is small enough so the this "inclined plane" vectorized force can be overcome by the bigger friction force. As long as the materials friction coef is good enough. Make the bump too big after a certain point depending on the friction coef of the materials and the belt would be just thrown away and would never stick there.

So diameter is measured in cm, and cm is not a measure of force, hence regardless of how many cm u get of "something" it cant make things move by itself. Belt tension is like a spring, but also doesnt mean anything by itself except that at a point the belt mai fail.

The only force that is actually a force and as such, it is capable of moving things here is the friction force. It increases in the bump area because the belt increases its vectorized tension effect there. It presses more on the bump, so the friction force is directly proportionally biger. Not much, just a % hint, but enough as it only needs to be bigger with a minimal increment. Friction by definition oposes the movement, hence the belt gets stuck at that point because the biggest friction force 1) first wins out as a vector against all other forces, and 2) afterwards succeds in opposing to movements in all other directions.

The thing with "belt finds the bigger diameter" is a sort of a big overlook/shortcut. Exactly what kind of explanation you receive from some1 that doesnt want to give explanations. Its counterintuitive and doesnt help understanding. Sorry to resurect the old thread but would of been a shame to leave it at that.

Edited 2 time(s). Last edit at 07/10/2012 09:15AM by NoobMan.