belt/pulley radius

I was just wondering if anyone knows how to work out what the outer radius of a gt pulley with a belt wrapped around it should be. I cant seem to find an answer to this with some googling and was wondering if anyone else knew. I need this little bit of information so i can figure out where to position some idlers and maintain a straight belt path.

I think you'll find that different belt makers make them different thicknesses. When I was laying out drilling locations I had both belt and pulley in front of me, wrapped the belt around the pulley and measured. Steel core belts are thicker than glass core, and the Gates belts I have are slightly thicker than the chinese glass core belts, IRIC.

If you already have the belt you can get a close enough estimate by folding it over on itself and measuring the thickness. That thickness will add to the pulley diameter. Belt that's 1.4 mm thick will end up about 2.2 mm thick when folded over on itself. Unless you have a milling machine on which you can drill holes very accurately, that's as close as you'll need or be able to get.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Ahh, thanks for the info. I thought there was some kind of nominal value for these things that I just wasn't finding. I'll just have to measure the pulleys and belts when I get them.

Gates info is here.

Sdp-si has the pulley info.

I wouldn't trust their info to match the probably Chinese parts that are going into the printer. It's safer to get the parts and measure.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Nominally, a GT2 timing belt has 2mm tooth spacing. The teeth are spaced so that centre to centre there should be 2mm of spacing. This results in the diameter being approximately 2mm times the number of teeth. A 20 tooth gear should result in about 40mm of travel for one revolution. At 200 full steps per revolution and 16X microstepping, this SHOULD result in about 80 steps/mm. With different belt material, this will be somewhat greater, since there is a bit of adjustment for the additional travel that the outside of the belt does beyond this, therefore you can be assured that the actual value will be more than this.

If the gear spacing is significantly off of the 2mm spacing, the gear will chew the teeth off of the belt, so it's pretty safe to assume that this is correct. The radius at the surface of the teeth will be (2mm * tooth count / 2) / 3.15159 mm. To this, you can add the thickness of the belt backing (not including the teeth) to determine the effective radius of the gear for distance purposes.

It's still likely to be more accurate to start with an approximation, measure actual travel and determine a correction factor.

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I'm not looking for how to calculate steps/mm, it's relatively simple. What I'm looking for is the total radius of the pulley and belt so I can offset idlers correctly to keep the belt path straight. I'll probably just end up measuring the belts on my printer to find out. I was just hoping there was some kind of general formula I could use for a parametric openscad script, where I could just input the belt type (gt2, gt3 etc) and pulley tooth count to get an offset.

Did you read the specs in the links I provided? They have all of the data needed to make your calculations.

p.s. Gates belts are not that expensive.

Quote
etfrench
Did you read the specs in the links I provided? They have all of the data needed to make your calculations.

p.s. Gates belts are not that expensive.

And when you have done the computation, what do you do ? You just measure to make sure. then you wonder why there is a difference, then ?

An other amusing thread.

Edited 2 time(s). Last edit at 02/06/2018 04:09AM by MKSA.

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"A comical prototype doesn't mean a dumb idea is possible" (Thunderf00t)

Quote
etfrench
Did you read the specs in the links I provided? They have all of the data needed to make your calculations.

p.s. Gates belts are not that expensive.

Gates belts aren't that expensive on a per foot basis, but you have to buy a minimum of 50 feet. SDP/SI pulleys are pretty expensive and their shipping charges are pretty high.

For those reasons, the belts and pulleys will probably come from different chinese manufacturers and will probably not match the Gates and SDP/SI dimensions exactly. The goal here is to ensure that the belt clamp that attaches to the moving part of the axis holds the belt parallel to the guide rails. As long as you position the pulleys the same distance from the guide rails, the belt will be parallel to the axis. The attachment to the moving carriage should be at exactly the same level (or as close to it as you can get) or the belt won't stay parallel to the guide rails. That results in varying belt tension that depends on the carriage position along the axis and distortion in the prints because the steps per mm in that axis will vary a bit with the carriage position. Prints made near the edge of the bed will be different size from prints made near the center of the bed.

That's why it is best to get the parts first and measure the diameter with the belt wrapped around the pulley. Then you choose the pulley's offset from the guide rail(s), and the position of the belt clamp on the moving carriage to ensure that the belt stays parallel to the rail(s). Realistically, we're talking about a couple tenths of mm, but a 3D printed belt clamp can be made in whatever resolution your printer can handle, so you can get pretty close to the exact value needed if you measure and print carefully.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Normally, when you design something you base it relative to known dimensions. In the case of GT2 pulleys, the known dimensions are the root diameter and the diametrical pitch. If you need to allow for different thickness belts, then the part securing the outside of the belt should be adjustable. The thickness of the belt should not affect how it tracks.

In some corexy printer builds the back side of the belt rides on some pulleys and the teeth ride on others. That can affect the design of the belt clamps.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

^That right there is what I'll be doing, just not for coreXY

@MKSA
I'm trying to make the openscad script easy to use and user friendly, some people can't be bothered and would rather it automated. Besides, these would be very small differences, a couple of mm at most. This would result in minuscule triangulation errors for a result machine with a 200-300mm belt span, let along the 1500mm belt span I'll be using in my build, so the approximate value from the calculations will be good enough. The carriage also wont get within 150mm or so of the idlers, so the worst of the triangulation will be avoided.

When it says outer radius in the spec sheet, does anyone know if that's the tips of the teeth on the pulley or the roots?

Edited 1 time(s). Last edit at 02/06/2018 06:27PM by Trakyan.

It's the outside of the teeth.

Quote
Trakyan
^That right there is what I'll be doing, just not for coreXY

@MKSA
I'm trying to make the openscad script easy to use and user friendly, some people can't be bothered and would rather it automated. Besides, these would be very small differences, a couple of mm at most. This would result in minuscule triangulation errors for a result machine with a 200-300mm belt span, let along the 1500mm belt span I'll be using in my build, so the approximate value from the calculations will be good enough. The carriage also wont get within 150mm or so of the idlers, so the worst of the triangulation will be avoided.

When it says outer radius in the spec sheet, does anyone know if that's the tips of the teeth on the pulley or the roots?

I know a bit about the where and why about these belts. I use them, but before that did a lot a reading. You should. Timing belts are a very smart design. It is not just a belt !
See, I am old school. I don't learn from youtube or forum and don't expect others to do what I should do.

As for the formula, you have been given links to the pertinent doc, links you should have found by yourselves.
From that you can define the required formula, simple, unless you want to account for the swelling/stretching effect due to the bend around the pulley.

Or you can sample a few belts and pulley, measure, then make up a close enough formula. Imported stuff varies so much as written above.

Anyway, at the end, you better measure the real thing as written above.

And there are smooth and toothed pulleys, mounted inside or outside, belt that works in one direction or both, slack side etc... All this info on the net.

Fact is, you should design the system to be adjustable.
Funny the number of belt systems I see in the 3D realm where there is no belt tension adjustment or a very cumbersome one. Not to mention the canted pulleys etc...

Besides, I don't know how your machine looks like.

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"A comical prototype doesn't mean a dumb idea is possible" (Thunderf00t)

My previous one was aimed at steps/mm, but it also has all of the information to calculate the radius.

Or, you can take the nominal diameter of the GT2 timing wheel, which is the number of teeth X 2mm. This is the diameter at the surface, which will be the base of the teeth for the belt itself. Divide that by 2Xpi will give you the gear diameter, and add in the thickness of the belt, less the tooth depth.

A quick Internet search seems to indicate that this is about 0.63mm. Hmmm. Looking at the pulley dimensions, it also appears that the diameter is slightly off. A 20 tooth gear has a nominal diameter by these calculations of 12.73mm, but the physical dimensions show as 12.22mm. The discrepancy of 0.51mm is listed as a part of the belt dimensions, for the gear center. The reference that I found above lists that factor as 0.254mm, which jives, since that would account for a difference of 0.508 (Close enough to the 0.51 for all intents and purposes.)

I would therefore subtract the 0.254mm from the calculated radius of the gear, and from the belt thickness.

So for our 20 tooth gear, the gear radius of 6.11mm + the belt thickness of (0.63mm - 0.254mm) = an overall radius of 6.49mm (6.486, rounded). Doing the math for the gear diameter, I get 6.4882mm keeping more significant digits, but this is probably more precision than you are going to be able to actually manufacture anyway, and 6.5mm will be a functional answer.

Of course, an 18 tooth gear will yield a different answer. You never specified.

Edited 2 time(s). Last edit at 02/07/2018 11:04AM by SupraGuy.

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MBot3D Printer
MakerBot clone Kit from Amazon
Added heated bed.

Leadscrew self-built printer (in progress)
Duet Wifi, Precision Piezo parts

Or you could just use a program like Gearotic to create your pulleys and/or verify your results:

GT2-2mm 20 teeth:
Outside Diameter: 12.2244
Pitch Radius: 6.3662
Root Radius: 4.1122