How to calculate timing belt lengths / diameters?

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jonnybischof
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How to calculate timing belt lengths / diameters?

Post by jonnybischof » March 7th, 2016, 5:32 am

I'm trying to solve the following problem:
screen.png
warthog extruder belt drive, WIP
I'm making a GT2 belt drive, and now I want to calculate the exact needed belt length, or rather the exact needed spacing between the two axes.

Does anyone have a formula for this calculation?
Maybe also some rules of thumb to account for proper belt tension?
Best regards,
Jonny

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Re: How to calculate timing belt lengths / diameters?

Post by jonnybischof » March 7th, 2016, 5:50 am

As always, I trust Misumi to be a very good source for information:

http://uk.misumi-ec.com/vona2/detail/11 ... 96%3A%3Aag

So, the important decisive dimension is the length and position of the core wire.
The length is ( n * 2 ) with n being the number of teeth, and 2 being the "GT2" 2mm pitch

This means that if I were to wrap a 60T belt around that 60T pulley, I would have a 120mm belt circumference, which results in a belt ( = core wire) diameter of 38.2 mm (120mm / pi)

Doing the same for the 20T Pulley, I get 40mm circumference and a core wire diameter of 12.7mm

Now, I just add tangents to the two circles, and measure their length:
belt overall length - before correction.png
Then select the nearest valid belt length, which would be 154mm (77 teeth) in my case, and adjust the axis spacing until I get the correct value:
belt overall length - spacing corrected.png
Does that sound ok, or am I missing something?

Now, I have a very nice CAD program that lets me do this comfortably. But is there a general way to mathematically describe those tangents? It would be really nice to have an Excel spreadsheet where you can enter two diameters and a spacing and get the belt length...

/edit:
About belt tension:
Mounting the motor (smaller pulley) with slotted holes should solve that problem without having to do a lot of calculations. I actually have slotted holes in the parts that I already had lasercut. I just noticed that there's an error in my SpaceClaim drawing where the slotted holes are actually round holes there. Gonna fix that error.
Best regards,
Jonny

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jonnybischof
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Re: How to calculate timing belt lengths / diameters?

Post by jonnybischof » March 7th, 2016, 6:46 am

timing belt final.png
Finished. I added the slotted holes like they were in my first prototype. It looks like it will actually work as a direct replacement to my horrible lasercut steel gears. Ofc I would now center the slot holes to their correct position, but as I've already got a few parts produced, I will not do that until the thing gets a revision and a new set of lasercut steel parts.

For the belt thickness, I offset the initial curve inwards by 0.25mm (0.254mm as per Misumi spec, leaving the 0.004mm away), then from that new curve outwards by 0.65mm (belt thickness). Then deleted the initial curve (or you could leave it for future modifications) and extruded the result by 6mm. I left the teeth away, seemed unnecessary...
warthog wip - belt drive done.png
Best regards,
Jonny

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Amedee
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Re: How to calculate timing belt lengths / diameters?

Post by Amedee » March 7th, 2016, 8:10 am

If you look at this, there are plenty of online calculators -- e.g. this one, it is in JavaScript so you can look at the sources for the formulas.
Phil.

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Re: How to calculate timing belt lengths / diameters?

Post by jonnybischof » March 7th, 2016, 10:13 am

Shit, I just got lmgtfy'd :-?

The results of the linked calculator are accurate, so it succeeds in calculating those tangents. What I don't like about that one is that you have to know your pulley diameter (which you usually don't).
If I can extract that formula into Excel, I can extend it to accept "pulley style & number of teeth" --> pulley diameter.

** working **
Best regards,
Jonny

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Re: How to calculate timing belt lengths / diameters?

Post by Amedee » March 7th, 2016, 10:30 am

Yes absolutely -- the main thing was to get the math for the tangents in an easy way...

And pulleys are a great when you don't need a big conversion ratio
Phil.

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