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How do I Calculate Pulley Diameter for Timing Belts

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Neil Wyatt23/05/2020 15:33:04
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I 3D printed a timing pulley, calculating the diameter as:

pitch x number of teeth / PI

The result was a (100 tooth) pulley that was about two pitches too large in circumference. (A 20-tooth pulley seems fine as the error is too small to have an effect).

I couldn't find a clear calculation online, but measured a real 66 tooth pulley which was just over 98.2% of the calculated diameter.

I did find a diagram that showed how the pitch line is some distance 'up' the teeth, but no formula for calculating the amount of compensation for this.

I'm printing a second pulley using the empirical figure of 98%, as this seems right if the original size was two pitches too large for a 100 tooth pulley.

But it would be nice to know a formula for calculating the correct figure, especially if I create machine pulleys in the future.

Neil

HOWARDT23/05/2020 15:45:34
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Can’t remember the dimensions, but you may find it here Transdev. I used to use these in the past as they made any pulleys from supplied drawings when I did a lot of special pulley and belt assemblies.

Michael Gilligan23/05/2020 15:46:24
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Don’t forget there are different types of timing belt, with different geometries.

Probably best to look at reference material from Gates, or one of the other big manufacturers.

MichaelG.

blowlamp23/05/2020 15:56:28
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Gearotic should have what you need.

 

Martin.

Edited By blowlamp on 23/05/2020 15:57:01

Neil Wyatt23/05/2020 16:00:35
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Posted by Michael Gilligan on 23/05/2020 15:46:24:

Don’t forget there are different types of timing belt, with different geometries.

Probably best to look at reference material from Gates, or one of the other big manufacturers.

MichaelG.

I did spend about 20 minutes looking.

I've now found this:

Pitch Diameter (P.D.) = (Pitch x Number of teeth) / Pi (3.14159)

Timing belt pulley Outside Diameter (O.D.) further builds upon the relationship between the timing belt pulley and timing belt. The Outside Diameter (O.D.) of the timing belt pulley is in contact with the tooth bottom of the timing belt while meshing with it. The distance from the timing belt tooth bottom to the tensile cord (pitch line) will determine the Outside Diameter (O.D.) of the timing belt pulley for any timing belt pitch/timing belt tooth profile.

Outside Diameter (O.D.) = Pitch Diameter (P.D.) – (2 x U)
Note: “U” = distance between the tensile cord and the bottom of the timing belt tooth

The challenge is now finding 'U' for a 1.5mm belt, which seems to be a bit obscure...

Michael Gilligan23/05/2020 16:10:23
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Not quite, Neil ... There are different geometries of tooth available

You may need to identify which 1.5mm belt you are using

MichaelG.

.

Edit: This looks quite useful

https://www.instructables.com/id/Types-of-Timing-Belts/

Edit: is this the belt profile you are using ? 

https://uk.misumi-ec.com/vona2/detail/221000230640/

 

Edited By Michael Gilligan on 23/05/2020 16:13:44

Edited By Michael Gilligan on 23/05/2020 16:21:23

Michael Cox 123/05/2020 16:12:27
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Hi Neil,

You can look up the outside diameter of standard pulleys in manufacturers literature, see for example:

**LINK**.

When I have machined timing belt pulleys I use the given outside dimension for the number of teeth and then cut the grooves to give the require angular pitch.

Should be possible to use the same method to 3D drawing and then print.

Mike

blowlamp23/05/2020 16:36:14
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From Gearotic:

HDT5 100 tooth wheel.

O/D 158.0119

Outside Radius 79.006

Pitch Radius 79.5775

Root Radius 76.846

Edited By blowlamp on 23/05/2020 16:59:23

John P23/05/2020 16:49:38
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Hi Neil

From an article that i wrote in MEW 164 there are some calculations for 1/5 xl 3/8L and 5 mm htd i can't find the article among my notes .For 1/5 xl it is .200 x number of teeth divide by Pi - .020 inch = OD,

100 tooth pulley = .200 x 100 = 20 inches divide by Pi =6.366 inch - .020 inch = 6.346 inch ,in all

cases the pitch diameter is always is always greater than the OD.

John

John Haine23/05/2020 16:50:35
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There are several online calculators around associated with different suppliers. A while back I produced my own spreadsheet which I recently resurrected to work out the pulley spacing for power power feed (yes it worked but I did slightly reduce the spacing and added a belt tensioner). I'd be happy to share that with anyone that wants it.

Neil Wyatt23/05/2020 16:52:41
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It seems U is about 0.5, but that's me trying to measure it with a calliper!

Still my new pulley seems OK. 0.1mm nozzle is very precise, but very, very fussy about settings!

large pulley.jpg

Neil Wyatt23/05/2020 21:39:39
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I see that several folks posted while I left the window open to sort a photo!

I wasn't ignoring you all!

It seems the calculations are different for different pulley sizes. For the 1.5mm belt the 66 tooth pulley is allowing about a ~0.5mm reduction.

The 100 tooth pulley was designed with a greater reduction than that but printed slightly oversize soworked out with a 0.5mm eduction below theoretical size.

That's not what I expected from the print, but the ridged surface does mean that prints are often slightly oversize, even with me using a correction, its the one for a larger nozzle.

I tried to arrange a click and collect of 18mm play for the platform from B&Q but they cancelled it and returned my money without explanation.

Looks like Wickes may have it but not as click and collect.

Neil

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