Double-Belt for LR2

frosty · September 19, 2019, 2:52pm

Since the issue of belt stretch (or perhaps zip-tie stretch) has been in the news lately, I’ve been thinking about variations on the double-belt concept developed by @braunscnc and how it could be adapted to the LR2.

Here’s my latest thought: Add a 2nd Steel reinforced GT2 belt (teeth interfacing with the Fiberglass one to the) to the Y axis. This belt would be shorter than the fiberglass belt and would run straight from one end of the table to the other. The arrangement would end up being similar to Leon’s in the sense that the straight through belt acts as a bit of a rack gear, but doesn’t require an extra rail.

Other required modifications to make this work:

New Belt-end holders. Perhaps a printed part with two self-locking hairpins facing each other which can be zip tied as a unit to the existing end blocks.
Tension adjustment of driven belt. Since the belt loop around the pulley can only be tensioned in belt-tooth increments some other means will be needed to snug the belt up against the drive pulley. Perhaps having one of the idlers mounted in a slot so it can move in and out with an adjustment screw?
Means to ensure the two belts remain meshed. Two extra holes could be placed in the end plate to mount an idler (2x 608? or another gt2 idler) to pull the belt a little closer to the plate and put a bit of 'squeeze' on the belt to keep it together.

Just throwing that out there. Thoughts?

jeffeb3 · September 19, 2019, 3:33pm

The look of that would be really neat. Is the distance between the pulleys a multiple of the teeth? It would need that to mesh, right?

frosty · September 19, 2019, 3:57pm

Total distance around the idlers and drive gear must be an even number to teeth longer than the distance between the idlers. That is what makes #2 above is necessary. Could also contrive some other way to change overall drive-loop length without moving the idlers, I guess. Mount the motors in oblong holes?

jeffeb3 · September 19, 2019, 4:53pm

Probably would help if I read it more carefully.

vicious1 · September 20, 2019, 9:25pm

I guess more importantly what is a good way to actually test belt stretch? I have thought about this since the very first lowrider and some even earlier comments I didn’t believe. I figure you could mount a belt vertically and preload it with 3-5lbs (whatever the gt2 is rated for). Add one of the endstop blocks at a very specific distance and a dial indicator on it. Then add something like 1-2kg, something slightly above max expected load.

I really don’t think there is much. The gt2 6mm belt on the first lowrider at a little over 9’ seemed to have 1-2mm stretch if pushed hard, if it was only a belt issue. Swap to 10mm belt an I don’t notice any. I actually think running 2 6mm belts would be better as you would get rid of harmonics at the same time. This works well on 3D printers with moving beds. Each belt gets a slightly different tension.

I have regular 6mm, premium 6mm, and 10mm. I should really do a quick and dirty test if nothing else. Maybe it is an issue and I was completely wrong this whole time.

jeffeb3 · September 20, 2019, 9:35pm

How do you feel about counting teeth? I would like to know about stretch, but also about the accuracy of the teeth over a distance like the 60" of the LR.

jamiek · September 21, 2019, 2:21pm

I like these ideas. I’ve been contemplating the question of belt stretch and what might reduce it. There are already enough ideas out there so I won’t add more but one thing I will point out is that the effect of belt stretch changes with position.

The stiffness changes with length because a given force will stretch the belt by a certain percentage. Near one end, you will effectively have a short belt to one end and a long belt to the other end, and most of the stiffness is contributed by the short belt, whereas in the middle, you have two medium-length belts and the stiffness of two medium belts could be lower than the stiffness of one short belt.

I measured about 4mm stretch on a 1220 mm length at 5.5kg of tension, or a stretch ratio of about 0.0006 (i.e. 0.06 percent) per kg of tension. This is for a 6 mm belt. Under 2kg of tension, considering each segment separately, the segment from X=0 to the tool has length = X and the stretch is 2kg * X mm * 0.0006 per kg. If the table were 1000 mm long, then the segment of the belt from the tool to X=1000 would have length (1000-X) and under 2kg of force the stretch would be (2kg * (1000-X) mm * 0.0006 per kg).

To calculate the combined deflection of both belts, the question is, under what deflection is the combined force equal to 2 kg. I won’t derive it here but the combined deflection is 1/(1/d₁ + 1/d₂), where d₁ and d₂ are the hypothetical deflections of each belt individually.

The outcome is shown here for a 1000 mm travel and my 6mm belts that stretch by 0.0006 per kg.

[attachment file=114955]

For a longer table, say 3000 mm for LR2, the same formulas produce higher worst-case deflection:

[attachment file=114956]

Also note that these assume a perfectly rigid mounting at both ends. If there is some stretch in the anchors then the orange and blue plots would be shifted upward by the amount of deflection at 2 kg.

I tried measuring this nonuniformity of stiffness and I did find it was slightly less stiff in the middle, but the numbers didn’t exactly reflect the theory. But then there were other things deflecting at the same time and I wasn’t looking for a quantitative confirmation.

Also, the position of the tool in the perpendicular direction has an effect. Near one end in the perpendicular direction, one belt is supporting the majority of the load, but when the tool is in the middle, both belts share the load equally and with half the load should come half the deflection. I also tried to measure this effect, but the results were inconclusive. I am not very skilled at taking these measurements and my setup is pretty janky.

I bought some expensive name brand belts but I have not yet measured their stiffness. I am hoping they are not much better because it’s simpler for everyone if it doesn’t become another variable.

jeffeb3 · September 21, 2019, 3:46pm

When the machine is at rest, there will be some tension in the belts from the two endpoints. That would change the overall steps/mm. I’ve been saying that is negligible, but maybe that’s wrong.

When you’re milling, you will have some load on the belts. When you’re slotting, the load will be highest. When you’re doing a finishing pass, it will be basically zero. If you’re milling aluminum, and doing trichoidal milling and a small finishing pass, you will end up with two kinds of cuts. The trichoidal part, which will be high load, and so you’ll get some flex. And the finishing pass, where you will need accuracy. As long as the high load parts aren’t doing things like grabbing too much material, you’ll be fine and finish with an accurate part.

This sort of supports my gut on the sizes too. At 1m, the mpcnc will have a tough time with aluminum. The LR is bigger than that, but uses 10mm belts. At 1m, other parts, like the conduit, start adding more errors too.

The onky reason I hope the genuine belts are better is if they have basically no flex.

jamiek · September 21, 2019, 3:58pm

I made a measurement and it is looking like high quality belts are stiffer by roughly 2x. The Gates belts sold by E3D (https://e3d-online.com/gates-powergripr-gt2-belt-6mm-x-100mm) are showing roughly 2mm of stretch instead of 4mm, over a 45" length and 5.5kg of load. I want to construct a better setup to measure this more accurately, but at a gross level it looks like there is a difference large enough to make it worth considering.

vicious1 · September 21, 2019, 5:28pm

Where does that stretch start? 12lbs seems pretty big, I think 7 would still be excessive but the number I always had in mind for tests. If we use that 1.9kg rough number I got for aluminum and a tension of under 7lbs. I would really hope to see a preloaded belt with 5lbs and then add some weight as a load?

vicious1 · September 21, 2019, 5:36pm

As for the belt accuracy itself. Without some really large calipers (my last job had a 1M set I think, so cool) I think the only way to test them would be the machine itself. No load, mark out as far as possible, and tension until you get that exact number with a manual move.

I would really like to believe from like 1lb-5lb tension the teeth would be super accurate.

vicious1 · September 21, 2019, 5:39pm

Shoot…Did I just send you a box today Jamie? I could have put in a sample of the import “premium” belt. I believe it is 2x the cost, but if it is 2x as rigid that is a no brainier. Shoot If gates is really 2x…that is significant.

jamiek · September 22, 2019, 2:18am

After measuring more precisely and re-testing the other belts, the difference is smaller than I thought. It appears my previous measurement of 0.0006 per kg was for some reason worse than reality. Measuring with the same setup as the Gates belt, the stretch is more like 0.00040 per kg while the gates belt is 0.00032 per kg.

It’s hard to see the construction by eye, but with enough zoom and flash from my phone camera, I can see the cords in the three belts. In the Gates belt I count 12 cords and in the other two I count 10. In no-name belt 2, they appear smaller in the picture but I’m not 100% confident that’s real. The belts with fewer/thinner cords seem to have less stiffness but I am wary of confirmation bias so I won’t draw a conclusion from that.

Anyway bottom line it looks like the difference is only about 25%, not 2x like I thought. The previous stretch measurement seems to have been somehow inflated by the way it was measured and it wasn’t as bad as 0.0006 per kg.

And yes I just placed an order recently. I’m planning to make lots more mistakes cutting steel, and many tools could die. Although it’s tough because the 4th and 5th axis are fighting for priority, so the steel might end up taking a back seat.

vicious1 · September 23, 2019, 8:49am

I am shocked that it is so linear. I would assume there would be some stretch, then some sort of level-ish spot and then more stretch.

frosty · September 23, 2019, 9:24am

Do you have a steel-reinfoced belt to test as “best case” for stiffness?

Also, I wonder if there is any difference in stretch between clamped belt ends and a belt running over a 16 or 20 tooth gear. Seems like the clamped end would have more clamping force on it than the pulleys would have under ‘normal’ tension and might be stiffer as a result. You could measure the deflection of an MPCNC axis with a dial indicator and a fish scale and compare those values to the baseline established by the above tests and come up with an additional ‘squish’ factor introduced by the teeth deforming around the pulley (if there is any). You could also do the test with differeng levels of ‘static tension’ to see how much a tighter belt will help.

frosty · October 16, 2019, 8:57am

Cross-link to a related thread: