Tuning Timing Belt Tension

So just throwing this out there to see if anyone has tried this. I ended up tuning the tension of my timing belts by tightening them up and using a guitar tuning app on my phone to ensure they all produced the same D# note with the gantry at the same location on X and Y. I want to get the belts as close to equal as possible, what are some ways other people get the tension balanced?


Interesting, pretty good idea.

There should not be a noticeable stretch so close is plenty good, too tight and you will lose steps, too loose and things will be undersized, super loose and you will skip teeth. I keep trying to come up with some sort of 3D printable belt tension gauge, but heck a guitar tuner should at least equalize each axis.

Yeah, found out my belts were not tight enough when two halves of a box with 1/32" clearance would not fit together. I couldn’t figure out a good way to measure the belt tension either, I was trying to draw up some kind of gauge in fusion to do it but came up with this idea and it worked nicely. This of course assumes you want to have enough tension to make notes. I use a bolt type belt tightener, so not sure how easy this would be using zip ties.

It also assume a very similar belt length. But 1/32" is pretty tight for wood a slight change in humidity and that is not going to work for long, I wouldn’t think. That is about what I use for similar plastic parts, dissimilar and I would use more.

The tone should change with length, so you have to make sure the distance from the gantry to the ends are consistent. And there won’t be a good comparison between machines. I guess you could use a calculator to put in a length and it would tell you a ballpark note to shoot for.

Really though, that might just bring out the crazies (present company excluded of course).

Wood can support very tight tolerances if you design it right. The fingers in a box joint that wrap around a box will need to be very tight. The grain is going around the same way, so as long as they are similar boards, they will shrink and expand the same, keeping a tight fit. Plus, plywood is pretty much stable (and actually expands most along it’s thickness). I can’t say for sure if you should be expecting 1/32" (I don’t think I get that consistently on my table saw) but if you had that quality, wood can benefit from it.

I suppose the sound would probably be different for each machine, but I was primarily concerned with getting consistency for all 4 belts. The belts seem to be pretty evenly tightened now, when I finish my homing switches I’ll be doing some more testing on the cut tolerances. Here is the piece I was running with the 1/32" gap for the two halves of the er11 collet holder box. That first picture there is the last cut I ran when I noticed the belts were loose, you can see the poor quality of the cut if you look at the piece on the right.

Before this gets too crazy, there is a proper tension for these belts. Off the top of my head 5-6lbs. Below that and you might get some smaller than expected dims, above that and nothing…as the belts should not stretch at all until you start breaking the banding inside before that happens you will stall the steppers and/or wear them prematurely from to high of a load.

What is usually the problem is people do some crazy things with the cable ties and leave them like giant springs. The cable ties should be short and rigidly bent and lined up as show in the instructions to minimize any bounce.

You are moving around a pretty heavy double gantry unless you turned down the accelerations for that axis I have a feeling that is a bigger contributor to each belt having a different tension. Or perhaps spindle perpendicularity to the work piece, feeds and speeds, or even bit selection. At such low tolerances everything has to be pretty perfect with such deep cuts.

I am not trying to sound like a punk about this. I want people to understand you are chasing pretty serious tolerances and this is not usually a necessary step, and this is also a heavily modified machine. I am just making sure that this doesn’t go like last time and everyone was 100% sure zipties was there issues and everyone switched to screw mounted belts. You could also have people misunderstanding and trying to match all 4 belts no matter what shape there machines were. For the record, I have to reinstall belts all the time for various prototypes and all I have ever done is place the cable ties as I show in the assembly instructions and click them until they feel right. I can only tell if they are too loose so I start there. I also have never tried for 1/32" in wood, so you might very well be right.


Totally agree about having them be the proper tension, and not overdone. On my first machine, I founn that the zip ties worked very well once I shortened them up and removed the ‘spring’ in them. Currently, my belts are tight enough that I cannot feel or see any give to them if I pull on them, but the gantry still moves smoothly and easily by hand with the motors off.

There are a LOT of variables here, and I am pretty much having to make sure I check them all, primarily due to the modifications I have made. Personally think that your original design is best for what most people are looking to do, my machine has a cut area of only 8.5"x11.5" and is intended for small mechanical parts made from harder materials such as acrylic and aluminum.

Could one quantify the belt tension by counting the number of teeth in, say, a carefully measured 400 mm segment? Or are the 200 teeth in a 400 mm segment not enough precision?

I would like to think that would not measurably change. If you try it out and have a way to measure that I would love to know!

I’ve often wondered why it couldn’t be as simple as the way you measure the tension on a motorcycle chain…”it’s right when you have XX” total deflection” up to down. But it’s also affected by the length of the belt which is different on all machines.


What was wrong with the old motorcycle chain tension rule of thumb was the deflection was totally arbitrary, based on how much effort you put into deflecting it. IIRC Honda at one point was using a specific weight hanging from the middle of the chain span, but they stopped giving that spec when people started changing the sprocket size…
Maybe Ryna could do a quick experiment on his machines by hanging a 1kg weight between various length MPCNC sides. :slight_smile:

It has not ever really seemed to matter too much, the “correct” tension window seems to be huge. The spec for genuine 6mm gt2 belt is like 5lbs or something, with zip ties that should actually be easy to set with a scale. I have it listed in the instructions I think.

Assuming belt stretch follows Hooke’s Law, if a belt is suspended by two fixed points (not quite right because of the effect of the rollers, but maybe it’s a good approximation), one can calculate the stiffness coefficient k and the rest length L0 if one measures (a) the undeflected length L, and (b) the respective deflections d1 and d2 for two different weights w1 and w2 in the middle. And from these one gets the tension as k(L-L0).

I may have made some mistake in the algebra, but if I didn’t, the formula for the tension is this big nasty mess: [deleted, as the mess was just plain wrong].

Unfortunately, I think this formula may be really sensitive to small differences, and so it may require weight and length precisions that are really impractical to measure. I haven’t actually tried this in practice.

My formula was wrong. When I corrected it, and tried hanging about 50-150g weights, I got results that seemed reasonable (8.5lbs), but which were more sensitive to measurements than I would trust my measurements. For instance, changing a deflection measurement by 0.01 inches resulted in a tension estimate change of about a pound. The reason for this is that I have two unknowns: the rest length and the stiffness coefficient of the belt.

Moreover, the belt is not very stretchy: if my calculations are right, which they may well not be, the rest length of my cable is only 0.5 mm less than its actual length.

Audio frequency might be a better approach. There is a standard formula for the relationship between frequency, tension, density and length: http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/string.html . We can measure the density and length quite easily, so from the frequency we can get the tension. Unfortunately, the audio tuner app I’ve been trying doesn’t seem to pick up the low frequency of the belt very well. :frowning:

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It should not be, it is belted.



I see what you are trying to do, get some sort of exact number, but we already have one. The belts are rated at 1-5lbf tension. Anything between 2-5 has very little difference in tooth jump torque. With a window that large it is very hard to miss it. Too loose and you will have smaller than expected accuracy, too tight and you will stall your stepper.

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Not a problem. The formula I linked to takes length into account. The frequency scales inversely linearly with length.

Here is another approximate method. Hang one small weight–say, 10-50 grams–in the middle of the belt. Using the deflection and an easy bit of statics gives us a direct calculation of the tension in the belt with the extra weight:

tension = (1/2) * weight * sqrt((length/2)^2 + deflection^2) / deflection

Unfortunately, this is the tension in the belt when it is stretched by the weight, rather than the tension in the belt in its original configuration. But if the weight and deflection are small, and the belt is already under some significant tension, this should be pretty close to the original tension. If we want more precision, we could take measurements with different weights and try to extrapolate to zero weight, but I expect that’s overkill.

As I said, the error in this estimate comes from the fact that putting the weight on the belt changes the tension. And one cannot quantify how much it changes the tension on the basis of a single measurement, because the change in tension depends on two variables: the stiffness constant in Hooke’s Law and the rest length. The error in the estimate is of the same magnitude, however, as the error in the frequency method when the amplitude of vibrations in that method is of the same order of magnitude as the deflection in this method, I suspect. (The frequency formula also doesn’t take the extra tension from the extra stretch into account.)

Yeah, one can probably just eyeball all this. But I’m a mathematician, not an engineer. :slight_smile:

If you’re interested in knowing the tension, then you can do it.

I think that’s probably missing the point. It doesn’t have to be perfect, or even really in a specific range. It just needs to be tight without breaking anything. There isn’t much stretch and there isn’t much force, so it really just needs to be a little past taught to be good enough and not so tight that it’s breaking.

What I do is just pluck it. If it makes a note, then it’s tight enough. If it thuds, then it’s not tight enough. My low rider makes bass notes. My printer makes guitar notes. I’m an engineer (not a mechanical one) not a musician. :slight_smile:

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I had a musician pluck my belts…sounds odd…but he heard a specific note then plucked the rest and they were all different. Can’t win em all.

Using deflection could work if there was a calculator somewhere to type in a few variables but I doubt many can measure weight, deflection and overall length to enough accuracy to get a valid calculation? Then throw in all the various sources of belts and it is game over. I can get a km of two worth of belt and have it be two different kinds in the same batch.

Welcome to my world, of trying to make it work easily over the entire globe with any possible combination of parts imaginable. Engineering…the science of compromises, Math… the science of 100% certainty, Coding…the science of tabs over spaces in your language of choice.

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The tension formula can be made a slightly closer approximation and a lot simpler (by going with the horizontal component of the tension vector). It’s still a bit of an overestimate, but it’s going to be close if the weight hanging on it is small:

tension = (1/4) * weight * length / deflection

This seems simple enough that one doesn’t need an online calculator. The length is the length of the belt from a fixed end to the idler. The weight is the weight of the item hanging in the middle of the length (half-way between the fixed end and the idler). The deflection is the difference between the rest height and the deflected height at the mid-point where the weight is hanging. The length and deflection need it be in the same units and the tension will be in the same units as the weight (e.g., lbs or Newtons).

But if you do want an online calculator, you can use the “Highline tension calculator” here: https://www.ropelab.com.au/two-point-anchor-calculator/ (What I call deflection, they call sag, what I call length, they call span, and what I call weight, they call load.)

Using the deflection method, we don’t need any data specific to the particular belt.

It’s easy to measure the length to within 1% with measuring tape or a long ruler.

The weight can easily be measured with a small kitchen scale to within 5-10%.

The deflection is the hardest to measure, but I expect one can do it to within 10-20% with calipers as long as the belt doesn’t get twisted under the weight.

All this will give us a tension value within 30% or so. From what I hear in the thread, 30% should be good enough.

There will be a small overestimate in the tension due to the tension formula being approximate because it measures the tension of the belt with the extra weight.

The advantage of doing this is that it would reduce anxiety in new builders like me who are not sure if the tension is in the right range and close enough between the four belts.

You can also go backwards. You decide what tension you need, and then you adjust until you have the right deflection using the formula:

deflection = (1/4) * weight * length / tension

(I am not promising I didn’t make some mistake. It’s been three decades since first year physics, and I’ve made mistakes in this before.)