Steps Per Millimeter

[Trampas Stern]

I am wondering how many people have to tweak their steps per millimeter beyond what the gearing would indicate? 

Specifically if I have a 20 tooth gear, 400 steps per rotation motor, 16x driver  and 2mm belt, then I would end up with (400*16)/(20*2) = 160 steps/mm. 

So I was wondering how many people have to tweak the actual number to get system working correctly and if so where is the error? That is is the issue people see that the gear diameter is not correct, or other? 

Thanks

[Bernd Walter]

There can't be anything wrong with the motor or the pulley.
Tooth and steps are fixed.
If you stepper has 400 steps per revolution and your gear 20 teeths, then there can't be anything wrong.
What can happen is that you've got an MXL instead of GT2, which has 2.032mm spacing instead of 2mm.
But what will happen for sure is that a standard belt will be stretched depending on the tension, so that the belt over 500mm distance only takes 249 teeths.
Most evil is if your belt tension changes because your slider mount isn't in a straight line with the belt path between the pulleys.
Normal GT2 have fabric inlay, but you can also get GT2 with steel inlay, which isn't stretching as much.

[Jason von Nieda]

It is common to have to adjust steps per mm per each installation. The pulley diameter gets you close, but there are a number of tolerances that have to stack up just right for that to be perfect. I highly recommend measuring and correcting the error yourself: https://github.com/openpnp/openpnp/wiki/Setup-and-Calibration%3A-Steps-Per-Mm

FWIW, this is also very common for 3D printers and really any belt driven system if you want high accuracy.

Jason

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[Mark Harris]

Even ballscrew systems need to be setup with steps per mm different to the theoretically ideal. No mechanical system is perfect. 

On Mar 22, 2017 8:36 AM, "Jason von Nieda" <ja...@vonnieda.org> wrote:

It is common to have to adjust steps per mm per each installation. The pulley diameter gets you close, but there are a number of tolerances that have to stack up just right for that to be perfect. I highly recommend measuring and correcting the error yourself: https://github.com/openpnp/openpnp/wiki/Setup-and-Calibration%3A-Steps-Per-Mm

FWIW, this is also very common for 3D printers and really any belt driven system if you want high accuracy.

Jason

On Wed, Mar 22, 2017 at 8:48 AM Trampas Stern <tra...@gmail.com> wrote:

I am wondering how many people have to tweak their steps per millimeter beyond what the gearing would indicate? 

Specifically if I have a 20 tooth gear, 400 steps per rotation motor, 16x driver  and 2mm belt, then I would end up with (400*16)/(20*2) = 160 steps/mm. 

So I was wondering how many people have to tweak the actual number to get system working correctly and if so where is the error? That is is the issue people see that the gear diameter is not correct, or other? 

Thanks

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[Trampas Stern]

I was noticing on my machine the steps per mm were 161.42 for X axis with a GT2 steel core belt.  The only reason I can figure that I have a value larger than 160 is that the pulley diameter is smaller than spec. 

[Mark Harris]

It can be many things, pulley diameter is a really easy one - stepper motor manufacturing can be another one, each step isnt reallllly 1.8 degrees, it could be more or less. Belt manufacturing is another one, they are decent but not exactly precise. The parts are only good as the machine that built them, and the machines which built them are only as good as the machines which built them, and so on - this is why every mechanical drawing has allowable tolerances.

On 22 March 2017 at 10:33, Trampas Stern <tra...@gmail.com> wrote:

I was noticing on my machine the steps per mm were 161.42 for X axis with a GT2 steel core belt.  The only reason I can figure that I have a value larger than 160 is that the pulley diameter is smaller than spec. 

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[Bernd Walter]

On Wednesday, March 22, 2017 at 10:16:49 PM UTC+1, Mark Harris wrote:

It can be many things, pulley diameter is a really easy one - stepper motor manufacturing can be another one, each step isnt reallllly 1.8 degrees, it could be more or less. Belt manufacturing is another one, they are decent but not exactly precise. The parts are only good as the machine that built them, and the machines which built them are only as good as the machines which built them, and so on - this is why every mechanical drawing has allowable tolerances.

No, motor and pulleys are technically impossible to be causing this.

A motor with 400 steps per revolution has exactly 400 steps per revolution (he is using a 0.9° stepper).
There is no manufacturing tolerance in the number of steps.
There are tolerances how evenly the steps (especially the microsteps) are spread, but the number per revolution is exact.
The same goes with the pulleys.
A 20 teeth pulley will transport exactly 20 teeth belt per revolution, neither more nor less.
It really is just the tooth distance of the belt, which matters.
And the tooth distance of the belt is part manufacturing plus part tension related.
Maybe the belt is that much off tolerance, or the manufacturer assumed the belt to be used with more tension.

[Mark Harris]

Actually a 20 tooth pulley can move more than 20 tooth pitches per revolution. The pulley is a wheel, and its diameter is all that determines the distance travelled (ie: the circumference of the pulley). The teeth are just there to make it non slip, the belt is perfectly able to stretch and bend to the diameter of the pulley. A pulley is NOT a gear.

If your pulley diameter is say 15mm, then each revolution it will move 2.pi.radius == 47.1239mm (0.11780975mm/step @ 400 step/rev). If it's actually machined to say 15.1mm it will move 47.4380mm per revolution (0.118595mm/step @ 400 step/rev). Then you can get even more fun of a pulley's outside face not being concentric with the bore, at which point your diameter technically changes at each point of the revolution, so if you use a 25mm/1" dial gauge to measure steps/mm you could be off by quite a few steps depending on where in the rotation of the pulley you take your reading. Peter Betz had a lot of issues with his machine's calibration until he used a precision 300mm ruler to set his step count over a longer distance, this of course could be from many things, or many combinations of things, such as tolerance on the belt or concentricity of the pulley.

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[Bernd Walter]

On Wednesday, March 22, 2017 at 11:00:48 PM UTC+1, Mark Harris wrote:

Actually a 20 tooth pulley can move more than 20 tooth pitches per revolution. The pulley is a wheel, and its diameter is all that determines the distance travelled (ie: the circumference of the pulley). The teeth are just there to make it non slip, the belt is perfectly able to stretch and bend to the diameter of the pulley. A pulley is NOT a gear.

If your pulley diameter is say 15mm, then each revolution it will move 2.pi.radius == 47.1239mm (0.11780975mm/step @ 400 step/rev). If it's actually machined to say 15.1mm it will move 47.4380mm per revolution (0.118595mm/step @ 400 step/rev). Then you can get even more fun of a pulley's outside face not being concentric with the bore, at which point your diameter technically changes at each point of the revolution, so if you use a 25mm/1" dial gauge to measure steps/mm you could be off by quite a few steps depending on where in the rotation of the pulley you take your reading. Peter Betz had a lot of issues with his machine's calibration until he used a precision 300mm ruler to set his step count over a longer distance, this of course could be from many things, or many combinations of things, such as tolerance on the belt or concentricity of the pulley.

 

Sorry, but this is BS.
Of course behaves as a "gear" in that situation.
If the pulley won't transport exactly 20 teeth belt per revolution then the belt has skipped, which is a fatal error condition.
Yes that can happen when the tolerances are way off, but otherwise it is just a wear issue.
A pulley, which is too big, will have to stretch the belt while it is running over it.

There is no question that calibration is required, but this is just because of the belt tolerances and nothing else.
Of course a too big pulley can wear out a belt to be stretched permanently, but then again the result is a longer belt.

Concentricity of the pulley is a problem for say half a revolution, but those errors won't sum up, because the
second half revolution has the opposite error.

[Michael Anton]

I agree.  The diameter of the pulley doesn't matter much with toothed belts, as long as the belt teeth engage the belt properly, so this would not be the source of error.  Belt stretch, or inaccurate tooth spacing would be a problem though.  If you have a 20 tooth pulley, there is no way it can move more or less belt teeth than that, unless the belt slips.

As Bernd pointed out, there may be a periodic error within one revolution, but that wouldn't accumulate.  Perhaps you are calibrating for this periodic error, rather than for the tooth spacing error.  The only way to know if this is the case is to calibrate at multiple positions, and it would help if these positions were at a multiple of the distance moved per revolution.  I'd be curious to see results from this.

When I built my 3D printer using GT2 belts, I just put in the ideal values, and the measurements of the printed parts worked out pretty perfectly.  There wouldn't be much I could do to calibrate it any better.

[Mark Harris]

I'm not saying that concentricity error would accumulate, I'm saying if you measure less than one revolution you may measure an incorrect distance, and then set the steps/mm wrong.

You can certainly have a 20 tooth pulley that is wider or narrower diameter, and as the belt is rolling around the diameter that is what determines the distance travelled. Belts are relatively squishy, they will squash their teeth into pockets that are a little too small, and stretch to fit pockets that are spaced a little too far apart. 0.1mm of diameter change is *nothing* to the belt, and not exactly a great tolerance for a pulley either - but at a dollar or two per pulley I honestly wouldnt be surprised to see this much variation.  I can stretch a GT2 belt 0.1mm over a short distance just by pulling on it - belts are not steel, and will stretch  or compress to suit the pockets in the pulley, if the distance is small enough. The 0.1mm tolerance I used as an example adds up to a lot of error pretty quickly.

If we were talking metal gears meshing together, then no, you can't have more or less than a tooth. But a 20 tooth belt pulley can have its pockets a tiny fraction too big or small, or the spacing between pockets a tiny fraction too big or small - still being a 20 tooth pulley but causing the belt to travel further or shorter each rotation. The lathes turning and hobbing the pulley, if they are not just extruded and cut to length, are not perfect. Extruded aluminium is also not perfect. Thermal expansion will also change the size of the pulley and the stretch of the belt.

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[Michael Anton]

I don't think it would happen the way you think though, as it wouldn't be cumulative.  Again, you would see a periodic error during a revolution, but it wouldn't accumulate, since there really isn't anything forcing the belt to stay out of position.  The motor is after all driving a load that will move, so it will not resist the forces that would be required to pull the belt out of alignment by large amounts.

Think about it this way: if you have an error of 0.1mm per revolution, then after 10 revolutions (or 320mm of travel on a 16 tooth pulley) you would be out by 1mm, which is half of the belt pitch.  After 20 revolutions, you are out by a full tooth, which means that it had to skip a tooth.  That just doesn't happen in real life when there is appropriate tension on the belt.  If it did happen, then the load on the belt would be far higher than it was designed for.

The diameter of a pulley only really matters for smooth belts.  If toothed belts suffered from the same problem, these things wouldn't work anywhere near as good as they do.

I still think the error if any has more to do with the belt, than the pulley (stretch, accuracy, temperature, etc.).  The pulley will force the belt to move the correct number of teeth, and any errors in this process will not be cumulative.

If you don't believe me, here is a reference from the people that ought to know: http://www.sdp-si.com/PDFS/Technical-Section-Timing.pdf.

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[Trampas Stern]

I went back and check my calibration of the axis. 

I have about 0.1mm of backlash that I can tell. and using 200mm as the calibration distance I ender up with 160.7585 for the X axis and 80 for the Y. 

The images below shows the calibration and the relative offsets in bottom left of screen. 

I am still having issues trying to get board aligned correctly, which I will discuss in another thread.. 

[Juha Kuusama]

The issue are belt manufacturing accuracy, belt stretch and the accuracy of the reference. Don't rule out the last point! When I was calibrating my machine the first time, I found it surprisingly difficult to find a reasonably priced ruler with specified accuracy. Turned out that when I bought my long ruler, I made a good (not!) deal, as I got significantly more steel than I paid for. :-/

A tip: By far the most accurate ruler with a sensible price tag that I'm aware of, come from http://www.schaedlerprecision.com. No affiliation, just a customer.

[Jason von Nieda]

I will second Juha's comments on accuracy of reference! I wasted nearly a week of debugging and work because I had a 300mm ruler that turned out not to be quite 300mm. I now use a name brand ruler and I trust it much more! https://www.amazon.com/gp/product/B0002FS9HE/ref=oh_aui_search_detailpage?ie=UTF8&psc=1

Jason

On Thu, Mar 23, 2017 at 3:35 PM Juha Kuusama <ju...@kuusama.com> wrote:

The issue are belt manufacturing accuracy, belt stretch and the accuracy of the reference. Don't rule out the last point! When I was calibrating my machine the first time, I found it surprisingly difficult to find a reasonably priced ruler with specified accuracy. Turned out that when I bought my long ruler, I made a good (not!) deal, as I got significantly more steel than I paid for. :-/

A tip: By far the most accurate ruler with a sensible price tag that I'm aware of, come from http://www.schaedlerprecision.com. No affiliation, just a customer.

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[Michael Anton]

Now that looks like a good ruler!!!

[Mark Harris]

Just to follow up on this - the mechanical engineers at work unanimously agree that tooth count has nothing to do with the distance travelled, its all about the pulley diameter and belt height - within reason... ie: belt pitch needs to be somewhat represented by the size of the teeth on the pulley, but the pulley's diameter plus the belt determine the distance. The belt will conform to the pulley, there's no way the pulley made of a harder material can conform to the belt.

Also, on rulers, agreed with the Mitutoyo. Any manufacturer that sells NIST certified rulers, will be vastly superior to any ruler you can buy at a hardware store or office supply/similar store :) It doesn't need to be NIST certified... the other rules they sell should all be well within the tolerances specified. When comparing rules before I bought mine, the Mitutoyo's claims to accuracy were a smidge better than other similarly priced rules. You can also find them on McMaster from various brands, but amazon is cheaper :)

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[Michael Anton]

There will never be a cumulative error, unless the belt is allowed to slip and skip teeth, and that doesn't happen unless you overload the belt, or don't have it tensioned properly.  If you move the belt one tooth, that is the distance moved, as long as the belt can engage the pulley properly (how much the belt distorts on the pulley doesn't actually matter).  Now, there may be error in the actual tooth spacing on the belt, due to manufacturing tolerances, or stretch, but that has nothing to do with the pulley.  Think of it this way, if you have a tooth right at the top of the pulley, and you advance by exactly one tooth, so the next tooth is again at the top, how can this move by more or less than one tooth, as the only thing that has changed between the two situations, is that a different part of the belt is now on the pulley?

If the engineers you work with are correct, then there is little point to toothed belts, as they would need to slip in order to have the distance moved not be related to the teeth on the belt.  Do any of them have a reference that demonstrates their claims?  I'd like to see that if they have one.

[Paul Kelly]

Not disagreeing with anything, just pointing out that, in practice, belt pitch is limited to a few options (2mm, 5mm, 5.08mm are the most common at this scale). For a given tooth pitch, more teeth==more diameter...

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[Michael Anton]

Well, that is certainly true.  What I don't agree with (and it's not something you said) is that small variations in actual diameter affect actual belt travel.  Timing belts are not subject to this, like V type belts are.  That is one of the advantages of having belt teeth.  One can calculate the ratio between two timing pulleys by just using the number of teeth on each of them.  The actual diameter doesn't factor into the calculation.

[Cri S]

What is you'r difference of visual adjusted step/mm and calculated step/mm on a 300mm lenght ?

[Juha Kuusama]

On Tuesday, March 28, 2017 at 12:08:27 PM UTC+3, Cri S wrote:

What is you'r difference of visual adjusted step/mm and calculated step/mm on a 300mm lenght ?

One datapoint: My machine uses GT2 belts from RobotDigg. With 20 teeth pulley, I should get 40mm per revolution. I actually got 39.983mm on X (longer) and 39.954mm on Y (shorter, dual belts). Maybe a few crashes during the development has stretched the X belt a bit more than the Y belts. On 300mm travel, these would be 299.87mm and 299.65mm.

[Cri S]

The most worse error i have seen was on chinese small pnp,
on 300mm the error is 4.8mm more travel as calculated using teeth calculation.
When helping setup pnp from remote, i have seen errors 2-3mm on 300mm several times
when there have used chinese pulley.

[Michael Anton]

Wow, that is a significant difference.  Were you also using Chinese belt with the Chinese pulleys?

So just for fun, I compared some open loop belt I have from Robotdigg, with a Gates Unitta belt (made in Japan I think).  There is a significant difference in pitch between the two, though I couldn't test these under appropriate tension so they were just stretched taut by hand.  I'd say that after about 300mm of length, the Chinese one was shorter by around 0.5mm.  I'm running the Gates belts in my 3D printer, so perhaps that is the reason that it seems to be fairly accurate.  I certainly haven't measured any major inaccuracies in it over the 200mm bed size, and I just used the expected steps/mm when setting it up.  I've been running the same set of belts on my printer for about 4 years, with over 1000 printing hours on it.  I've always thought that at some point the belts would wear out, but there haven't been any signs of that.  Perhaps this is due to using good belts, which I wasn't even aware that I had done...

I'm wondering if the pitch of the belt is manufactured to account for expected belt stretch?  Perhaps in Juha's case, since his travel is shorter than expected, he could use a bit more tension on his belts to bring it into spec.

[Bernd Walter]

On Tuesday, March 28, 2017 at 11:23:55 PM UTC+2, Michael Anton wrote:

Wow, that is a significant difference.  Were you also using Chinese belt with the Chinese pulleys?

300 + 4.8mm is perfectly on spot if you expect a GT2 belt, but instead have an MXL, which has 2.032mm pitch.
300 / 2 * 2.032 = 304.8.

[Michael Anton]

MXL would probably run perfectly fine on GT2 pulleys too...

[Bernd Walter]

On Tuesday, March 28, 2017 at 11:36:44 PM UTC+2, Michael Anton wrote:

MXL would probably run perfectly fine on GT2 pulleys too...

I have two different sets of 20 teeth pulleys from china, which just won't fit a GT2 belt in half
turn, so around 10-12 teeth contact.
It all looks great at first glance, but doesn't run smooth and eventually skips.
They may have been horribly manufactured, but since I got exactly the same problem with two
sets my assumption always had been that two suppliers send me MXL pulleys instead.

[Cri S]

That explain it. It was the only case where the travel was longer as it should move, the other was always less then 300mm.

[Paul Kelly]

At the risk of sounding like I’m arguing against myself (and agreeing with a previous post). If the belt pitch changes from 2mm to 2.05mm as it is stretched, this won’t make any difference to the distance the head moves per step or over a commanded difference.  It will offset the move, but deltaX/Y/Z will stay the same. Moves per step is determined by solely by pulley OD (within reason).

As an example:

 

A 22 tooth, 2mm pitch pulley might have a nominal diameter of 14.006mm.

At that diam we see 44mm of travel per rev.

 

If the pulley had a manufacturing tolerance of +-0.02mm (which it easily could) then the pitch would stay the same, but the teeth would just be a tiny amount taller. The belt (and the operator) isn’t ever going to notice a 0.02mm diameter change.

However, the head will now move between 43.937mm and 44.063mm per revolution.   Over 300mm that works out to +-0.42mm of error.

That’s the difference between the best and worst placement of a TQFP…

 

This is why precision ground ballscrews and 10minute machine warmup cycles exist..

 

From: ope...@googlegroups.com [mailto:ope...@googlegroups.com] On Behalf Of Michael Anton
Sent: Wednesday, 29 March 2017 5:37 AM
To: OpenPnP <ope...@googlegroups.com>
Subject: Re: [OpenPnP] Steps Per Millimeter

 

MXL would probably run perfectly fine on GT2 pulleys too...

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[Bernd Walter]

On Wednesday, March 29, 2017 at 1:16:48 AM UTC+2, PK wrote:

At the risk of sounding like I’m arguing against myself (and agreeing with a previous post). If the belt pitch changes from 2mm to 2.05mm as it is stretched, this won’t make any difference to the distance the head moves per step or over a commanded difference.  It will offset the move, but deltaX/Y/Z will stay the same. Moves per step is determined by solely by pulley OD (within reason).

As an example:

 

A 22 tooth, 2mm pitch pulley might have a nominal diameter of 14.006mm.

At that diam we see 44mm of travel per rev.

 

If the pulley had a manufacturing tolerance of +-0.02mm (which it easily could) then the pitch would stay the same, but the teeth would just be a tiny amount taller. The belt (and the operator) isn’t ever going to notice a 0.02mm diameter change.

However, the head will now move between 43.937mm and 44.063mm per revolution.   Over 300mm that works out to +-0.42mm of error.

That’s the difference between the best and worst placement of a TQFP…

Amazing how difficult this simple thing is.
Yes - if the pulley is bigger it transports more belt - the circumference is bigger, right?
But at the same time it transports a well known number of teeth, right?
The thing is really that simple that the belt is slightly more or less stretched "over the pulley".
So yes - the belt has more mm/teeth "while it is over an oversized pulley"
The outside of the belt even moves faster than the inside ;-)
But the transport mm per teeth is how the belt is stretched over the transport path and not what it is over the pulley.
And the number of teeth per revolution is independent of the precision of the pulley diameter.

 

This is why precision ground ballscrews and 10minute machine warmup cycles exist..

Yes - temperature and ballscrew precision matters - if it is longer it transports more mm per revolution.
Same for the belt - if it is longer for the same number of teeth it transports more mm/teeth.
If you have an asymetric tension system also the temperature matters for belts.

[Paul Kelly]

Amazing how difficult this simple thing is.

J

Yes - if the pulley is bigger it transports more belt - the circumference is bigger, right?

Agree

But at the same time it transports a well known number of teeth, right?

Yep

The thing is really that simple that the belt is slightly more or less stretched "over the pulley".
So yes - the belt has more mm/teeth "while it is over an oversized pulley"

I see what you’re saying, I think the tooth profile on the pulley and the compressibility of the rubber teeth on the belt might compensate for these tiny differences whilst the fibre reinforcing in the belt remained unstretched..  If we really look at it, those fibres ARE the belt, their pitch diameter is the one that matters because everything else is made of rubber..  Of course, even those fibres stretch which is why Kevlar and steel belts exist...

But that’s just speculation

The outside of the belt even moves faster than the inside ;-)
But the transport mm per teeth is how the belt is stretched over the transport path and not what it is over the pulley.
And the number of teeth per revolution is independent of the precision of the pulley diameter.

 

This is why precision ground ballscrews and 10minute machine warmup cycles exist..

Yes - temperature and ballscrew precision matters - if it is longer it transports more mm per revolution.
Same for the belt - if it is longer for the same number of teeth it transports more mm/teeth.
If you have an asymetric tension system also the temperature matters for belts.

 

I was more saying that ball screw errors are  measured in um. A C5 screw, the worst ground grade you can get, is rated to a 23um (0.023mm) over 300mm, the best is 4um (0.004)

Once you get over 1m then rolled screws can be more accurate because the way they are made doesn’t result in cumulative error.

Ref: https://tech.thk.com/en/products/pdf/en_a15_011.pdf

 

Back to point A, belts and pulleys have no grades beyond price and brand. If we are generous and assume that they only have an order of magnitude more error than a cheap ground screw, then you could  seeing 0.23mm error over 300mm or 50% of a 0.5mm pitch part.

Add in different thermal expansion coefficients (which you don’t get with a steel screw, on a steel frame pushing a steel linear bearing) and we find ourselves back to:

 

“Belt driven machines with cheap bearings and aluminium extrusion frames will struggle to place many common parts”.

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[Michael Anton]

You put this very well.  This is what I've been trying to describe the whole time.

Of course there is distortion of the belt around the pulley, but the teeth lock it into place regardless of inaccuracies in the pulley diameter.  To have cumulative error after the belt leaves the pulley, would require the belt to slip, and skip a tooth.  In this regard, a toothed belt behaves very much like a geared system.