Resolution along X and Y vs Z: are belts precise enough?

I wonder why in most printers GT2 belts are used for X and Y axes, which give a quite "low" resolution, while so much care is taken for Z axis. A typical GT2 pulley has a diameter of 12 mm, which gives about 40mm for a full turn. If we ignore microstepping, this corresponds (again: usually) to 200 steps / 40mm = 5 steps per millimeter for X and Y axes. If for Z a threaded rod with 6mm diameter is used (metric thread), this gives about 200 steps per turn = 200 steps per millimeter along Z.
So:

X/Y: 5 steps per millimeter ==> 1 step is 0.2 mm = 200 micron
Z: 200 steps per millimeter ==> 1 step is 0.005 mm = 5 micron

Does this make sense in terms of control on printing quality?

If we ignore microstepping (for example if microsteps are not too precise), it seems to me that the X/Y resolution is definitely too low unless one is printing with 0.8mm or bigger nozzle. On the other hand, Z resolution is far too high unless one wants to print at very very low layer height. If we consider microstepping, then Z resolution is just wasted.

Moreover, belts have quite big teeth that may leave some traces on the surfaces of the prints, since I would expect that the pitch of a (tightened) belt is different from the pitch of the pulley by some microns at least.

What do you think?

Quote
cristian
I wonder why in most printers GT2 belts are used for X and Y axes, which give a quite "low" resolution, while so much care is taken for Z axis. A typical GT2 pulley has a diameter of 12 mm, which gives about 40mm for a full turn. If we ignore microstepping, this corresponds (again: usually) to 200 steps / 40mm = 5 steps per millimeter for X and Y axes. If for Z a threaded rod with 6mm diameter is used (metric thread), this gives about 200 steps per turn = 200 steps per millimeter along Z.
So:

X/Y: 5 steps per millimeter ==> 1 step is 0.2 mm = 200 micron
Z: 200 steps per millimeter ==> 1 step is 0.005 mm = 5 micron

Does this make sense in terms of control on printing quality?

If we ignore microstepping (for example if microsteps are not too precise), it seems to me that the X/Y resolution is definitely too low unless one is printing with 0.8mm or bigger nozzle. On the other hand, Z resolution is far too high unless one wants to print at very very low layer height. If we consider microstepping, then Z resolution is just wasted.

Moreover, belts have quite big teeth that may leave some traces on the surfaces of the prints, since I would expect that the pitch of a (tightened) belt is different from the pitch of the pulley by some microns at least.

What do you think?

the main thing is that we aren't ignoring microstepping in practice when operating our printers ,

Quote
belts have quite big teeth that may leave some traces on the surfaces of the prints

have you got any evidence of this occurring ?

i think you are overthinking it .....

---

-=( blog )=- -=( thingiverse )=- -=( 3Dindustries )=- -=( Aluhotend - mostly metal hotend)=--=( Facebook )=-

Given there are plenty of examples of good quality prints from belt driven printers, the answer would seem to be yes. It's an interesting question as to why though. Part of it is that micro-stepping works pretty much as advertised, provided that the torque requirements are still met. And even when the per-step torque requirements aren't met the errors are non-accumulating, so amount to a form of dithering. I think the relatively low resolution in x & y would be more obvious if 3d printers were pixel based - stopping the head at every point to place a dot of plastic at each point. In that case you'd have to overcome axis stiction on every microstep and the torque limitations would likely show up badly. But since filament printing is based on segments the head keeps moving most of the time and overcoming stiction is not so much of a problem. The Z axis has very different requirements to X & Y for most printer designs as it usually carries a lot more weight and performs more limited movements. Lead screws make sense for Z, while the lighter & faster belt drives make sense for X & Y. Not that you couldn't use lead screws everywhere, but you'd have to spend a lot more to get the same dynamics.

Edited 1 time(s). Last edit at 05/29/2015 01:22PM by JamesK.

Quote
JamesK
The Z axis has very different requirements to X & Y for most printer designs as it usually carries a lot more weight and performs more limited movements. Lead screws make sense for Z, while the lighter & faster belt drives make sense for X & Y. Not that you couldn't use lead screws everywhere, but you'd have to spend a lot more to get the same dynamics.

On a delta printer, the Z axis drive relies on belts too. I have found this quite adequate down to layers heights of 0.1mm. I haven't tried lower.

---

Large delta printer [miscsolutions.wordpress.com], E3D tool changer, Robotdigg SCARA printer, Crane Quad and Ormerod

Disclosure: I design Duet electronics and work on RepRapFirmware, [duet3d.com].

Quote
dc42
On a delta printer, the Z axis drive relies on belts too. I have found this quite adequate down to layers heights of 0.1mm. I haven't tried lower.

Good point. Deltas are really an ideal proof point of how well you can do with belt drives. It's such a cool design. Deltas are what got me excited about building a printer, even though I eventually opted to build a Prusa.

... belt drives are been used mostly for higher possible speeds than with spindles.

As the Z-axe can be much slower and the steppers with spindles can withstand the gravity with motors off, this is the most practical solution for the standard machines ...

---

Viktor
--------
Aufruf zum Projekt "Müll-freie Meere" - [reprap.org] -- Deutsche Facebook-Gruppe - [www.facebook.com]

Call for the project "garbage-free seas" - [reprap.org]

Wouldnt flex, backlash, and other undesirable movements have more negative impact than belts and pulleys? Inkjet printers use belts and they get pretty nifty resolution but they also benefit from multiple nozzles firing off at precise timings. They also use dc motors with encoders so there are some parallels but big differences too.

One thing people seem to forget is that once you start counting microns a 3d printer really isn't that rigid. If your nozzle is too close to the previous layer the plastic will both push the nozzle upwards and spread out more, making it somewhat self correcting.

Once your layer height gets small enough you basically need to imagine every linkage as a spring. The hotend in most printers will move a few microns when exposed to a strong breeze.

Quote
thejollygrimreaper

Quote
belts have quite big teeth that may leave some traces on the surfaces of the prints

have you got any evidence of this occurring ?

I think I do. I have seen vertical stripes on many printed objects with glossy surface from different printers and I cannot find any other reason for their existence. I cannot quantify the stripes in terms of microns, though. For sure they do not affect the printed objects in terms of functionality, but they do exist, and quality is not necessarily just "being functional" mechanically.

Quote
JamesK
The Z axis has very different requirements to X & Y for most printer designs as it usually carries a lot more weight and performs more limited movements. Lead screws make sense for Z, while the lighter & faster belt drives make sense for X & Y.

The difference in resolution between Z and X/Y is about 40 times. I agree that Z is different from X and Y, but not "40 times" different. The weight of my bed is more than 0.5kg and it relies on a belt to move horizontally. Please show me a printer that has a bed lighter than 0.5kg and something to move along Z that weights 40 times 0.5 kg = 20 kg.

I am not telling that it does not work, I am trying to understand why it is usually done like that, even it were just to reduce the costs.

Quote
dc42
On a delta printer, the Z axis drive relies on belts too. I have found this quite adequate down to layers heights of 0.1mm. I haven't tried lower.

In this sense, a delta printer seems "better proportioned" to me.

Edited 1 time(s). Last edit at 05/29/2015 01:50PM by cristian.

Quote
VDX
... belt drives are been used mostly for higher possible speeds than with spindles.

As the Z-axe can be much slower and the steppers with spindles can withstand the gravity with motors off, this is the most practical solution for the standard machines ...

To withstand gravity, a lever corresponding to 20 steps per millimeter is more than enough (I tried), which is a resolution 10 times smaller.

And is it really so practical, given that instead of lead screws people tend to use cheap threaded rods with all their consequences of wobble and backlash? Which makes even more nonsense having 5 microns per full step as Z resolution.

Edited 1 time(s). Last edit at 05/29/2015 02:01PM by cristian.

Quote

The difference in resolution between Z and X/Y is about 40 times. I agree that Z is different from X and Y, but not "40 times" different. The weight of my bed is more than 0.5kg and it relies on a belt to move horizontally. Please show me a printer that has a bed lighter than 0.5kg and something to move along Z that weights 40 times 0.5 kg = 20 kg.

The weight of the bed isn't supported by the belts, it's supported by the smooth rods (or other linear bearings). On the Z axis the weight bears directly on the movement system, and in many designs is transferred directly to the stepper motors. None of the weight on the Z axis is supported by the smooth rods. It's this primary factor that makes the difference in gearing between XY and Z appropriate. I guess this also factors into why Delta style printers aim to keep the moving mass as light as possible, along with the speed benefits that go hand in hand and are normally given as primary motivation.

Another factor is that for Z micro-stepping is used for smoothness of motion, but layer heights are recommend to be multiples of the full step distance in order to avoid vertical banding. So for this case your suggestion of ignoring micro-stepping is entirely accurate, and a lower physical gearing is needed to maintain precision.

Quote
JamesK
The weight of the bed isn't supported by the belts, it's supported by the smooth rods (or other linear bearings). On the Z axis the weight bears directly on the movement system, and in many designs is transferred directly to the stepper motors. None of the weight on the Z axis is supported by the smooth rods. It's this primary factor that makes the difference in gearing between XY and Z appropriate. I guess this also factors into why Delta style printers aim to keep the moving mass as light as possible, along with the speed benefits that go hand in hand and are normally given as primary motivation.

Smooth rods support the weight of the bed, but the force applied during the changes of printing direction is much higher than the weight itself, even at normal printing speeds. The fact that the Z motor has to withstand gravity is relevant only because the Z axis (or better whatever moving along it) should not fall down when the motor is powered off.

Quote
JamesK
Another factor is that for Z micro-stepping is used for smoothness of motion, but layer heights are recommend to be multiples of the full step distance in order to avoid vertical banding. So for this case your suggestion of ignoring micro-stepping is entirely accurate, and a lower physical gearing is needed to maintain precision.

This point holds only if bed auto-tramming/leveling is never used. And if lower gearing were absolutely necessary, delta printers would not print so well I guess.

Um, so I don't want to seem argumentative, but a 1G acceleration equates to 9800mm/s2 - is that considered normal printing speed? I confess to a lack of knowledge, but that sounds on the high side to me. Your points about auto-levelling and the deltas are well made. I've often wondered what auto-levelling does to the "use full steps' line of reasoning. I guess it's one of those cases where the benefits out-weigh any disadvantages. Perhaps it comes back to a form jittering and that's sometimes not a bad thing. I think most Deltas use ABL, not sure how that plays into the situation.

[edited for typos - sorry]

Edited 2 time(s). Last edit at 05/29/2015 02:23PM by JamesK.

Quote
JamesK
I think most Deltas use ABL, not sure how that plays into the situation.

Best practice on delta machines is to use the Z probe to perform delta calibration, but not to use ABL. People using ABL on deltas generally haven't calibrated them properly.

---

Large delta printer [miscsolutions.wordpress.com], E3D tool changer, Robotdigg SCARA printer, Crane Quad and Ormerod

Disclosure: I design Duet electronics and work on RepRapFirmware, [duet3d.com].

Quote
JamesK
Um, so I don't want to seem argumentative

Please be argumentative, I am trying to understand the "state of the art" to avoid naive mistakes in the printer I am going to build, so even Devil's advocates are welcome in the thread.

Quote
JamesK
but a 1G acceleration equates to 9800mm/s2 - is that considered normal printing speed? I confess to a lack of knowledge, but that sounds on the high side to me.

My bad, it is high indeed (2000mm/s2 looks "normal" to me). But the acceleration needed for the X and Y axes movement is much, much higher than for Z, so the gearing seems not justified in that respect anyway.

So maybe threaded rods are (or were?) just the cheapest way, and easiest to implement for Z movement on cartesian printers?

Edited 1 time(s). Last edit at 05/29/2015 02:46PM by cristian.

Quote
cristian
If we ignore microstepping (for example if microsteps are not too precise), it seems to me that the X/Y resolution is definitely too low unless one is printing with 0.8mm or bigger nozzle. On the other hand, Z resolution is far too high unless one wants to print at very very low layer height. If we consider microstepping, then Z resolution is just wasted.

Cost, speed, resolution. Pick 2. Belts enable a cheap stepper motor to move things faster. The same motor enables a lead screw to move things with better resolution. If you want to move things fast and with higher resolution, you'll need something better than a standard NEMA 17 motor as a starting point. Yes there's a big difference in accuracy between belt driven X and Y and lead-screw driven Z. But it works, and for a vast majority, is good enough. Z doesn't need to move fast, so going overboard with resolution is better than not enough. You could replace all three axis with a more custom screw with a larger lead distance, but then your costs go up considerably as compared to standard threaded rod available in many hardware stores.

Quote

Moreover, belts have quite big teeth that may leave some traces on the surfaces of the prints, since I would expect that the pitch of a (tightened) belt is different from the pitch of the pulley by some microns at least.

Get a belt and pulley that's made for bidirectional positioning and it shouldn't be an issue.

Quote
cdru
Cost, speed, resolution. Pick 2. Belts enable a cheap stepper motor to move things faster. The same motor enables a lead screw to move things with better resolution. If you want to move things fast and with higher resolution, you'll need something better than a standard NEMA 17 motor as a starting point. Yes there's a big difference in accuracy between belt driven X and Y and lead-screw driven Z. But it works, and for a vast majority, is good enough. Z doesn't need to move fast, so going overboard with resolution is better than not enough.

In other words: belts and threaded rods are the cheapest solutions, threaded rods are better in terms of resolution but they are too slow for X and Y, so they are used only on Z. That makes sense.

Quote
cdru
You could replace all three axis with a more custom screw with a larger lead distance, but then your costs go up considerably as compared to standard threaded rod available in many hardware stores.

I would really like to see if they make some difference on the printed objects...

Quote
cdru
Get a belt and pulley that's made for bidirectional positioning and it shouldn't be an issue.

May you post a link to some example? I did not know the existence of such stuff.

Mark's (digital dentist) build uses a ball screw on Y with very impressive results. He posted a writeup [www.instructables.com]

If you can't glean what you want to know from there I'm sure he'd be happy to answer questions.

Edited 1 time(s). Last edit at 05/29/2015 03:56PM by JamesK.

Quote
JamesK
Mark's (digital dentist) build uses a ball screw on Y with very impressive results. He posted a writeup [www.instructables.com]

If you can't glean what you want to know from there I'm sure he'd be happy to answer questions.

Many thanks!

Quote
cristian

Quote
thejollygrimreaper

Quote
belts have quite big teeth that may leave some traces on the surfaces of the prints

have you got any evidence of this occurring ?

I think I do. I have seen vertical stripes on many printed objects with glossy surface from different printers and I cannot find any other reason for their existence. I cannot quantify the stripes in terms of microns, though. For sure they do not affect the printed objects in terms of functionality, but they do exist, and quality is not necessarily just "being functional" mechanically.

those vertical stripes/ridges are actually the belts vibrating/ringing on a direction change, (eg on corners and such, ) , it's a side effect of a lot of the high speed printing people seem to like to do these days however the solution i found is rather simple and doesn't involve spending days tuning acceleration values , you just slow down the perimeter speed , on my printer i go down to 15mm/sec for the perimeters and the effect is all but eliminated.

---

-=( blog )=- -=( thingiverse )=- -=( 3Dindustries )=- -=( Aluhotend - mostly metal hotend)=--=( Facebook )=-

... vertical stripes on the surface, corresponding with teeth spacing, are caused mostly by the belts, running around smooth bearings - the tension of the belt changes with the count of teeth or gaps pressing on the bearings.

To avoid this, you'll need pulleys with the correct form ...

---

Viktor
--------
Aufruf zum Projekt "Müll-freie Meere" - [reprap.org] -- Deutsche Facebook-Gruppe - [www.facebook.com]

Call for the project "garbage-free seas" - [reprap.org]

Quote
thejollygrimreaper
those vertical stripes/ridges are actually the belts vibrating/ringing on a direction change, (eg on corners and such, ) , it's a side effect of a lot of the high speed printing people seem to like to do these days however the solution i found is rather simple and doesn't involve spending days tuning acceleration values , you just slow down the perimeter speed , on my printer i go down to 15mm/sec for the perimeters and the effect is all but eliminated.

I don't think we are talking about the same stripes. Those that come from vibration on a direction change follow the corners of the printed object, and obey some sort of exponential attenuation the same way spring oscillations do. The stripes I am talking about do not depend on that, they are present all over the object and have no attenuation. Sorry not to be able to provide a picture, I will take one if I have the chance.

Quote
VDX
... vertical stripes on the surface, corresponding with teeth spacing, are caused mostly by the belts, running around smooth bearings - the tension of the belt changes with the count of teeth or gaps pressing on the bearings.

To avoid this, you'll need pulleys with the correct form ...

Thank you for the tip, I cannot confirm or disprove it yet but I will pay attention to it the next time to see if that is actually the source of those stripes.

Quote
dc42

Quote
JamesK
I think most Deltas use ABL, not sure how that plays into the situation.

Best practice on delta machines is to use the Z probe to perform delta calibration, but not to use ABL. People using ABL on deltas generally haven't calibrated them properly.

Ah, thanks for the clarification - I hadn't appreciated the difference between auto-calibration and ABL.

Quote
cristian

Quote
thejollygrimreaper
those vertical stripes/ridges are actually the belts vibrating/ringing on a direction change, (eg on corners and such, ) , it's a side effect of a lot of the high speed printing people seem to like to do these days however the solution i found is rather simple and doesn't involve spending days tuning acceleration values , you just slow down the perimeter speed , on my printer i go down to 15mm/sec for the perimeters and the effect is all but eliminated.

I don't think we are talking about the same stripes. Those that come from vibration on a direction change follow the corners of the printed object, and obey some sort of exponential attenuation the same way spring oscillations do. The stripes I am talking about do not depend on that, they are present all over the object and have no attenuation. Sorry not to be able to provide a picture, I will take one if I have the chance.

Quote
VDX
... vertical stripes on the surface, corresponding with teeth spacing, are caused mostly by the belts, running around smooth bearings - the tension of the belt changes with the count of teeth or gaps pressing on the bearings.

To avoid this, you'll need pulleys with the correct form ...

Thank you for the tip, I cannot confirm or disprove it yet but I will pay attention to it the next time to see if that is actually the source of those stripes.

what type of belt are you using? and on what size pulleys?

---

-=( blog )=- -=( thingiverse )=- -=( 3Dindustries )=- -=( Aluhotend - mostly metal hotend)=--=( Facebook )=-

My printer has a 10mm pitch ball screw driving the Y axis and 1/2" lead acme screws in the Z axis, and a 2mm pitch belt driving the X axis. I don't see much difference in performance between the X and Y axes, but I limit print speed to about 50mm per sec.
Here are some microscope photos of some vases I recently printed. I've looked at all the flutes under the microscope and they all look the same in terms of positional accuracy and uniformity of layer thickness. IRIC these were all printed with a 0.4mm nozzle and 0.3 mm layer thickness so they'd finish quickly.

The X and Y axes use DSP drivers running at 64:1 microstepping and have 32V power supplies. The z axis and extruder are driven by the 8825 chips on the smoothieboard with 16:1 microstepping.















I have printed down to 50 um layers with the 0.4mm nozzle, but extruder calibration was off a little and the prints looked a little blobby. I have a 0.25mm nozzle that I'll put on the machine one of these days and then I'll calibrate the extruder at 20 or 50 um and try a small print.

Quote
VDX
... vertical stripes on the surface, corresponding with teeth spacing, are caused mostly by the belts, running around smooth bearings - the tension of the belt changes with the count of teeth or gaps pressing on the bearings.

To avoid this, you'll need pulleys with the correct form ...

Or you can use a $0.10 spring to "smooth out" any variations in tension of the belt(s):

[www.youtube.com]

And just my $0.02 regarding the OP's original question in his first post:

Yes, GT2 (and I suppose some other types, but I have only used GT2) belts are more than precise enough when used to provide linear motion along the X and Y axis in a Prusa i3-style printer, or along the three X, Y and Z towers in a linear delta, at least as far as current FDM technology is concerned (I mean, with current layer thicknesses and nozzle diameters). This can be demonstrated both by calculating the theoretical precision of belt drives, but also by empirical observation of printed objects on printers that use belt systems (the calculations in the OP's first post are missing microstepping considerations as already remarked, leading to incorrect conclusions).

There is strictly nothing to gain (in terms of resolution) by using more expensive linear drive mechanisms.

... this "tension-waves" will occur with the spring too, as it's not only tension, but more a minimal displacing of the printhead, when the belt moves around the bearings.

Imagine a gear, rolling on a table - the center distance from the table changes with every tooth or gap ... this will be the same, but with much lower effect, when you bend a belt around a smooth bearing/cylinder and move it around - so the distance of the printig head in relation to the bearings will change slightly, what's only visible in this sort of vertical waves ...

---

Viktor
--------
Aufruf zum Projekt "Müll-freie Meere" - [reprap.org] -- Deutsche Facebook-Gruppe - [www.facebook.com]

Call for the project "garbage-free seas" - [reprap.org]

Quote

the center distance from the table changes with every tooth or gap ... this will be the same, but with much lower effect, when you bend a belt around a smooth bearing/cylinder and move it around

Hmm, I can visualize the effect for one side of the bearing, but can't intuit how the two sides interact for different diameters. The maths looks marginally painful for a Friday evening (where's the embarrassed smiley when I need it?). I'm guessing the effect is quite small for anything other than the smallest of bearing diameters - the change in effective diameter being dictated by the relative curvature of the bearing vs the pitch of the teeth. Hmm, when the rest of the parts arrive I will have a spare GT2-20 pulley, perhaps I should make up an idler with that and see if I can spot any difference. Certainly a toothed idler should in principle be better than a smooth bearing.

Quote
thejollygrimreaper
what type of belt are you using? and on what size pulleys?

I noticed these stripes on other printers besides my own. It does not make sense to talk about my printer (GT2 2mm belts with 24 teeth pulleys, if I counted well) since it is so unreliable that those stripes may even come from the transit of the Moon or some nearby asteroid, and I have currently no access to the other printers so I cannot answer such a question right now.

Quote
the_digital_dentist
I've looked at all the flutes under the microscope and they all look the same in terms of positional accuracy and uniformity of layer thickness.

Many thanks for your detailed reply.

Quote
the_digital_dentist
I have printed down to 50 um layers with the 0.4mm nozzle, but extruder calibration was off a little and the prints looked a little blobby. I have a 0.25mm nozzle that I'll put on the machine one of these days and then I'll calibrate the extruder at 20 or 50 um and try a small print.

If you are posting the results online please let me know where, I am looking forward to knowing them.

Quote
AndrewBCN
Yes, GT2 (and I suppose some other types, but I have only used GT2) belts are more than precise enough when used to provide linear motion along the X and Y axis in a Prusa i3-style printer, or along the three X, Y and Z towers in a linear delta, at least as far as current FDM technology is concerned (I mean, with current layer thicknesses and nozzle diameters). This can be demonstrated both by calculating the theoretical precision of belt drives, but also by empirical observation of printed objects on printers that use belt systems (the calculations in the OP's first post are missing microstepping considerations as already remarked, leading to incorrect conclusions).

There is strictly nothing to gain (in terms of resolution) by using more expensive linear drive mechanisms.

As I said in the first post, if microstepping is to be considered reliable, then my only observation is that the driving mechanism with threaded rods on Z gives a resolution so high that it is mostly wasted. Besides that (and again, by considering microstepping) I agree that belts are good enough in terms of resolution: 1/16 microstepping gives a resolution of about 13 microns per microstep, which is more than enough.

But belts are elastic, no matter how taut they are. And judgements based on empirical observation depend on the eye of the observer and his/her expectations.

On the other hand, 20 microns layer height and 0.25mm nozzle diameter are probably the best quality I may ever hope to achieve with this technology (yes, 0.1mm nozzles do exist and I read about people printing at 5 micron layer height, but I don't want to wait weeks for a print...) so if the_digital_dentist finds no difference between belt and ball screw drive at that resolution, I will definitely buy GT2 belts. So, I am really looking forward to his results.

In any case, thank you all for your replies, as usual this has been very, very instructive, far more than I expected.

Edited 1 time(s). Last edit at 05/29/2015 07:57PM by cristian.

@ Viktor,

Interesting!

I guess I will have to test a couple of toothed pulleys in one of my printers to verify this. Here is a vertical flat surface and indeed, one can see a very faint vertical wave pattern. I confess I never paid any attention to this because the vertical wave pattern cannot be felt by running a fingernail along the surface, contrarily to the horizontal pattern formed by the layers themselves: