What is the smallest practical XY step size? When does accuracy become overkill?

So for my next build I will be using titanium thread instead of belts and was trying to think of what size drum to print. If I just wrapped it around the shaft of the motor, I did the math and with 1/16 microstepping I would be getting over 200 steps PER MM. Meaning I could theoretically partition one single millimeter into 200 different sections. On the other hand, a 100 mm drum would only get me ~10 steps per mm and be inaccurate. It would be fast as hell (My motors are very nice and have plenty of torque) but would be inaccurate and unrealistic.

Where is the middle ground, quantitatively? I understand that other limiting factors could be whatever the tolerance of my machine is, firmware, etc. I want to pick a number that, no matter how well I tune my machine, will never realistically become the limiting factor. Thanks.

Edited 1 time(s). Last edit at 12/27/2013 02:50PM by SamS.

Every time you double your accuracy, you increase voxel count by a factor of 8. So that means for example, a slicer has to work 8 times as long to render a 50 micron (approx .002) reasonable over kill in my estimation, as it would for a makerbot's .004 resolution. So say you want to go to .001, the average resolution on say a manual milling machine. It will now take 64 times as long to render a slice as for a makerbot (which seems to me to take a rather long time) How perfectly can you measure your filament? The answer is you can only roughly estimate, so you will never get practical results @.001, especially given the fact that it will take longer to render a slice than to print the output. A smooth running machine will give the best output, remember you are dealing more with lines here than points. Just my opinion.

The short answer is it's a trade-off between speed and accuracy.

For the 3D printer I'm designing it has 160 steps/mm with 1/16 microstepping. Personally I wouldn't go any higher resolution that that otherwise you start to sacrifice speed too much. With that resolution I'm able to achieve at least 200mm/s. I haven't yet tested at any higher speeds (my firmware maximum speed limit needs increasing), although 250-300mm/s might be possible.

Thanks, but as I mentioned I understand the qualitative limits of accuracy. Also I'm curious- can you manually specify accuracy in other slicing programs? I use slic3r and my only control there is layer height, which I am not concerned about.

I thought of an easier way to explain it. Say I had only one step per cm: the object would come out looking like it was made out of legos. The sides might be smooth because the z steps are .2 (what I print at.) Now say step size is one step per mm. Suddenly I have ten times the resolution, but circles and arcs still have hundreds of tiny "sides" and objects will appear to be made out of thousands of micro-legos. If you keep going down in step size, eventually it's so small that it appears perfectly round. At what point does it get to this? Because as you get rid of unnecessary accuracy, you increase speed. I want some input so I can find that perfect middle ground. I'll be trying several sizes around a range, but I'm looking for somewhere to start. (10mm? 50mm? 100mm?)

samp: Just read your post, thanks! This is really helpful. You get good prints at 200 mm/sec? Very impressive. Do you have any pictures of your design?

EDIT 2: Samp, another quick question- do you think you would be losing anything if you theoretically doubled your pulley size and went down to 80 steps/mm? I feel like even then there is precision you'll never touch on.

Edited 2 time(s). Last edit at 12/27/2013 06:40PM by SamS.

Sorry, I was a bit vague with my post. The 200mm/s is the maximum travel speed before the motor starts skipping steps, not printing speed. It's still in progress so I don't have any printing results yet. All the progress is on the reprap wiki here: [reprap.org]. It's a bit of a non-standard design because it uses leadscrews for all the axes instead of belts. This will likely result in a lower maximum speed than an equivalent belt or thread drive.

For another comparison my current Prusa Mendel i2 is set at 71.11 steps/mm for the X and Y axes. That's with a pulley diameter of approximately 14mm (2.5mm belt with an 18 tooth pulley).

EDIT: You've read my post by now, so the pulley size isn't relevant in my scenario. I designed my printer to be more towards precision since I wanted to do more than 3D printing. Also although the motor drivers have 1/16th microstepping, I would expect only the accuracy of 1/4 or 1/8 microstepping since the incremental torque between two microsteps is tiny. You are correct to some extent. I wouldn't need all of the precision I have currently, although I think it's better to have too much than not enough.

Edited 3 time(s). Last edit at 12/27/2013 07:07PM by samp20.

You are pushing plastic out the end of a nozzle. The diameter of the "track" is going to be 0.3 to 0.6 mm +/- 5%. You *might* get to +/- 2%. Extruders are only just so good. That puts a limit on your resolution in the 0.01 mm range. Anything over 100 steps per mm is simply wasted.

If you go to precision thread rod for all your drives (normal thread rod won't be good enough) the speeds will drop a lot. Look at your Z speed compared to X and Y on a normal printer. On a real printer you will need a screw with a 20 to 40 mm pitch to hit ~ 100 to 200 mm/ sec under load. I'm in the middle of building a printer like that.

This is kinda of a perennial question, but I guess is never fully resolved because of several unknowns. However, I think it's true to say that very few 3d printers (maybe 2?) out of the 100s on the market use screws for X and Y. That is a useful data point, but it is still possible there is something overlooked.

I think that repeatability of position is more of a factor in terms of print accuracy, which is probably where leadscrews win, not because of the finer resolution. Belts, especially with printed pulleys and a not very rigid frame, combined with microstepping, lead to quite a lot of positioning innaccuracy even if the resolution is good enough on paper.

The draw back of leadscrew is high step rates and slower "rapids", unless you fork out for high lead screws.

I think if I was designing from scratch, I would want something between leadscrew and belts, but I don't know what that is. Rack and pinion perhaps? High end pick and place machines which need both speed and accuracy use linear motors I think.

I think ultimately screws vs belts will never be resolved, since they both have advantages. The path to accuracy and speed is to allow for their respective deficiences. In the case of leadscrew, that probably means a more expensive design with high lead screw and fast stepper drivers, bigger motor drivers.

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For enough money, you can get lead screws with 50mm (2") pitch. That's quite adequate to move a "what ever" at the speeds normally seen in printers. The down side is that you likely will spend $500 to $2,000 on a set of them and all the nuts that go with them (~$60 a foot and $150 each for nuts). They also are a bit heavy (1" diameter steel rod isn't light stuff).

I think the leadscrew thing is distracting from SamS' original question. I only mentioned the leadscrews since it was an example I had of a maximum resolution limit that you don't want to go any higher than. SamS was asking what diameter of pulley to use with a titanium thread. If the 100 steps/mm limit was chosen then that would result in a pulley diameter of 10.19mm.

bobc, Thanks for the input! That's really interesting. Uncle_bob, THANKS. That makes sense and is very much what I'm looking for.

I think I'm going to try a few different sizes. Attached is a graph of pulley diameter vs. accuracy. (In mm.) I'll try a few around the 10-20 range and see If there's a noticeable difference.

Unless you have a way to eliminate all the other sources of error (backlash being a big one), you likely will see more from other contributions (that also vary) than you will from fine grain resolution changes.

Exactly. I want to find out how big of a drum I can use before the resolution comes out over those other sources of error.

I believe someone was saying that as low as 20 steps per mm it was hard to tell the difference, this was using gt2 2mm belt and 20 tooth pulleys, with only 4x micro-stepping. 4x micro-stepping with a 20 tooth wheel will be more accurate than 16x micro-stepping and an 80 tooth wheel, however the movements on the 80 tooth wheel will be smoother because the change in angle will be smaller with the16x micro-stepping.

there are two ways to get a smooth motion from a stepping motor:

1. The motors need to be moving with enough steps per second that there are no noticible steps. as you increase the speed of the stepper it actually vibrates less per step, because the momentum of the moving mass smooths out the motor steps, another reason why micro-stepping is a good idea, because it gives more steps per distance, which means less time in between steps.

2. The second way to get smoother motion is actually to have a larger moving mass, because the mass will naturally keep moving in the direction it is going in, and average out the jerky motions that the stepper makes. Think of a Cadillac, its heavy but its really smooth over the bumps and in turns.

Basically this is a sort of formula if you will: if the moving mass is close to zero and the speed of the stepper is close to zero you will get a cartesian looking pattern out of your prints. If the moving mass and speed are high, the momentum of the moving mass will smooth out the steps of the stepper motors.

There is a limitation to this formula and it is the more momentum you have the more rigid your rails must be, if your rails are not rigid, the momentum that smooths out the steps will wiggle your linear rails around, and you will still have the the cartesian pattern in your print along with some other artifacts. so basically instead of the momentum smoothing out the motors steps it will wiggle your printer.

so in summary by using a bigger wheel you need to have a larger mass to get smoother steps. and to have a larger mass you need to have stronger rails.

From my experience it would be wise to have a regular sized drum say about 15mm or something, and use a higher voltage to drive your motors. this will give you good resolution and a higher rpm and smoother motion because the smaller step size.

If I tear down my printer and put it back together with exactly the same parts, things will change. I will get a different set of results simply because I can't put it back together *exactly* the same way. If I do so a few times I *might* be able to measure the error from my unavoidable variation in assembly technique.

Toss in something like a different gear and even more variables get into the mix. A "better" gear tooth ratio might be mounted so it binds a bit more. A tooth ratio change in the "right" direction might get obscured because the specific gear I have in my had does not match the spacing on your belt quite as well as another gear.

This is why people get into a topic called "design of experiments". You can *never* vary just one thing....

I agree, I was just stating a scenario where the variables were controlled.

Any *practical* test of this is not going to be easy to do.

You could test the smoothness of your printer by doing this

attach a pen to your print head, level the z axis so then pen can draw onto a sheet of paper that will be attached to the print bed.

make a pattern for the printer to sketch out, one continious smooth curved line.

Use a 2d printer with a high dpi and print out a scale image of the sketch.

place the paper under the pen at the beginning of the pattern, make sure its square with the x and y axis, and tape it down as flat as you can.

Run the gcode and see how closely the printer follows the pattern, you could probably even measure the largest deviation from the line.

The simplest answer IMO is to recreate what works for gt2 and then dial it in thrrogh iteration. Not enough work has been done to really give you a rule of thumb.

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This is interesting, this is the second thread where my post has vanished. Let's see if it re-apperars at some point in the future .....