Accuracy of the cartesian bot

In reading through some of the builders blogs I have been curious how to maximize the positioning accuracy of my to be built cartesian bot.

The reason I have been thinking about accuracy is due to reading through Nophead's blog: his pieces look amazing, but he started with a commercial table and microstepping positioning system (not that he cheated, just that I am really hoping to build my table :-) ).

What steps have you taken to increase the accuracy of your cartesian bot? Do you find that accuracy and speed are inversely proportional?

---

Robert Carpenter
[www.robertcarpenter.net]

robacarp Wrote:
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>
> What steps have you taken to increase the accuracy
> of your cartesian bot?
>
I used non-captive linear stepper motors which use accurate lead screws and anti-backlash thrust collars instead of belts and gears.

[www.hsi-inc.com]
>
> Do you find that accuracy
> and speed are inversely proportional?
>
Not really, when I stay within the speed ranges my machine is really capable of, viz, 0-15 mm/sec. Beyond that, the linear steppers tend to miss steps when they have to deal with abrupt changes in direction. I don't think I'm too far off the 0.1 mm resolution of my coarsest resolution stepper (Y-axis).

Edited 1 time(s). Last edit at 09/29/2008 03:58PM by Forrest Higgs.

Forrest Higgs Wrote:
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> [...] I don't think I'm too far off the
> 0.1 mm resolution of my coarsest resolution
> stepper (Y-axis).


Do you find that 0.1mm resolution is enough? I ask because nophead's commercial table has, iirc, 0.001mm resolution.

I'll be honest though, I've not really read any other builder's blogs.

---

Robert Carpenter
[www.robertcarpenter.net]

Quote

Do you find that 0.1mm resolution is enough? I ask because nophead's commercial table has, iirc, 0.001mm resolution.

For thermoplastic extrusion, this level of resolution should be fine. After all, STL models are quantised to a grid during the slicing and dicing process... I don't recall the resolution of the grid, but it is probably somewhere between .1 and .01mm. Finer positioning than that is wasted. Admittedly, you could alter this value, at the cost of a lengthened slice/dice time.

The print detail is also somewhat restricted by the fact that you're extruding a .3mm thick filament, or whatever. This is going to limit the vertical resolution of any printed part... to increase it, you'll need to print finer filament which is going to drastically increase your slice/dice/print time. But is that extra resolution needed? I don't recall anyone complaining about the coarseness of a print yet.

I guess you can just tune stuff to suit your own needs. What do you anticipate making? There's nothing to stop you setting up a nice precision manufactured ballscrew driven cartesian bot with a bunch of monster servos driving fancy harmonic gearboxes, apart from your wallet.

Quote

Do you find that accuracy and speed are inversely proportional?

Not at current resolutions without our current steppers, certainly... the speed is limited by extrusion rates.

It is not unreasonable to say that cost and accuracy are inversely proportional, however

Ru Wrote:
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> It is not unreasonable to say that cost and
> accuracy are inversely proportional, however


I've always found them to be directly proportional...

robacarp Wrote:
-------------------------------------------------------
> Forrest Higgs Wrote:
> --------------------------------------------------
> -----
> > [...] I don't think I'm too far off the
> > 0.1 mm resolution of my coarsest resolution
> > stepper (Y-axis).
>
>
> Do you find that 0.1mm resolution is enough?
>
I can always trade out my linear steppers for a finer lead screw. I can buy such steppers with resolutions down to 0.01 mm. I'll take it on the chin for print/cutter speed with that, however. Actually, though, I've found that most of the Haydon Linear Stepper's run about 20% faster at 0.05 mm/step than at 0.1 mm/step. I don't know why that is, but it is.

Given that extruded filament currently has a 0.5 mm^2 cross-section (0.5 mm diameter orifice) I think it's pointless trying to go for finer resolution for extrusion. For cutting, my standard cutter head is 3.175 mm in diameter. I can cut HDPE and HPP as thick as 12 mm with that. If I am willing to limit myself 6 mm plastic sheet, I have a smaller, 1.59 mm cutter head. As you see, however, my cutter head is between 7-15 times bigger than my resolution. It doesn't make too much sense to go for finer resolution in that sense. Any addition resolution would probably be lost in the natural flex of my positioning robot.
>
> I ask because nophead's commercial table has, iirc,
> 0.001mm resolution.
>
There's nothing stopping anybody from going Nop's route. It's certainly been a very successful one. I didn't have the money to invest that he did, nor did I have his extensive experience to bring to bear on my decisions, either. You will notice, however, that Nop is building a Darwin with his commercial positioning table. The goal is to move towards having reprap machines that can replicate bigger and bigger percentages of their own parts. That's why I've been positioning Tommelise to do things like cut steel. I want to make the steppers and mill the PCB's as as well as the structure of Tommelise's next generation.

Quote

I've always found them to be directly proportional...

Heh, guess it depends how you do the maths. Being able to work to 1/10 of the scale would suggest a tenfold increase in price. It made sense to me at the time, anyway

Ru Wrote:
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> I've always found them to be directly
> proportional...
>
> Heh, guess it depends how you do the maths. Being
> able to work to 1/10 of the scale would suggest a
> tenfold increase in price. It made sense to me at
> the time, anyway

Well, I agree that they aren't technically proportional according to the mathematical definition (y=kx) (since a linear increase in cost does not necessarily bring a linear increase in accuracy), but inversely proportional means that when one goes up the other goes down.

I really, really wish that accuracy and cost were inversely proportionate. That would be awesome.

So, the more steps the stepper can make the more accurate it is? How accurate can RepRap get before adding more stepper steps stops making a difference?

The thing you have to keep in mind is that the more steps to your stepper motor, the slower it goes all things being equal. On my linear steppers I rarely use less than a 15 degree step. It just doesn't pay.

BTW, if you want to see how accurate a 15 degree stepper can be...

[www.3dreplicators.com]

There is also a teaser for the article on the main Reprap blog.

[blog.reprap.org]

I really like Vik's plastic cat!

Stepper motors are accurate to +-5% of step angle so any more then 1/10 micro-stepping will not increase accuracy but it will make the motor run smoother.

Micro-stepping does not make the motor run slower as long as your controller is fast enough to send out more pulses.

---

Ian
[www.bitsfrombytes.com]

So, removing the steppers from the equation, what steps have you taken to maximize your accuracy?

I'd think backlash is a concern which, from what I can tell, is not addressed by the McWire cartbot. Is it something addressed by others repstraps? Does darwin address it on the X-Y plane?

What about precision threads? Ball screws are ridiculously overpriced: I am not entirely sure but I get the feeling that if I put together one axis on ball screws I'd be looking at around $300...let alone all three axes.

Acme screws are much better priced, and from what I hear, they are a big improvement over your average 1/4*20 threaded rod. I think I priced an Acme axis set at about $12 -- much more respectable.

What about slop in the table itself? A few of the builders blogs have commented that they are having problems with the z-axis being incorrectly aligned and/or that it has play in it, especially when doing milling. For those repstrappers out there, how are you making sure your table is where you are hoping it is? I've only seen a few mentions of positioning systems...

Then again, is precision at that level an issue when the width of our extrusion is 0.5mm?

---

Robert Carpenter
[www.robertcarpenter.net]

robacarp Wrote:
-------------------------------------------------------
>
> I'd think backlash is a concern which, from what I
> can tell, is not addressed by the McWire cartbot.
> Is it something addressed by others repstraps?
>
Yeah, the Haydon linear steppers that I use have built-in anti-backlash thrust collars inside the steppers
>
> What about precision threads? Ball screws are
> ridiculously overpriced: I am not entirely sure
> but I get the feeling that if I put together one
> axis on ball screws I'd be looking at around
> $300...let alone all three axes.
>
The precision lead screws that come with the linear steppers that I use cost about $1.35/inch in six foot lengths. If you want Haydon to cut them for you they do it for about $5/inch, iirc.
> Acme screws are much better priced, and from what
> I hear, they are a big improvement over your
> average 1/4*20 threaded rod. I think I priced an
> Acme axis set at about $12 -- much more
> respectable.
>
> What about slop in the table itself? A few of the
> builders blogs have commented that they are having
> problems with the z-axis being incorrectly aligned
> and/or that it has play in it, especially when
> doing milling. For those repstrappers out there,
> how are you making sure your table is where you
> are hoping it is? I've only seen a few mentions
> of positioning systems...
>
> Then again, is precision at that level an issue
> when the width of our extrusion is 0.5mm?

Quote
Forrest Higgs
Given that extruded filament currently has a 0.5 mm^2 cross-section (0.5 mm diameter orifice)

Does that not translate to the width of the extrusion being 0.5mm?

---

Robert Carpenter
[www.robertcarpenter.net]

robacarp Wrote:
-------------------------------------------------------
> Given that extruded filament currently has a 0.5
> mm^2 cross-section (0.5 mm diameter orifice)
>
> Does that not translate to the width of the
> extrusion being 0.5mm?
>
No. For most plastics, PLA being an exception I'm told, the extruded filament swells significantly after leaving the extruder orifice. Adrian tells me that this is because molten plastic is a non-Newtonian fluid. I've noticed that with a 0.5 mm orifice HDPE and HPP swells to about 0.8 mm. That works out to a cross-sectional area of right at 0.5 mm^2. I've noticed that ABS and PLC also swell about this much. I've also noticed that the degree of swelling is a function, at least in part, of the melt temperature and the extruder barrel operating pressure. It also seems to have something to do with the depth of the orifice bore, that is the distance that the molten plastic has to travel at the extrusion orifice diameter.

Because of that last, I've always tried, at Adrian's urging, to keep that distance as short as possible. For that reason, my extruder barrel design is quite heterodox when compared with conventional Mk II extruder barrel designs.

[3dreplicators.com]

The way that I build mine insures that that distance doesn't exceed 0.025 inches (0.635 mm) which is a close shout from the width of the orifice. I expect that this lets me expend a lot less energy in pumping filament into my heated extruder barrel than conventional designs made from drilled-out brass bolts. My extruder barrel also has a lot less metal in it as well. That means that it is much more responsive to thermal input from the nichrome wire than conventional designs.

Edited 1 time(s). Last edit at 10/01/2008 11:36AM by Forrest Higgs.