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# Steps per mm vs theoretical resolution

Posted by PDBeal
 Steps per mm vs theoretical resolution November 26, 2018 09:43PM Registered: 5 years ago Posts: 558
I've been searching and haven't been able find this, but what's the equation for steps per mm to theoretical resolution? I'm interested in understanding the theoretical resolution of a z axis using GT2 20T pulley between 1/16 microstepping and a 1.8 degree motor and a 0.9 degree motor. Primarily for what the resolution is for a full step.

Edited 1 time(s). Last edit at 11/26/2018 09:44PM by PDBeal.
 Re: Steps per mm vs theoretical resolution November 26, 2018 09:59PM Registered: 10 years ago Posts: 6,076
see [reprap.org]

steps/mm is the theoretical resolution, in reality it will not move every micro step, and when it does the inter step spacing is not uniform.

or re you just meaning this?

there are N steps per mm, so each mm can be divided by N for the theoretical resolution

eg 80 steps/mm
1/80 = 0.0125

ie 1 step = 0.0125 mm movement

Edited 2 time(s). Last edit at 11/26/2018 10:04PM by Dust.
 Re: Steps per mm vs theoretical resolution November 26, 2018 10:08PM Registered: 5 years ago Posts: 558
Sort of, but not exactly. I've seen people mention a z axis that uses 1.8 degree motors with GT2 20T pulleys is only really capable of 0.2mm layer heights with it being a full step. I'm wanting to understand how that is calculated or connected to the step per mm calculation.
 Re: Steps per mm vs theoretical resolution November 26, 2018 10:12PM Registered: 10 years ago Posts: 6,076
replace the microstpping value with 1 for full step.
 Re: Steps per mm vs theoretical resolution November 26, 2018 11:23PM Registered: 6 years ago Posts: 5,232
It's a matter of reliability. Hard to calculate 'luck'.
Moving 1/16 step only might or might not work, but moving 17/16th step sure works. How can you put that in a formula?

Best practice would be to drop the axis a few steps, then move up to the desired position.
Just guessing here...
 Re: Steps per mm vs theoretical resolution November 27, 2018 02:47PM Admin Registered: 13 years ago Posts: 13,118
... the problem with "not moving every microstep" is assigned with the common used steppers, which are sort of "underpowered" for the target application/mechanics.

I'm driving my "sub-micro-stages" with much stronger steppers and/or gearing - e.g. NEMA-23- or NEMA-36-steppers with 1 to 2 Nm torque when driven direct or up to 5x (5 to 10 Nm!) with 5:1 gearing ... and driver voltages and currents with up to [email protected] or with [email protected],5A (Berger-Lahr/Precitec drivers+motors).

This massive "overpowered" drives can handle microstepping with "real" micro-positioning - have different types of drives and drivers vor sub-micron positionig -- e.g. the BergerLahr-drives were meant for 0,001mm repeatable precision at an "accuracy" of 0,1 micron (=0,0001mm) per step!!

So you have on your own to decide, which scenario to use - either cheap/leightweight ... or "beefy"

Viktor
--------
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 Re: Steps per mm vs theoretical resolution November 29, 2018 04:25AM Registered: 6 years ago Posts: 752
If a full rotation of the 20 teeth pulley covers 40mm, ie 20 teeth at 2mm per tooth, the number of steps a 1.8 degree per step stepper motor needs to do for 1mm is 200 steps per full rotation / 40mm per rotation= 5 steps per mm. so a single full step covers 1/5 = 0.2mm.

2x and 4x microstepping is also reasonably accurate so you could push it to 0.1 and 0.05mm per layer.

--
Kind regards
Imqqmi

NFAN CoreXY printer:
[reprap.org]
 Re: Steps per mm vs theoretical resolution November 29, 2018 07:45AM Registered: 3 years ago Posts: 1,716
Quote
imqqmi
If a full rotation of the 20 teeth pulley covers 40mm, ie 20 teeth at 2mm per tooth, the number of steps a 1.8 degree per step stepper motor needs to do for 1mm is 200 steps per full rotation / 40mm per rotation= 5 steps per mm. so a single full step covers 1/5 = 0.2mm.

I understood this but could you explain the 2x and 4x microstepping or point me to where I could read more about 2x and 4x microstepping.

Computer Programmer / Electronics Technician
 Re: Steps per mm vs theoretical resolution November 30, 2018 02:37AM Registered: 6 years ago Posts: 752

It uses more voltage levels that approximates sine waves for driving the motor coils. The higher the microstepping, the closer it gets to a sine wave as opposed to a square wave.

--
Kind regards
Imqqmi

NFAN CoreXY printer:
[reprap.org]
 Re: Steps per mm vs theoretical resolution December 01, 2018 09:24AM Registered: 5 years ago Posts: 558
Quote
imqqmi
If a full rotation of the 20 teeth pulley covers 40mm, ie 20 teeth at 2mm per tooth, the number of steps a 1.8 degree per step stepper motor needs to do for 1mm is 200 steps per full rotation / 40mm per rotation= 5 steps per mm. so a single full step covers 1/5 = 0.2mm.

2x and 4x microstepping is also reasonably accurate so you could push it to 0.1 and 0.05mm per layer.

That was exactly the information I was after. This makes sense and why people have said 0.2mm is the realistic layer height with that setup. I knew microstepping can get you smaller layer heights, but also knew that microstepping at small distances isn’t an exact science.

So if I change my Z motor to a 0.9, it takes 400 steps per full rotation / 40mm per rotation = 10 steps per mm, so a single full step covers 1/10 = 0.1mm. Which should be a better consistency for smaller layer heights with microstepping because the micro steps moved would be twice as many now.

Thanks.
 Re: Steps per mm vs theoretical resolution December 01, 2018 10:48AM Registered: 6 years ago Posts: 752
Yes, that's exactly right!

I think there's a speed penalty to 0.9 degrees per step stepper motors though but I can't say from experience since I don't own one. Better to aim for 24V drivers, they can reach higher speeds.

And there are 16 teeth pulleys too (with an inner diameter of max. 6mm or 1/4"), gaining 25% more theoretical resolution. Don't use steel reinforced PU belts thouhg, they will slip out of the teeth and may break/wear more quickly than glass fiber reinforced rubber belts.

--
Kind regards
Imqqmi

NFAN CoreXY printer:
[reprap.org]
 Re: Steps per mm vs theoretical resolution December 01, 2018 11:22AM Registered: 5 years ago Posts: 558
In my case, these are only going on my Z axis, so speed isn’t going to be an issue.
 Re: Steps per mm vs theoretical resolution December 02, 2018 02:49AM Registered: 6 years ago Posts: 5,232
Quote
PDBeal
In my case, these are only going on my Z axis, so speed isn’t going to be an issue.

You can use "Z-lift on layer change' to move the bed away some extra steps, then move back to next layer height. That should give you the extra peace of mind about microstepping does or doesn't really work. and you don't have to care about the ratio between fullsteps vs layer height.
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