Steps per mm vs theoretical resolution

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.

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.

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.

replace the microstpping value with 1 for full step.

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...

... 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 70V@6A or with 325V@2,5A (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"

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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.

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Kind regards
Imqqmi

NFAN CoreXY printer:
[reprap.org]

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.

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Computer Programmer / Electronics Technician

Google microstepping.

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.

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Kind regards
Imqqmi

NFAN CoreXY printer:
[reprap.org]

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.

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.

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Kind regards
Imqqmi

NFAN CoreXY printer:
[reprap.org]

In my case, these are only going on my Z axis, so speed isn’t going to be an issue.

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.