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. https://reprap.org/forum/read.php?1,839723,839723#msg-839723 Sun, 19 Jul 2026 02:52:46 -0400 Phorum 5.2.23 https://reprap.org/forum/read.php?1,839723,840151#msg-840151 Re: Steps per mm vs theoretical resolution https://reprap.org/forum/read.php?1,839723,840151#msg-840151
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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.]]> o_lampe General Sun, 02 Dec 2018 02:49:15 -0500 https://reprap.org/forum/read.php?1,839723,840127#msg-840127 Re: Steps per mm vs theoretical resolution https://reprap.org/forum/read.php?1,839723,840127#msg-840127 PDBeal General Sat, 01 Dec 2018 11:22:12 -0500 https://reprap.org/forum/read.php?1,839723,840124#msg-840124 Re: Steps per mm vs theoretical resolution https://reprap.org/forum/read.php?1,839723,840124#msg-840124
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.]]> imqqmi General Sat, 01 Dec 2018 10:48:34 -0500 https://reprap.org/forum/read.php?1,839723,840115#msg-840115 Re: Steps per mm vs theoretical resolution https://reprap.org/forum/read.php?1,839723,840115#msg-840115
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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.]]> PDBeal General Sat, 01 Dec 2018 09:24:27 -0500 https://reprap.org/forum/read.php?1,839723,840039#msg-840039 Re: Steps per mm vs theoretical resolution https://reprap.org/forum/read.php?1,839723,840039#msg-840039
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.]]> imqqmi General Fri, 30 Nov 2018 02:37:15 -0500 https://reprap.org/forum/read.php?1,839723,839962#msg-839962 Re: Steps per mm vs theoretical resolution https://reprap.org/forum/read.php?1,839723,839962#msg-839962
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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.]]> Roberts_Clif General Thu, 29 Nov 2018 07:45:15 -0500 https://reprap.org/forum/read.php?1,839723,839947#msg-839947 Re: Steps per mm vs theoretical resolution https://reprap.org/forum/read.php?1,839723,839947#msg-839947
2x and 4x microstepping is also reasonably accurate so you could push it to 0.1 and 0.05mm per layer.]]> imqqmi General Thu, 29 Nov 2018 04:25:31 -0500 https://reprap.org/forum/read.php?1,839723,839793#msg-839793 Re: Steps per mm vs theoretical resolution https://reprap.org/forum/read.php?1,839723,839793#msg-839793
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" B)]]> VDX General Tue, 27 Nov 2018 14:47:04 -0500 https://reprap.org/forum/read.php?1,839723,839729#msg-839729 Re: Steps per mm vs theoretical resolution https://reprap.org/forum/read.php?1,839723,839729#msg-839729 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...]]> o_lampe General Mon, 26 Nov 2018 23:23:23 -0500 https://reprap.org/forum/read.php?1,839723,839727#msg-839727 Re: Steps per mm vs theoretical resolution https://reprap.org/forum/read.php?1,839723,839727#msg-839727 Dust General Mon, 26 Nov 2018 22:12:51 -0500 https://reprap.org/forum/read.php?1,839723,839726#msg-839726 Re: Steps per mm vs theoretical resolution https://reprap.org/forum/read.php?1,839723,839726#msg-839726 PDBeal General Mon, 26 Nov 2018 22:08:28 -0500 https://reprap.org/forum/read.php?1,839723,839725#msg-839725 Re: Steps per mm vs theoretical resolution https://reprap.org/forum/read.php?1,839723,839725#msg-839725 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]]> Dust General Mon, 26 Nov 2018 21:59:43 -0500 https://reprap.org/forum/read.php?1,839723,839723#msg-839723 Steps per mm vs theoretical resolution https://reprap.org/forum/read.php?1,839723,839723#msg-839723 PDBeal General Mon, 26 Nov 2018 21:43:04 -0500