Steps per mm calculation help

I've seen all the online calculations for steps per mm however I'm a bit confused about something since my setup has one size pulley on the motor and a different size on the linear rods. I have a setup like an Ultimaker where you have a belt between two linear rods and a motor with a smaller belt attached to one of the rods. My motor has 20 teeth and the linear rods have 16 teeth. I'm using TMC2208 at 1/16 and GT2 2mm belt pitch. What would be the steps per mm since there's two pulley sizes involved here? How to calculate?

On another note, I have a separate setup for X axis with 16 teeth pulleys on motor and idler and 100 steps calculated per mm with GT2 2mm pitch belt. But when I tell it to move say 10mm, it moves more like 50mm. What's wrong? I'm pretty sure my micro stepping is correct at 1/16 because it's hardwired with both MS1 and MS2 connected to 3.3V on the TMC2208 as per the bottom on this page: https://learn.watterott.com/silentstepstick/pinconfig/tmc2208/

All my motors are standard Nema 17 1.8 degree angle.

Edited 4 time(s). Last edit at 07/11/2020 02:30AM by shai.

20:16 ratio or simplified 5:4

so every rotation of the 20 tooth results in 1.25 rotations of the 16 tooth.

so instead of using 200 steps per rotation use 4/5 of that ie 160 step per rotation.. This effectively puts the stepper motor on the 16 tooth side for the maths.

so it should be (steps_per_rotation * micro_stepping) / ( tooth_pitch * number_of_teeth_on_the_pulley)

ie (160 * 16) / ( 2 * 16) = 2560/32 = 80 steps/mm (unless i'm having a bad math day...)

As for you second problem the most common issue is people update the steps/mm in their firmware, but forget to update the setting in their eeprom which takes precedence.

Send the machine a M502 - Factory Reset then a M500 to save all setting into eeprom.

Edited 4 time(s). Last edit at 07/11/2020 03:10AM by Dust.

So do we care what tooth count the idler is or it doesn't matter? Since the motor pulley and idler are different tooth count.

so it should be (steps_per_rotation * micro_stepping) / ( tooth_pitch * number_of_teeth_on_the_pulley)
ie (160 * 16) / ( 2 * 16) = 2560/32 = 80 steps/mm (unless i'm having a bad math day...)

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16, the Number of teeth on the "idler"

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160, 200 steps per revolution * (16 teeth / 20 teeth)

so yes the number of teeth are very important.

Edited 3 time(s). Last edit at 07/11/2020 12:02PM by Dust.

Hello,

Motor step angle = 1.8°
Micro steps @ 16 (8/16/32/64)
Pitch 2mm
(20 teeth / 16 teeth = 1,25) = 20*1,25 =25 teeth

360/1,8 = 200 steps * 16 micro steps = 3200 / (25 (teeth) x 2 (mm pitch) = 50) = 64

may this helps [reprap.org]

Edited 1 time(s). Last edit at 07/11/2020 02:18PM by 3D-Freak.

Sorry but seems both of these steps/mm are wrong. It's neither 64 or 80. The carriage does not reach the end of the linear rail and I'm telling it to move the correct distance. 80 steps is closer to what it should be, but there's still about 5mm left.

Hello,

1.
you have 1 gear with 20 teeth and 1 gear with 16 teeth with 2mm pitch, so when your motor makes 1 360° turn, your second gear have 450° !
calculate 100mm with 2mm pitch
config: 80steps/mm *100mm = 8.000 steps | Q1 what is real mm

so what we calculate ?

if we calculate 100mm with 2mm pitch like above then 8000steps / 160steps /r = 50 360° revolutions
but on second gear you have 450° so you have 62,5 360° revolutions, and that must be 125mm by 2mm pitch
if you have 1,25mm pitch then we are calc. 62,5 r *1,25 mm = 78,125 mm

so we calculate now 8000steps = 78,125mm that is 8000 / 78,125 = 102,4 steps insted of 80.

Also take a look at in configuration_adv.h
#if AXIS_IS_TMC(X)
#define X_CURRENT 1620 // (mA) RMS current. Multiply by 1.414 for peak current.
#define X_CURRENT_HOME X_CURRENT // (mA) RMS current for sensorless homing
#define X_MICROSTEPS 256 // 0..256 -> i have TMC5160
#define X_RSENSE 0.075 -> this i must set for TMC5160
#define X_CHAIN_POS -1 // <=0 : Not chained. 1 : MCU MOSI connected. 2 : Next in chain, ...
#endif

Edited 1 time(s). Last edit at 07/12/2020 06:12AM by 3D-Freak.

@3D-Freak please re read original post. we are not talking about lead screws here.

uups, that coms from to mutch calculate and
the prerequisite of false facts.

i am sorry.

Q1 is valid

If you set 80 steps/mm and move 100mm how far does it move in reality
As from that you can correct the value.

Say for eg you move 96mm

You can then do (100/96) * 80 = 83.33 steps/mm