Calculation for MOD1 spur linear travel distance per rotation

Hi,

I'm trying to confirm my calculations for the travel distance per rotation on my CNC machine

I have MOD1 rack and pinion on x-axis and dual y-axis. All of them are driven by NEMA34 (200 steps per rotation), 50:10 pulley reduction gearbox with the output shaft equped with MOD1 15T spur.

My calculation is as follows:
Pitch Diameter (d) for MOD1 15T is 15mm.
Travel distance per rotation of end shaft MOD1 gear is from the circle circumference =>
2 * Pi * r
or
Pi * d

So in my case 47.1238898mm.

The output shaft is connected to the motor via 5:1 reduction, so one rotation of the motor is 9.424777961mm of the linear travel.

I found the following formula for setting the scale:
Following this example, I will have SCALE value for INI file as 200 / 9.424777961 = 21.22065908.
BTW - The calculated value do not correspond to my current INI values. Current INI does work with massive inaccuracy in the travel distance .

Am I right or my calculation is totally incorrect?

P.S. Later on I will feed these details into stepconf and will see if it will get the same result.

For "scale" i use "40" since i have full step drives connected to 200 step/rev
(1.8 degre/step) motors attached to 5mm/rev ballscrews. This is simple
math: steps per rev/mm per rev, in my case 200/50=40.

Note that the math at the end is wrong: it should be 200/5=40

So your calculation should be 200 / 9.424777961 = 21.22065908 to get steps/mm

Yeh, I've just spotted it and edited my post with the correct math

Can you confirm that my logic and the calculation formula correct?

Are you not using microstepping?

seems all right to me. Do you have micro stepping activated?

The empirical way is to set scale to, for example 10, and command a move say 10mm and measure the length actually traveled and then calculate the correction required.
This is my usual method.

Got the same.
There is a unite easy way to do this. The tooth pitch ist module x pi

So the circumference here is 1xpix15

So travel per step is 200x5/15pi = 21,2206591 steps / mm

But i would always double check by going 10mm with a dail indicator as a reference.

I'm a complete newbie - so sorry for the lame answer - Yes, I think I'm microstepping as my driver settings are 400 steps (min on DM860A) and in the stepconf I have put 200 steps and 2 in "Driver Microstepping" filed...

So, that means I need to use calculation based on 400 steps per revolution?

(2 * 200) / ((15 * Pi) / 5) = 42.44131816

(<microstepping> * <steps per rev>) / ((<pitch diameter> * Pi) / <gear reduction ration>)

yes.

scale tells linuxcnc how many steps it needs to send to the motor drive to move the axis 1mm.

I sanity checked your math and concur...your setup is very similar to mine (only I'm 20T on the MOD1, and geared 4:1).

Wow!
What a big surprise - the theoretical calculation of the SCALE checked in the reality was spot-on on 1600mm of x-axis movement and just a few mm out of expected move on 3100mm on y-axis!

Again - thank you for your support!