Useful CNC formuals

Leadscrew Formulas

Linear Speed:

These equations will calculate the linear speed along the axis (direction of yellow arrow in figure) of a leadscrew. Both metric and imperial units are given.


$Linear Speed (\frac{mm}{sec}) = \frac{SPS\frac{steps}{second}}{SPR\frac{steps}{rev}}\times Pitch\frac{mm}{rev}$
$Linear Speed (\frac{in}{min}) = \frac{SPS\frac{steps}{second}}{SPR\frac{steps}{rev}}\times 60\frac{sec}{min}\times \frac{1}{TPI\frac{threads}{in}}$
TPI: Threads Per Inch is the standard thread dimension for imperial units
Efficiency: Efficiency of leadscrew (Ballscrew = 85-95%, Acme screw with metal nut = 35-55%, acme and plastic nut = 50-85%)

Axial Force and Torque:
The axial force is a force along the axis of the leadscrew (direction of yellow arrow in figure above). This formula is either used to calculate the axial force when a torque is given or calculate the torque that is generated from an axial force.

$Force(N) = Torque(N\cdot m) \times \frac{1}{Pitch\frac{mm}{rev}}\times \frac{1000mm}{1m}\times 2\pi (\frac{rad}{rev})\times Efficiency (\%)$
$Force(Lb) = Torque(oz\cdot in) \times TPI(\frac{rev}{in})\times \frac{lb}{16oz}\times 2\pi (\frac{rad}{rev})\times Efficiency (\%)$

Smoothieboard

In this post, we will go over some of the things we have learned with the Smoothieboard.

1. Connecting the Smoothieboard to Windows as of April 1, 2014:
- Go to this link and download the zip file. Extract the contents out with a zip program like 7-zip (free) or Winzip (paid). The file names we used are "cdc_vista" and "smothieware"
- The files will say vista but I have tested that it works on Windows 7
- Plug in your smoothieboard and open up device manager.
- Find the smoothieboard device which will be labelled "Smoothieboard USB Serial" and right click on it. Select update driver software and browse my computer for driver software. Then browse to the folder where you extracted the files to and click "Next".
- Now you should be able to connect to the smoothieboard through a serial terminal like PuTTY. Just take note of the COM port (eg "COM5") in device manager and the baudrate which is 115200.