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.

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