The Physics of Rotary-to-Linear Motion
A power screw converts motor rotational torque ((T)) into linear axial force ((F)). The theoretical relationship is governed by the screw lead ((L) in meters per revolution) and mechanical efficiency ((eta)):
Thrust_Force (N) = (2 × π × Torque_Nm × η) / Lead_meters
Sliding Friction (Lead Screw) vs Rolling Contact (Ball Screw)
- Acme Lead Screws: Feature trapezoidal threads sliding against brass, bronze, or Delrin plastic nuts. Sliding friction limits efficiency to only 30% to 45%. Over half of your stepper motor's torque is converted into heat and wear!
- Ball Screws: Feature hardened recirculating steel ball bearings rolling inside ground raceways. Rolling friction boosts efficiency to 90% to 95%, delivering over 2.5 times higher thrust force from the exact same motor!
The Danger of Ball Screw Vertical Z-Axis Drop
Because lead screws have low efficiency (<50%), they are usually self-locking: the weight of a heavy CNC spindle cannot back-drive the screw when power is removed. Ball screws, however, have near-zero friction ((eta = 90%)) and are freely back-drivable.
If you install a ball screw on a vertical CNC Z-axis without an electromagnetic brake, the instant you power down the machine, gravity will send your 20-lb heavy spindle crashing into the table!