What force does this lead screw produce?

A screw is an inclined plane wrapped around a cylinder. One revolution of the screw moves the nut one lead along the axis, so the work done by the torque over one turn, which is 2π times the torque, equals the work done by the axial force over one lead, minus whatever friction takes. Rearranged, the force is 2π times the torque times the efficiency, divided by the lead. The mechanical advantage is large: a 2 mm lead turns a hundredth of a newton metre into several newtons even at poor efficiency.

Lead is the term that gets confused. Lead is axial travel per revolution. Pitch is the distance between adjacent threads. On a single-start screw they are equal, which is why the confusion survives; on a four-start screw the lead is four times the pitch, and using the pitch gives an answer four times too large. This is the most common error in the calculation and it is always in the unsafe direction.

Efficiency in a sliding-contact lead screw is genuinely low, commonly 20 to 50%, and it depends on the lead angle and the friction coefficient of the screw and nut pair. Fine leads have shallow helix angles and low efficiency. Coarse leads and ball screws are far more efficient, and consequently back-drive freely. The efficiency figure entered here is the screw pair only: if a gearhead drives the screw, its efficiency is already accounted for in the torque you enter, and applying it again double-counts the loss.

Back-driving is the property that decides whether the axis needs a brake. A screw is self-locking when the lead angle is below the friction angle, roughly when efficiency is under about 35 to 40%, but the boundary depends on lubrication, load and vibration, and a screw that holds statically can walk under vibration. Self-locking cannot be read off an efficiency number and it must be verified on the real assembly if anything depends on it.

Three limits live outside this equation and each one can be the binding constraint. Column buckling: a long screw in compression fails by Euler buckling at a load that depends on the root diameter to the fourth power, the unsupported length squared, and the end fixity, and for a thin screw it is often far below the force this page reports. Bearing axial rating: the force has to react somewhere, and a small ball or sleeve bearing usually reaches its axial limit first. Critical speed: a long screw has a whirl speed that caps rpm regardless of load.

Finally, the force here is quasi-static. Accelerating the carriage adds force, guideway friction adds force, and any side load from misalignment adds torque the motor has to supply and wear the nut has to absorb. A lead screw axis that is sized to the static force alone will be undersized.