Lead Screw Speed, Torque and Force Calculator

How is a lead screw calculated?

A lead screw turns rotation into straight line motion. One turn of the screw moves the nut by one lead, so linear speed is v = P_h × n. A screw with a 10 mm lead turning at 600 rpm moves the nut 6 metres per minute.

Force and torque

The work done in one turn is the same on both sides: 2 × π × T from the motor and F × P_h on the load. Losses enter through the efficiency: T = F × P_h / (2 × π × η). For 5000 N, a 10 mm lead and 90 percent efficiency the torque is 8.84 N·m. The same relation works in reverse: F = 2 × π × η × T / P_h.

A smaller lead gives more force for the same torque but less speed.

Trapezoidal screws and self locking

For a sliding nut trapezoidal screw the efficiency depends on friction, and the calculator derives it from the friction coefficient. With enough friction the load cannot turn the screw backwards. This is self locking, and the condition is π × μ × d_m × sec α > P_h. Jacks and vices rely on it. Ball screws have very low friction and do not self lock, so a vertical axis needs a brake.

Example

A Tr 20×4 screw (mean diameter 18 mm, lead 4 mm) with a friction coefficient of 0.15 under 10 kN: the torque to raise is 20.6 N·m, the torque to lower is 7.5 N·m and the efficiency is 31 percent. Because the lowering torque is positive, the screw is self locking.

Limits

The calculator gives torque at constant speed. Motor selection also needs acceleration torque, and the screw needs checks for buckling, critical speed and nut life. Follow the method in the manufacturer's catalogue for those.