Lead Screw
Size a trapezoidal lead screw for a jack, a press or a linear axis. Check the nut pressure, the stress, buckling and the critical speed, and get the drive torque, the efficiency and whether it holds its load by itself — or let the calculator find the smallest thread that works.
How Does a Lead Screw Work?
A lead screw turns rotation into straight-line motion: every turn moves the nut by the lead. The thread is a ramp wrapped around a cylinder, so a small torque produces a large force — the reason a car jack or a vice can be turned by hand.
The flanks slide over each other, so a lot of energy goes into friction: efficiencies of 20–50% are normal. The upside is that a screw with a small lead angle is self-locking: the load cannot turn it backwards, so a jack holds the car without a brake. Long, thin screws can also buckle under compression or start to whip at high speed.
Screw and Thread
TrLead-Screw Formulas
| Quantity | Formula |
|---|
Worked Techniques
The load is spread over every thread turn in the nut. Too short a nut wears quickly; much longer than 2.5 d hardly helps, because the turns no longer share the load evenly.
If the lead angle φ is smaller than the friction angle ρ′, the load cannot drive the screw backwards. Vibration can still make it creep, so safety-critical lifts get a brake anyway.
Both depend on the core diameter d₃ and the supports. Fixing both ends instead of one quadruples the buckling load. Short, thick screws fail by crushing instead, which the calculator handles with Tetmajer’s formula.
Sources & Verification
- R. G. Budynas & J. K. Nisbett, Shigley’s Mechanical Engineering Design, 10th ed., McGraw-Hill, 2015 — Ch. 8 (Screws, Fasteners, and the Design of Nonpermanent Joints).
- R. C. Hibbeler, Mechanics of Materials in SI Units, 10th ed., Pearson, 2018 — Ch. 13 (Buckling of Columns).
- S. S. Rao, Mechanical Vibrations, 6th ed., Pearson, 2017 — Ch. 8 (Continuous Systems).