Lead Screws

Pitch is thread spacing; lead is travel per revolution

Lead = pitch × number of starts. This is the distinction to get right before calculating either speed or force.

A start is one continuous helical ridge. A single-start screw has one ridge, so its lead equals its pitch. A triple-start screw has three interleaved ridges: follow one ridge through a full turn and it advances three pitch distances.

At the same pitch, adding starts increases travel per turn. At the same torque it reduces theoretical force. The thread's cross-sectional form and its number of starts are separate choices; see Screw Threads.

Check the definition, not just the label on a catalog

Thomson: Screw Pitch and Lead defines lead as nut travel per screw revolution and states the pitch-times-starts relationship. A supplier may list lead directly. Do not multiply a value already labelled lead by the number of starts a second time.

Multiply rpm by lead to find linear speed

For an engaged screw and nut, with the nut restrained from rotating, v = nL. Here n is screw speed in revolutions per minute and L is lead in distance per revolution. The result is distance per minute. Divide by 60 for distance per second.

Do not multiply that speed by efficiency. The teaching rule is: “RPM → velocity is 100% efficient unless the screw is malfunctioning; all efficiency losses are found in the torque → force conversion.” This describes a positive-drive motion relationship, not 100% energy efficiency. It is the same tooth-count principle used in Gear Ratios.

Use the actual screw rpm. If the motor slows under load, the lower rpm gives a lower travel speed. Backlash at reversal and elastic deflection can affect positioning without being an efficiency factor on speed. These calculations describe steady engaged travel, after clearance is taken up. See Rotation and Linear Speed for the general rotation-to-travel connection.

Divide torque times 2π by lead, then apply efficiency

For steady motion driving a resisting axial load, Ftheoretical = 2πT / L and Factual = η × Ftheoretical. Here T is input torque and η (eta) is efficiency written as a decimal: 40% is 0.40.

To find the torque required for a target actual force, rearrange: T = FL / (2πη). For the same load and lead, lower efficiency requires more torque. Keep the efficiency boundary consistent: a whole screw assembly efficiency includes losses in the bearings or collar (a supporting thrust-contact surface) as well as the threads.

Derive the 2π from equal power, or one revolution of work

Ideally, power in equals power out: Tω = Fv. With n in rpm, ω = 2πn/60 rad/s and v = nL/60. Cancel n/60 at nonzero steady speed to get F = 2πT/L. Equivalently, one revolution puts in work 2πT and moves the load through L, doing work FL.

With losses, Fv = ηTω. The motion ratio stays fixed, so the reduction appears in force. See Power and Efficiency. At zero speed both powers are zero; this derivation does not predict breakaway torque or static holding capacity. Lowering a load that drives the screw requires a different friction analysis.

IIT Kharagpur: Power Screw Drives and Their Efficiency, section 6.1.2, relates output work, input work and friction. The calculator uses a given efficiency, not a friction coefficient or a thread-strength model.

Worked actuator: keep inch torque and inch lead together

A single-start ACME actuator has 0.20 in pitch, runs at 900 rpm and receives 12 lbf·in of torque. Its assembly efficiency is given as 60%. Find travel speed and useful axial force.

1. L = 0.20 × 1 = 0.20 in/rev.
2. v = 900 × 0.20 = 180 in/min = 3 in/s.
3. Ftheoretical = 2π × 12 / 0.20 = 376.99 lbf.
4. Factual = 376.99 × 0.60 ≈ 226 lbf.

The 60% belongs in step 4, not step 2. It is an example input, not an efficiency assigned to every ACME screw.

Practice actuator force

Worked vise: turn hand force into torque before finding clamp force

For an illustrative square-thread vise, a 120 N hand force acts perpendicular to the handle at a radius of 0.18 m from the screw axis. Pitch is 4 mm with one start. Assume a given overall tightening efficiency of 30%; this is not a measured or universal vise efficiency.

1. Use torque = radius × perpendicular force: T = 0.18 × 120 = 21.6 N·m. Radius is the distance from the axis to the hand, not necessarily the full handle length.
2. L = 4 mm/rev = 0.004 m/rev.
3. Factual = 0.30 × 2π × 21.6 / 0.004 ≈ 10,179 N = 10.18 kN.

This is a tightening estimate using the supplied efficiency. It is not a vise rating or a prediction of residual force after the hand stops turning. A separate free-travel calculation at 24 rpm gives 24 × 4 / 60 = 1.6 mm/s; the jaws do not continue at that speed through a rigid clamped part.

Practice handle torque and clamp force Practice a triple-start CNC screw