Power Screw Torque, Self-Locking, and Collar Friction Checks

A power screw is often selected because it can turn a modest motor or handwheel torque into a large linear force. That advantage is useful in screw jacks, presses, vises, clamps, lift tables, valve actuators, and machine-tool feed drives. It also creates a design trap: the screw may look strong enough in compression, while the drive torque, collar friction, heating, or self-locking behavior is the actual limiting feature.

This article gives a practical calculation workflow for a square or Acme-style power screw. The wording, worked example, and engineering comments are original for EnggTools. The local Shigley mechanical design reference was used only to ground the standard mechanics: lead angle, raising torque, lowering torque, self-locking, collar friction, efficiency, and nominal screw-body stress checks.

1. Start with the motion requirement

Before calculating torque, write down what the screw must do in service. A lifting screw and a feed screw are not judged the same way. A screw jack may need to hold a load safely when the drive stops. A CNC feed screw may intentionally back-drive under some conditions and may be judged more by efficiency, backlash, wear, and positioning stiffness.

The minimum input set is:

• Axial load F.
• Major diameter, pitch, and number of starts.
• Mean thread diameter dm and root diameter dr.
• Thread friction coefficient f.
• Collar or thrust-bearing friction coefficient fc and mean collar diameter dc.
• Required raising speed or duty cycle, if power and heating matter.

For a square thread, a quick geometric estimate is dm = d - p/2 and dr = d - p. For Acme or trapezoidal threads, use the actual thread data instead of forcing square-thread geometry into the design.

2. Lead is not always pitch

Lead is the axial travel per revolution. For a single-start thread, lead equals pitch. For a two-start thread, lead equals two times pitch. This matters because the lead angle controls the mechanical advantage and the chance of back-driving.

The lead-angle tangent is:

tan(lambda) = lead / (pi x dm)

A larger lead gives faster travel but needs more torque and is less likely to be self-locking. A smaller lead gives higher mechanical advantage but can be slow and inefficient.

3. Separate thread torque from collar torque

The thread torque is the torque used at the screw thread interface. For a square thread raising a load, a practical form is:

Tr = F dm / 2 x (lead + pi f dm) / (pi dm - f lead)

The lowering torque term for the thread is:

Tl = F dm / 2 x (pi f dm - lead) / (pi dm + f lead)

If Tl is positive, the thread friction is high enough that the screw tends to hold the load rather than run down freely. If it is zero or negative, the load can back-drive the screw unless another brake or holding device is provided.

Most real lifting screws also have thrust collar friction. The collar torque is often a large part of the handle or motor torque:

Tc = F fc dc / 2

The torque required to raise the load is therefore:

Total raising torque = Tr + Tc

Do not hide collar friction inside a vague service factor. If the thrust surface changes from a plain collar to a rolling thrust bearing, the required torque can change enough to affect motor selection, handwheel force, heat, and user feel.

4. Self-locking is a design decision, not a bonus

The classic self-locking check is:

f > tan(lambda)

This check is useful, but it should not be treated as the only safety device for lifting equipment. Friction varies with lubrication, wear, vibration, contamination, surface finish, temperature, and manufacturing scatter. If a suspended or hazardous load must not fall, use a brake, locking device, ratchet, redundant support, or code-approved holding method. Self-locking from thread friction is a helpful behavior, not a substitute for a safety system.

5. Efficiency explains where the power went

The ideal no-friction torque to raise the load is:

T0 = F x lead / (2 pi)

Thread efficiency is approximately:

eta = T0 / Tr

This efficiency excludes collar friction. The full drive efficiency is lower when collar torque is included. Low efficiency is not automatically bad; it may be acceptable for an occasional jack. It is a problem for continuous-duty motion because the lost power becomes heat at the threads and thrust bearing.

6. A quick stress screen

A power screw under load sees axial compression and torsion at the same time. A first-pass screw-body screen uses the root diameter:

Axial stress = 4F / (pi dr^2)

Torsional shear stress = 16T / (pi dr^3)

Von Mises screen = sqrt(axial stress^2 + 3 torsional shear stress^2)

This is only a nominal check. Long screws need buckling checks. Threads need bearing, bending, and shear review. Nuts need enough engaged thread length and a material pair that will not gall. Reversing duty needs fatigue and wear checks. Still, this nominal screen quickly tells you whether the torque and root diameter are in the right neighborhood.

7. Worked example: small lifting screw

Assume a square-thread lifting screw raises 18 kN. Use a 24 mm major diameter, 5 mm pitch, single-start thread, thread friction f = 0.12, collar friction fc = 0.10, and mean collar diameter dc = 36 mm.

For the square thread:

• lead = 5 mm
• dm = 24 - 5/2 = 21.5 mm
• dr = 24 - 5 = 19 mm
• tan(lambda) = 5 / (pi x 21.5) = 0.074, so lambda = 4.23 degrees

Because f = 0.12 is greater than tan(lambda) = 0.074, the thread passes the simple self-locking check. That does not remove the need for a holding brake if the application has a personnel or equipment hazard.

The thread torque to raise the load is:

Tr = 37.9 N-m

The collar torque is:

Tc = F fc dc / 2 = 18,000 x 0.10 x 36 / 2 = 32.4 N-m

The total raising torque is therefore:

Ttotal = 37.9 + 32.4 = 70.3 N-m

This is the main practical lesson from the example: collar friction is almost as large as the thread torque. If a designer sizes the motor from thread torque alone, the actuator will be underpowered.

The ideal no-friction thread torque is:

T0 = 18,000 x 5 / (2 pi) = 14.3 N-m

The thread efficiency is:

eta = 14.3 / 37.9 = 0.38, or about 38 percent.

Using the full 70.3 N-m raising torque for a conservative nominal body screen:

• Axial stress = 4F / (pi dr^2) = 63.5 MPa
• Torsional shear stress = 16T / (pi dr^3) = 52.2 MPa
• Von Mises screen = 110 MPa

If the screw material yield strength were 250 MPa, this nominal combined stress would look acceptable. The engineer should still check buckling length, thread bearing pressure, nut material, lubrication, wear, end fixity, handle or motor torque, and stopping/holding safety.

8. Practical review checklist

1. Confirm whether the screw must be self-locking or intentionally back-drivable.
2. Use lead, not pitch, for multi-start screws.
3. Calculate thread torque and collar torque separately.
4. Check the lowering torque sign before assuming the screw will hold.
5. Estimate efficiency and heat for repeated or continuous operation.
6. Screen axial plus torsional stress at the screw root diameter.
7. Check buckling for long screws and thread stresses for heavily loaded nuts.
8. Specify lubrication and material pairing; friction is an input, not a constant of nature.

A power screw is a compact machine, not just a threaded rod. Treat the thread, thrust bearing, nut, lubrication, and holding method as one system, and the calculation becomes much easier to review.