Power Screw Calculator — Raise/Lower Torque, Efficiency & Self-Locking (Shigley §8-2)

Governing standard: Shigley §8-2 · ASME B1.5 / DIN 103 thread forms· Method: Shigley's Mechanical Engineering Design (Budynas & Nisbett, 11th ed., §8-2) — power-screw raise/lower torque, thread efficiency, self-locking, bearing pressure and root stresses. Thread GEOMETRY: ASME B1.5 (Acme, α = 14.5°) · DIN 103 / ISO 2901 (metric trapezoidal Tr, α = 15°) · ANSI B1.9 (buttress, 7°/45°). Those are dimensional standards and contain no torque or efficiency model.

Page last updated 18 October 2026

How ASME B1.5 works — the method explained

Video walkthrough (3:25)

Read the transcript

Here's a screw jack: a 40 mm Acme screw lifting 25 kN. The tool says it's OK, and raising it takes 157 N·m.

Raise the load to 55 kN, and the screw fails.

This is the MechanixCalc power screw calculator. It finds the torque and the efficiency, checks self-locking, and checks the screw and the nut against their limits. Let's go through it, step by step.

A thread is a ramp wrapped around a shaft. The load sits on the ramp, each turn lifts it by one lead, and friction decides how much torque it takes.

If the ramp is shallow, friction holds the load by itself. That's self-locking. Too steep, or too slippery, and the load drives the screw back down.

Step one is the thread: an Acme screw, 40 mm across, with an 8 mm lead and a 60 mm bronze nut. The tool adds the standard root clearance, so the screw's core is 31.5 mm.

Step two is friction: 0.12 on the thread and 0.10 on the collar. It's the biggest unknown here, so check both ends of the range.

Step three is the load: 25 kN, at 30 rpm.

Step four is the limits. The nut pressure and the thread shear have defaults, but the screw's yield is blank.

So the verdict is CHECK. Every limit is met, but the von Mises stress, 110.4 MPa, is only judged against a generic reference.

Enter the screw's yield, 355 MPa, and the verdict turns OK.

Raising it takes 157 N·m, the thread efficiency is 36%, and the screw is self-locking, with a margin of 1.75.

The nut pressure is 7.9 MPa, within the 9.6 allowed at this speed.

Now run it at 120 rpm. The allowed nut pressure falls to 1.6 MPa, so the verdict is CHECK.

The thread now rubs too fast for a bronze nut. Slow it down, or choose a ball screw.

Back at 30 rpm, lower the friction to 0.06. The efficiency climbs to 53%, but the screw is no longer self-locking. Under load, it would turn back down by itself.

Now raise the load to 55 kN.

The von Mises stress at the thread root is 242.9 MPa, above the 200 MPa reference, and the screw fails.

The fix is a bigger thread: a trapezoidal Tr 60 by 9, with a 90 mm nut.

At 55 kN, the stress is 129.6 MPa and the nut pressure 7.0 MPa. The verdict is OK, and it still self-locks.

What the tool does not check is listed too: column buckling, fatigue, shock loads, whirling at speed and the nut's own thread bending. So silence never reads as a pass.

Every input, every formula and every check goes into a PDF report. A report your reviewer can follow.

That's a power screw, checked. Try it on your own design, on MechanixCalc.com.

The MechanixCalc power screw calculator sizes and verifies lead screws and screw jacks using the power-screw torque model of Shigley's Mechanical Engineering Design (§8-2), applied to the thread forms defined by ASME B1.5 (Acme), DIN 103 / ISO 2901 (metric trapezoidal) and ANSI B1.9 (buttress). Enter the thread geometry, friction coefficients and axial load, and the tool returns the raising torque, lowering torque, collar torque, mechanical efficiency, the self-locking / overhauling verdict, and the combined Von Mises stress at the screw root — all in a single calculation pass.

It is built for machine designers and mechanical engineers who need a defensible, textbook-method (Shigley §8-2) number for a screw jack, linear actuator, vise, press, or any power-transmission lead screw — and who need to hand a reviewer a worked, methodology-shown calculation rather than a spreadsheet. The tool covers Acme, trapezoidal (Tr), square and buttress thread forms and includes an efficiency map, a mechanical-advantage analysis and a thread-strength / Archard wear life panel.

What this calculator does

Raise and lower torque with collar friction — Shigley §8-2, for Acme (ASME B1.5, α = 14.5°), metric trapezoidal (DIN 103 / ISO 2901, α = 15°), square (α = 0°) and buttress (ANSI B1.9, α = 7°) thread forms
Mechanical efficiency and self-locking / overhauling check (λ vs arctan μ′)
Efficiency map — η vs lead angle and vs friction coefficient across five μ values
Mechanical advantage analysis — ideal and actual MA, handle force, back-drive torque
Thread strength and wear life — shear-stripping stress, contact pressure and Archard wear criterion
Von Mises combined stress — the worse of the thread root (first-thread share 0.38, Shigley §8-2 method) and the screw core at the minor diameter
Branded PDF engineering report with full methodology and substituted values

Method & formulas

Raise and lower torque (Shigley §8-2)

The torque required to raise a load W on a lead screw follows from the friction-circle model at the thread mean radius r_m (Shigley 11e §8-2, Eqs. 8-1 to 8-6). For flanked thread forms — Acme at α = 14.5°, metric trapezoidal at α = 15°, buttress at α = 7° on the load flank — the friction coefficient is elevated to μ′ = μ / cos(α) to account for the radial force component on the inclined flank. Square threads use μ′ = μ (flat flanks, α = 0). The collar torque T_c = μ_c · W · (d_c / 2) is added in series to represent thrust-bearing or flat-collar friction. ASME B1.5 and DIN 103 supply the flank angle and the thread dimensions; the torque relations above are not part of either standard.

The self-locking condition is tan(λ) < μ′, where λ is the lead angle. When this inequality holds the screw does not back-drive under a steady load in static friction; the tool prints the margin μ′ / tan(λ) beside the verdict, because self-locking is a static-friction result: vibration, shock or lubricant change can back-drive a self-locking screw — fit a brake for a suspended or safety-critical load. When it does not hold the screw overhauls and a brake or holding device is needed. The tool evaluates both conditions and shows them as a badge alongside the efficiency.

Raise torque — thread plus collar

T_raise = W · r_m · (l + π·μ′·d_m) / (π·d_m − μ′·l) + μ_c · W · (d_c / 2)

where W = axial load (N); r_m = mean thread radius = d_m / 2 (mm); d_m = mean diameter = d − h (mm); l = lead (mm/rev); μ′ = modified thread friction coefficient; d_c = collar (thrust bearing) diameter (mm); μ_c = collar friction coefficient

Lower torque — thread plus collar

T_lower = W · r_m · (π·μ′·d_m − l) / (π·d_m + μ′·l) + μ_c · W · (d_c / 2)

where T_lower < 0 means the load OVERHAULS — it drives the screw down by itself and the magnitude is the braking torque you must hold. A positive T_lower means torque is required to lower it. Note that this total includes the always-positive collar term, so its sign can mask a thread that overhauls; the self-locking verdict is decided on the thread alone, tan λ vs μ′.

Mechanical efficiency

Thread efficiency is the ratio of ideal (frictionless) raising work to the actual thread-raising work. It EXCLUDES collar losses, so it is always higher than the overall drive efficiency: at the tool's default screw the thread efficiency is 36.0 % while the overall figure including the thrust collar is 20.3 %. Size a motor from the overall figure — the calculator shows both, and the mechanical-advantage panel prints the overall one as η_total. An optimal lead angle that maximises efficiency exists at λ_opt = 45° − φ′/2, where φ′ = arctan(μ′) is the friction angle; the efficiency map plots η against λ for five standard friction levels so the designer can see whether a coarser or finer lead would improve drive efficiency.

Thread mechanical efficiency

η = (W · l) / (2·π · T_raise_thread) × 100 %

where T_raise_thread = thread torque component only (excluding collar). η peaks at λ_opt = 45° − φ′/2 with φ′ = arctan(μ′) — 41.5° at the default μ′ = 0.124. At the self-locking boundary λ = arctan(μ′) the raising efficiency is (1 − μ′²)/2, i.e. just under 50 % — a self-locking screw is at best about half efficient, and it is the LOWERING efficiency that is undefined there.

Thread stress and contact pressure

The screw root (core) diameter d3 = d − 2h − 2·a_c carries the combined compressive load and torsional torque over the loaded length between the thrust collar and the nut. Von Mises theory combines these into a single equivalent stress for comparison against material yield, and the thread ROOT is checked the same way with the thread-bending stress of the most heavily loaded (first) thread added — often the governing value. The root clearance a_c is how much deeper the screw is cut than the basic profile: the standard value is applied automatically — DIN 103 / ISO 2901 trapezoidal 0.25 mm for pitch 2–5 mm and 0.5 mm for 6–12 mm, ASME B1.5 general-purpose Acme 0.010 in (10 tpi and coarser) — and it moves only the root stresses, never the pitch diameter or the bearing depth; enter your drawing's value to override it. Thread contact pressure — bearing pressure on the nut flank — is limited to 15 MPa (recommended) or 24 MPa (bronze-nut maximum) after Shigley Table 8-4, but that table is a function of RUBBING SPEED: it falls to about 17 MPa above 10 ft/min and about 9.6 MPa at 20–40 ft/min, and the calculator de-rates accordingly and against the permissible pressure you enter for your own material pair. Thread shear-stripping strength is checked at the root of the FIRST engaged thread, which carries the largest share of the load (0.38 of it on one thread by the Shigley §8-2 method), as the transverse shear at the centre of the root — never as an average over the nut; the count of fully formed engaged threads n_t = floor(L_nut / l) sets the bearing pressure, and below one full lead the exact fractional engagement is used and the result is flagged. COLUMN BUCKLING of the screw under its own thrust is NOT checked here and is frequently the governing failure mode for a long unsupported screw.

Von Mises combined stress — thread root and screw core, governing value

σ_vm = max( √(σ_b² + σ_c² + σ_b·σ_c + 3·τ_drive²) , √(σ_c² + 3·τ_body²) , √3·τ_drive )

where σ_c = W / (π·d_r² / 4) = compressive stress (MPa); d_r = d3 = d − 2h − 2·a_c = the screw's root (core) diameter (mm), a_c the root clearance. A screw has two distinct sections: the LOADED length between the thrust collar and the nut carries the full axial load plus whichever friction torque lies further from the drive, τ_body = 16·max(T_thread, T_collar)/(π·d_r³); the unloaded DRIVE length between the input and the first friction sink carries no axial load but the whole input torque in pure torsion, τ_drive = 16·T_raise/(π·d_r³). The THREAD ROOT follows the Shigley §8-2 method: the first engaged thread carries 0.38 of the load (more when fewer than three threads engage — the shares sum to one), bent as a cantilever at the root, σ_b = 6·F₁/(π·d_r·p) with p the pitch (for a thread deeper than p/2 the general cantilever 12·F₁·h/(π·d_r·p²) is used; p = lead/starts when the starts are given), and combined at the root fibre with the axial stress and the torsion of the total raising torque. The calculator reports the worst of the three and names which one governs.

Thread contact (bearing) pressure

p_c = W / (π · d_m · h · n_t)

where h = thread depth (mm); n_t = fully formed engaged thread count = floor(L_nut / l), taking the lead as the pitch — for a multi-start screw the true count is higher, so the reported pressure is conservative; p_c ≤ 15 MPa recommended and ≤ 24 MPa bronze-nut maximum at low rubbing speed, de-rated with speed per Shigley Table 8-4 and against your own permissible pressure

Worked example

A steel Acme-thread screw jack (α = 14.5°) must raise a W = 10 000 N load. Thread: d = 40 mm, l = 8 mm, h = 4 mm (so d_m = 36 mm, d_r = 32 mm). Thread friction μ = 0.12, collar diameter d_c = 60 mm, collar friction μ_c = 0.10. Find the raising torque and thread efficiency.

Given

Axial load W10 000 N
Nominal diameter d40 mm
Lead l8 mm
Thread depth h4 mm → d_m = 36 mm, d_r = 32 mm
Thread friction μ (Acme α = 14.5°)0.12
Collar diameter d_c60 mm
Collar friction μ_c0.10

Result

Modified friction μ′≈ 0.124
Lead angle λ≈ 4.05°
Self-lockingYes (tan λ < μ′)
Thread raise torque T_thread≈ 35.35 N·m
Collar torque T_collar30.00 N·m
Total raise torque T_raise≈ 65.35 N·m
Thread efficiency η36.015 %
Overall efficiency (thread + collar)19.48 %

Compute modified friction: μ′ = μ / cos(α) = 0.12 / cos(14.5°) = 0.12 / 0.968148 = 0.123948.
Compute lead angle: λ = arctan(l / (π·d_m)) = arctan(8 / 113.097) = arctan(0.0707355) = 4.0461°.
Self-locking check: tan(λ) ≈ 0.0707 < μ′ ≈ 0.1239 → SELF-LOCKING in static friction, margin μ′ / tan λ = 0.1239 / 0.0707 ≈ 1.75 (vibration or shock can still back-drive it — fit a brake for a suspended load).
Thread raise torque: T_thread = W·r_m·(l + π·μ′·d_m) / (π·d_m − μ′·l) = 10 000·18·(8 + π·0.1239·36) / (π·36 − 0.1239·8).
Numerator factor: 8 + π·0.1239·36 = 8 + 14.019 = 22.019; denominator: π·36 − 0.1239·8 = 113.097 − 0.991 = 112.106.
T_thread = 10 000 · 18 · (22.0182 / 112.1057) = 180 000 · 0.196406 = 35 353.0 N·mm = 35.35 N·m.
Collar torque: T_collar = μ_c · W · (d_c / 2) = 0.10 · 10 000 · 30 = 30 000 N·mm = 30.00 N·m.
Total raise torque: T_raise = 35.35 + 30.00 = 65.35 N·m.
Thread efficiency: η = (W·l) / (2·π·T_thread) × 100 = (10 000·8) / (2·π·35 353) × 100 = 80 000 / 222 129 × 100 = 36.015 %.
Overall drive efficiency, which is what a motor must be sized from: η_total = (W·l) / (2·π·T_raise) × 100 = 80 000 / 410 625 × 100 = 19.48 %. The collar costs more than the thread here.

Illustrative example — verify against your actual thread geometry, surface finish, lubrication condition and material pair. The calculator uses the same formulas with your exact inputs.

Frequently asked questions

Which standard does this power screw calculator use?

The governing METHOD is the power-screw friction-circle model of Shigley's Mechanical Engineering Design (Budynas & Nisbett, 11th ed., §8-2) — raise and lower torque, thread efficiency, the self-locking criterion, bearing pressure and the root stresses all come from there. ASME B1.5 (Acme), DIN 103 / ISO 2901 (metric trapezoidal) and ANSI B1.9 (buttress) are DIMENSIONAL thread standards: they supply the flank angle α and the thread dimensions, and contain no torque or efficiency model of their own. The modified friction coefficient μ′ = μ / cos(α) is applied to every flanked form; square threads use α = 0. The full method, with the substituted values, is printed in the generated PDF report.

How is the self-locking condition determined?

A power screw is self-locking when the lead angle λ is less than the friction angle φ′ = arctan(μ′), which is equivalent to tan(λ) < μ′. When this condition holds a steady load does not back-drive the screw in static friction — but that is all it guarantees: vibration, shock or lubricant change can back-drive a self-locking screw — fit a brake for a suspended or safety-critical load. The calculator prints the margin μ′ / tan(λ) with the verdict. When λ > φ′ the screw overhauls and will back-drive under load unless a separate braking torque is applied. The calculator evaluates this in real time and shows SELF-LOCKING or OVERHAULING on the drawing and in the verdict.

What thread forms are supported?

Four power-thread forms: Acme (ASME B1.5, 29° included, α = 14.5° — the most common inch form), metric trapezoidal Tr (DIN 103 / ISO 2901, 30° included, α = 15° — the metric equivalent), square (α = 0°, the highest efficiency, no flank force component) and buttress (ANSI B1.9, asymmetric with a 7° load flank and a 45° back flank, for unidirectional load; the DIN 513 variant uses a 3° load flank instead). Select the thread form in step 1 (Thread); the flank half-angle and the modified friction coefficient μ′ = μ / cos(α) follow automatically. Only the LOAD flank angle enters μ′, because that is the flank carrying W.

What is the difference between thread efficiency and total efficiency?

Thread efficiency η counts only the work done at the thread helix — it excludes collar (thrust-bearing) losses. Total or handle-referred efficiency is lower because it includes the collar torque μ_c·W·(d_c/2) in the denominator. On the tool's default screw the thread efficiency is 36.0 % while the overall figure is 20.3 %: sizing a motor from the thread figure would undersize it by about 44 %. The efficiency map plots thread efficiency; the mechanical-advantage panel and the hero sub-line both show the overall handle-referred figure (MA_actual / MA_ideal × 100), and the reported shaft power P is always computed from the TOTAL torque.

Does the calculator check the screw for buckling?

No — and for a long unsupported screw in compression, column buckling is frequently the failure mode that governs, well before the torque or thread limits are reached. This tool computes the axial and torsional stresses at the root diameter and combines them by Von Mises; it has no slenderness or end-condition input. Take the root diameter d_r it reports, together with your axial load and the unsupported length, to the Euler/Johnson buckling calculator. The tool links to it directly, and the assumptions section of the PDF report states the omission.

Why does the contact-pressure limit change when I change the speed?

Because the safe bearing pressure for a sliding screw and nut is a function of rubbing speed, not of the material pair alone. Shigley's Table 8-4 gives roughly 17–24 MPa for a steel screw on a bronze nut at low speed, about 11–17 MPa above 10 ft/min, about 5.5–9.7 MPa at 20–40 ft/min and far less beyond that. The calculator computes the rubbing velocity at the mean diameter from your speed and de-rates the permissible pressure accordingly, and it also compares against the permissible pressure you enter for your own material pair in step 4 (Nut & thread limits) — a cast-iron or PTFE-lined nut is governed by a lower figure than the built-in bronze one.

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