Power Screw Calculator — Raise/Lower Torque, Efficiency & Self-Locking (ASME B1.5 / DIN 103)
Governing standard: ASME B1.5 / DIN 103· ASME B1.5 (Acme threads) · DIN 103 (trapezoidal threads) · ISO 2901 · Shigley's lead-screw torque model (Budynas & Nisbett, 11th ed., §8-2)
The MechanixCalc power screw calculator sizes and verifies lead screws and screw jacks to ASME B1.5 (Acme threads) and DIN 103 / ISO 2901 (trapezoidal threads). Enter the thread geometry, friction coefficients and axial load, and the tool instantly 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, standard-cited 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, 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 — ASME B1.5 / DIN 103 / ISO 2901 Acme, square and buttress 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 (compressive + torsional shear) at the screw minor diameter
- Branded PDF engineering report with full methodology and substituted values
Method & formulas
Raise and lower torque (ASME B1.5 / Shigley)
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. For flanked thread forms (Acme at α = 14.5°, buttress), 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 at the screw base.
The self-locking condition is tan(λ) < μ′, where λ is the lead angle. When this inequality holds the screw cannot back-drive under load — no brake is required. 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.
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
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 indicates the screw is self-locking — the load cannot back-drive the screw unaided
Mechanical efficiency
Thread efficiency is defined as the ratio of ideal (frictionless) raising work to the actual thread-raising work — it excludes collar losses, which are accounted for separately. An optimal lead angle that maximises efficiency exists at λ_opt ≈ 45° − α/2 for a given thread form; 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.
η = (W · l) / (2·π · T_raise_thread) × 100 %where T_raise_thread = thread torque component only (excluding collar); η = 0 at the self-locking boundary and peaks near λ_opt ≈ 45° − α/2
Thread stress and contact pressure
The screw minor (root) diameter d_r = d − 2h carries the combined compressive load and torsional torque. Von Mises theory combines these into a single equivalent stress for comparison against material yield. Thread contact pressure — bearing pressure on the nut flank — is limited to 15 MPa (recommended) or 25 MPa (bronze nut maximum per Shigley) to prevent wear and galling. Thread shear-stripping strength is checked on the shear plane at the root diameter with the number of engaged threads n_t = L_nut / l (Shigley §8-2).
σ_vm = √(σ_c² + 3·τ²)where σ_c = W / (π·d_r² / 4) = compressive stress (MPa); τ = 16·T_raise_thread / (π·d_r³) = torsional shear stress (MPa); d_r = d − 2h = minor (root) diameter (mm)
p_c = W / (π · d_m · h · n_t)where h = thread depth (mm); n_t = engaged thread count = round(L_nut / l); p_c ≤ 15 MPa recommended, ≤ 25 MPa bronze-nut maximum
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 η≈ 36 %
- Compute modified friction: μ′ = μ / cos(α) = 0.12 / cos(14.5°) = 0.12 / 0.9686 ≈ 0.1239.
- Compute lead angle: λ = arctan(l / (π·d_m)) = arctan(8 / (π·36)) = arctan(0.07074) ≈ 4.047°.
- Self-locking check: tan(λ) ≈ 0.0707 < μ′ ≈ 0.1239 → SELF-LOCKING (no brake needed).
- 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 · (22.019 / 112.106) = 180 000 · 0.19641 ≈ 35 354 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·35 354) × 100 = 80 000 / 222 108 × 100 ≈ 36.0 %.
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 torque and efficiency model follows ASME B1.5 (Acme threads) and DIN 103 / ISO 2901 (trapezoidal threads), using the lead-screw friction-circle method from Shigley's Mechanical Engineering Design (Budynas & Nisbett, 11th ed., §8-2). Thread geometry (flank angle α) and the modified friction coefficient μ′ = μ / cos(α) are applied consistently for Acme and buttress forms; square threads use α = 0. The governing method 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 the load cannot back-drive the screw — no brake or holding device is needed. 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 displays a SELF-LOCKING / BACK-DRIVES badge.
What thread forms are supported?
The calculator supports three power-thread forms: Acme (ASME B1.5, α = 14.5° flank angle — the most common), square (α = 0°, highest efficiency, no flank force component) and buttress (asymmetric, α = 3° / 45°, used where load is unidirectional). Select the thread type in the input panel; the flank angle and the modified friction coefficient are applied automatically.
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 efficiency is lower because it includes the collar torque μ_c·W·(d_c/2) in the denominator. The efficiency map plots thread efficiency; the mechanical-advantage panel shows the total handle-referred efficiency (MA_actual / MA_ideal × 100).
Is the power screw calculator free?
You can run a full calculation during a free 30-minute preview with no sign-up required, and a free 14-day account trial (no credit card) unlocks every calculator on the platform. The branded PDF engineering report and saved / shareable calculations are part of a paid plan.
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