Power/Lead Screw Design and Service-Life Calculator

Screen trapezoidal power-screw geometry, forward and backdrive torque, combined stress, efficiency, thread pressure, and wear-limited service events.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Power-screw inputs

Use positive load magnitudes and a standard metric trapezoidal thread. Select whether one service event is a one-way move or a complete out-and-back cycle.

Trapezoidal thread d × PmmNominal diameter d and standard pitch P; table range Tr8–Tr120.Thread starts n—Positive integer starts; lead is nP.Screw yield strength R_p0.2MPaVerified 0.2% proof/yield strength; positive.Axial load FkNPositive compressive/tensile load magnitude; constant during the event.Stroke length L_smmPositive axial travel for one one-way movement.Nut engagement length L_nmmLoaded thread engagement; uniform load sharing is assumed.Specific wear rate km²/NPositive validated Archard-type wear coefficient for the pair and conditions.Allowable wear ratio h′× 0.5PAllowable thread wear depth divided by half-pitch; 0 < h′ ≤ 1.Thread friction coefficient μ—Effective flank friction; 0 ≤ μ ≤ 1 and constant.Service-event basis —A cycle uses twice the sliding distance of one move.

Design and life screen

Forward-drive torque T₊—N·m

Service events—events

Efficiency—%

Safety factor——

Backdrive torque T₋—N·m

Thread pressure—MPa

Equivalent stress—MPa

Total sliding distance—km

Sliding per event—m

Pitch diameter d₂—mm

Root diameter d₃—mm

Lead angle φ—rad

Self-locking—

—

How to use

This calculator has one power-screw design model. Select the metric trapezoidal thread and the number of starts; pitch and root geometry follow the selected size table.
Enter screw yield strength in MPa, positive axial load in kN, positive stroke and nut engagement in mm, wear coefficient in m²/N, allowable half-pitch wear ratio, and effective friction coefficient.
Select One-way move when one event covers one stroke, or Out-and-back cycle when one event includes two strokes.
Select Calculate or edit a field to update the result. Reset restores the displayed Tr20 example and recalculates.
Read forward torque as the canonical drive requirement, then inspect efficiency, equivalent stress, yield safety factor, contact pressure, signed backdrive torque, self-locking screen, sliding distance, and service-event estimate.
Correct red input or yield warnings. A negative backdrive torque means the applied load alone does not overcome modeled thread friction; it is not a guaranteed holding-brake rating.
Verify the effective friction and wear coefficient for the actual material pair, lubrication, finish, pressure, speed, temperature, and contamination.
Do not use this model for ball screws, non-trapezoidal geometry, buckling, critical speed, fatigue, thread stripping with nonuniform load sharing, thermal growth, lubricant starvation, transient shock, or safety-critical holding without separate analysis and tests.

Worked example

1. Select Tr20 × 4, one start, R_p0.2 = 295 MPa, F = 20 kN, 50 mm stroke, 44 mm nut, k = 5×10⁻¹⁵ m²/N, h′ = 0.1, μ = 0.1, and one-way move.

2. The expected screen is 31.6 N·m forward torque, −5.9 N·m signed backdrive torque, 40.3% efficiency, 16.1 MPa thread pressure, safety factor about 2.27, and about 3,520 one-way moves.

3. Interpret this as a static/wear screen only. The negative backdrive torque supports the static self-locking screen, while the life estimate remains only as credible as the entered wear rate.

Equations used

Lengths are evaluated in mm, forces in N, stresses in N/mm² = MPa, and torque in N·mm before conversion to N·m. Axial load is an unsigned magnitude. Positive T₊ drives the load forward; signed T₋ is positive only when the load can backdrive under the friction model.

H₁ = P/2; d₂ = d − H₁; d₃ = d − 2h₃; lead = nP

Aₜ = πd₃²/4; i = Lₙ/P; Aₘ = iπd₂H₁; pₘ = F/Aₘ

ρ = atan[μ/cos(15°)]; φ = atan[nP/(πd₂)]

T₊ = F(d₂/2) tan(φ + ρ); T₋ = F(d₂/2) tan(φ − ρ)

T₀ = F(d₂/2) tan φ; η = T₀/T₊

σₜ = F/Aₜ; Wₚ = πd₃³/16; τ = T₊/Wₚ; σₑ = √(σₜ² + 3τ²); S = Rₚ₀.₂/σₑ

h = h′P/2; s = h/(kpₘ); s₁ = πd₂Lₛ/P; s_cycle = 2s₁; N = round(s/s_event)

Symbols: d is nominal diameter; P pitch; h₃ selected root-depth parameter; H₁ loaded flank height; d₂ pitch diameter; d₃ root diameter; n starts; Lₙ nut engagement; i engaged turns; Aₜ tensile area; Aₘ idealized thread support area; F load; μ friction; ρ friction angle; φ lead angle; T₊/T₋ forward/backdrive torque; T₀ ideal torque; η efficiency; σₜ tensile stress; τ torsional stress; σₑ von Mises stress; S yield safety factor; h allowable wear depth; k specific wear rate; s total sliding distance; Lₛ stroke; and N service events.

Theory and method

The trapezoidal flank angle is 30°, so the effective friction angle uses the 15° half-angle. Torque follows the classical inclined-plane screw relation at pitch diameter. The stress screen combines axial stress at the calculated root area with torsion from forward torque using von Mises equivalence. Contact pressure assumes every engaged turn shares load uniformly. Wear life applies the linear Archard depth relation h = k pₘ s and therefore assumes constant pressure and wear coefficient.

Assumptions and limits

Rigid, aligned screw/nut; standard listed trapezoidal geometry and constant pitch.
Uniform thread load sharing, constant Coulomb friction, steady axial load, and no collar/bearing torque.
Wear is linear with sliding distance; running-in, debris, lubrication changes, temperature, and geometry evolution are omitted.
The static self-locking check is φ ≤ ρ. Vibration, inertia, lubrication changes, manufacturing tolerances, and external torque can defeat holding.
No buckling, column stability, critical speed, fatigue, stripping concentration, PV/thermal rating, deflection, or drive duty-cycle analysis is included.

References

ISO 2904, ISO metric trapezoidal screw threads — Basic dimensions.
ISO 2903, ISO metric trapezoidal screw threads — Tolerances.
Budynas and Nisbett, Shigley’s Mechanical Engineering Design, power-screw mechanics.
Archard, J. F. (1953), “Contact and Rubbing of Flat Surfaces,” Journal of Applied Physics 24(8), doi:10.1063/1.1721448.

Continue in TriboSolver

Use TriboSolver to refine friction, contact pressure, wear, thermal behavior, and duty-dependent service estimates with geometry and material evidence.

Thread self-locking Archard wear Shaft buckling