Trapezoidal thread power screw — fixed nut length

Tightening/loosening torque, thread efficiency, contact pressure and sliding-wear service life of a trapezoidal-thread power screw (nut length fixed at 44 mm, matching the original locked demo).

✓ validated against legacyoriginal: /calculators/e3_7.htm

Trapezoidal thread power screw — fixed nut length — original diagram from /calculators/e3_7.htm

Trapezoidal threadNumber of thread starts, nYield strength, R_p0.2MPaAxial load, F10³ NStroke length, L10⁻³ mSpecific wear rate, k10⁻¹⁵ m²/NRelative wear depth, h/0.5PFriction coefficient, μ

Pitch, P4 10⁻³ m

Pitch diameter, d₂ = d − 0.5P18 10⁻³ m

Root diameter, d₃ = d − 2h₃15.5 10⁻³ m

Thread depth, H₁ = 0.5P2 10⁻³ m

Tensile stress area, A_t = π/4·d₃²188.7 10⁻⁶ m²

Tensile stress, σ_t = F/A_t106 MPa

Torsion stress, τ = T/W_p43.2 MPa

Equivalent stress, σ_e129.8 MPa

Safety factor, S_v = R_p0.2/σ_e2.27

Thread contact area, A₁1244.1 10⁻⁶ m²

Tightening torque, M_G+31.599 Nm

Loosening torque, M_G--5.86 Nm

Thread efficiency, η40.3 %

Thread contact pressure, p_m16.1 MPa

Total sliding distance, s = h/(k·p)2.49 10³ m

Sliding distance per stroke, s₁ = π·d₂·L/P0.71 m

Number of strokes, L_n = s/s₁3520

Nut length is fixed at 44 mm (not exposed as an input): the legacy "please login" demo lock freezes the L_nut variable, but the source never actually uses that variable in the formula — the engaged-thread-count term `i = 44/P` hardcodes the literal 44 directly, so L_nut has no effect on the result even with the lock lifted. Exposing an editable-but-inert control would be misleading, so this port fixes it accordingly. All other inputs were genuinely free under the lock and remain so.

Method & references

Trapezoidal power-screw thread: tightening/loosening torque, efficiency, contact pressure and sliding-wear service life.

The computation is a literal port of the original client-side JavaScript from /calculators/e3_7.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.

Trapezoidal thread power screw — fixed nut length — Engineering ABC