Engineering ABC

Calculators · Power transmission

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
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 and documents the reasoning here (see header comment). 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