Power screw — torque, safety factor and service life
Forward/back-drive friction torque, screw efficiency, thread contact pressure, safety factor and sliding-wear service life of a trapezoidal power screw, from thread size, material grade, axial load, friction and nut geometry.
Pitch, P4 mm
Pitch diameter, d₂ = d − 0.5P18 mm
Root diameter, d₃ = d − 2h₃15.5 mm
Tensile stress area, A_s = π/4·d₃²188.69 mm²
Thread depth, H₁ = 0.5P2 mm
Tensile stress, σ_m = F/A₃10.6 MPa
Torsion stress, τ = T/W_p5.6 MPa
Equivalent stress, σ_e14.4 MPa
Ultimate tensile strength, R_m490 MPa
Yield strength, R_p0.2295 MPa
Safety factor, S_v = R_p0.2/σ_e20.49
Forward-drive friction torque, T+4.113672365499433 Nm
Back-drive friction torque, T--1.5054691338493733 Nm
Screw efficiency, η31 %
Thread contact pressure, p1.6 MPa
Total sliding distance, s = h/(k·p)24.88141381643116 km
Sliding distance per cycle, s_i = 2(π·d₂·L_lift/P)1.413716694115407 m
Number of cycles, L_n = s/s_i17600
Method & references
- Power-screw torque (raising/lowering), efficiency, contact pressure and sliding-wear service life for a trapezoidal thread.
The computation is a literal port of the original client-side JavaScript from /calculators/e4_6.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.