Size a round-wire cylindrical helical compression spring per GB/T 23935-2009. Calculates spring rate, working load, maximum shear stress (with Wahl curvature correction), solid height, travel margin and buckling stability in one pass. Formula: τ = K·8FD/(πd³), k = Gd⁴/(8D³n).
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K = (4C−1)/(4C−4) + 0.615/C corrects for stress concentration at the inner coil surface, where the wire bends tightest.
k = Gd⁴/(8D³n) links stiffness directly to wire diameter, mean coil diameter, active coils and shear modulus.
τ = K·8FD/(πd³) at the inner coil — the critical check against material allowable stress [ τ ].
Lsolid = (n + nend)·d prevents coil binding — the travel margin must stay positive through full compression.
L0/D ≤ 3.7 keeps a both-ends-guided spring from lateral buckling under axial load.
G ≈ 78500 MPa preset for spring steel (oil-tempered / Si-Mn / Cr-V); reduce to 69–73 GPa for stainless grades.
Input wire diameter d, mean coil diameter D and active coil count n.
Enter shear modulus G (steel default 78500 MPa) and allowable [ τ ].
Specify working deflection δ, free length L0 and end coils (closed+ground = 2).
Read spring rate, load, stress, solid height, margin and buckling pass/fail.
Enter wire diameter, coil diameter and active coils to get spring rate, load, stress and pass/fail.
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