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Compression spring

A real spring works between two positions: installed (preload) and working (max). Set both and this gives the force and stress at each, the clearance left to solid, and — the part that decides whether it survives — a fatigue safety factor cycling between the two loads. Wire strength is taken from the actual wire diameter, so thin wire is correctly stronger.

Compression spring — working stroke k = —

Wire diameter d mm

Mean coil diameter D mm

Active coils n_a turns

Free length L₀ mm

Preload deflection δ₁ mm

Working deflection δ₂ mm

Material

Surface finish

Engineering notes

Two operating points

Rate k = G·d⁴ / (8·D³·n_a); forces F = k·δ at preload (δ₁) and working (δ₂).
Shear stress τ = K_W · 8·F·D / (π·d³), K_W = (4C−1)/(4C−4) + 0.615/C.
Tensile strength is size-dependent: S_ut = A / d^m (A, m per material). Static shear yield ≈ 0.45·S_ut.

Fatigue (Goodman + Zimmerli)

Alternating / mean shear τ_a = (τ₂−τ₁)/2, τ_m = (τ₂+τ₁)/2.
Endurance from Zimmerli (size-independent): unpeened S_sa=241, S_sm=379 MPa; shot-peened 398 / 534 MPa. Goodman: S_se = S_sa/(1−S_sm/S_su), S_su=0.67·S_ut.
Fatigue factor n_f = 1 / (τ_a/S_se + τ_m/S_su). n_f ≥ 1 means infinite life (>10⁶ cycles); shot-peening roughly doubles the alternating endurance.
Keep index C in 4–12, the working point clear of solid, and L₀/D < 4 to avoid buckling.

Result

Live