Spring geometry & loading
mm
mm
D = D_outer − d
—
mm
N
e.g. preload / assembly
N
e.g. maximum operating force
Results
Formulas & notes
Spring rate
k = G · d⁴ / (8 · D³ · n)G = shear modulus, d = wire diameter, D = mean coil diameter, n = active coils.
Shear stress (Wahl corrected)
C = D / d (spring index)K_W = (4C−1)/(4C−4) + 0.615/C
τ = K_W · 8·F·D / (π·d³)
K_W accounts for curvature and direct shear effects. Valid for C = 4…12.
Solid length
Closed & ground: Ls = n_t · dClosed not ground: Ls = (n_t+1)·d
Open: Ls = (n_t+1)·d
n_t = n + 2 (2 dead end coils for closed ends). Solid stress τ_s must stay below τ_allow.
Buckling
λ = L₀ / DBuckling risk if λ > 2.6 (fixed-free)
or λ > 5.3 (fixed-fixed)
For slender springs consider end conditions and use a buckling guide pin. Rule of thumb: L₀ < 3·D.
Material G values
- Spring steel wire: 81 500 MPa
- Cr-V 51CrV4: 80 000 MPa
- Stainless 1.4310: 73 000 MPa
- Phosphor bronze: 41 000 MPa
Design tips
- Spring index C = 4…12 (preferred 6…9)
- Active coils n ≥ 3
- f₂ / L₀ ≤ 0.8 (avoid coil clash under max load)
- τ at solid < τ_allow (no set)
- Standard: DIN EN 13906-1