Spring geometry & loading
mm
mm
D = Douter − d
N
Built-in pretension(typ. 10–40 N)
N
Must be ≥ F0
N
Design maximum load
Results
| Parameter | Value | Unit | Formula / note |
|---|
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 corrects for wire curvature and direct shear. Valid for C = 4…12.
Free length & extension
L₀ = (n+1)·d + 2·h_hookδ = (F − F₀) / k
L_F = L₀ + δ
h_hook = hook length (D, D/2 or 1.5D depending on hook type). Initial tension F₀ must be overcome before extension starts.
Initial tension
τ₀ = K_W · 8·F₀·D / (π·d³)τ₀ typical: 20–45% of τ_allow
Initial tension is built in during coiling. Too high = brittle hooks; too low = spring doesn't stay closed under vibration.
Material G & strength
- Spring steel EN 10270-1: G = 81 500 MPa
- Cr-V 51CrV4: G = 81 500 MPa
- Stainless 1.4310: G = 73 000 MPa
- Phosphor bronze: G = 43 000 MPa
- τ_allow = 0.45 × Rm (static loading)
Design tips
- Spring index C = 4…12 (preferred 6…9)
- Active coils n ≥ 3
- Hook stress is often the limiting factor — inspect hook bend stress separately
- Extension springs are susceptible to fatigue at hooks
- Related: 🌀 eng-015 Compression Spring