| name | compression-spring |
| description | Helical compression spring design — spring rate, stress, Wahl factor, solid length, buckling, fatigue, material selection, tolerances, preferred sizes (ASME B27.1). |
| metadata | {"priority":7,"promptSignals":{"phrases":["compression spring","coil spring","spring rate","Wahl factor","spring index","solid length"],"minScore":3}} |
Compression Spring Design — Complete Skill
Geometry and Spring Rate
Basic Parameters
d = wire diameter [mm]
D = mean coil diameter [mm]
C = spring index = D/d (ideal: 4-12; C < 4 difficult to manufacture; C > 12 tangles)
N_a = number of active coils
End types: open, closed, closed+ground (closed+ground most common)
L_free = free length [mm]; L_solid = solid length = (N_total) × d
Spring rate:
k = Gd⁴ / (8 D³ N_a) [N/mm]
G = shear modulus: steel 79 GPa; stainless 316 73 GPa; phosphor bronze 44 GPa
Deflection: δ = F/k = 8 F D³ N_a / (G d⁴)
Stress Analysis
Torsional Shear Stress
τ = K_w × 8FD / (π d³) [corrected by Wahl factor]
Wahl correction factor:
K_w = (4C-1)/(4C-4) + 0.615/C [stress concentration + curvature]
K_w values: C=4 → K_w=1.40; C=6 → K_w=1.25; C=8 → K_w=1.18; C=12 → K_w=1.12
Allowable stress:
Static: τ_allow = 0.45 S_u (cold-wound, set removed); 0.35 S_u (no set)
Fatigue: τ_allow = 0.36 S_u (10⁷ cycles, S_e estimate from Zimmerli)
Wire S_u (Shigley spring wire tables):
Music wire (A228): S_u = A/d^b where A=2061, b=0.163 (d in mm, S_u in MPa)
Hard-drawn (A227): A=1753, b=0.183
Chrome-vanadium (A232): A=2000, b=0.167
Chrome-silicon (A401): A=1974, b=0.108
302 SS: A=1867, b=0.146
Deflection and Operating Conditions
Shut height (solid length):
L_solid = d × N_total
N_total: closed+ground = N_a + 2; open = N_a; closed (not ground) = N_a + 2 but varies
Working deflection:
δ_working < L_free - L_solid - 25%clash allowance
Clash allowance: 10-25% of working deflection (prevents coil clash at overload)
Initial tension: not applicable for compression springs (no initial tension)
Buckling
Spring can buckle if free length is too large relative to spring diameter
Buckling ratio: L_free/D < 2.63 for fixed ends (stable)
L_free/D < 4 for one end pinned
For L_free/D > 4: guide rod or tube required
Critical force for buckling (conservative):
F_cr = k × δ_cr where δ_cr = L_free [1 - √(1 - (C₁D/L_free)²)] / C₂
C₁ = 0.5 (both ends fixed), C₂ = π²/2 (typically)
Fatigue Design (Zimmerli Data)
For spring steel (N = 10⁷ cycles):
S_su ≈ 0.67 S_u (ultimate shear)
Fatigue limit (unpeened): S_sa ≈ 241 MPa (corrected amplitude stress)
Fatigue limit (shot peened): S_sa ≈ 379 MPa
Modified Goodman (shear):
τ_a/S_su + τ_m/S_su = 1 → use Goodman for mean+alternating stress
Energy Stored
U = F² / (2k) = k δ² / 2
Material Comparison
| Wire | G [GPa] | Cost | Temp | Notes |
|---|
| Music wire (A228) | 79 | Low | -40 to 120°C | Best fatigue |
| Hard-drawn (A227) | 79 | Low | -40 to 120°C | Static loads |
| Cr-V (A232) | 79 | Med | -50 to 220°C | Elevated temp |
| Cr-Si (A401) | 79 | Med-Hi | -50 to 250°C | Highest strength |
| 302 SS (A313) | 68 | Med | -250 to 260°C | Corrosion |
| Inconel 718 | 75 | High | to 540°C | High temp |
Output
Provide: wire diameter d [mm], mean diameter D [mm], C (spring index), N_a (active coils), k [N/mm], τ_max [MPa] vs. τ_allow, L_free [mm], L_solid [mm], buckling check, fatigue safety factor.
