Springs — Complete Guide
A complete engineering reference for springs: compression, extension, torsion, Belleville, leaf, gas, and wave springs, design formulas, spring materials, fatigue and stress relaxation, manufacturing, standards, and interactive spring-rate calculators.
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Springs
Types · Compression · Extension · Torsion · Belleville · Materials · Fatigue · Manufacturing · Standards · Calculators
🌀 Spring Types
Compression Spring
Most Common
PrincipleA force opposing compression — F = k × δ
End ShapeOpen · Closed · Closed Ground · Pigtail
ProfileCylindrical · conical · Barrel · Hourglass
Solid Length LsLs = n_total × d
⚠️ BucklingL/D > 4 → risk of lateral buckling!
UsesValves, steering, presses, products
▶ YouTubeExtension Spring
Initial Tension
PrincipleA force opposing extension · Initial Tension Ti
F = Ti + k × δ
EndsMachine Hook · Full Loop · Half Loop · Crossover
⚠️ Weak PointHook ends! High stress concentration
Initial TensionTi = τi × πd³ / (8D) per Wahl
UsesClosing mechanisms, garage doors, trampolines
▶ YouTubeTorsion Spring
MomentBending!
PrincipleBending stress (not shear!) · T = k_θ × θ
k_θk_θ = E×d⁴ / (10.8×D×n) [N·mm/°]
Winding DirectionRH (Right Hand) · LH — direction matters!
⚠️ TighteningD shrinks under load → ↑stress
UsesHinges · gun hammers · clutches · control mechanisms
▶ YouTubeBelleville Washer
High LoadSmall Space
PrincipleA conical plate that flattens under load
AdvantageVery high load / small deflection
Parallel Stack↑↑load · ↓deflection
Series Stack↑↑deflection · = load
DIN 2093International standard · 3 series A/B/C
UsesBolt preload · seatbelts · valves
▶ YouTubeLeaf Spring
Automotive · Vehicles
PrincipleA Cantilever/Simply Supported beam
Multi-leafLayered leaves ← ↑load · ↑damping
Mono-leafA single leaf · less damping · lighter
MaterialCr-Si (9254) · Cr-V (6150) · Composite GFRP
UsesRear axle · trucks · trailers
▶ YouTubeSpiral / Flat Spring
Clocks · Mechanisms
Power SpringStored energy · clocks · products
Constant Force SpringConstant force across the full deflection
Volute SpringCylindrical-conical · heavy loads
Hair SpringWatch · very precise · Ni-Span-C
UsesWatches · retractors · reels · instrumentation
▶ YouTubeGas Spring
N₂ / Oil
PrincipleCompressed N₂ + oil → a uniform force
AdvantageMore constant force · ↓space · ↓damping
CompressionGas compresses on compression → ↑force
ExtensionPulls back — trunk lid opening
Force Range50-60,000N · Stroke 25-1000mm
Manufacturers: Stabilus · ACE Controls
▶ YouTubeWave Spring
↓SpaceSmalley
PrincipleA strip coiled into a wave shape
Advantage↓50% space vs. Coil Spring
Single TurnSmall deflection · preload
Multi-TurnGreater deflection
UsesBearing preload · retaining trays · instrumentation
Manufacturer: Smalley Steel Ring
▶ YouTube⬇️ Compression Spring Design
Geometric Parameters
ISO 10243
d — Wire Diameter0.1-50mm (depending on load)
D — Mean DiameterD = D_outer - d = D_inner + d
C = D/dSpring index: 4-12 ideal
n — Active Coils3-20 typical
n_totaln + 2 (Closed Ground end)
Ls = d × n_totalSolid Length
Lf = Ls + δ_max + clearanceFree Length
Stress Formulas
Wahl Correction
k = G×d⁴/(8×D³×n)Spring rate [N/mm]
Kw = (4C-1)/(4C-4) + 0.615/CWahl Factor
τ = Kw × 8FD/(πd³)Shear stress [MPa]
δ = F/k = 8FD³n/(Gd⁴)Deflection [mm]
τ_static ≤ 45% SutStatic stress limit
τ_fatigue ≤ 35% SutFatigue stress limit
Buckling — Lateral Buckling
L/D > 4 → danger!
Buckling ConditionL₀/D > 2.62 (Free-Free) · >4.0 (Free-Fixed)
SolutionsInternal guide (Arbor) · external guide · Conical
Arbor DiameterDi - 1.0 to Di - 0.5 mm
Guide I.D.Do + 1.0 to Do + 0.5 mm
Rule of thumb: L/D ≤ 3 safe · 3-4 check buckling · >4 = use a guide
▶ YouTubeEnd Types
4 Types
Plain (Open)Open end · n_dead=0 · less stable
Plain ClosedClosed end · n_dead=1 ← squared
Closed Ground ✅Closed + ground · n_dead=1 · flat!
PigtailA reduced end · prevents lateral catching
Closed Ground = the default for most applications
For the manufacturer, specify: "Both ends closed and ground"
▶ YouTubeFor the manufacturer, specify: "Both ends closed and ground"
Presetting
↑Durability
PrincipleCompress beyond the elastic limit → residual stress
Result↑load range · ↑fatigue durability
MethodCompress to Solid → release → a smaller Lf
Shot Peening↑20-40% fatigue life
Presetting + Shot Peening = a recommended combination for fatigue springs
▶ YouTubePractical Design Rules
Rules of Thumb
Index C4 ≤ C ≤ 12 (ideal C=6-9)
Coil Spacinga gap ≥ 0.1×d between coils at full compression
Max Deflection≤ 80% of (Lf - Ls) — never to Solid
Natural Frequencyfn = (d/πDn²) × √(G/8ρ) → avoid resonance!
Stabilizing at 60°C+Stress Relaxation → choose a suitable material
↔️ Extension Spring Design
Initial Tension
Ti
PrincipleTight coils → a built-in initial tension Ti
F = Ti + k × δTotal force
Typical Tiτi = 0.3 × Sut for Music Wire
LengthL = n×d + 2×r_hook (without pre-tension)
⚠️ HookThe point of failure! High SCF at the hook end
Hook Types
4 Main Types
Full Loop (Machine Hook)Most common · high SCF · cheap
Half LoopLower SCF · ↑hook strength
Extended HookAccess for connection ← a long end
Crossover Center↓SCF · more expensive to manufacture
For fatigue: Half Loop is preferred! Crossover = the best
▶ YouTubeSCF at the Hook — Stress Concentration
⚠️ Critical Point
K_hook = (4R1-d)/(4R1-4d)Wahl at the hook
σ_hook = K_hook × 32F×R/(πd³)Bending!
Limitσ_hook ≤ 0.5×Sut (fatigue: ≤0.35)
Solution↑d · ↑R1 · a special hook
🔄 Torsion Spring Design
Torsion Spring Formulas
Bending, Not Shear!
k_θ = E×d⁴/(10.8×D×n)Rate [N·mm/°]
T = k_θ × θMoment [N·mm], θ=[°]
Ki = (4C²-C-1)/(4C(C-1))Bending concentration factor
σ = Ki × 32T/(πd³)Bending stress [MPa]
σ ≤ 0.78×SutStatic stress limit
E=207GPa for steel (not G!) — because it's bending stress
D Changes Under Load
Important for Design!
RH Winding (rotates CW)D shrinks under load
LH Winding (rotates CCW)D expands under load
D_loadedD' = D×n / (n + θ/360°)
Arbor DiameterDi_loaded - 0.5mm at minimum
⚠️ The Arbor must accommodate D shrinking under load!
Leg Angles
Relative Position
0° (Straight)Both legs straight in the same direction
90°One leg ← 90° → the other leg
180°Opposing ends — a common hinge
Body TorsionThe spring holds itself ← needs an Arbor
Specify to the manufacturer: "Body: RH · Leg A: 90° · Leg B: straight"
🫸 Belleville Washer
DIN 2093 — Series
A · B · C
Series Ah₀/t ≈ 0.4 · a linear force-deflection curve
Series Bh₀/t ≈ 0.75 · a non-linear trend
Series Ch₀/t ≈ 1.5 · a constant-force zone at peak
h₀ = tConstant force — ideal for preload!
OD/IDCommon ratio: OD/ID ≈ 2.0
Stack Arrangements
Parallel × Series
Parallel↑↑force · deflection = single unit
Series↑↑deflection · force = single unit
MixedTwo parallel + two series = ×2 force ×2 deflection
⚠️ FrictionA stack ← ↑friction = ↑hysteresis
Oil/grease between washers reduces friction and hysteresis
▶ YouTube🔩 Spring Materials
Music Wire — EN 10270-1
Most Common
G80 GPa
E207 GPa
τ_max1400-1700 MPa (depends on d)
Sut2170 MPa at d=0.5mm · ↓ as ↑d
T_max120°C — not for high temperature!
ManufacturingCold Drawn · Patented · very flexible
UseGeneral springs · products · tools
Cr-V Steel — 6150 / EN 10270-2
Automotive · Performance
Composition0.5%C · 1%Cr · 0.15%V
G80 GPa
τ_max1100-1300 MPa
T_max220°C
Advantage↑fatigue durability · ↑toughness
UseAutomotive springs · valves · high loads
Cr-Si Steel — 9254 / Si-Cr
Defense↑↑Strength
Composition0.54%C · 1.4%Si · 0.7%Cr
τ_max1200-1450 MPa
T_max250°C
Advantage↑↑strength · ↑sag resistance
UseDefense · aircraft engines · high performance
SS 302 / 304 — EN 10270-3
CorrosionFood · Marine
G69 GPa (lower than steel!)
E193 GPa
τ_max800-1000 MPa
T_max260°C
⚠️ Low Gk is 14% lower vs. Carbon → recalculate!
UseCorrosion · food · marine · medical
SS 17-7PH — AMS 5678
Defense + SS
G72 GPa
τ_max1100-1300 MPa
T_max315°C
ConditionCH900 · RH950 — Precipitation Hardened
UseDefense · aerospace · half the price of Inconel
Inconel 718 / X-750
High TUp to 550°C
G 71877 GPa
G X-75075 GPa
τ_max900-1100 MPa
T_max 718550°C
T_max X-750650°C
UseJet engines · turbine valves · extreme conditions
| Material | G (GPa) | E (GPa) | τ_max (MPa) | T_max (°C) | Use |
|---|---|---|---|---|---|
| Music Wire SW | 80 | 207 | 1400-1700 | 120 | General use |
| Oil Tempered OT | 80 | 207 | 1000-1300 | 150 | Large springs |
| Cr-V 6150 | 80 | 207 | 1100-1300 | 220 | Automotive, loads |
| Cr-Si 9254 | 80 | 207 | 1200-1450 | 250 | Defense |
| SS 302/304 | 69 | 193 | 800-1000 | 260 | Corrosion |
| SS 17-7PH | 72 | 203 | 1100-1300 | 315 | Defense+SS |
| Inconel 718 | 77 | 200 | 900-1100 | 550 | High T |
| Phosphor Bronze | 44 | 110 | 600-800 | 95 | Electrical |
| Beryllium Cu | 48 | 131 | 900-1100 | 200 | Max conductivity |
📊 Spring Fatigue
Goodman Line — Springs
Modified Goodman
τ_a/S_e + τ_m/S_ut = 1/SF— Goodman line
τ_aStress amplitude = (τ_max-τ_min)/2
τ_mMean stress = (τ_max+τ_min)/2
S_e for Springs0.45×Sut (Shear endurance, R=-1)
Minimum SF1.3 general · 1.5 defense
Goodman: Zimmerli Line for steel springs:
τ_a = 241 MPa (Music Wire, corrected)
τ_a = 241 MPa (Music Wire, corrected)
Zimmerli / Wahl Fatigue Lines
Spring-Specific
Music Wire (Shear)τ_a = 338 MPa (R=0) · 241 MPa (corrected)
Hardened Alloyτ_a = 310 MPa (R=0)
SS 302τ_a = 207 MPa (R=0)
Non-Ferrousτ_a = 186 MPa (R=0)
10⁷ cycles · Not Shot Peened. Shot Peened: ×1.3
Stress Relaxation
Sag at Temperature
PhenomenonA spring loses length under temperature + sustained load
Music Wire >70°C↑↑Sag — not suitable!
Cr-Si <250°C≤2% Sag — acceptable
Inconel 718 <500°C≤1% Sag — excellent
PreventionPresetting · a suitable material · ↓τ_max
▶ YouTubeShot Peening for Springs
↑↑Durability
PrincipleCompressive stress in the outer layer → opposes cracking
Improvement↑20-40% fatigue life
Almen StripA/N/C — intensity gauging
Peening MediaSteel Shot S110-S330 · Glass Bead
AMS 2430Shot Peening standard for aerospace
Presetting after Shot Peening = the optimal combination!
▶ YouTube🏭 Spring Manufacturing
Cold Coiling
Up to d=16mm
ProcessWire ← feeding · coiling · cutting
CNC CoilingComputer control ← every parameter · ↑↑precision
Stress Relief150-250°C · 20-30 min · mandatory!
Precisionk: ±10% (general) · ±5% (select) · ±2% (specific)
Always specify Stress Relief on the drawing!
▶ YouTubeHot Coiling
d > 16mm
Working Temp.900-1100°C
ProcessHeating ← hot coiling ← Q&T
MaterialsCr-Si · Cr-V · En45/46
UseTruck springs · heavy pressure
Precision±5% Lf · ±10% k
▶ YouTubeGrinding — End Grinding
Closed Ground
PurposeA flat end ← accurate seating ← ↑stability
Squareness≤1.5°/mm diameter (DIN 2095)
Ground EndMinimum 3/4 coil
⚠️ Grinding Heat↑temp = ↓Sut! Strict cooling required
▶ YouTubeDIN 2095 / 2096 — Coiling Standard
SN Tables
DIN 2095Static/Quasi-Static — static force
DIN 2096Dynamic — cyclic stress
d=2mm DIN 2095490-640 N/mm²
d=2mm DIN 2096610-760 N/mm²
↑d → ↓Sut (Sut decreases with wire thickness)
Coatings for Springs
Corrosion · Appearance
Zinc PhosphateA paint base · not for exposure
Hot Dip Zinc⚠️ HE risk! Not for springs!
Cadmium (EU banned)Replaced by Zinc-Nickel
Zinc-NickelA Cadmium replacement · aerospace · ±200h SS
PTFE Coating↓friction · chemical resistant · non-conductive
E-CoatElectrophoretic paint · 500h SS · automotive
⚠️ Hydrogen Embrittlement! A bake-out after electroplating is mandatory!
🏆 Standards & Manufacturers
International Standards
ISO · DIN · EN
ISO 10243Compression Springs — dimensions
ISO 2162Spring Drawing Standards
DIN 2095Cold Coiled Compression — Static
DIN 2096Cold Coiled Compression — Dynamic
DIN 2097Extension Springs
DIN 2093Belleville Washers
EN 10270Spring Steel Wire — Part 1/2/3
Associated Spring — Barnes
Global Leader
CompanyBarnes Group · SPEC Engineering Springs
CatalogStandard Springs Catalog — millions of items
ToolsSpring Design Software — SPEC
Lesjöfors · Mubea · Lee Spring
Europe · Global
LesjöforsSweden · Standard + Custom · Europe
MubeaGermany · Disc Springs · Automotive
Lee SpringUSA · a huge catalog · ISO 9001
Century SpringUSA · Standard Catalog
Suppliers in Israel 🇮🇱
Local
Kfitzei IsraelLocal manufacturing · Custom · Standard
Avner-GalSprings + spring products
TelescopeGas springs · Stabilus Israel
ImportsAssociated Spring · Lee Spring — available
Spring Design Software
CAD · FEA
SpringulatorLee Spring — free · online
SPEC (Barnes)Associated Spring — professional
KISSsoftA complete spring module + FEA
ANSYS MechanicalFEA — full fatigue analysis
🧮 Spring Calculators
Compression / Extension Spring Calculator
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Torsion Spring Calculator
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