Comprehensive catalog of mechanical springs: helical (compression, extension, torsion, conical/barrel), Belleville disc, wave/finger, constant-force Negator, volute, leaf, gas-strut, air-spring bellows; design standards (SAE J1122, ASTM A227/A228/A229/A231/A232/A313, EN 10270, JIS G 3522), end conditions, manufacturers, design equations including Wahl/Curtis/Bergsträsser correction factors, fatigue criteria (Goodman, Sodorberg, Wöhler S-N), applications, and exotic materials. Both SI and US units; ASTM material specs cross-linked to EN/JIS equivalents.
Most common — last ½ coil pitch reduced to touch adjacent coil
Closed and ground
n_a = n_t − 2
Closed + ground flat at both ends; best squareness + seating; aerospace + critical valve springs
2.2 Standard Specifications
Standard
Topic
SAE J1122
Helical compression spring design (US automotive)
ASTM A125
Hot-coiled steel springs
ASTM A267
Spring testing
SAE-AMS 7472
Aerospace cold-coiled compression
DIN EN 13906-1
Helical compression spring design (Europe)
DIN EN 13906-2
Helical extension spring design
DIN EN 13906-3
Helical torsion spring design
DIN EN 15800
Cylindrical helical compression spring quality
ISO 26909
Spring vocabulary
JIS B 2704
Helical compression spring design (JP)
2.3 Conical / Barrel / Hourglass
Profile
Use
Conical (tapered)
Telescopes into shorter solid height (battery contacts, retractable mechanisms)
Barrel (convex)
Reduced lateral buckling tendency
Hourglass (concave)
Decreasing rate at full compression
Variable pitch
Progressive rate (suspension, valve spring)
Mini-block coil-over
Truck suspension (Fiat/IVECO mini-block)
3. Helical Extension Springs
Standard / topic
Notes
Initial tension
Built-in preload from cold winding (typically 10-25% of max load)
ASTM E2769
Extension spring testing
DIN EN 13906-2
Extension spring design
End loop types
Machine half-loop, full loop over center, side hook, raised hook, swivel hook, threaded plug end (Lee Spring), screw-in plug end
Stress concentration at hook: hook stress can be 1.5-3× body stress; specify generous hook radius + cross-over for fatigue service.
4. Helical Torsion Springs
Parameter
Definition
Body diameter
Reduces as spring is wound; design for max wound diameter
Leg orientation
Straight, hinged, axial, tangential, special
End deflection
Angular: θ (deg or rad)
Spring rate
k_t = M / θ (Nm/rad) = E·d⁴ / (10.8 · D · n_a) — approximate
ASTM
A229 oil-tempered, A228 music wire, A313 stainless
DIN EN 13906-3
Torsion spring design
Wound direction: clockwise (RH) or counterclockwise (LH); spring is loaded only in the winding direction (closing).
5. Conical / Volute / Constant-Force
5.1 Volute Spring
Tapered strip wound on edge into a truncated cone; high deflection in small package; vibration damping from inter-coil friction. Heritage US tank suspension (M4 Sherman); modern niche use.
5.2 Constant-Force Spring (Negator)
Pre-stressed flat strip wound onto small drum; force ≈ constant over extended travel.
Same strip mounted to provide constant winding torque to drive a shaft — used in mechanical timers, escape mechanisms, satellite deployment.
6. Belleville (Disc Spring) — Conical Washer
6.1 Standards
Standard
Topic
DIN 2092
Belleville design
DIN 2093
Belleville dimensions + material (Group 1/2/3 standard sizes)
DIN EN 16983
Belleville (replaces DIN 2092 + 2093 future)
DIN 6796
High-load conical washer (M3-M48)
DIN 2096
Spring washer (low-load lock variant)
ASTM B485
Belleville (US)
JIS B 2706
Belleville (JP)
SAE-AMS 5520
Aerospace nickel + Inconel Belleville
6.2 Stack Arrangements
Stack
Description
Effect
Single
One disc
Baseline F + δ
Parallel (cup-to-cup, ↑↑↑)
n discs stacked nesting
Force × n, deflection unchanged
Series (alternating, ↑↓↑↓)
n discs alternating
Deflection × n, force unchanged
Parallel-series combination
combination
Both scaled
Pre-loaded (with washer in middle)
adds preload
linear rate
6.3 Force-Deflection Behavior
Per DIN 2092 / Almen-Laszlo formula, the F-δ curve depends on h₀/t ratio:
h₀/t (cone height / thickness)
Curve
<0.4
Nearly linear
0.4-0.75
Progressive
0.75-1.41
Plateau (near-constant force over part of range)
1.41-2.83
Snap-through (bistable)
>2.83
Snap-action
OEMs: Schnorr (the original German Belleville inventor, now part of Heico Group), Christian Bauer, Mubea (auto), Solon Manufacturing (US), Spirol International, Key Bellevilles, BelleStock, Springmasters.
7. Wave Springs (Smalley, Crest-to-Crest)
Type
Stack
Use
Single-turn wave
one ring with multiple waves
Light axial preload (bearing preload, retainer)
Multi-turn wave (crest-to-crest)
Multiple flat-wire turns stacked crest-on-crest
Replaces multi-coil compression with ~50% less axial length
Linear wave
Custom rate
Specific design
Nested wave
Multiple stacked rings nested for higher rate
Higher force
Snap-ring wave (Spirolox + wave)
Combined retainer + spring
Bearing preload
OEM: Smalley Steel Ring Company (now part of Bauer Engineering / TFI Group) — invented crest-to-crest wave springs; manufactures Spirolox retaining rings + Crest-to-Crest, Nested, Linear, Interlace, Single-Turn waves in carbon, stainless 17-7PH, Elgiloy, Inconel X-750 + Hastelloy. Sizes: 0.250” - 79” diameter.
Other mfrs: RotoClip, Associated Spring Raymond (Barnes Group) wave springs, Murata Springs (JP), Sodemann (DK).
8. Leaf Springs
Type
Use
Multi-leaf (laminated)
Heritage truck + railroad freight car suspension
Mono-leaf (parabolic, taper-rolled)
Modern truck — lighter, longer life
Half-elliptic
Standard truck axle
Full-elliptic
Heritage carriage
Quarter-elliptic
Vintage
Volute leaf (Belleville disc stack)
Heavy machinery
Composite (GFRP / CFRP transverse leaf)
Corvette transverse mono-leaf, Volvo rear
OEMs: Eaton (Stanley Eaton, Pacific Heavy Duty), NHK Spring (JP, world’s largest auto spring mfr), Hendrickson, Mubea, Krupp Hoesch Federn (ThyssenKrupp Federn), Yamato Spring, Inka, Sogefi (Allevard Rejna), Jamna Auto (India), Liteflex (composite leaf).
Specify Almen strip + intensity (0.006-0.020 A) + coverage (>100%)
Dual peening (large media + fine media)
Smoother finish + higher residual compression
Premium valve springs
Stress-peening (peen under preload)
Higher compressive stress in critical zone
Aerospace + racing
Pre-setting (scragging)
Plastically deform to permanent set, then operate within elastic range
All medium/high-stress springs
Heat setting (warm + cold)
Stress-relieve coiling residual stress
Standard for music wire after forming
Black oxide
Cosmetic + light corrosion
Standard finish
Zinc-plate + chromate (Cr3+)
Galvanic corrosion protection
Industrial commodity
Mechanical zinc (no H-embrittlement)
For high-strength springs
ASTM B695
Cadmium (legacy)
Aerospace heritage
Restricted (REACH)
Powder coat / electrostatic paint
Cosmetic + corrosion
Auto suspension
Hot-dip galvanize
Heavy corrosion
Heavy industrial leaf springs
Phosphate + oil
Lubricant + light corrosion
Auto
Magni 565
Zn-Al flake + organic topcoat
Auto OEM
Geomet
Cr-free Zn-Al flake
Auto suspension
Nickel + chrome plate
Decorative + corrosion
Light
PTFE coat (Xylan)
Low friction
High-cycle
Electroless nickel
Uniform corrosion + hardness
Specialty
Tin-zinc
Solderable, corrosion
Electronic relay springs
H-embrittlement caution: high-tensile (≥ 1400 MPa) springs electroplated in acid bath → baking 190-230°C × 4-24 hr within 4 hours of plating, per ASTM B850 / ISO 9587. Music wire + high-Cr-Si steel especially sensitive.
12. Fatigue Design
12.1 Stress Diagrams
For helical compression spring under cyclic load between F_min and F_max:
OEMs (die springs): Associated Spring Raymond (Raymond Die Spring), Danly IEM (Connell), Anchor Lamina (Bahco), Special Springs, Hunter (Ametek), Misumi (catalog), Diamond Wire, Lawson Springs, AccuPress, AMTECH, Korema, Forkardt.
15. Application Cross-Reference
Application
Spring type
Material
Engine valve (gasoline)
Helical compression (variable pitch); valve spring
Cr-Si A401 / VDSiCr
Engine valve (high-rpm racing)
Beehive single + sometimes dual; titanium retainer
VDSiCrV, Ti-Beta
Diesel injector
Helical compression high-stress
Cr-V A232, peened + stress-peened
Suspension coil
Helical compression with variable pitch
SAE 9254 / EN 54SiCr6 oil-tempered
Stabilizer bar
Torsion bar
5160 spring steel
Leaf spring (truck)
Parabolic mono-leaf or multi-leaf
SAE 5160, 51CrV4
Clutch diaphragm
Belleville disc (one large disc with fingers)
Cr-Si / Cr-V
Brake return
Extension helical
ASTM A228 music wire (chromate-plated)
Bearing preload
Wave spring (Smalley)
17-7PH stainless
Valve actuator return
Helical compression
Stainless 17-7PH
Watch hairspring
Spiral flat
Nivarox / Glucydur (Elgiloy-derivative)
Clock mainspring
Spiral wound
Carbon steel; modern Nivaflex (Elgiloy)
Switch contact
Cantilever flat (leaf)
Phosphor bronze C51000
Relay armature
Flat or compressed coil
BeCu C17200
RFI gasket
Compressed knit / spring contact
BeCu, stainless
Door closer
Helical torsion
Cr-V
Mousetrap
Wide-coil torsion
Hard-drawn carbon
Tape measure / window shade
Constant-force Negator
Stainless 301 / 17-7PH
Garage door
Torsion (large dia)
Oil-tempered
Trampoline
Extension
ASTM A229 hot-dip galv
Crash buffer (dies, presses)
Pierce-die polyurethane
TPU 90 Shore A
Vibration isolator (rotating equipment)
Helical compression + rubber + air
varies
EV battery cell pressure
Belleville stack
Stainless
16. Calculation Worked-Example Snippets
16.1 Helical Compression — Sizing
Given: F = 200 N at δ = 25 mm, music wire ASTM A228, target k ≈ 8 N/mm
$\text{Try } d = 2.0 \text{ mm}, D = 16 \text{ mm}, G = 79,300 \text{ MPa}$
For k = 8 N/mm: n_a = 4.84 ≈ 5 active coils. Closed-and-ground ends → n_t = 7 coils total.
Spring index C = D/d = 8 → Wahl K_w = (4·8−1)/(4·8−4) + 0.615/8 = 31/28 + 0.077 = 1.184.
Stress at F = 200 N: τ_c = 1.184 × (8 × 200 × 16)/(π × 2³) = 1.184 × 25 600/25.13 = 1.184 × 1019 = 1206 MPa. For music wire 2 mm: S_y ≈ 1700 MPa → OK with reasonable safety.
16.2 Belleville Stack
Three discs in series stacked alternately give: F same as one disc, δ = 3 × δ_single. Two such stacks placed in parallel (series-parallel combo): F = 2 × single, δ = 3 × single.
17. Common Pitfalls
Spring index C < 4: hard to coil, work-hardens unevenly, residual-stress overshoot at ID; aim 5-12
Buckling: free length / mean diameter L_f/D > 5.26 (fixed-fixed) or > 2.63 (fixed-free) — design lateral support or reduce length
Solid-stress check overlooked: must verify stress at solid length doesn’t exceed yield, otherwise permanent set after handling
Helical extension hook stress not corrected: failures occur at hook radius before body; specify hook with radius ≥ wire diameter
Music wire used above 120°C: rapid loss of strength; switch to chrome-silicon or stainless 17-7PH
Stainless 302 spring in chlorine environment: stress-corrosion cracking; switch to Inconel X-750 or Elgiloy
Belleville stack without guide rod or sleeve: discs slip + jam; always pilot
Belleville stack with parallel + series count miscalculated: gives wrong F-δ — count carefully (parallel multiplies force, series multiplies deflection)
Wave spring in compressed coil’s place without verifying load capacity: wave springs trade space for slightly lower force capacity
Gas strut sized only for static load: needs ~30% more force to overcome stiction + accelerate; size lift-off force properly
Air spring without surge tank: rate too stiff; auxiliary reservoir tunes natural frequency
Constant-force Negator extended beyond rated length: yields and loses force constant
Shot-peening missed on critical-fatigue spring: cuts life 50%; specify Almen + coverage
Compression spring with non-uniform pitch and unground ends: misalignment + buckling
Mating spring seat with sharp edges: chafes spring at contact, initiates fatigue; specify washer or rounded seat
Spring under cyclic + impact in stainless 302: cold-work-induces martensite phase that increases magnetic permeability + reduces ductility — use 316 if needed
Plating high-strength spring without bake: H-embrittlement failure within hours; ASTM B850 / ISO 9587 mandatory bake
Phosphor bronze spring used as battery contact in deep discharge: tin migration / whiskers; use BeCu C17200
Coiled spring loaded in reverse direction: torsion springs are unidirectional; extension springs cannot be compressed (initial tension would invert)