Compression Springs (`compression-springs`)

Check	IND	US	EU	ISO
Shear stress utilization	implemented	implemented	implemented	—
Solid height margin	implemented	—	—	—
Surge frequency margin	implemented	—	implemented	—
Fatigue life (EN 13906)	implemented	—	implemented	—

Purpose

Design helical compression springs per EN 13906-1 and Shigley methods:

s p r in g r a t e, so l i d h e i g h t, s h e a r s t r ess, b u c k l in g scr ee n, s u r g e f r e q u e n cy, an d o pt i o na l E N 13906 f a t i g u escr ee nin g . S u pp or t s A S T M s p r in g w i r e g r a d es, E N 10270 w i r ec a t a l o g p i c k er, an d A u t o - d es i g n w i r e / co i l s w ee p s

Physics & theory

A helical compression spring wound from wire diameter $d$ on mean coil diameter $D$ with $n$ active coils behaves as a linear spring with rate $k = G d^{4} / (8 D^{3} n)$ , where $G$ is shear modulus. Wahl factor $K_{w} = (4 C - 1) / (4 C - 4) + 0.615/ C$ with spring index $C = D / d$ corrects for curvature and direct shear in maximum wire shear stress $τ = K_{w} \cdot 8 F D / (π d^{3})$ .

EN 13906-1 allowable shear for cold-coiled springs is $τ_{zul} = 0.56 R_{m}$ , where $R_{m}$ follows size-effect fit $R_{m} = A / d^{m}$ for standard wire grades. Buckling when free length $L_{0}$ exceeds $2.63 D / ν$ with end condition coefficient $ν$ .

Optional fatigue screening uses characteristic shear fatigue strength $τ_{k 0}$ with life-class reduction and Goodman mean-stress correction when minimum deflection is specified (life classes VL/LH/MH/HH).

Governing equations

k = \frac{G d ^{4}}{8 D ^{3} n}

τ = K_{w} \frac{8 F D}{π d ^{3}} \leq 0.56 R_{m}

f_{surge} = \frac{1}{2} \frac{k}{m _{active}}

\frac{L _{0}}{D} \leq \frac{2.63}{ν} (buckling screen)

Numerical method

Closed-form EN 13906-1 / Shigley equations. Wire ultimate from Shigley Table 10-4 fits or springWireCatalog.ts (EN 10270 / ASTM stock). Active coil mass computed for surge frequency. Fatigue via en13906Fatigue.ts when enabled.

Inputs

Parameter	Description
`wireDiameter`, `meanDiameter`	$d$ , $D$
`activeCoils`	Active turn count
`modulus` $G$	Shear modulus
`deflection`, `freeLength`	Operating deflection and $L_{0}$
`wireType`	ASTM wire grade or custom $R_{m}$
Wire stock picker	Optional catalog designation → auto-fill $d$ , $G$ , $R_{m}$
`endCondition`	Buckling end condition (ν coefficient)
`operatingFrequencyHz`	Forcing frequency for surge margin (target 10×)
Fatigue panel	Life class, wire quality 1–3, minimum deflection

Outputs

Spring rate, solid height, loaded length, solid height clearance, max load, shear stress, static SF
Surge frequency and margin, buckling limit, spring index, Wahl factor
Optional fatigue SF and utilization; governing failure mode
Load–deflection and stress plots; spring outline preview

Design codes & checks

Indicative: Shear stress utilization, solid height, surge margin, fatigue life (when enabled)
EU: EN 13906-1 cold-coiled helical compression springs
US: SAE AMS spring wire specifications (reference)

Design workflow

Validate: Forward check on entered geometry.
Auto-design: Sweeps springWireCatalog wire diameters and active coils within max OD for target rate and stress.
Compare: Ranked wire/coil alternatives with Apply.

Assumptions & limitations

Circular wire, closed and ground ends (solid height includes 2d end allowance).
Fatigue uses simplified τk0 + Goodman screening — verify critical designs against EN 13906 nomographs.
Surge margin requires operating frequency input; default 10× margin target.
Not for extension or torsion springs (see dedicated modules).

Verification

CI: compression-springs-indicative-01.json, compression-springs-indicative-fatigue-01.json
Vitest: src/lib/springs/compression-springs/engine.test.ts, en13906Fatigue.test.ts
Engineer sign-off: spring-modules-user-tasks.md, validation-master-checklist.md

References

EN 13906-1:2013. Cylindrical helical springs — Part 1: Compression springs.
Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 10.
Wahl, A. M. Mechanical Springs, 2nd ed. McGraw-Hill.
ASTM A228/A227/A229. Steel Wire for Mechanical Springs.

Compression Springs

Assumptions

Limitations

Engineering checks