Extension Springs (`extension-springs`)

Extension Springs

Tension spring rate and stress screening

Standards catalog

Validation: indicative · Method band: formula

Open calculator

Indicative method: Body shear + hook stress screening with rate and surge checks

Assumptions

Linear elastic material behavior unless noted otherwise.
User is responsible for load combinations and load factors per the selected design code.
Design standard (US/EU/ISO) sets unit defaults and screening check labels — not a full code worksheet.

Limitations

Hook stress uses closed-form factors — not FEA of the hook junction.
Professional screening — verify critical extension springs with manufacturer worksheets.

Engineering checks

Check	IND	US	EU	ISO
Body shear stress utilization	implemented	—	implemented	—
Hook stress safety factor	implemented	—	implemented	—
Surge frequency margin	implemented	—	—	—
Fatigue life (EN 13906-2)	—	—	implemented	—

Purpose

Design helical extension (tension) springs including initial tension, hook stress, spring rate, EN 13906 fatigue screening, and wire catalog selection. Used for assemblies requiring pull force with near-zero free length.

Physics & theory

Extension springs are wound with initial coiled tension $F_{i}$ that must be overcome before coils separate. Total force at extension $x$ is $F = F_{i} + k x$ , with rate $k = G d^{4} / (8 D^{3} n)$ identical to compression spring formula.

Maximum shear stress in the body uses Wahl correction on the coil body load. Hook stress concentrations often govern failure; standard hooks (machine, cross-over, extended) use empirical stress factors $K_{hook}$ . Initial tension is user-specified or estimated from the manufacturable limit (Shigley screening).

Governing equations

F = F_{i} + k x, k = \frac{G d ^{4}}{8 D ^{3} n}

τ_{body} = K_{w} \frac{8 ( F _{i} + k x _{m a x} ) D}{π d ^{3}}, τ_{hook} = K_{hook} \cdot τ_{body}

S F = min (\frac{τ _{allow}}{τ _{body}}, \frac{τ _{allow}}{τ _{hook}})

Numerical method

Closed-form rate and body stress with Wahl factor. Hook factors from wireStrength.ts. Fatigue on body stress range when minimum extension is set. Auto-design sweeps catalog wire sizes and coil counts for target rate, hook SF, and optional fatigue margin.

Inputs

Parameter	Description
Wire and coil geometry	$d$ , $D$ , $n$
`initialTension`	Coiled-in preload $F_{i}$
`hookType`	Machine, cross-over, extended, or body-only
Extension at load	Operating stroke
`wireType` / wire stock picker	Grade or catalog designation
`operatingFrequencyHz`	Surge margin (optional)
Fatigue panel	Life class, wire quality, minimum extension

Outputs

Spring rate, initial tension, max manufacturable $F_{i}$ , force at extension
Body and hook shear stress and separate safety factors
Coil bind length, extended length, surge frequency
Optional fatigue SF; governing failure mode
Load–extension plot (F = Fi + kx)

Design codes & checks

Indicative: Body shear utilization, hook stress SF, surge margin, fatigue life (when enabled)
EU: EN 13906-2 extension springs (reference)

Design workflow

Validate: Forward check with hook type and Fi validation flag.
Auto-design: Wire/coil sweep from springWireCatalog for target rate, max force, hook SF.
Handoff: Fatigue module receives body shear as alternating stress input.

Assumptions & limitations

Hook stress uses empirical factors — not a substitute for hook FEA on critical applications.
Initial tension validated against manufacturable estimate; not auto-sized.
Fatigue simplified per EN 13906-2 screening; full hook fatigue nomograph not embedded.

Verification

CI: extension-springs-indicative-01.json
Vitest: src/lib/springs/extension-springs/engine.test.ts
Engineer sign-off: spring-modules-user-tasks.md

References

EN 13906-2:2013. Cylindrical helical springs — Part 2: Extension springs.
Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 10.
Wahl, A. M. Mechanical Springs, 2nd ed.
Associated Spring Raymond. Design Handbook.

Maintainer note: Extension spring screening.

Extension Springs

Assumptions

Limitations

Engineering checks

Extension Springs (extension-springs)

Extension Springs (`extension-springs`)