Torsion Springs (`torsion-springs`)

Torsion Springs

Leg geometry, rate and bending stress

Standards catalog

Validation: indicative · Method band: formula

Open calculator

Indicative method: Bending stress and rate screening for round-wire torsion springs

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

Arbor friction, leg bending detail, and fatigue spectra are simplified.
Professional screening — verify critical torsion springs against EN/ASME spring standards.

Engineering checks

Check	IND	US	EU	ISO
Coil bending stress utilization	implemented	—	implemented	—
Fatigue life (EN 13906-3)	—	—	implemented	—

Purpose

Design helical torsion springs loaded by bending in the coil wire (typically via legs). Computes spring rate, curvature-corrected coil bending stress, leg stress estimate, EN 13906 fatigue screening, and wire catalog selection.

Physics & theory

Torsion springs store energy through wire bending rather than torsion shear along the coil axis. Spring rate in terms of angle $θ$ is:

k = \frac{E d ^{4}}{64 D n _{a}}

(Shigley Eq. 10-37), for $n_{a}$ active coils. Bending stress uses curvature factor $K_{b}$ on the mean-diameter stress:

σ = K_{b} \frac{32 M}{π d ^{3}}

Legs act as cantilever beams; leg bending stress is estimated separately. Allowable bending stress screening uses $σ_{zul} = 0.8 R_{m}$ .

Governing equations

k = \frac{E d ^{4}}{64 D n _{a}}, M = k θ

σ_{coil} = K_{b} \frac{32 M}{π d ^{3}}

K_{b} = \frac{4 C ^{2} - C - 1}{4 C ( C - 1 )}, C = D / d

Numerical method

Closed-form bending-based rate and stress with Shigley curvature factor. Optional EN 13906 bending fatigue when minimum wind angle is specified. Auto-design sweeps wire diameter, coil count, and leg length for target rate and bending SF.

Inputs

Parameter	Description
`wireDiameter`, `meanDiameter`	Coil geometry
`activeCoils`	Active coil count
`legLength`	Leg geometry
`deflectionAngleDeg`	Operating wind angle
`wireType` / wire stock picker	Grade or catalog designation
Fatigue panel	Life class, wire quality, minimum angle (deg)

Outputs

Spring rate (N·m/rad), torque at angle, coil bending stress with $K_{b}$
Leg force and leg bending stress estimate, static SF
Optional fatigue SF; spring index, governing failure mode
Torque–angle and stress–angle plots

Design codes & checks

Indicative: Coil bending stress utilization, fatigue life (when enabled)
EU: EN 13906-3 torsion springs (reference)

Design workflow

Validate: Forward check on entered geometry and angle.
Auto-design: Wire/coil/leg sweep for target rate (N·m/rad) and bending SF.
Handoff: Fatigue module receives coil bending stress.

Assumptions & limitations

Circular wire; rectangular wire requires different section modulus.
Leg stress uses simplified cantilever model; coil–leg junction not FEA’d.
Rate formula updated to Shigley Eq. 10-37 (re-baseline saved projects from older builds).
Fatigue simplified per EN 13906-3 screening.

Verification

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

References

EN 13906-3:2013. Cylindrical helical springs — Part 3: Torsion springs.
Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 10.
Wahl, A. M. Mechanical Springs, 2nd ed.
Spring Manufacturers Institute. Handbook of Spring Design.

Maintainer note: Torsion spring leg bending.

Torsion Springs

Assumptions

Limitations

Engineering checks

Torsion Springs (torsion-springs)

Torsion Springs (`torsion-springs`)