Source: https://guthlabs.ai/docs/instruments/helical-compression-extension-spring-designer/mechanism/

instrument mechanism / verified-clean

# Helical Compression/Extension Spring Designer mechanism

The inspectable method record for Helical Compression/Extension Spring Designer, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

NEEDS_REVIEW because deflection and solid-height formulas are missing, the solid-height convention is undefined, and compression and extension springs do not share the same complete design model. The listed k, Wahl factor, and Wahl-corrected axial-wire-stress formulas are valid only under the stated unit and geometry assumptions.

- The spring-rate formula k=Gd^4/(8D^3N) is standard for a close-coiled helical spring under axial load when d and D use the same length units, G is shear modulus, and N is the number of active coils.

- The Wahl-corrected shear-stress formula τ=Kw·8FD/(πd^3) is standard for axial spring force F, mean coil diameter D, and round wire diameter d. It does not cover hook stresses, bending stresses, or other local stresses in extension-spring ends.

- The Wahl factor Kw=(4C-1)/(4C-4)+0.615/C with C=D/d is standard, but its applicability requires a physically valid spring index; the specification gives no admissible C range.

- Deflection is listed as an output but its formula is omitted. For the stated linear axial model it should be δ=F/k=8FD^3N/(Gd^4), subject to the correct force reference for compression versus extension springs.

- Solid height is listed as an output but no formula or end-coil convention is supplied. For a compression spring with closed ends and an assumed total-coil count Nt=N+2, a common estimate is Hs=Nt·d=(N+2)d; it is not determined by active-coil count alone for arbitrary end configurations.

- The specification combines compression and extension springs, but solid height is primarily a compression-spring concept, while extension springs require initial tension and may require separate end-hook stress checks. A single unqualified model is therefore incomplete.

## Units and conventions

- Vectors 1, 2, and 4 use d and D in mm, G in N/mm^2 (MPa), F in N, k in N/mm, τ in MPa, deflection in mm, and solid height in mm.

- Vector 3 uses d and D in inches, G in psi, F in lbf, k in lbf/in, τ in psi, deflection in inches, and solid height in inches; no mixed-unit arithmetic is permitted.

- D is assumed to be mean coil diameter, not outside or inside diameter.

- G is assumed to be shear modulus, not Young's modulus.

- N is assumed to be the number of active coils.

- Solid-height test vectors assume a compression spring with closed ends and Nt=N+2 total coils, so Hs=(N+2)d.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "spring_type": "compression",
    "d_mm": 2,
    "D_mm": 16,
    "N_active": 8,
    "G_MPa": 79000,
    "F_N": 100,
    "solid_height_assumption": "closed ends, total coils=N+2"
  },
  "expected_outputs": {
    "k_N_per_mm": 4.82177734375,
    "tau_MPa": 603.015343,
    "deflection_mm": 20.7392405063,
    "solid_height_mm": 20,
    "Kw": 1.1840178571
  },
  "working": "C=D/d=16/2=8. Kw=(4C-1)/(4C-4)+0.615/C=(32-1)/(32-4)+0.615/8=31/28+0.076875=1.1071428571+0.076875=1.1840178571. d^4=2^4=16 and D^3=16^3=4096. k=79000×16/(8×4096×8)=1264000/262144=4.82177734375 N/mm. τ=1.1840178571×8×100×16/(π×2^3)=1.1840178571×12800/(8π)=603.015343 MPa. δ=F/k=100/4.82177734375=20.7392405063 mm. Hs=(N+2)d=(8+2)×2=20 mm."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specified Wahl factor is undefined at C=1 and produces mathematically evaluable but physically nonsensical values for C<1; the instrument should enforce a valid spring-index range rather than blindly performing arithmetic. Signed-force handling is also convention-dependent.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/helical-compression-extension-spring-designer/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/helical-compression-extension-spring-designer/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/helical-compression-extension-spring-designer/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`