Torsion (Helical) Spring Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration

Tranche

tranche-5

Evidence ID

t5-009

Ledger rows

1

No ledger note is attached.

Review findings

The specification is not an honest complete calculator definition: the honest_label field is empty, the rate formula is incorrect or at least critically unit-ambiguous, Kb is omitted from the inputs, and angular deflection is omitted from the formulas. The instrument should not be labeled production-ready until these definitions and design constraints are corrected.

Formula and scope findings

• The spring-rate formula k=Ed⁴/(10.8DN) is not the standard elastic helical torsion-spring rate formula. For E in N/mm², dimensions in mm, and angular rate in N·mm/rad, the standard formula is k=Ed⁴/(64DN).
• The declared output 'k(per turn)' is inconsistent with the formula and lacks a defined angular unit. Rate per turn is k_turn=2πk_rad, while rate per degree is k_degree=πk_rad/180.
• The bending-stress formula is structurally standard, σ=32KbM/(πd³), but Kb is required and is absent from the listed inputs.
• Angular deflection has no formula specified. Under linear elastic behavior it should be θ=M/k, with the angular unit matching the spring-rate unit.
• The coil diameter D is not defined; torsion-spring formulas normally require mean coil diameter, not outside or inside diameter.

Unit assumptions

• Test vectors use the corrected standard rate formula k_rad=Ed⁴/(64DN).
• For SI-style vectors, E is in N/mm² (MPa), d and D are in mm, M is in N·mm, k is in N·mm/rad, and σ is in MPa.
• For the inch-based vector, E is in psi, d and D are in inches, M is in lbf·in, k is in lbf·in/rad, and σ is in psi.
• D is assumed to be mean coil diameter.
• N is assumed to be the number of active coils.
• Kb is dimensionless and must be supplied or calculated from a clearly defined spring-index correction model.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

Zero wire diameter produces k=0, stress division by zero, and undefined angular deflection; the calculator must reject it. The specification also omits the definition or input source for Kb and does not state whether coil diameter is mean or outside diameter, so finite results are not uniquely determined without assumptions.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "wire_diameter": 2,
    "wire_diameter_unit": "mm",
    "mean_coil_diameter": 20,
    "mean_coil_diameter_unit": "mm",
    "active_coils": 8,
    "E": 200000,
    "E_unit": "N/mm^2",
    "applied_moment": 1000,
    "moment_unit": "N·mm",
    "Kb": 1.15
  },
  "expected_outputs": {
    "spring_rate_Nmm_per_rad": 312.5,
    "bending_stress_MPa": 1464.2255,
    "angular_deflection_rad": 3.2,
    "angular_deflection_deg": 183.3465,
    "angular_deflection_turns": 0.5092958
  },
  "working": "d⁴=2⁴=16. k=Ed⁴/(64DN)=(200000×16)/(64×20×8)=3200000/10240=312.5 N·mm/rad. σ=32KbM/(πd³)=(32×1.15×1000)/(π×2³)=36800/(8π)=4600/π=1464.2255 MPa. θ=M/k=1000/312.5=3.2 rad. θ_deg=3.2×180/π=183.3465°. θ_turns=3.2/(2π)=0.5092958."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

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

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json