Torsion (Helical) Spring Calculator mechanism

Model scope

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.

• 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.

Units and conventions

• 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.

Inspectable vector

One of 4 source-bound review vectors:

{
  "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."
}

Failure boundary

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.

Other records

Sources and evidence

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

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