Spring Fatigue Life Estimator (Wahl + Goodman) mechanism

Model scope

The arithmetic and Wahl/Goodman structure are conditionally correct. Verdict is NEEDS_REVIEW because the specification names Se/Sut without stating whether they are shear properties, and spring-wire data tables commonly list tensile rather than torsional strengths. The instrument should explicitly require torsional Se and torsional Ssu (or document a material-specific conversion), define the applicable wire/material table and design-life convention, and retain the stated honest label that this is an estimate requiring physical verification for critical applications.

• The Wahl factor Kw=(4C-1)/(4C-4)+0.615/C with C=D/d is the standard curvature correction for a round-wire helical spring in torsion, and tau=Kw*8FD/(pi*d^3) is correct for load-induced shear stress.
• The alternating and mean stresses must be tau_a=(tau_max-tau_min)/2 and tau_m=(tau_max+tau_min)/2; this is correct for a constant spring geometry under force cycling.
• The Goodman equation SF=1/(tau_a/Se+tau_m/Sut) is valid only when Se is a torsional shear endurance strength and Sut is a torsional shear ultimate strength. Spring-wire tables commonly provide tensile Sut, not torsional Sut; using tensile Sut directly in this shear Goodman equation is incorrect unless a documented conversion is supplied.
• The specification does not identify the fatigue-life target, stress ratio, reliability, surface condition, shot peening, residual stress, or whether Se is a corrected endurance strength. Therefore the reported value cannot be treated as a generally valid fatigue safety factor.
• The calculation omits possible effects of coil clash, inactive coils, spring index limits, buckling, surge, stress concentration at hooks or ends, and finite-life S-N behavior.

Units and conventions

• For the test vectors, force is in N, wire diameter and mean coil diameter are in mm, and calculated shear stress is in N/mm^2=MPa.
• The diameter ratio is C=D/d, with D as mean coil diameter rather than outside or inside diameter.
• Se=550 MPa and Sut=2300 MPa are treated here as torsional shear endurance and torsional shear ultimate strengths, respectively, solely for formula verification; this interpretation must be confirmed before implementation.
• The table fragment uses music-wire values represented as widely tabulated standard design values for ASTM A228 music wire; actual allowable values depend on wire diameter, surface condition, reliability, and loading history.
• pi is taken as 3.141592653589793.
• The third vector explicitly converts kN to N before stress calculation.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "material": "music wire ASTM A228",
    "F_min_N": 100,
    "F_max_N": 200,
    "wire_diameter_mm": 2,
    "mean_coil_diameter_mm": 16,
    "Se_MPa": 550,
    "Sut_MPa": 2300
  },
  "expected_outputs": {
    "spring_index_C": 8,
    "Wahl_factor_Kw": 1.1840178571,
    "tau_min_MPa": 603.015343,
    "tau_max_MPa": 1206.030686,
    "tau_a_MPa": 301.507671,
    "tau_m_MPa": 904.523014,
    "fatigue_safety_factor": 1.062172
  },
  "reference_data": {
    "music_wire_Se_MPa": 550,
    "music_wire_Sut_MPa": 2300,
    "source_convention": "widely tabulated standard spring-wire design values for ASTM A228 music wire; interpreted as torsional shear strengths for this vector"
  },
  "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=1.1840178571. Base stress at F=1 N is 8D/(pi*d^3)=8(16)/(pi*2^3)=128/(8pi)=16/pi=5.092958179 MPa/N. Stress coefficient=Kw*5.092958179=1.1840178571*5.092958179=6.030153430 MPa/N. tau_min=6.030153430*100=603.015343 MPa. tau_max=6.030153430*200=1206.030686 MPa. tau_a=(1206.030686-603.015343)/2=301.507671 MPa. tau_m=(1206.030686+603.015343)/2=904.523014 MPa. Goodman denominator=301.507671/550+904.523014/2300=0.548195766+0.393270876=0.941466642. SF=1/0.941466642=1.062172."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The estimator breaks or must reject inputs at the Wahl singularity C=1 and when the Goodman denominator is zero. Its result also changes materially under plausible signed-force versus load-magnitude conventions, and the specification does not define how negative mean stress is branched or handled.

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-tranche7/tranche7-results.json
• BOUNDARY_HAZARD_CATALOG.json