Source: https://guthlabs.ai/docs/instruments/torsional-vibration-natural-frequency/mechanism/

instrument mechanism / verified-clean

# Torsional Vibration Natural Frequency mechanism

The inspectable method record for Torsional Vibration Natural Frequency, kept separate from implementation and qualification.

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

## Model scope

Core shaft-disk formula is standard under the stated idealized assumptions, but the specification needs the explicit fn=ωn/(2π) formula, required unit conventions, and the exact shaft boundary/model assumptions before it can receive PASS. The empty honest_label is inadequate; it should disclose the fixed-end, rigid-disk, massless-shaft, undamped single-degree-of-freedom assumptions.

- The listed formulas define kt and ωn but omit the formula for the declared output fn; the standard relation must be stated explicitly as fn=ωn/(2π).

- The model scope is not stated: these formulas assume a uniform, massless shaft fixed at one end with a rigid disk inertia J at the other, and negligible damping and shaft distributed inertia.

- Jp must mean the shaft Saint-Venant torsional constant. Calling it a polar second moment is valid directly for circular shafts, but not generally for noncircular sections.

## Units and conventions

- Use G in Pa (N/m²), Jp in m⁴, and L in m; kt then has units N·m/rad, with radians treated as dimensionless.

- Use J as the disk mass moment of inertia in kg·m²; it must not be confused with the shaft torsional constant Jp.

- ωn is in rad/s and fn is in Hz, using fn=ωn/(2π).

- For noncircular shafts, Jp requires the appropriate Saint-Venant torsional constant rather than the ordinary geometric polar second moment.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "G_Pa": 80000000000,
    "Jp_m4": 1e-8,
    "L_m": 1,
    "J_disk_kg_m2": 0.02
  },
  "expected_outputs": {
    "kt_Nm_per_rad": 800,
    "omega_n_rad_per_s": 200,
    "fn_Hz": 31.83098862
  },
  "working": "kt=(G·Jp)/L=(80,000,000,000·0.00000001)/1=800 N·m/rad. ωn=√(kt/J)=√(800/0.02)=√40,000=200 rad/s. fn=ωn/(2π)=200/6.283185307=31.83098862 Hz."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specification provides no stated domain-validation rules. L = 0 causes division by zero and must be rejected; negative stiffness inputs produce an undefined real square root. The formulas also do not define an actual piecewise branch at the sign switch.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/torsional-vibration-natural-frequency/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/torsional-vibration-natural-frequency/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/torsional-vibration-natural-frequency/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-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`