Rotating Unbalance Force Calculator mechanism

Model scope

The formulas are conditionally standard, but the specification is not implementation-ready because M, r, ω_n, and ζ are undefined and the symbol m is reused for different masses. The empty honest_label should be replaced with a clear statement that this is an ideal linear SDOF steady-state model, that angular speed must be supplied in rad/s or explicitly converted, and that resonance behavior is model-dependent.

• F0=m e ω² is the standard rotating-unbalance force-amplitude formula, but the notation "me" is ambiguous and must explicitly mean unbalance mass m_u multiplied by eccentricity e.
• The displacement formula is standard for a linear single-degree-of-freedom system only when M is the total participating system mass, r=ω/ω_n, ω_n=√(k/M), and ζ=c/(2Mω_n). These definitions are absent.
• The input description uses m for both unbalance mass and system mass, while the displacement formula uses M. The two masses must be distinct and explicitly named.
• The formula computes steady-state displacement amplitude under harmonic rotating-unbalance excitation; it does not by itself provide phase, transient response, or vibration velocity/acceleration.
• The formula must state that k is positive and that the model is linear SDOF. For an undamped system at r=1, the steady-state amplitude is unbounded rather than finite.

Units and conventions

• Unbalance mass m_u and system mass M are in kilograms.
• Eccentricity e is in metres.
• Rotor angular speed ω is in radians per second, not revolutions per minute.
• Stiffness k is in newtons per metre and damping c is in newton-seconds per metre.
• F0 is in newtons and X is a displacement amplitude in metres.
• The system mass M is the total modal or participating mass used in ω_n=√(k/M).

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "unbalance_mass_kg": 0.02,
    "eccentricity_m": 0.001,
    "omega_rad_s": 100,
    "system_mass_kg": 10,
    "stiffness_N_per_m": 10000,
    "damping_Ns_per_m": 20
  },
  "expected_outputs": {
    "F0_N": 0.2,
    "steady_state_amplitude_X_m": 0.00000222167
  },
  "working": "ω_n=√(k/M)=√(10000/10)=√1000=31.6228 rad/s. r=ω/ω_n=100/31.6228=3.16228, so r²=10. ζ=c/(2Mω_n)=20/(2×10×31.6228)=0.0316228. F0=m_u e ω²=0.02×0.001×100²=0.2 N. Numerator for X=(m_u e/M)r²=(0.02×0.001/10)×10=0.00002 m. Denominator=√[(1−10)²+(2×0.0316228×3.16228)²]=√[81+0.04]=√81.04=9.00222. X=0.00002/9.00222=0.00000222167 m."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The ideal undamped resonance input r=1 and ζ=0 produces a zero denominator and an undefined steady-state amplitude. A second hazard is that negative eccentricity has incompatible magnitude-versus-direction interpretations.

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