Screw Jack / Power Screw Torque Calculator mechanism

Model scope

The specification is not honest as written for its stated square/ACME capability: the thread angle input is unused, T_lower is claimed but not formulated, and efficiency is thread-only unless collar and other losses are added. Leave honest_label empty is inappropriate; it should state the supported thread geometry, the angle convention, and that torque/efficiency exclude collar friction.

• T_raise is the standard square-thread raising-torque formula when F is axial load, dm is mean pitch diameter, l is lead, and μ is the thread friction coefficient; it is not directly valid for ACME/V-threads without replacing μ by an effective friction coefficient, commonly μ_eff=μ sec(α), where α is the thread half-angle.
• The specification claims T_lower but provides no lowering-torque formula. For a square thread, the standard thread-only formula is T_lower=(F dm/2)[(μπdm-l)/(πdm+μl)].
• The thread angle input is unused and its meaning is ambiguous: thread included angle versus half-angle. For ACME/V-threads, the angle changes the effective friction coefficient and therefore raising torque, lowering torque, efficiency, and self-locking.
• The self-locking condition μ>tan(λ) is valid for a square thread, with tan(λ)=l/(πdm), but for an angled thread it should use the effective friction coefficient and the specification does not state whether equality is treated as self-locking.
• The efficiency formula e=Fl/(2πT) is the screw-thread mechanical efficiency for raising torque only and excludes collar/bearing friction, gearbox losses, and other losses. It is not a complete screw-jack efficiency unless those exclusions are honestly stated.

Units and conventions

• F is an axial force in N, dm and l are lengths in the same unit, and torque is returned in force-length units; using N and m returns N·m.
• l is lead, not pitch. For a single-start screw they are equal; for a multi-start screw, lead equals pitch multiplied by the number of starts.
• μ is dimensionless thread friction coefficient; it must be nonnegative.
• The test calculations using the supplied formula treat the thread as square-thread geometry, so thread angle is set to 0° unless specifically illustrating the ACME ambiguity.
• The helix angle is λ=atan(l/(πdm)).
• Efficiency is dimensionless and is normally reported as a fraction or multiplied by 100 for percent.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "F_N": 10000,
    "dm_m": 0.05,
    "l_m": 0.0157079633,
    "mu": 0.2,
    "thread_angle_deg": 0
  },
  "expected_outputs": {
    "T_raise_Nm": 76.530612,
    "T_lower_Nm": 24.509804,
    "efficiency": 0.326667,
    "self_locking": "yes"
  },
  "working": "πdm=π(0.05)=0.157079633 m; l/(πdm)=0.1. T_raise=(10000×0.05/2)[(0.0157079633+π×0.2×0.05)/(π×0.05-0.2×0.0157079633)]=250[(0.1+0.2)/(1-0.2×0.1)]=250(0.3/0.98)=76.530612 N·m. T_lower=250[(0.2-0.1)/(1+0.2×0.1)]=250(0.1/1.02)=24.509804 N·m. e=Fl/(2πT_raise)=0.1(1-0.2×0.1)/(0.1+0.2)=0.098/0.3=0.326667. Since μ=0.2>tanλ=0.1, self-locking=yes."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The raising-torque denominator vanishes when pi dm=mu l, producing an undefined result. The calculator must reject that input rather than return a finite torque. The thread-angle input also has an unresolved convention because it is supplied but absent from the stated formulas.

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-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json