Source: https://guthlabs.ai/docs/instruments/dc-motor-starting-current-back-emf-estimator/mechanism/

instrument mechanism / verified-clean

# DC Motor Starting Current & Back-EMF Estimator mechanism

The inspectable method record for DC Motor Starting Current & Back-EMF Estimator, kept separate from implementation and qualification.

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

## Model scope

The simplified separately-excited DC motor label is honest only if the instrument clearly states that it uses a steady-state model with supplied speed and combined SI-compatible motor constant K_e=kΦ. Define the warning rule, the speed unit, the motor-constant definition, the locked-rotor condition, and the allowed sign/range constraints before release.

- Ia=(V−Eb)/Ra is the standard steady-state armature-current relation for a separately excited DC motor, provided Ra is the total armature circuit resistance and Ra>0.

- The back-EMF relation is standard as Eb=K_e·ω, or Eb=k·Φ·ω when k·Φ is not already combined. The specification writes Eb=kΦN without defining whether N is angular speed in rad/s or rotational speed in rpm; using rpm requires a 2π/60 conversion or an rpm-specific motor constant.

- The listed inputs provide a motor constant but do not explicitly provide flux Φ. The formula is complete only if motor constant means the combined constant kΦ, equivalently K_e.

- The claimed locked-rotor current requires the explicit condition speed=0, giving Eb=0 and I_start=V/Ra; this condition is implied but not stated as a separate formula.

- The claimed armature current under load is only estimated from a supplied speed. No load torque, mechanical losses, or speed-dynamics relation is included, so the instrument does not calculate speed or current from load.

- The starting-current warning has no defined threshold, trigger condition, or output semantics, so it cannot be verified.

## Units and conventions

- V is terminal armature voltage in volts.

- Ra is total armature-circuit resistance in ohms and must be strictly greater than zero.

- The motor constant used in these vectors is K_e=kΦ in volts per radian per second, numerically V·s/rad.

- Speed is angular speed ω in rad/s unless explicitly converted from rpm.

- Eb is in volts and Ia is in amperes.

- For rpm input, ω=rpm·2π/60 must be used before applying Eb=K_e·ω.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "V_V": 240,
    "Ra_ohm": 1.2,
    "motor_constant_Vs_per_rad": 0.8,
    "speed_rad_per_s": 0
  },
  "expected_outputs": {
    "Eb_V": 0,
    "Ia_A": 200,
    "starting_current_warning": null
  },
  "working": "Eb=K_e·ω=0.8·0=0 V. Ia=(V−Eb)/Ra=(240−0)/1.2=240/1.2=200 A. Speed is zero, so this is the locked-rotor case; the warning result is null because the specification defines no warning policy."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specification provides no stated validation for Ra=0, which makes Ia undefined. It also leaves the speed and motor-constant units unspecified, allowing materially different back-EMF and current results.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/dc-motor-starting-current-back-emf-estimator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/dc-motor-starting-current-back-emf-estimator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/dc-motor-starting-current-back-emf-estimator/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-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`