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FLUX

Interactive laboratory

Model & method

Electricity → rotation

Brushed DC motor.

Three coils. Two permanent poles. One mechanically switched circuit.

Rotor topology3 teeth · 3 coils · 3 bars

Rotor poles (wound teeth)

Rebuilds the armature and its electrical circuit. Changing configuration restarts the experiment and clears the trace.

Dynamic rotor N / S colors

Red N / blue S: armature excitation. Gray: near zero. Select a tooth card to track it.

DC supply

Applied voltage9.0 V

0 V12 V

Shaft load8.0 mN·m

Free runningBrake

Reference air-gap field0.45 T

0 T0.60 T

Brush and shaftNormal

Experiment presets

Each preset restores the reference supply, load and field, then changes one condition.

Restores the reference supply, load, field, views and study time, keeps the rotor topology and starts a new trace.

Assembly view

Visualize

Magnetic fieldConventional currentLorentz forcesComponent labels

Trace a winding

Drag to orbit · Shift + drag to pan · double-click to reset the view

Record

Clears only the rolling trace and starts a new run number; the motor state is unchanged.

Model reference

vⱼ − vⱼ₊₁ = R iⱼ + L diⱼ/dt + ω ∂λⱼ/∂θ
τ = Σ iⱼ ∂λⱼ/∂θ · eⱼ = ω ∂λⱼ/∂θ
J dω/dt = τ − bω − τ_load − τ_friction

Winding topology: 3 branches in a closed ring; 72 turns per branch
Winding resistance / inductance: 2.4 Ω / 1.2 mH per branch
Full-face brush contact resistance: 0.12 Ω per brush
Inertia / viscous friction: 2.8 × 10⁻⁵ kg·m² / 1.5 × 10⁻⁵ N·m·s
Integrator: Backward-Euler circuit; semi-implicit rotor; at most 20 μs per step
Reference magnetic materials: μᵣ: rotor 500; yoke 900; magnets 1.05
Reference air-gap flux density: 0.45 T at the pole-axis sample point

Not modeled: mutual inductance, armature reaction in the field display, iron saturation, hysteresis, eddy currents, end leakage, brush arcing, wear, contact bounce and thermal limits. The 1 nF node capacitances are circuit regularization.

Model self-checks

Runs the source laboratory checks for the 2-, 3- and 4-tooth circuits in a background worker. It can take several seconds and does not change the experiment.

Spacepause / resume time

The working principle

Current. Field. Motion.

A physical circuit, switched by the shaft itself.

3-pole rotor / 3-bar commutator

Shaft speed

0rpm

Supply current

0.00A

Electromagnetic torque

0.0mN·m

Back-EMF · equivalent

0.00V

Click a component in the scene to inspect its function.

B fieldCurrent IForce F

N → S through the rotor; S → N through the steel return.
2D stator-field approximation · arrowheads indicate direction, not motion.

Turn on the B-field probe; it measures in the field-section camera.

Brush contact / live cross-section

Orbit · zoom · inspect
Shift + drag to pan · double-click to reset view

Constructing the motor and its magnetic circuit.

Self-contained WebGL 2 / no network required

Physical time0.000 s

Rotor15.0°

Winding currents / physical time

A B C

Delta winding / 3 copper bars

Electrical power balance

Electrical input

Converted · τω

Winding heat

Brush heat

Storage + solver

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Educational reference · Power

Brushed DC Motor Laboratory

Rebuild a 2-, 3- or 4-tooth brushed DC motor and watch commutation, load, stall and coasting come out of one solved circuit.

This laboratory is a purpose-built educational permanent-magnet brushed DC motor, not a dimensional replica or a validated performance model of a commercial product. The selected 2-, 3- or 4-tooth armature has exactly that many continuous 72-turn windings and copper commutator bars, joined in a closed ring. Changing the rotor rebuilds the tooth meshes, coils, leads, bars, circuit matrix, trace channels and labels.

Two stationary carbon brushes make angle-dependent contact with the commutator. Kirchhoff’s equations for every winding branch are solved implicitly at each step, and back-EMF and electromagnetic torque use the same field-derived flux-linkage derivative, so the electrical power converted equals torque times speed. No target speed or animation timer drives the rotor: its speed comes from torque, bearing friction and the selected load.

The magnetic field is a precomputed two-dimensional, stator-only reference from a finite-volume vector-potential solution, rescaled linearly by the field setting. It omits armature reaction, iron saturation, hysteresis, eddy currents and end leakage. Rotor tooth colors show armature excitation computed from winding currents with an equal-reluctance approximation, not a measured field. Brush arcing, wear, contact bounce and thermal limits are not simulated.

Try the experiments: add shaft load and watch speed fall while current rises, reverse the supply and see the rotor brake before it reverses, retract a brush or open the supply to let the rotor coast, or lock the shaft to compare stall current with running current. The two-tooth rotor has real dead positions where neither brush can drive it.

Specifications

Rotor options: 2, 3 or 4 wound teeth, coils and commutator bars
Winding: 72 turns per coil; 2.4 Ω and 1.2 mH per branch
Supply: 0–12 V, reversible
Reference air-gap field: 0.45 T at the pole axis (0–0.60 T adjustable)
Integrator: Backward-Euler circuit, semi-implicit rotor, at most 20 μs per step
Field reference: 2D finite-volume magnetostatic solution, 321 × 321 grid

All exhibits

Current. Field. Motion.

In the current issue