Induction Motor Simulation — Slip, Torque and Rotating Field

physical time

Drag to orbit ·scroll to zoom · click any part
One clock drives the rotor, field and current waveforms.

Industrial materials · physical finishPainted cast iron / enamelled copper / laminated steel
Teaching colors are overlays, not colored metal.

U phaseV phaseW phaseNSbore poles

B-field · projected transverse slice➜ conventional current

Building the induction laboratory

Procedural geometry · coupled electrical and mechanical states · no network required

Rotor speed—rpm

Synchronous field—rpm

Slip—%

Electromagnetic torque—N·m

Instantaneous phase currents

120° apart

Rotating field

electrical angle

Torque–speed characteristic

SI model

Three-phase supply

Balanced sinusoidal AC

Star-connected · no rotor supply

Supply frequency

Line-to-line voltage

Maintain V/f below base speed

Mechanical load

Resisting shaft torque

No load

A smooth friction load opposes either direction of rotation.

Lock the rotornᵣ = 0

Bench experiments

The initial state is a settled 50 Hz operating point. Start from rest to watch induction build and the rotor accelerate.

Stator phase current: —
Rotor current frequency: —
Electromechanical power: —
Simulated time: —

At 1/25×, a real 50 Hz supply is displayed at 2 Hz. Instrument values remain in real SI units.

Model, equations and limits

Asynchronous, by construction.

Three distributed AC windings create a four-pole rotating field. Slip induces current in the closed cage. The resulting electromagnetic torque accelerates the rotor against load and friction.

nₛ = 120 f / P
s = (nₛ − nᵣ) / nₛ
fᵣ = |s| f
J dωᵣ/dt = Tₑ − Tₗ − bωᵣ

The display, electrical waveforms and mechanical motion use one slowed physical clock. At 1/25×, a real 50 Hz supply is displayed at 2 Hz. Instrument values remain in real SI units.

Electrical and mechanical equations

The state solver uses an amplitude-invariant, stationary αβ frame. Rotor variables are referred to the stator.

ψₛ = Lₛ iₛ + Lₘ iᵣ
ψᵣ = Lₘ iₛ + Lᵣ iᵣ
dψₛ/dt = vₛ − Rₛ iₛ
dψᵣ/dt = −Rᵣ iᵣ + j p ωᵣ ψᵣ
Tₑ = (3/2)p(ψₛα iₛβ − ψₛβ iₛα)

Fourth-order Runge–Kutta integration with a maximum 83.33 μs step. P = 4 poles; p = P/2 = 2 pole pairs. Resistance values are per phase, referred to the stator. Rₛ = 1.4 Ω; Rᵣ = 1.0 Ω; Lₘ = 180 mH; Lₗₛ = Lₗᵣ = 6 mH; J = 0.032 kg·m²; b = 0.003 N·m·s/rad.

Winding and cage topology

24 slots, 4 poles, 3 phases: q = 2 slots per pole per phase. A single-layer winding contains 12 coils, four in series in each phase, connected in star. The full coil pitch is six slots (180° electrical). Six continuous turns are explicitly drawn per illustrative coil.

Positive U sides: slots 1, 2, 13, 14. V: 5, 6, 17, 18. W: 9, 10, 21, 22. Each negative side lies six slots away, modulo 24. Phase belts advance U+, W−, V+, U−, W+, V−.

The cage has 28 bars skewed by 15° mechanical and two continuous end rings. Bar-current arrows use the rotor αβ current’s spatial fundamental. Ring currents satisfy nodal continuity; their displayed magnitude is normalized, not a calibrated bar ampere measurement.

What the field lines mean

The transverse field is reconstructed from the solved magnetizing flux. Closed lines are contours of A_z = F(r) sin(2θ), with piecewise permeability in rotor iron, air gap, stator iron and exterior air. Interface conditions are solved analytically; arrows follow B = ∇×A.

This is a circular, fundamental-harmonic field model with an equivalent stator bore current sheet—not a finite-element solution of individual teeth. The slice is projected slightly in front of the core for visibility. Pole labels indicate instantaneous resultant stator-bore polarity. Field lines return through iron; there are no permanent rotor magnets.

Schematic relative iron permeability: 400. Absolute flux density is not calibrated in tesla. The visible air gap is enlarged. Slot harmonics, end fringing, leakage-field detail and iron saturation are not solved.

Experiments and important limits

Open supply: ideal stator open circuit; rotor flux decays and the shaft coasts. Open cage: every bar is disconnected from one end ring, so no closed rotor current path remains. Lock: an external mechanical constraint holds the shaft. Synchronism: an external servo imposes field speed; transient rotor current decays rather than disappearing instantly.

Ideal opening projects the disconnected winding current to zero. Arc energy, switch transients, temperature rise, saturation, deep-bar effects, acoustic noise, elastic contact and mechanical tolerances are omitted. Geometry is an educational reference assembly, not a dimensionally certified commercial motor or a protective-device simulator.

The torque–speed line is the steady-state equivalent-circuit curve of the same R/L parameters. During transients, the live operating point can depart from that curve. Low-speed friction uses a smooth tanh transition; it is not a detailed stiction model.

Physical materials and rendering

The housing and end shields use dielectric epoxy paint over cast iron. Copper winding has an enamel / varnish appearance, separate from colored phase sleeves. Rotor bars and end rings use a die-cast aluminum reference finish. Exposed electrical-steel stack edges, ground steel, brass, zinc plating, insulating liners, lacing, fan polymer and rubber have separate surface responses.

Metallic/roughness GGX shading with directional metal highlights, a clearcoat approximation, object-space procedural height and roughness, filtered lamination seams, analytic rectangular studio reflections and filtered shadow maps. This is not ray tracing, measured spectral rendering, finite-element material identification or a scanned production motor.

The grain texture and identification plate are generated locally. No images, fonts, libraries or other resources are fetched. The nameplate is labeled as an educational reference and is not a certified product rating.

Reference sources

Simulation-software reference: squirrel-cage induction machine model — flux-linkage, voltage and torque equations; reference-frame modeling.

Motor manufacturer’s technical library: the three-phase induction motor — induction, slip, cage construction and torque–speed behavior.

Motor manufacturer’s technical library: rotation principle of the induction motor — induced rotor currents and electromagnetic torque.

Motor manufacturer’s catalogue: three-phase industrial motor, construction pages — cast-iron frame, aluminum cage, impregnated winding, steel shaft, fan and nameplate materials. This model is not a replica of any product.

Motor manufacturer’s catalogue: general-performance motors — cast-iron construction, copper winding and protective paint.

These references are listed for further reading. The exhibit itself needs no network.

Controls

Drag: orbit. Scroll or pinch: zoom. Right-drag or Shift-drag: pan. Click a part: inspect. With the 3D model focused: Space runs or pauses, R resets the camera, X toggles X-ray, F shows the field section, and Escape closes the inspection and releases the keys. Step advances 1 ms of physical time.

Numerical self-checks

No self-check report in this session.

Three-phase induction motor

Instantaneous phase currents

Rotating field

Torque–speed characteristic

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