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VECTOR

Electromechanics / Motion laboratory

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Model & sources ↗

Causal-step lesson

Why does a stepper motor turn?

Change the stator field first, then watch torque pull the rotor toward the next equilibrium.

1
Start: phase A energized and aligned
The field exists, but the torques balance. Staying energized does not mean turning.
2
Commutate: see the stator act first
The shaft is held for a moment: current commutates and the stator pole changes before the rotor can move.
3
Release: torque turns the rotor
Watch the gold tangential arrows. Their direction and size follow the computed result.
4
Aligned: the rotor stops at the next position
This beat moves only 1.8°. Only another commutation moves the equilibrium on.

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Next step direction

Rebuild to a stage

Re-integrates from the lesson start with the native 100 µs step. This is not a reversal; the records of this run are replaced.

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Causal mechanism · one beat at a time

Torque first, then motion.

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Equivalent tangential actionLocal flux sketch N → SEquilibrium tooth position for the present current—

Why does it turn? Look at the slope of the energy curve.τ = −∂U / ∂θ

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Constructing the motor laboratory

Solid geometry · copper windings · magnetic field solver

Rotor angle and phase current—

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Solver rotor angle · simulated encoder, not used by the driver

Command angle—

Command error—

Phase A current—

Phase B current—

Motor torque—

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Computed winding currents

Phase A——

Phase B——

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Magnified pole—

Stator color follows the actual current. The rotor N / S comes from the axial magnet and does not flip on commutation.

Motion set by torque, not by an assigned angle

Net magnetic torque on the shaft—

Phase A / phase B torque—

Actual rotor angle θ—

Next equilibrium θ*—

Travel this beat—

Playback / model time—

Settling check—

Where does 1.8° come from?

Each rotor stack has 50 teeth, so the tooth pitch is 360° ÷ 50 = 7.2°. The four beats of two phases each move a quarter pitch, so one step is 1.8°. The rear stack is offset from the front by half a pitch, 3.6°.

Component inspector

A hybrid, not an alternating-pole ring

Every tooth on the front rotor stack is north; every tooth on the rear stack is south. A single axial magnet supplies both stacks, staggered by half a tooth.

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A sample is recorded every 5 ms of model time from the same state that drives the 3D model. Clearing removes samples only.

Run numerical checks

Deterministic checks run on independent simulation states; the live motor is not reset. They validate implementation consistency, not agreement with a manufactured motor or a calibrated field measurement.

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contemporary model · Electronics

VECTOR Hybrid Stepper Motor

Two phases, fifty teeth and one axial magnet: current commutates first, then torque carries the rotor one 1.8° step.

A hybrid stepper motor does not jump to a commanded position. Its driver changes the current in two phase windings, the stator field moves the rotor's equilibrium, and torque, inertia and damping then carry the rotor there. This exhibit separates that causal chain: an optional teaching lock holds the shaft while current commutates, then releases it so the integrated torque turns the rotor one 1.8° step.

The model is a 42 mm educational reference motor with eight stator poles carrying five teeth each, two 50-tooth rotor stacks offset by half a tooth, and an axially magnetized ring. A voltage-limited current regulator drives each resistive–inductive phase at a fixed 100 µs integration step. Back EMF, detent torque, viscous damping and the load decide the actual shaft angle; it is never assigned from the step command, and the displayed encoder does not feed the driver.

The simplifications are deliberate and labeled. Torque comes from a permanent-magnet-dominant co-energy model rather than a finite-element solution; field traces are normalized Biot–Savart and dipole approximations; the magnified tooth view is a schematic with an enlarged gap; and the lesson's stage windows are instructional constraints. The parameters are plausible teaching values, not a manufacturer data sheet.

Specifications

Construction: Two-phase hybrid: 8 stator poles, 2 × 50-tooth rotor stacks
Full step: 1.8°, a quarter of the 7.2° tooth pitch
Rotor stagger: 3.6° between the north and south stacks
Solver: Fixed 100 µs step; circuit and rigid-rotor dynamics in SI units
Drive modes: Wave, full step, half step and 1/4 to 1/32 microstepping
Modeled: Current regulation, back EMF, detent torque, load, shaft lock and open phases

All exhibits

Torque first, then motion.

Hybrid stepper motor

In the current issue