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DC motor, 12 V

A small 12 V DC motor to drive a table-top blade, and the first design on my motor roadmap. The specification is written; the electromagnetic, mechanical and thermal design come next. The model and the derivation come from my Electric Machines notes.

ARMATURE MODEL+−V112 VRaarmatureIa+−Ekφω / 2πMτ, ωto the bladeTHE PLAN: FIVE PHASES, FROM MY MOTOR-DESIGN ROADMAP1 ElectromagnetismcourseworkMaxwell, flux,magnetic circuits,Lorentz force2 Electrical machinescourseworkDC, induction,synchronous;torque–speed, losses3 Motor designnot startedair gap, slots andpoles, windings; abasic BLDC4 Advanced systemsnot startedthermal, FEA,field-oriented control5 Tools and projectsnot startedMATLAB, FEM, anArduino-driven motor▸ Hover a wire to name its net.NET SUPPLY 12 V into the armature resistanceNET ARMATURE after R_a, where the back-EMF E pushes against the supplyNET RETURN back to the supply

DERIVATION, FROM MY ELECTRIC MACHINES NOTES

  1. One conductor passes a pole in half a turn, so T = 1/2n and E = φ/T = 2nφ, with n in revolutions per second.
  2. With p poles and As conductors in series, E = 2pAsnφ = kφn, where k = 2pAs.
  3. Since ω = 2πn, E = (k/2π) φ ω.
  4. Electrical power becomes mechanical power, IaE = τω, so τ = (k/2π) φ Ia.

One constant ties the two halves: the same k/2π that makes voltage from speed makes torque from current.

SPECIFICATION, APRIL 2026

Supply12 V DC
Rotor diameter60 mm
Shaft5 mm
Loada table-top blade

FROM THE COURSE

Electric Machines, 2026: rotational motion, torque and power; the magnetic field in machines; armature EMF. Self-study alongside it from MIT's course on electric machines.

NEXT, IN MY OWN HEADINGS

  1. Electromagnetic design
  2. Mechanical design
  3. Thermal design
  4. Simulation
  5. Documentation

PRINCIPLES

Derive, don't memorise. Visualise fields, not circuits. Connect theory to real systems. Depth over speed.

REVISIONSREVDATEDESCRIPTIONA2026-02-18Notes: rotational motion, torque and powerB2026-02-23Notes: the magnetic field in machinesC2026-03-19Armature EMF and torque, derivedD2026-04-0412 V motor for a table-top blade: specificationE2026-04-12Motor-design roadmap, five phasesTITLEDC motor, 12 VSHEET/ dc-motorNO.6 of 7REVEDATE2026-04-12DRAWND. BrownSIZEA3GO TO◂ sheet 5sheet 7 ▸OTHER VIEWSDEVPHYSICSACADEMICee.desmondbrown.me

/ ROOT / DC-MOTOR

DC motor, 12 V

A small 12 V DC motor to drive a table-top blade, and the first design on my motor roadmap. The specification is written; the electromagnetic, mechanical and thermal design come next.

SHEET6 of 7REVEDATE2026-04-12
OTHER VIEWSDEVPHYSICSACADEMIC
ARMATURE MODEL+−V112 VRaarmatureIa+−Ekφω / 2πMτ, ωto the blade

Drag sideways to see the motor and its shaft.

DERIVATION, FROM MY ELECTRIC MACHINES NOTES

  1. One conductor passes a pole in half a turn, so T = 1/2n and E = φ/T = 2nφ, with n in revolutions per second.
  2. With p poles and As conductors in series, E = 2pAsnφ = kφn, where k = 2pAs.
  3. Since ω = 2πn, E = (k/2π) φ ω.
  4. Electrical power becomes mechanical power, IaE = τω, so τ = (k/2π) φ Ia.

One constant ties the two halves: the same k/2π that makes voltage from speed makes torque from current.

SPECIFICATION, APRIL 2026

Supply12 V DC
Rotor diameter60 mm
Shaft5 mm
Loada table-top blade

THE PLAN: FIVE PHASES

1Electromagnetism. Maxwell, flux, magnetic circuits, Lorentz force.coursework
2Electrical machines. DC, induction, synchronous; torque–speed, losses.coursework
3Motor design. air gap, slots and poles, windings; a basic BLDC.not started
4Advanced systems. thermal, FEA, field-oriented control.not started
5Tools and projects. MATLAB, FEM, an Arduino-driven motor.not started

FROM THE COURSE

Electric Machines, 2026: rotational motion, torque and power; the magnetic field in machines; armature EMF. Self-study alongside it from MIT's course on electric machines.

NEXT

  1. Electromagnetic design
  2. Mechanical design
  3. Thermal design
  4. Simulation
  5. Documentation

PRINCIPLES

Derive, don't memorise. Visualise fields, not circuits. Connect theory to real systems. Depth over speed.

REVISIONS

A2026-02-18Notes: rotational motion, torque and power
B2026-02-23Notes: the magnetic field in machines
C2026-03-19Armature EMF and torque, derived
D2026-04-0412 V motor for a table-top blade: specification
E2026-04-12Motor-design roadmap, five phases
TITLEDC motor, 12 V
◂ sheet 56 / 7sheet 7 ▸