An brushed DC motor is an electromechanical actuator that converts electrical energy into rotation through magnetic forces and a mechanical commutator.
At a basic level it’s simple: you put electricity in, you get rotation out. It’s a machine of dynamic equilibrium between magnetic and electrical forces.
The physical principle: the Lorentz force
Everything is based on the Lorentz force: a conductor with current inside a magnetic field experiences a force.
The vector formula is:
Where:
- F: Force (Newtons).
- I: Current (Amperes).
- L: Length of the wire.
- B: Magnetic Field (Teslas).
To maximize the force, we need a lot of current (I), many meters of coiled wire (L) and very powerful magnets (B).
Internal anatomy: stator and rotor
To convert that linear force into rotation, we build an intelligent structure:
- The Stator (The stationary part): Creates the fixed magnetic field (B). In small motors these are permanent magnets; in industrial ones they can be electromagnets (field coils).
- The Rotor or Armature (The rotating part): It’s a copper coil wound around a laminated iron core. We inject current (I) here.
- The Brushes: Carbons that make physical contact by sliding on the shaft to inject electricity while it rotates.
The reversal problem: the commutator
Here lies the ingenuity of the design. If we inject DC into a coil inside a magnet, the coil will rotate half a turn until it aligns with the magnet (North with South)… and then stop dead. That’s useless!
For it to keep rotating, we have to reverse the polarity of the current just as it passes the midpoint.
The Commutator is a copper ring cut into segments.
- As the motor rotates, the brushes touch one segment (+) and then the other (-).
- This mechanically reverses the direction of current in the coil every half turn.
- Thanks to this, the magnetic field of the rotor is always “chasing” that of the stator without ever catching it.
Back electromotive force (Back-EMF)
A spinning motor is not just an energy consumer. It is also a generator. When the coil rotates inside a magnetic field, by Faraday’s Law, a voltage is induced in it.
This voltage opposes the voltage we are supplying from the battery. That’s why it’s called Back ElectroMotive Force (
The electrical equation of the motor is:
Where
What does this imply in reality?
The motor is stopped (𝜔 = 0), so
Result: a current close to the stall current appears. The driver, power supply, and protections must be sized to handle it.
The motor spins very fast. The
Result: The current consumed is minimal. The motor is “self-regulating.”
If you stall a drill with your hand, the speed drops →
The drill heats up because it is trying to regain its speed by drawing amps (this is a mental exercise, don’t hold a drill with your hand).
The characteristic curve: torque vs. speed
DC motors have a linear inverse relationship between Speed and Torque.
- Maximum Speed (No-Load Speed): Occurs when Torque is zero (motor spinning in the air).
- Maximum Torque (Stall Torque): Occurs when speed is zero (motor stalled). This is the maximum brute force the motor can exert before burning up.
- Maximum Power: Curiously, it is obtained at 50% of the maximum speed.
Disadvantages: the price of brushes
The DC motor design is brilliant, but it has an Achilles’ heel: Physical contact.
- Sparks: When jumping from one commutator segment to another, electrical arcs occur. This generates electromagnetic interference (EMI) that can drive your microcontroller crazy (that’s why we solder ceramic capacitors across the motor terminals).
- Wear: The carbon brushes wear down due to friction. The motor has a limited lifespan.
- Dust: The wear generates conductive dust inside the motor.
