DC machines and brushless motors
A DC motor is most efficient when only lightly loaded: the maximum efficiency of a small motor is at one tenth of its stall current, far from the maximum torque.
01The easiest motor to control
In a DC motor, the rotor conductors carry current inside the stator field and experience a force. A segmented commutator with brushes reverses the current in each coil just as it passes from one pole to the other, so that the torque always pushes in the same direction. As they turn, the same conductors generate a back EMF proportional to the speed. Two equations describe the whole motor:
This simplicity made the DC motor the favorite for speed and position control for a century, and it remains in millions of small applications: toys, battery-powered tools, windshield wipers.
02Forms of excitation
| Excitation | Behavior | Use |
|---|---|---|
| Permanent magnet | Constant flux: speed almost proportional to voltage | Small motors, servos, tools |
| Separately excited or shunt | Like the magnet type, with the flux adjustable through the field | Older machine tools, rolling mills |
| Series | The same winding carries the field and armature current: very high starting torque, and the speed runs away at no load | Traction, starters for combustion engines, universal motors in appliances |
| Compound | Combines series and shunt | Cranes, older elevators |
03Curves, control and efficiency
Solving, the speed falls in a straight line with torque, from the no-load speed \( V/k \) to zero at the stall torque \( kV/R \). Changing the voltage shifts the line in parallel: that is why the speed is controlled with an H-bridge that applies the supply voltage modulated by pulse width, with an average value proportional to the duty cycle. The efficiency depends on the operating point and has a maximum:
A permanent-magnet motor with R = 1.2 Ω, k = 0.05 N·m/A and a friction of 5 mN·m, fed by an H-bridge. The gray lines are the characteristic at 6, 12, 18 and 24 V; the blue one, at the chosen voltage. The dot is the operating point at the load torque.
04Brushless motors
Brushes wear out, produce sparks and interference, and limit the speed. The brushless motor (BLDC) turns the construction inside out: the magnets go on the rotor and the windings on the stator, and the commutation is done by an electronic circuit that knows the rotor position from Hall-effect sensors or from the back EMF of the phase that is not conducting. With six-step commutation, the behavior is that of a DC motor; with vector control and sinusoidal currents (permanent-magnet synchronous motor), the torque is smoother and the efficiency higher.
| Brushed | Brushless | |
|---|---|---|
| Control | A DC voltage or an H-bridge | A three-phase inverter with position feedback |
| Service life | Limited by the brushes | Limited by the bearings |
| Typical efficiency | 60 to 80% | 85 to 95% |
| Applications | Toys, inexpensive tools, auto parts | Drones, disk drives, computer fans, electric vehicles |
05In the laboratory
Measure the winding resistance with the rotor locked and the constant k as the generated voltage divided by the speed, spinning the motor with another one.
Control a motor with an H-bridge and a microcontroller, and measure the speed as a function of duty cycle with and without load.
Observe with the oscilloscope the three phases and the Hall signals of a computer fan or a drone motor with its controller.
06Common mistakes
- Sizing the H-bridge for the rated current. At startup the stall current flows, V/R.
- Running a series motor without load. The speed runs away and can destroy it.
- Forgetting the diode or the freewheeling path. The winding inductance generates overvoltages when switching off.
- Braking a DC motor abruptly. It acts as a generator and returns energy to the supply.
07Self-assessment
What no-load speed does a motor with k = 0.05 V·s/rad have at 12 V?
240 rad/s, about 2290 rpm.
What stall torque does the same motor give with R = 1.2 Ω?
\( kV/R = 0.05 \cdot 12/1.2 = 0.5 \) N·m, with 10 A.
What maximum efficiency does it have if the no-load current is 0.1 A?
\( (1 - \sqrt{0.1/10})^2 = 0.81 \): 81%.
How does a BLDC know when to commutate?
From the rotor position, measured with Hall sensors or estimated from the back EMF.
08Further reading
- Stephen J. Chapman. Electric Machinery Fundamentals (Spanish edition: “Máquinas eléctricas”). 5th ed., McGraw-Hill, 2012. DC machines with their different excitations and their curves.
- Austin Hughes and Bill Drury. Electric Motors and Drives. 5th ed., Newnes, 2019. Motors seen from the electronic drive, with DC, induction and brushless.
- Padmaraja Yedamale. Brushless DC (BLDC) Motor Fundamentals (AN885). Microchip, 2003. The classic application note on the commutation of brushless motors.