Principios, construcción y guía de ingeniería de los motores de corriente continua con escobillas

Introduction

The brushed DC motor is the oldest and most fundamental form of rotary electromechanical energy converter still in widespread use today. Invented in the early 19th century and refined through generations of engineering, it remains the go-to solution for applications requiring simple control, high starting torque, and minimal system cost.

This article provides a comprehensive technical overview of brushed DC motor principles, construction, commutation physics, speed control methods, and the engineering trade-offs that determine when a brushed motor is the optimal choice.

1. Operating Principle: The Lorentz Force

At the heart of every DC motor lies the Lorentz Force Law, which describes the mechanical force experienced by a current-carrying conductor in a magnetic field:

Where: 
F = Force on conductor (Newton, N) 
B = Magnetic flux density (Tesla, T) 
I = Current through conductor (Ampere, A) 
L = Active conductor length in magnetic field (meter, m)

The direction of this force is determined by Fleming's Left-Hand Rule: extend the thumb, index finger, and middle finger of your left hand mutually perpendicular. The index finger points in the direction of the magnetic field, the middle finger in the direction of current, and the thumb indicates the direction of the resulting force.

In a practical motor, multiple conductors are wound around a laminated iron core (the armature or rotor) and placed within a stationary magnetic field. The collective force on all active conductors produces a driving torque that rotates the armature.

2. Construction and Components

A brushed DC motor consists of five essential components:

The Commutator: Mechanical Intelligence

The commutator is a segmented copper cylinder mounted on the rotor shaft. Each segment connects to a specific armature coil. As the rotor turns, the brushes slide across the commutator surface, sequentially connecting different coils to the power supply. This mechanical switching action ensures that current always flows in the correct direction to maintain continuous rotation.

Key Insight: The number of commutator segments equals the number of armature coils. More segments produce smoother torque with reduced ripple.

3. Fundamental Equations

Back EMF

As the armature rotates, its conductors cut through the magnetic field, inducing an electromotive force (EMF) by Faraday's Law. This back EMF ($E_b$) opposes the applied voltage:

Where: 
P = Number of poles 
Φ = Flux per pole (Weber, Wb) 
Z = Total number of armature conductors 
N = Rotational speed (RPM) 
A = Number of parallel paths in armature winding

For practical engineering, this simplifies to:

Where Ke is the back EMF constant (V·min/rpm or V·s/rad).

Voltage Equation

Applying Kirchhoff's Voltage Law to the armature circuit:

Where: 
V = Applied terminal voltage (V) 
Ia = Armature current (A) 
Ra = Armature resistance (Ω) 
Vbrush = Brush contact voltage drop (typically 0.5–2 V per brush set)

Critical Startup Condition: At standstill ($N=0$), back EMF is zero. The starting current is limited only by Istart=V/Ra, which can be 10–20× the rated current. This is why starting resistors or electronic current limiting are essential.

Torque Equation

The electromagnetic torque developed is:

For permanent magnet (PM) brushed motors (where $\Phi$ is constant):

This linear torque-current relationship makes PM brushed motors exceptionally predictable and easy to control—ideal for servo applications and simple speed regulation.

Speed Equation

Rearranging the voltage equation:

Or equivalently:

This reveals the two primary methods of speed control: 
• Armature voltage control: Reducing $V$ decreases speed while maintaining torque capability 
• Field flux control: Weakening $\Phi$ increases speed at the expense of torque

4. Types of Brushed DC Motors

Brushed motors are classified by how their magnetic field is produced:

Permanent Magnet DC Motors

PM motors dominate modern low-to-medium power applications because they eliminate the field winding losses and complexity of wound-field designs. Key advantages include:

• Higher efficiency (no field copper losses)
• Linear torque-speed characteristic
• Smaller size and lighter weight for equivalent output
• No risk of runaway (unlike series motors)

5. Performance Characteristics

Torque-Speed Curve

The torque-speed relationship of a brushed DC motor is fundamentally linear:

Efficiency and Power Flow

Example Calculation

Consider a 24 V PM brushed motor with: 
Ra=0.8 Ω
Ke=0.05 V·min/rpm (=0.477 V·s/rad)
Kt=0.477 N·m/A
Brush drop = 1.5 V 
No-load current = 0.5 A 
Rated current = 10 A

At rated load:

• Back EMF: Eb=24-10*0.8-1.5=14.5 V
• Speed: N=14.5/0.05=290 RPM
• Torque: T=0.477*10=4.77 N·m
• Output power: Pout=4.77*(290*2*Pi/60)
• Input power: Pin=24*10=240 W
• Efficiency: eta=144.8/240*100%=60.3%

Note: This relatively low efficiency is typical for small brushed motors. Larger, optimized designs achieve 75–85%.

6. Speed Control Methods

Armature Voltage Control

The most common and effective method. By varying the applied voltage below the rated value:

Implementation methods:

Field Flux Control

Applicable only to wound-field motors. By inserting a variable resistor in series with the shunt field winding, the field current (and thus flux) is reduced:

This method increases speed above the base (rated) speed, but torque capability decreases proportionally. It is commonly used in constant-power applications such as machine tool spindles.

7. Commutation and Brush Wear

The Commutation Process

Commutation is the process of reversing current direction in an armature coil as it passes from one pole to the next. Ideally, this reversal is instantaneous. In practice:

• Sparkless commutation requires the current to reverse while the coil is temporarily short-circuited by the brush spanning two adjacent commutator segments.
• Reactance voltage ($L\frac{dI}{dt}$) opposes this rapid current change, causing arcing.
• Interpoles (commutating poles) are small auxiliary windings placed between main poles to generate a counter-flux that neutralizes reactance voltage.

Brush Materials and Selection

Factors Affecting Brush Life

Typical brush life ranges from 500 to 5,000 hours depending on operating conditions.

8. Advantages and Limitations

Why Choose Brushed DC?

Key Limitations

9. Brushed vs. Brushless: Selection Guide

When to Choose Brushed

10. Modern Developments

Despite the dominance of brushless technology, brushed DC motors continue to evolve:

Conclusion

The brushed DC motor remains a viable and often optimal solution for applications where simplicity, cost, and high starting torque outweigh the benefits of brushless technology. Understanding the fundamental equations—back EMF, torque production, and the voltage balance—enables engineers to select, size, and control brushed motors effectively.

While brushless motors dominate continuous-duty, high-speed, and high-efficiency applications, the brushed DC motor's straightforward operation and minimal system complexity ensure its continued relevance in the electromechanical landscape.