A few characteristics of dc motors maintain linear relationships that allow for very predictable operation. First, if enough voltage is applied across the terminals of a dc motor, the output shaft will spin at a rate proportional to that applied voltage. A designer can determine the ratio of the applied voltage to rated voltage, multiply that value by a dc motor's no-load speed, and derive running speed. Second, measuring and plotting current and torque also gives a straight line — another directly proportional relationship. This means that current demand simply increases with that for torque. Finally, plotting motor torque and speed requires only two points of data: no-load speed and stall torque.

The entire motion control world, including manufacturers and designers, depends greatly on the premise that all these linear relationships hold true. Thankfully, they do because the laws of physics do not change. Even so, despite their simplicity, selecting a dc motor for an application can still be a daunting task. Many variables must be taken into account: dimensions, load, duty cycle, environment, feedback considerations, and so on. Let us decode some motor-operation mysteries to shed some light on the selection process.

Going for simplicity: Brushed motors

If an application demands reliable, time-tested, low-cost motion, then brushed dc motors may be the technology of choice. The key here is simplicity: A brushed motor is designed to run on straight-line dc voltage and can even be connected directly to a properly sized battery.

When dc voltage is applied across a brushed motor's terminals, a potential difference develops, and current is induced in the rotor windings. The brushes allow this current to flow through a rotating mechanical switch called a commutator. Rotor windings act as electromagnets and while powered, they form two poles that terminate at the commutator segments. (This entire assembly is known as an armature.)

While rotating, the commutator allows the direction of the current to reverse twice per cycle, in turn permitting current to flow through the armature and electromagnet poles, to attract and repel permanent magnets that encompass the motor's inner housing. As the armature's energized windings pass the permanent magnets, the polarity of the windings reverses at the commutator. This process is called mechanical commutation and is only found in brushed motors.

The instant that polarity switches, inertia keeps the rotor spinning in the proper direction and the motor turning. The result is power in its mechanical form, measured in Watts. Mechanical power is the product of torque multiplied by rotational distance per unit time (or speed.) Torque is the force vector component that rotates a load about an axis and is inversely proportional to speed:

P_rot = M × ω

From this equation, we see that there is a price to pay for how much power a motor can deliver: The amount of current that flows through the windings directly affects the torque the motor can produce. Adjusting supply voltage forces a proportional change in motor speed, so the output shaft's angular velocity (or speed) must be sacrificed as torque demands increase.

Other factors also come into play — for example, static friction. This is defined as the friction torque a motor must overcome for the shaft to begin turning. In addition, there are brush-contact losses caused by the friction of the brushes upon the commutator.

Other losses are in the form of heat. This dissipated electrical power is also somtimes called I²R loss:

P_diss = I²·R

Here, current I is that running through the motor, and R is the teminal resistance.

When torque and speed are measured empirically, the result is not always perfectly linear. Even so, from the equation above, we see that both torque and speed are inversely proportional and that a theoretically linear relationship exists. Because of this, feedback provided by an encoder, tachometer, or resolver is not even necessary in all cases. Where feedback is employed, it reports motor position and angular shaft speed to the servosystem.

In summary, a properly designed closed-loop servosystem gives predictable response to controlled input. What is more, thanks to the directly linear relationships, a servo can easily compensate for any disturbances introduced into the system.