Sizing a DC motor to accurately meet a set of requirements can be a thankless task. Having to choose between brush-type or brushless motors can complicate the selection. Even experienced designers may sometimes overlook critical motor parameters and find problems after the system is up and running. In the worst case, starting over may be the only alternative.

Experts, however, use an expedient procedure to properly size and select dc motors. This procedure is based upon an accurate definition of the target system parameters and designer experience.

Dc motor parameters: Fortunately, several motor parameters are the same for both brush-type and brushless dc motors. One of these is motor constant, Km. It is important but widely overlooked. It is used during motor sizing because it is a figure of merit of the motor power-to-torque ratio. Km is proportional to the ratio of peak torque, Tp, to peak power, Pp, at stall: Km = Tp / optionvPp. Km is also proportional to the ratio of torque sensitivity, Kt, to motor terminal resistance, Rm:Km = Kt / optionvRm.


Winding resistance is a major factor in motor selection because it seriously affects Km. Winding resistance and motor current produce power loss in the form of heat and motor temperature rise (TPR). These losses are also referred to as I2R losses and directly degrade motor efficiency.


A three-step procedure determines the value of resistance change from a specified initial power input. First, a quality factor, F, is computed from known wattage and temperature. Second, the hot-condition wattage, Wh is calculated. Third, the quality factor is used to find final temperature rise, Trf.

  • Quality factor is:

where Wc = initial input power, cold, W; TPR = motor temperature rise, °C/W; and Tamb = ambient temperature, °C.

  • Hot wattage is Wh = (F)(Wc).
  • The final temperature is Trf = (Wh)(TPR).

However, factor F is valid only over a restricted range of values for a part of the denominator, where n = Wc(TPR)/(234.5 + Tamb). If n >1, then F is negative or infinity, signifying thermal runaway that burns open the motor. But if n <1, then F is positive and the motor will stabilize at Trf or less.

Core losses: Hysteresis and eddy currents in the core also make motor temperature rise. At high speeds, these losses can produce as much or more heat than I2R losses.

Core losses depend primarily on the motor design. Design factors affecting those losses include lamination thickness, flux densities in the armature, and frequencies generated in the core that depend upon the number of poles and speed. Catalog specifications may not include core loss data, so designers must measure it by testing several sample motors. The data may also be available directly from the motor manufacturer.

Ambient temperature is the third most important factor determining motor temperature rise. A motor having a winding temperature rating of 155°C and operating in an ambient temperature of 100°C has only a 55°C allowable temperature rise. Core losses and I2R losses quickly cut the 55°C margin under load. An ideal room ambient temperature of 25°C, by comparison, allows a 130°C temperature rise.

Use of heat sinks and air or fluid cooling moderates the temperature rise value considerably. The TPR rating of the motor per watt of input power, °C/W, is usually in the catalog or data sheet for unmounted motors. The TPR for the same motor, but mounted, TPR can be 25% of the unmounted value. A conservative designer could ignore the reduced TPR in his calculations. But he would specify a motor much larger and more expensive than necessary.

Magnet properties: Dc motors use a variety of permanent-magnet materials. Early designs employed ceramic or ferrite and AlNiCo magnets. These materials are still widely applied, however, in automobiles and other areas where low cost as well as reliability is important. Newer designs use rare-earth samarium-cobalt and neodymium magnets.

Most magnets have stable magnetic properties within the normal operating temperature range of the motor. But some magnets have a higher temperature coefficient than others. High temperature-coefficient magnets may become too weak if operated at high temperatures for extended periods. Depending on the magnetic material and slope of the motor's magnetic circuit, torque degradation may result over a wide temperature range.

Ceramic or ferrite magnets lose about 0.13% / °C of their remanence above 25°C, while rare earth and AlNiCo may lose only 0.03% / °C. But this loss is generally reversible if the temperature is kept within the motor rating. Colder temperatures are seldom a problem. Since the coefficient curve is linear, magnets are stronger at lower temperatures.

Some grades of rare-earth magnets are more sensitive to temperature than others. Magnets in the neodymium family may have irreversible magnetic losses under wide temperature changes. These magnets have the highest maximum-energy product (MEP), a figure of merit, of any commercial magnet now available. High MEP comes at a premium and should not be lost to temperature extremes. Neodymium magnets are continually being improved with lower temperature coefficients to make them as stable as other rare-earth grades.

Peak loads applied to AlNiCo and ceramic dc motors can degrade their magnetic properties. AlNiCo motors have a peak current rating which usually corresponds to a point above the knee of the B/H curve. Current exceeding this rating, caused by either a current spike or a constant dc input, are over the knee and cause permanent demagnetization. A demagnetized AlNiCo motor may only provide 50 to 60% of its original torque. Fortunately, rare-earth magnets are not as sensitive to demagnetization as AlNiCo and ceramic.

Brushless versus brush-type: Designers planning to integrate a dc motor into a system usually work from a development specification. Constraints and limits in the specifications will largely determine whether a brush-type or a brushless motor is acceptable, based on the qualities of each.

Brush-type motors are generally used below 5,000 rpm. The actual operating speed depends upon the commutator diameter and brush material. Brush life decreases with higher commutator surface speed. Surface speed for silver-graphite brushes is usually below 650 fpm while paliney brushes are limited to only 50 fpm.

Other factors which limit brush motor life include commutator bar-to-bar voltage, brush current density, and power at the brush-commutator interface. High current and power at the brushes and commutator bar-to-bar voltage (not terminal voltage) greatly exceeding 15 Vdc produce excessive arcing. Arcing erodes brushes and commutators; wear accelerates once erosion begins.

On the other hand, electronic drives for brush motors are usually much simpler than for comparably sized brushless motors. No position sensors or electronics are required for commutation. But these components are mandatory for brushless operation. Unless used in a servocontrol loop, brush-type dc motors need no electronics other than a power source.

Since brushless dc motors have no commutators or brushes, brush and commutator arcing does not limit speed. Brushless dc motors are better suited for applications needing a wide speed range. Speeds from a stalled condition to more than 60,000 rpm are not unusual.

Brushless motors replace mechanical commutators with electronic switching. Brushless dc motor controllers require a position feedback signal from a sensor inside the motor. The sensor ensures that excitation to the electromagnetic armature field always leads the permanent-magnet field to produce torque. Power transistors drive the armature windings at a specified motor current and voltage level.

Most brushless dc motors are constructed with an outer-wound stationary armature and a rotor consisting of permanent magnets. Rotors of this type are small and have low inertias. And heat transfers more efficiently from the wound armature to ambient air in this configuration because heat dissipates from the armature core to the outer metallic housing, not conducted through the shaft like most brush-type configurations.

Motor sizing: Motor sizing takes into account all the above motor parameters and specifications. Also, the motor inertia and load must be defined for both transient and steady-state conditions. These inertia are critical since torque during acceleration exceeds torque at constant speed.

Two examples explain the sizing of dc motors for typical applications. The first example considers the selection and sizing of a brush-type dc motor. The second concerns a sterile outer-space environment requiring a brushless dc motor.