DC Motors: Performance

dc motors

U = I • R + UI

UI ... voltage induced in windings (back-EMF)

UI = k • ω (ω … angular speed, ω = 2 • π • n)


Torque generation is: T = k • I

Factor k depends on motor design features (number of winding turns, permanent magnet strength, air gap distance, rotor diameter, rotor length).
It is fixed with the design, but varies due to motor manufacturing tolerances.
There is also an influence of temperature (k gets lower at rising temperature, due to higher winding resistance and lower magnet strength).

Basic equation of DC motor is:

ω = U/k – R/k2 • T

It says that speed is highest at no load condition and decreases with rising load torque.


Performance Curve

dc motors


Manufacturing tolerance

Motors from serial production have a manufacturing tolerance, which should be considered.
Tolerance of no load speed is specified by +-10%, but is lower usually.

Rated operating point and overload

Rated operating point (rated torque) is defined for continuous duty cycle operation, usually. But motor design can be also made for low duty cycle operation or short time operation at rated point, especially for high speed motors.

Rated point is located at point of max.efficiency or between point of max.efficiency and point of max output power.

Lower duty cycle operation allows higher torque load (overload).

Permissible overload is restricted by winding temperature increase, but possibly also by

  • commutator/brush loadability (for low voltage / high current design)
  • de-magnetization of permanent magnets


A heat sink (metal flange to metal rack or gearbox) increases loadability.

Performance at increased motor temperature

An increase of motor temperature can be caused by

  • self-warming due to motor losses after some time of operation
  • high ambient temperature

 dc motors


Two effects cause the change of performance with temperature increase:

  • Permanent magnet strength decreases
  • Winding resistance increases
Both result in higher no load speed and lower stall torque



Performance at reduced supply voltage

The speed curve gets lower proportional to the voltage.
Vice versa, it increases with rising voltage (but to consider reduced lifetime or even thermal overloading of the motor).

dc motors