Analysis Approach for PMDC Motors

For a permanent-magnet DC motor, the stator is equipped with P pairs of permanent magnets, creating P pairs of alternating north and south poles. The distribution of the magnetic field produced by the permanent magnet’s field flux is fixed with respect to the stator. The rotor is equipped with a distributed winding connected to a commutator that revolves together with the rotor.

A system of brushes is kept in permanent electrical contact with the commutator. When DC current is applied to the rotor winding (via the brushes and commutator), a torque is produced by the interaction of the rotor (armature) currents and the field produced by the permanent magnets.

The commutator causes the armature to create a magnetic flux distribution that is fixed in space and whose axis is perpendicular to the axis of the field flux produced by the permanent magnets. For these motors, the commutator acts as a mechanical rectifier.

The performance of a permanent-magnet DC (PMDC) motor is computed by DC analysis only. The voltage equation of a PMDC motor is

U = Ub + R1 * I + E

where Ub is the voltage drop of one-pair brushes, R1 is the armature resistance, E = Ke * w is the back emf with Ke the back-emf constant in Vs/rad, and w is the speed in rad/s. For a given speed w, armature current can be computed based on the applied voltage U, as shown below:

I = (U - Ub - Ke * w)/R1

The shaft torque T2 is computed by

T2 = Kt * I - Tfw

where Kt is the torque constant in Nm/A, which is numerically the same as Ke, and Tfw is the frictional torque.

The output power (mechanical power) is

P2 = T2 * w

The input power (electrical power) is

P1 = P2 + Pfw + Pcua + Pb + PFe

where Pfw, Pcua, Pb, and PFe are frictional and wind loss, armature copper loss, brush drop-loss, and iron core-loss, respectively.

The efficiency is

eff = P2/P1 * 100%