DC series motor for starting heavy loads

A DC series motor is a DC motor whose field winding is connected in series with the armature, so the same current flows through both. The series field has a few turns of thick wire, so its resistance is very low.

   +o----[ Series field Rse ]----+
                                 |
                              ( A )  armature Ra
                                 |
   -o----------------------------+
        I = Ia = Ise

$$V = E_b + I_a (R_a + R_{se})$$

Why it is used for heavy starting loads

1. Torque varies as square of current. Since flux $\phi \propto I_a$ (before saturation), $T \propto \phi I_a \propto I_a^2$. If the current is doubled, the torque becomes about four times as large. A shunt motor would give only twice the torque for the same current.
2. Very high starting torque. At starting $E_b = 0$, so a large current flows (limited by the starter). This large current produces a strong field and a very large starting torque, which can accelerate heavy loads with high inertia.
3. Speed adjusts automatically to load. $N \propto E_b/\phi$; with heavy load the current and flux rise, so speed falls. Power ($T\omega$) stays roughly constant, so the motor is not overloaded much when the load torque rises.
4. Less current from the supply for the same torque. Because $T \propto I^2$, a given starting torque is obtained with less current than in a shunt motor.

Applications: electric traction (trains, trams), cranes, hoists, lifts, trolley buses, conveyors.

Caution: a series motor must never be started or run without load (or with a belt drive), because at light load the flux is very small and speed rises dangerously high ($N \propto 1/\phi$).