DC series motor should not start on no-load

In a series motor the field winding carries the armature current, so the flux depends on the load: $\Phi\propto I_a$ (below saturation). The speed is

$$N \propto \frac{E_b}{\Phi} \approx \frac{V - I_a(R_a + R_{se})}{\Phi}$$

• At no load $I_a$ becomes very small, so the flux $\Phi$ becomes very small (only the residual value).
• The numerator $E_b\approx V$ stays nearly constant, so the speed $N\propto 1/\Phi$ rises to a dangerously high value (several times rated speed).
• This is called racing. The centrifugal forces can burst the armature, throw the winding out of the slots and damage the commutator and bearings.
• The torque $T\propto\Phi I_a\propto I_a^2$ is small at no load, so the motor has no load to hold the speed down.

Hence a series motor must always be started and run with a load connected (preferably directly coupled or geared, never by a belt that may slip or break).