For the DC shunt motor, the speed equation is
N ∝ Eb/φ
N is the speed of the motor
Eb is back emf
Ï• is flux per pole
As we know, if the field winding of a running shunt motor suddenly breaks open. So, Flux is reduced and speed increase dangerously as flux is inversely proportional to speed.
In a DC shunt motor, Eb ∝ NÏ•
For a constant back emf, flux is inversely proportional to the speed of the motor.
If field winding is disconnected accidentally, the speed would dangerously increase in order to maintain the back emf of the motor. For a constant back emf, flux is inversely proportional to the speed of the motor.
In the case of a series machine if field winding is disconnected, then the motor circuit is open and no current will pass through the armature, for the operation of the machine interaction of two fluxes is necessary thus the machine won't operate.