The moment of inertia value is very important for the selection of a proper motor for drives involving many starts and stops or requiring very good speed control characteristics. The inertia can be determined by a retardation test. The test works on the principle that when a motor is switched off from the mains it decelerates and comes to rest. The angular retardation at any speed is proportional to the retarding torque and is inversely proportional to the inertia. The torque lost at any speed is calculated by running the motor at that speed steadily on no load and noting the power input. From this power the losses that take place in the armature and field are deducted to get the power converted into mechanical form.
All this power is spent in over coming the mechanical losses at that speed. This can be repeated at any defined speed to get the lost power (PL) and torque lost (Tlost) due to mechanical losses. In a retardation test the motor speed is taken to some high value and the power to the motor is switched off. The torque required by the losses is supplied by the energy stored in the motor inertia. The lost torque at any speed can be written as
PL = Tlost
Tlost = PL=w = Jdw/dt
Here the dw/dt is the slope of the retardation curve and the (Tlost) is the torque required to be
net at the given speed. From these values the moment of inertia can be computed as
J =Tlost/(dw/dt) = (PL/(w.dw/dt))kgm2