# Steady State speed of rotor in following doubly excited system

I'm trying to analyse following system -

A three phase armature winding on stator and on rotor field winding and both stator and rotor are cylindrical . And armature winding is connected to a three phase balance ACsupply while field winding is connected to a DC supply

At t=0 ;

Both supplies are open (off) and I start rotating rotor manually by applying external torque

At time t ;

When at time t rotor reaches to synchronous speed (equal to speed of rotating stator field ) at that instant I closed the both supplies and remove external torque

but I'm not sure what will be the steady State speed of rotor (what is best way to approach) whether it keeps rotating with synchronous speed or it will stop or reach at a speed in between zero to synchronous speed ?

Assuming following two cases -

1. a contant load torque after t
• " three phase armature winding on stator and on rotor field winding" does not describe a synchronous machine. Do you have a description of the angular relationship between the stator and rotor? If not, you should make an assumption and describe the results in terms of the angular position. – Charles Cowie Dec 30 '20 at 19:16
• You are a little bit confused, the DC motor doesn't have a synchronous speed nor the excitation field is rotating. – Marko Buršič Dec 30 '20 at 19:21
• @Charles Cowie relative angular position could be anything (except zero torque position ) ,I'm not saying this describes a synchronous machine rather how to analyse this system and what should be steady State speed of this doubly excited system – user215805 Dec 30 '20 at 19:27
• @Marko Buršič but DC motor doesn't have rotating magnetic field also ? – user215805 Dec 30 '20 at 19:28
• You applied the synchronous-motor tag to the question and mostly described a synchronous machine. Is this a homework or study question, or a machine that you are trying to identify? – Charles Cowie Dec 30 '20 at 19:40

Assuming that this is a synchronous motor, when AC stator power and DC rotor power is applied with no torque, the rotor will accelerate or decelerate very briefly to bring the rotor into alignment with the stator field.

When load is applied, the rotor will decelerate very briefly to achieve a torque angle required for the motor driving torque to match the retarding torque.

Re comment:

The motor torque is proportional to the product: the air gap flux X field winding magnetomotive force X sin torque angle. The torque angle is the phase angle between the rotor and stator fluxes. With the motor rotating without power applied, the initial torque would be determined by the the random angle of the rotor and would accelerate or decelerate the rotor to achieve a stable torque angle. That motion would be determined by the total load torque and inertia. It would tend to be a harmonic motion with a decreasing amplitude.

A lightly loaded motor would oscillate longer, but there would always be some friction load from motor bearing friction and aerodynamic drag even if it is not coupled to a load.

• Thanks for answer ! "Rotor will decelerate briefly " what briefly exactly is ? is there any limit of constant load torque until which we get a finite steady speed? I thought solving $$\frac{d^2 \theta}{dt^2} -ksin \theta =0$$ ,but this equation is non linear and approximating $$sin\theta$$ =$$\theta$$ gives solution similar to SHM motion ,but I don't know this is correct or not ? – user215805 Dec 31 '20 at 8:46
• thank you so much ! Is there any maximum limit of load torque for synchronous motors after which synchronization is impossible ? – user215805 Dec 31 '20 at 17:59
• My answer was only about the concept. I don't know if it is practically feasible to do what was described. When synchronous generators are connected to the grid, the phase relationship is matched before connecting. Synchronous motors are started with induction windings. When they pull into synchronism, the process is somewhat similar to what was described in this case. I believe inertia is a concern, but I think they can start with rated torque. Above some power level, I believe synchronous motors are electronically. – Charles Cowie Dec 31 '20 at 18:24