derive the torque equation of synchronous motor
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We know that torque equation in synchronous motor or generator is directly proportional to the stator filed strength, rotor field strength and the sine of angle between them. This is true for all rotating electrical machine.
If Fs, Fr and λ be the stator field strength, rotor field strength and angle between Fs & Fr, then the torque is given as
Te = FsFrSinλ
The above torque equation is a general equation applicable for all rotating electrical machine. In this post we will derive a general torque equation for synchronous machine. For this purpose, let us consider a uniform air gap two pole machine as shown below.
Current in the stator winding produces stator mmf which is assumed to be sinusiodally distributed in the air gap periphery. The peak value of this stator mmf Fs is directed along the stator winding axis as shown in figure. In the above figure, Fs is taken horizontal with Fs directed from left to right. Similarly, rotor current produces rotor mmf which is also assumed sinusiodally distributed in the air gap. The peak value of rotor mmf Fr is along the rotor winding axis as shown in figure. It should be noted that Fs and Fr is the peak value of resultant mmf due to all stator and rotor winding.
These stator and rotor mmf in turn causes appearance of stator and rotor poles. Stator mmf Fs causes appearance of North pole in the left side whereas South pole at the right side of stator. Similarly, North and South pole are produced due to rotor mmf as shown in figure. These stator and rotor magnetic poles interact with each other and tend to align their magnetic axis. This results in development of electromagnetic torque.
In the above figure, the length of air gap is ‘g’ and average radius i.e. average of stator and rotor radii is ‘r’. The effective axial length of synchronous machine is ‘l’.
If Fs, Fr and λ be the stator field strength, rotor field strength and angle between Fs & Fr, then the torque is given as
Te = FsFrSinλ
The above torque equation is a general equation applicable for all rotating electrical machine. In this post we will derive a general torque equation for synchronous machine. For this purpose, let us consider a uniform air gap two pole machine as shown below.
Current in the stator winding produces stator mmf which is assumed to be sinusiodally distributed in the air gap periphery. The peak value of this stator mmf Fs is directed along the stator winding axis as shown in figure. In the above figure, Fs is taken horizontal with Fs directed from left to right. Similarly, rotor current produces rotor mmf which is also assumed sinusiodally distributed in the air gap. The peak value of rotor mmf Fr is along the rotor winding axis as shown in figure. It should be noted that Fs and Fr is the peak value of resultant mmf due to all stator and rotor winding.
These stator and rotor mmf in turn causes appearance of stator and rotor poles. Stator mmf Fs causes appearance of North pole in the left side whereas South pole at the right side of stator. Similarly, North and South pole are produced due to rotor mmf as shown in figure. These stator and rotor magnetic poles interact with each other and tend to align their magnetic axis. This results in development of electromagnetic torque.
In the above figure, the length of air gap is ‘g’ and average radius i.e. average of stator and rotor radii is ‘r’. The effective axial length of synchronous machine is ‘l’.
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