Demagnetizing and Cross Magnetizing Ampere Turns

Armature reaction is defined as action of armature flux on the main flux. The armature reaction causes two effects – Demagnetizing effect and cross magnetizing effect
Demagnetizing effect of armature causes weaking of the main field thus reduce the Generated emf.

Cross magnetizing effect of armature reaction causes distortion of main field thus produces sparking on the brushes.
Armature reaction along the q-axis is cross magnetizing mmf.
Armature mmf has triangular wave form when geometrical neutral plane (GNP) coincides with magnetic neutral plane (MNP), Their is only cross magnetizing effect, there is no demagnetizing effect.

As soon as brushes are along the geometrical neutral plane (GNP) there are only cross magnetizing effect. when there is brush shift from the geometrical neutral plane (GNP), armature reaction has two effects – cross magnetizing effect and demagnetizing effect.

Demagnetizing and Cross Magnetizing Ampere turns

Demagnetizing Ampere Turns per Pole

Now consider two pole generator with brush shift of “θ_m” (mechanical degrees) from GNP. as shown in figure 1. The conductor lying in the angles AOC and BOD at the top and bottom of armature produce flux which are in direct opposition to the main flux and hence are called demagnetizing armature conductors.

Let
Z = Total number of armature conductors
I_a = current in armature
I = current in armature conductor
I = \frac{I_{a}}{2} = for simplex wave wound armature.
I = \frac{I_{a}}{P} = For simplex lap wound armature.

Total Demagnetizing armature conductors = Conductor in angle AOC and BOD = \frac{4\theta_{m}}{360} \times Z
Total demagnetizing turns = \frac{1}{2}\left[\frac{4\theta_{m}}{360} \times Z\right] =\frac{2\theta_{m}}{360} Z
Total demagnetizing Ampere turns = \frac{2\theta_{m}}{360} ZI

Total demagnetizing Ampere turns per Pole = \frac{\theta_{m}}{360} ZI
i.e. AT_d/Pole = \frac{\theta_{m}}{360} ZI

Demagnetizing Ampere turns can be neutralized by putting extra number of turns on each pole of generator.
Number of extra turns per pole (For Shunt generator)= \frac{AT_{d}}{I_{sh}}
Number of extra turns per pole (For Series generator)=\frac{AT_{d}}{I_{a}}

Relationship between Electrical Degrees (θ_e) and Mechanical degrees (θ_m)
\theta_{m}=\frac{2\theta_{e}}{P}

Cross Magnetizing Ampere Turns per Pole

Consider the figure 2 the armature conductor lying in the angles AOD and COB which are right angles to the main flux produce uneven flux distribution on each pole. They are called cross magnetizing armature conductors

Total Armature reaction ampere turns per pole (AT/Pole) = \frac{ZI}{2P}
Demagnetizing ampere turns per pole (AT_d /Pole) = \frac{ZI\theta_m}{360}
cross magnetizing ampere turns per pole = (AT/Pole) – (AT_d/Pole)

cross magnetizing ampere turns per pole = \frac{ZI}{2P} – \frac{ZI\theta_m}{360}
cross magnetizing ampere turns per pole (ATc/Pole) = ZI\left(\frac{1}{2P}-\frac{\theta_m}{360}\right)

Read Also

1. Armature Reaction | Armature Reaction in a DC Generator
2. Derive EMF Equation of DC Generator
3. Armature Winding | What is armature winding