Armature Reaction - Electrical Machines - Electrical Engineering (EE)

Numerical example - induced voltage in a DC armature

Consider a DC machine with the following data:

• Number of poles, p = 4
• Total number of armature conductors, Z = 1000
• Flux per pole, φp = 0.04 Wb
• Speed, N = 500 rpm

The induced EMF in the armature (generated voltage) is given by the relation

E_b = φp × Z × N / 60 × (p / a)

where a is the number of parallel paths in the armature (depends on winding: lap or wave).
Calculation for a lap-connected armature (for a lap winding, a = p, so p/a = 1):
φp × Z = 0.04 × 1000 = 40
40 × N = 40 × 500 = 20000
20000 / 60 = 333.33 V

Therefore, E_{b, lap} ≈ 333.3 V (≈ 330 V as an approximation).
Now for the same armature connected as a wave winding (for a simple two-circuit wave winding, a = 2):
p / a = 4 / 2 = 2
E_{b, wave} = E_{b, lap} × (p / a) = 333.33 × 2 = 666.67 V (≈ 660 V).

Although the induced voltage is higher for the wave-connected machine, the conductor current per conductor I_c and the number of parallel paths change the armature current and the total electrical power generated. If I_c is the current carrying capacity of one conductor and I_a the total armature current then:

• I_c = I_a / a
• For lap: I_a,lap = a × I_c = p × I_c = 4 I_c
• For wave: I_a,wave = a × I_c = 2 I_c

Power for lap connection = E_b,lap × I_a,lap = 333.3 × 4 I_c = 1333.2 I_c

Power for wave connection = E_b,wave × I_a,wave = 666.7 × 2 I_c = 1333.4 I_c

Thus, for the same armature conductor set the electrical power capability remains essentially the same; the choice between lap and wave depends on whether a higher voltage (wave) or higher current (lap) is required.

Why armature reaction occurs

In a practical DC machine both the main field winding and the armature winding carry currents simultaneously. The field winding produces the main flux; the armature current also produces an additional flux (armature flux). The resultant air-gap flux and induced voltage and torque are due to the superposition of the field flux and the armature flux. The modification of the main field flux distribution caused by the armature flux is called armature reaction.

Shape and spatial behaviour of armature mmf and flux

The armature magnetomotive force (mmf) wave is not sinusoidal but can be approximated as a triangular wave whose peaks coincide with the brush axis (the magnetic quadrature axis). The field flux produced by the main poles has its peak under the pole centre (the direct axis) and zero crossing at the interpolar region. The armature mmf is stationary in space because although individual conductors move, the pattern of dot and cross currents between the brushes remains fixed.

Superposition of the two mmf waves distorts the resultant air-gap flux density. Two main effects occur:

• Reduction of flux density on one side of a pole and an increase on the opposite side (uneven flux distribution under the pole shoe).
• Shift of the zero crossing (magnetic neutral axis) away from the position it would occupy without armature current; hence the resultant flux under the brushes is no longer zero.

These distortions affect generated voltage, torque and commutation.

Effect of armature reaction on induced voltage and commutation

The induced voltage in an armature coil depends on the flux per pole. Since the armature mmf and armature flux are stationary in space their superposition with the main field flux changes the flux per pole in a position-dependent manner. If the magnetic circuit were linear (unsaturated), the positive and negative changes in flux due to armature mmf under one pole would cancel and net flux per pole would remain unchanged. In most practical machines, however, the iron is operating in the saturation region of the B-H characteristic.

Because of saturation, equal positive and negative changes in mmf do not produce equal changes in flux density. The decrease of flux density on one side of a pole (demagnetizing effect) is larger than the increase on the other side, so that the net flux per pole reduces. Consequently the induced emf falls. Furthermore, the shift of the magnetic neutral axis means coils that are being commutated are not shorted when their induced voltage is zero; there will be a non-zero induced voltage during commutation, producing circulating currents and sparking at the brushes. The distortion also produces higher instantaneous voltages in some coils and greater voltage stress between adjacent commutator segments, increasing the risk of insulation breakdown.

Calculating armature ampere-turns (peak) and conductor current

Let the total number of conductors be Z. The total number of turns is Z/2. If the total armature current is I_a and the number of parallel paths is a, then the current in each conductor is

I_c = I_a / a

The armature ampere-turns per pole (peak) is given by the ampere-turns per pole:

A_{T,armature (peak) = (Z × Ia) / (2 a p)} 

This value is important because compensating measures must provide an equal and opposite ampere-turns (in the pole face region) to negate the demagnetizing effect of the armature mmf.

Compensation using pole-face (compensating) windings

To reduce the harmful effects of armature reaction a winding called the compensating winding (or pole-face winding) is placed in slots in the pole face and connected in series with the armature so that its mmf opposes the armature mmf under the pole.

The required ampere-turns of the compensating winding is approximately equal to the armature ampere-turns peak multiplied by the ratio of pole arc to pole pitch:

A_T,comp = A_{T,armature (peak)} × (pole arc / pole pitch)

Because pole shoes do not extend over the entire armature periphery, compensating windings can largely cancel the armature mmf directly under the pole shoe but cannot fully cancel armature mmf in the interpolar region. That remaining mmf in the interpolar region must be handled by a different measure (interpoles).

Residual armature reaction after compensation and use of interpoles

With compensating windings in place, the mmf under the pole face is largely neutralised but the interpolar region still sees some armature mmf. The residual mmf shifts the magnetic neutral axis slightly and leaves a small flux in the interpolar region. Interpoles (commutating poles) are used to cancel these residual ampere-turns exactly in the interpolar region; they are placed in the interpole space and are excited in series with the armature so that commutation is improved.

Brush shift, demagnetizing and cross-magnetizing ampere-turns

In practice it is sometimes convenient to physically shift brushes to the new neutral axis (brush shift). A brush shift of an angle β changes the distribution of dot and cross currents among armature conductors. Conductors that fall under the pole shoe and whose current is opposite to the main field produce a demagnetizing effect, while the rest produce a cross-magnetizing effect (aligned to the quadrature axis).

The demagnetizing ampere-turns produced by brush shift can be calculated (for small β) by:

A_T,demag = (Z / 4π) × (2 β) × I_c

Here β must be in radians and I_c = I_a / a. To maintain the required main flux, the field ampere-turns should be adjusted so that field ampere-turns = demagnetizing ampere-turns due to brush shift.

Summary

Armature reaction is the modification of the main field flux distribution by the mmf of the armature current. The armature mmf is triangular with peaks at the quadrature axis and a zero crossing at the direct axis; it is stationary in space because the pattern of dot and cross currents between brushes is fixed. The main consequences are distortion and shift of the air-gap flux distribution, reduction of net flux per pole (especially in saturation), reduction of induced emf, and adverse effects on commutation and commutator insulation.

Compensating windings in the pole face, connected in series with the armature, are used to cancel the armature mmf under the pole shoe; interpoles are used to cancel residual mmf in the interpolar region. Brush shift affects demagnetizing ampere-turns and must be countered by suitable field adjustments.

Understanding armature reaction is essential for correct design and operation of DC machines to ensure adequate generated voltage, efficient torque production and satisfactory commutation.