Basics of DC machines

DC machines are the first rotating electrical machines discovered. After the advent of AC machines use of DC machines were used only for specific applications. DC machines are used as prime movers of synchronos generators at power stations. They are also an important part of the excitation systems employed at generating stations.

Structure

The stator of a DC machine has projected poles (salient poles) and a coil is wound on these poles as shown in figure. When excited by DC current, air-gap flux distribution created by this winding is symmetric about the center line of the field poles. The field produced by the stator current is stationary with respect to stator. This axis is called the field axis or direct (d) axis. The rotor of DC machine has slots which contain a winding. This winding handles electric power for conversion to (or from) mechanical power at the shaft. In addition, there is a commutator affixed to the rotor.

The commutator on its outer surface contains copper segments, which are electrically insulated from each other by means of mica. The coils of the rotor (armature) winding are connected to these commutator segments. A set of stationary carbon brushes are placed on the rotating commutator. These brushes are fitted to the stator. It should be noted that the wear due to mechanical contact between the commutator and the brushes requires regular maintenance, which is the main drawback of these machines.

Principle of Operation of DC Machines

Consider a two pole DC machine as shown in figure below. The voltage induced in the rotor coil rotating in a uniform field established by the stator is alternating. The air gap flux distribution and the voltage induced in the coil are shown in figures (b) and (c).

Consider a coil a-b is placed on diametrically opposite slots of the rotor shown in figure (a) above. The two ends of this coil are two commutator segments which are rotating. Coil a is connected to segment C_a and coil b to segment C_b . Let B1 and B2 be the two carbon brushes. These brushes are stationary. For counterclockwise motion of the rotor the terminal under north pole is positive with respect to the terminal under south pole. Therefore, B1 is always connected to positive end of the coil and B2 to the negative end of the coil. Thus even though the voltage induced in the coil is alternating, the voltage at the brush terminals is unidirectional as shown in figure.
The rectified voltage across the brushes has a large ripple (magnitude is not constant, it is varying) as shown in figure (d) above. In a actual machine a large number of turns are placed in several slots around the periphery of the rotor. By connecting these in series through the commutator segments a reasonably constant DC voltage is obtained. The magnitude of the voltage induced in the armature is proportional to

where

is the airgap flux and

is the speed of rotation.

Now let's look at the role of commutator. Current reversal in a turn by commutator and brushes is shown in the figure below. The end 'a' touches the brush B1 . The current flows from a to b. As this coil rotates, at a particular position it gets short circuited (refer next figure).

The angle between the d-axis and this position is 90^o . As the coil rotates from this position, end 'a' now touches brush B2 . The current now flows from 'b' to 'a' as shown in figure. Hence, the commutator and brushes rectify the alternating voltage induced in the armature to DC. This combination is also known as mechanical rectifier. Though the current flowing in the armature conductors is AC, the current flowing in/out of carbon brushes is DC. The change over from positive to negative value takes place at a particular axis. The angle between this axis and the d-axis is always 90^o . Therefore, this axis is known as q-axis or the quadrature axis. Since, the armature mmf (F_a) is along this axis, the angle

is always 90^o .

Governing Equations

It is often convenient to discuss a DC machine in terms of its equivalent circuit shown in figure. which shows the conversion between electrical and mechanical power or vice-versa. Field produced by the stator is represented by current flowing in the coil. At steady state the equation relating this current and applied voltage to the field coil is , where is resistance of the field coil.

is the air gap flux, and

is the speed of rotation, the expression for the voltage induced in the armature is given by

, where

is a constant. Let

be the armature resistance and

be the armature current.

Equations for motor

Here the current is assumed to flow into the positive carbon brush (see figure (b)). The relationship between the steady state voltage induced in the armature

and the armature terminal voltage

Multiplying throughout by

, we get

The term on the LHS in above equation is the power input to the armature, first term on RHS is the power lost as heat in the armature resistance and last term is power developed in the armature. This developed power should be equal to the mechanical output power

if friction is neglected.

Equations for generator

In this case

is leaving the positive brush as shown (see figure (c)). The relationship between the steady state voltage induced in the armature

and the armature terminal voltage

The power balance equation would be then,

The following points may be noted from these equations

During motoring operation, armature current flows in opposition to the voltage induced in the armature (also known as speed voltage). Hence for motoring operation is called as back emf denoted by
when operated as generator, voltage induced in the armature is forcing the current to leave the positive brush. Hence for generator operation is called as induced emf and is denoted by

Also note that these equations are applicable only for the steady state operation of the machine.