Introduction to D.C. Machines

D.C. machines are characterized by their versatility. By means of various combinations of shunt-, series-, and separately excited field winding they can be designed to display a wide variety of volt-ampere or speed-torque characteristics for both dynamic and steady state operation. Because of the ease with which they can be controlled, systems of D.C. machines are often used in applications requiring a wide range of motor speeds or precise control of motor output.

The essential features of a D.C. machine are shown schematically. The stat-or has salient poles and is excited by one or more field coils. The air-gap flux distribution created by the field winding is symmetrical about the center line of the field poles. This is called the field axis or direct axis.

As we know, the A.C. voltage generated in each rotating armature coil is converted to D.C. in the external armature terminals by means of a rotating commutator and stationary brushes to which the armature leads are connected. The commutator-brush combination forms a mechanical rectifier, resulting in a D.C. armature voltage as well as an armature m.m.f. Wave then is 90 electrical degrees from the axis of the field poles, i.e. in the quadrature axis. In the schematic representation the brushes are shown in quadrature axis because this is the position of the coils to which they are connected. The armature m.m.f. Wave then is along the brush axis as shown. (The geometrical position of the brushes in an actual machine is approximately 90 electrical degrees from their position in the schematic diagram because of the shape of the end connections to the commutator.)

The magnetic torque and the speed voltage appearing at the brushes are independent of the spatial waveform of the flux distribution; for convenience we shall continue to assume a sinusoidal flux-density wave in the air gap.  The torque can then be found from the magnetic field viewpoint.

The torque can be expressed in terms of the interaction of the direct-axis air-gap flux per pole   and space-fundamental component  of the armature m.m.f.wave. With the brushes in the quadrature axis the angle between these fields is 90 electrical degrees, and its sine equals unity. For a   pole machine

               （1-1）

In which the minus sign gas been dropped because the positive direction of the torque can be determined from physical reasoning. The space fundamental   of the sawtooth armature m.m.f.wave is   times its peak. Substitution in above equation then gives 

              （1-2）

Where,  =current in external armature circuit;

        =total number of conductors in armature winding;

        =number of parallel paths through winding.

And

                  （1-3）

is a constant fixed by the design of the winding.

The rectified voltage generated in the armature has already been discussed before for an elementary single-coil armature. The effect of distributing the winding in several slots is shown in figure. In which each of the rectified sine wave is the voltage generated in one of the coils, commutation taking place at the moment when the coil sides are in the neutral zone. The generated voltage as observed from the brushes and is the sum of the rectified voltages of all the coils in series between brushes and is shown by the rippling line labeled   in figure. With a dozen or so commutator segments per pole, the ripple becomes very small and the average generated voltage observed from the brushes equals the sum of the average values of the rectified coil voltages. The rectified voltage   between brushes, Known also as the speed voltage, is