0.3 Chapter 4: introduction to rotating machines  (Page 4/9)

Figure 4.7 Typical induction-motor speed-torque characteristic.

§4.2.2 DC Machines

• DC Machines

• There are two sets of windings in a dc machine.

• • The armature winding is on the rotor with current conducted from it by means of carbon brushes.
  • The field winding is on the stator and is excited by direct current.
• An elementary two-pole dc generator is shown in Fig. 4.8.

• Armature winding: (a,a) , pitch  ${\text{180}}^o$
• The rotor is normally turned at a constant speed by a source of mechanical power connected the shaft.

Figure 4.8 Elementary dc machine with commutator.

• The air-gap flux distribution usually approximates a flat-topped wave, rather than the sine wave found in ac machines, and is shown in Fig. 4.9(a).
• Rotation of the coil generates a coil voltage which is a time function having the same waveform as the spatial flux-density distribution.
• The voltage induced in an individual armature coil is an alternating voltage and rectification is produced mechanically by means of a commutator. Stationary carbon brushes held against the commutator surface connect the winding to the external armature terminal.
• The need for commutation is the reason why the armature windings are placed on the rotor.
• The commutator provides full-wave rectification, and the voltage waveform between brushes is shown in Fig. 4.9(b).

Figure 4.9 (a) Space distribution of air-gap flux density in an elementary dc machine;

(b) waveform of voltage between brushes.

It is the interaction of the two flux distributions created by the direct currents in the field and the armature windings that creates an electromechanical torque.

• If the machine is acting as a generator, the torque opposes rotation.
• If the machine is acting as a motor, the torque acts in the direction of the rotation.

§4.3 MMF of Distributed Windings

• Most armatures have distributed windings, i.e. windings which are spread over a number of slots around the air-gap periphery.

• The individual coils are interconnected so that the result is a magnetic field having the same number of poles as the field winding.
• Consider Fig. 4.10(a).
  • Full-pitch coil: a coil which spans 180 electrical degrees.
  • In Fig. 4.10(b), the air gap and winding are in developed form (laid out flat) and the air-gap mmf distribution is shown by the steplike distribution of amplitude

Figure 4.10 (a) Schematic view of flux produced by a concentrated, full-pitch winding in a machine with a uniform air gap. (b) The air-gap mmf produced by current in this winding.

§4.3.1 AC Machines

• It is appropriate to focus our attention on the space-fundamental sinusoidal component of the air-gap mmf.

• In the design of ac machines, serious efforts are made to distribute the coils making up the windings so as to minimize the higher-order harmonic components.
• The rectangular air-gap mmf wave of the concentrated two-pole, full-pitch coil of Fig.4.10(b) can be resolved to a Fourier series comprising a fundamental component and a series of odd harmonics.

• The fundamental component $F_{\text{agl}}$ and its amplitude $(F_{\text{agl}}{)}_{\text{peak}}$ are

$F_{\text{agl}}=\frac{4}{\pi }(\frac{\text{Ni}}{2})\text{cos}{\theta }_a$ (4.3)