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D.C Machines
1 Introduction
The steam age signalled the beginning of an industrial revolution. The advantages of machines and gadgets in helping mass production and in improving the services spurred the industrial research. Thus a search for new sources of energy and novel gadgets received great attention. By the end of the 18th century the research on electric charges received a great boost with the invention of storage batteries. This enabled the research work on moving charges or currents. It was soon discovered ( in 1820 ) that, these electric currents are also associated with magnetic field like a load stone. This led to the invention of an electromagnet. Hardly a year later the force exerted on a current carrying conductor placed in the magnetic field was invented. This can be termed as the birth of a motor. A better understanding of the inter relationship between electric and magnetic circuits was obtained with the enumeration of laws of induction by Faraday in 1831. Parallel research was contem- porarily being done to invent a source of energy to recharge the batteries in the form of a d.c. source of constant amplitude (or d.c. generator). For about three decades the research on d.c. motors and d.c. generators proceeded on independent paths. During the second half of the 19th century these two paths merged. The invention of a commutator paved the way for the birth of d.c. generators and motors. These inventions generated great interest in the generation and use of electrical energy. Other useful machines like alternators, transformers and induction motors came into existence almost contemporarily. The evolution of these machines was very quick. They rapidly attained the physical configurations that are being used even today. The d.c. power system was poised for a predominant place as a preferred
system for use, with the availability of batteries for storage, d.c. generators for conversion of mechanical energy into electrical form and d.c. motors for getting mechanical outputs from electrical energy.
The limitations of the d.c. system however became more and more apparent as the power demand increased. In the case of d.c. systems the generating stations and the load centers have to be near to each other for efficient transmission of energy. The invention of induction machines in the 1880s tilted the scale in favor of a.c. systems mainly due to the advantage offered by transformers, which could step up or step down the a.c.voltage levels at constant power at extremely high efficiency. Thus a.c. system took over as the preferred system for the generation transmission and utilization of electrical energy. The d.c. system, however could not be obliterated due to the able support of batteries. Further, d.c. motors have excellent control characteristics. Even today the d.c. motor remains an industry standard as far as the control aspects are concerned. In the lower power levels and also in regenerative systems the d.c. machines still have a major say.
In spite of the apparent diversity in the characteristics, the underlying princi- ples of both a.c. and d.c. machines are the same. They use the electromagnetic principles which can be further simplified at the low frequency levels at which these machines are used. These basic principles are discussed at first.
where ψ is the flux linkages given by the product of flux lines in weber that are linked and N the number of turns of the coil. This can be expressed as,
e ∝ N d dtΦ (2)
Here N is the number of turns of the coil, and Φ is the flux lines in weber link- ing all these turns. The direction of the induced emf can be determined by the application of Lenz’s law. Lenz’s law states that the direction of the induced emf is such as to produce an effect to oppose this change in flux linkages. It is analogous to the inertia in the mechanical systems. The changes in the flux linkages associated with a turn can be brought about by (i) changing the magnitude of the flux linking a static coil (ii) moving the turn outside the region of a steady field (iii) moving the turn and changing the flux simultaneously These may be termed as Case(i), Case(ii), and Case(iii) respectively. This is now explained with the help of a simple geometry. Fig. 1 shows a rectan- gular loop of one turn (or N=1). Conductor 1 is placed over a region with a uniform flux density of B Tesla. The flux lines, the conductor and the motion are in mutually perpendic- ular directions. The flux linkages of the loop is BLN weber turns. If the flux is unchanging and conductor stationary, no emf will be seen at the terminals of the loop. If now the flux alone changes with time such that B = Bm. cos ωt, as in Case(i), an emf given by
e = (^) dtd(Bm.L.N cos ωt) = −(Bm.L.Nω). sin ωt. = −jBm.L.Nω. cos ωt volt (3)
4
L
X
B
Figure 1: Faraday’s law of Induction
appears across the terminals. This is termed as a ”transformer” emf. If flux remains constant at Bm but the conductor moves with a velocity v, as in Case(ii), then the induced emf is
e = dψdt = d(Bm dt.L.N )= Bm.L.N dXdt volts (4)
but dX dt =^ v^ ∴^ e^ =^ Bm.L.N.v^ volts^ (5) The emf induced in the loop is directly proportional to the uniform flux density under which it is moving with a velocity v. This type of voltage is called speed emf (or rotational emf). The Case(iii) refers to the situation where B is changing with time and so also is X. Then the change in flux linkage and hence the value of e is given by
e = dψdt = d(Bm.L.X.N. dt cos^ ωt)= Bm. cos ωt.L.N.dXdt − Bm.L.X.N.ω. sin ωt. (6)
In this case both transformer emf and speed emf are present.
cal energy conversion results in the generation of both transformer and rotational emf to be present in the coil moving under a changing field. This principle is utilized in the induction machines and a.c. commutator machines. The direction of the induced emf is
Force (^) Motion
B
emf and current
F
(a) (b)
Figure 2: Law of induction-Generator action
decided next. This can be obtained by the application of the Lenz’s law and the law of interaction. This is illustrated in Fig. 3.
In Case(i), the induced emf will be in such a direction as to cause a opposing mmf if the circuit is closed. Thus, it opposes the cause of the emf which is change in ψ and hence φ. Also the coil experiences a compressive force when the flux tries to increase and a tensile force when the flux decays. If the coil is rigid, these forces are absorbed by the supporting structure.
In Case(ii), the direction of the induced emf is as shown. Here again one could derive the same from the application of the Lenz’s law. The changes in the flux linkages is
7
Motion,Force
B
emf
current
F
(a) (b)
Figure 3: Law of interaction- Motor action
brought about by the sweep or movement of the conductor. The induced emf, if permitted to drive a current which produces an opposing force, is as shown in the figure. If one looks closely at the field around the conductor under these conditions it is as shown in Fig. 2(a)and (b). The flux lines are more on one side of the conductor than the other. These lines seem to urge the conductor to the left with a force F. As F opposes v and the applied force, mechanical energy gets absorbed in this case and the machine works as a generator. This force is due to electro magnetic interaction and is proportional to the current and the flux swept. Fig. 3(a)and (b) similarly explain the d.c.motor operation. The current carrying con- ductor reacts with the field to develop a force which urges the conductor to the right. The induced emf and the current are seen to act in opposite direction resulting in the absorption of electric energy which gets converted into the mechanical form.
In Case (iii) also the direction of the induced emf can be determined in a similar manner. However, it is going to be more complex due to the presence of transformer
