Dynamo electric machinery

Front matter

AW

ITS CONSTRUCTION, DESIGN, AND OPERATION

DIRECT CURRENT MACHINES

Preface

This book is intended to be used primarily in connection with instruction on courses of electrical engineering in institutions for technical education. It is laid out on the lines of the lectures and the instruction as given in the Polytechnic Institute of Brooklyn. It is intended equally as much for the general reader, who is seriously looking for information concerning dynamo electrical machinery of the types discussed, as well as a book of reference for engineers.

The first two chapters are devoted to a brief but logical discussion of the electrical and magnetic laws and facts upon which the operation of this class of machinery depends. Calculus methods have been employed in a few places in these chapters, but the results arrived at by use of them are in such a form that they can be utilized by the reader who is unfamiliar with the processes of the calculus.

In the chapter on design it has seemed advisable to express the flux density in lines per square centimeter. Both the square centimeter and the square inch are used in practice. The alteration of the formulas to square inch units is obviously simple.

We wish to express our thanks to the various manufacturing companies who have so courteously given information, and who have kindly loaned electrotypes of their apparatus.

Contents

CHAPTER PAGE

I. Electrical Laws and Facts i

II. Magnetic Laws and Facts . . . . 12

Chapter I. Electrical Laws And Facts

i. Mechanical Units Force is that which tends to

produce, alter, or destroy motion. The units of force are the pound and the dyne. The dyne is that force, which acting on one gram for one second, will produce a velocity of one centimeter per second.

Work is the production of motion against resistance. The units of work are the foot-pound and the erg. The foot-pound is the work done in lifting a body weighing one pound one foot vertically. The erg is the work performed by a force of one dyne in moving a body one centimeter in the direction of its acting. The joule is a larger unit much used, and is equal to io 7 ergs.

Energy is the capacity to do work. Energy is divided 'nto Kinetic energy and Potential energy. A body possesses kinetic energy in virtue of its motion, while potential energy is due to the separation or the disarrangement of attracting particles or masses. A wound up spring has potential energy because of the strained positions of the molecules, while a weight raised to a height has potential energy because of the separation of its mass from the attracting mass of the earth. The potential energy of a body is measured by the work required to put the body into its strained condition. Kinetic energy is measured by the product of the weight into the square of the velocity divided by twice the acceleration due to gravity, or

Wv 2 Kinetic Energy = .

Power is the rate of performance of work. Its units are the horse-power and the watt. A horse-power is 33,000 foot-pounds per minute. A watt is io 7 ergs per second. One horse-power is equivalent to 746 watts. The number of watts in an electrical circuit carrying a certain number of amperes of current under a pressure of a certain number of volts is expressed by the product of the amperes into the volts. If we let T equal the torque or twisting moment

and to equal the angular velocity (= where n is the

number of revolutions per minute), then the horse-power

60 o)T itmiT

33000 33000

In a belt-driven machine the torque in the shaft is equal to the difference in tension of the two sides of the belt multiplied by the radius of the pulley in feet, hence T={F-F')r.

2. Absolute and Practical Units Since distinction

must continually be made between the absolute units and the practical units, throughout this work the capital letters /, E, and R will be used for the practical units, the ampere, the volt, and the ohm, respectively, and the lowercase letters i, e, and r will stand for the absolute (C. G. S.) units of current, pressure, and resistance respectively.

The absolute unit of current is such that, when flowing through a conductor of one centimeter length, which is bent into an arc of one centimeter radius, it will exert a force of one dyne on a unit magnet pole (§ 10) placed at the center.

The absolute unit of difference of potential exists between two points when it requires the expenditure of one erg of work to move a unit quantity of electricity from one point to the other. This unit of quantity is the quantity which, in a second, passes any cross-section of a conductor in which a unit current is flowing.

The absolute unit of resistance is offered by a body when it allows a unit current to flow along it between its two terminals, when maintained at a unit difference of potential.

E.M.F., E = io 8 *.

Resistance, R = 10V.

It is convenient and rational to make a distinction between electromotive force and difference of potential. Electromotive force is produced when a conductor cuts magnetic lines of force, or when the electrodes of a primary battery are immersed in a solution. But a difference of potential may exist merely because of an electric current. Between any two points of a conductor carrying a current there is that which would send a current through an auxiliary wire connecting these points, and we call it difference of potential. If the current in the original conductor be doubled, the difference of potential between the same two points will be doubled, showing that this difference of potential exists because of the current flowing in the original conductor. The word pressure is used for either difference of potential or for E.M.F. with obvious relevancy. . k

3. Ohm's Law Ohm's law is expressed by the formula „ where / is the number of amperes flowing in an undivided circuit, E the algebraic sum of all the electromotive forces in that circuit, and R the sum of all the resistances in series in that circuit.

The form of the equation E = IR, as applied to a portion of a circuit, is much used under the name of Ohm's law. In this case, however, E is not E.M.F., but difference of potential, as explained in the last article.

If, in a house lighted by electricity, the service maintains a constant pressure of 100 volts at the mains where they enter from the street, and no lights be turned on, then at every lamp socket in the house there will be a pressure of 100 volts. If now a lamp be turned on, it will be working on less than 100 volts, because of the drop K ox fall of potential. If many lamps be turned on, a considerable drop may occur. The drop is caused by the resistance of the wires carrying the current from the place of constant potential to the place where it is used, and the volts lost have been consumed in doing useless work in heating the wires. That the drop is proportional to the current flowing is shown by a simple application of Ohm's law.

Let R be the resistance of the line, and E d the volts drop caused thereby when a current / flows. Then

E d = IR, from which it is evident that the drop varies as the current when the resistance in the line is constant.

4. Resistance of Conductors. — The resistance R of a conductor is expressed by the formula R = — -, where o- is a

constant called the resistivity, and depending upon the material and the temperature of the conductor, / is the length in centimeters, and A the cross-section in square

cms. The reciprocal of the resistivity, -, is called the conductivity of a substance.

The conductivity of copper depends on its purity, and on its physical condition, soft copper having 1.0226 times the conductivity of hard copper. Lake copper has a high conductivity because of its pureness. The same is true of electrolytic copper. This latter is now very largely used, though for a while there was a prejudice against it because it was said to be brittle. Temperature affects the resistance of metals. In pure metals the increase of resistance for a rise of i° C. is about .004 times their resistance at o° C. Various alloys of iron, nickel, and manganese have a high value for <r, and do not have so high a temperature coefficient as given above. Iron heated in contact with -copper gives a large thermal E.M.F., which militates against its alloys being used for resistances in measuring instruments.

If in the foregoing expression f or R the centimeter and square centimeter be the units of length and cross-section respectively, then the following list gives the value of o- for various metals in microhms (1 microhm = Tir ^ w ^ ohm).

Copper .... at o°C, I -594

Iron "

Steel "

18% German Silver " 30% "

9-5 13.0

A circular mil is a circle r ^ inch in diameter, and a wire one foot long and one circular mil cross-section is called a mil-foot. The resistance of a mil-foot at o° C. of

Copper = 9.59 ohms, Iron =58. ohms, Steel =82. ohms.

The American Institute of Electrical Engineers has adopted as its standard resistivity for soft copper one given by Matthiessen. A wire of standard soft copper, of uniform cross-section, of one meter length, and weighing one gram, should have a resistance of o. 141 729 international ohms at o° C. A commercial copper showing this resistivity is said to have 100 per cent conductivity. Copper is frequently found having a conductivity of 102 per cent. It is in these cases almost invariably electrolytic copper.

5. Insulating Materials. — Materials which are to be used for insulating from each other the various electrical circuits of dynamo electric machines should possess the following properties : —

They should have a high insulation resistance, and this resistance should be maintained high over the range of temperatures to be found in machines. They should furthermore have a dielectric strength sufficient to preclude any possibility of their being perforated by the voltages liable to exist between the conductors which they separate. This strength must also exist throughout all probable ranges of temperature. They must possess such physical properties as will permit of mechanical manipulation, as they must be oftentimes bent and twisted. Of course the chemical constitution should not be altered by any change of temperature to which they would be submitted.

Mica possesses the highest insulation resistance and the largest dielectric strength to be found. It requires iooo volts to perforate a sheet I mil in thickness. Its chemical constitution is unaffected by high temperatures. It is not, however, mechanically strong.

Preparations of fibrous materials with linseed oil, which, after being dried, have been thoroughly baked, are fairly good insulators. As water is generally present in their pores, their insulation resistance, upon heating, decreases until the temperature has reached ioo° C, and then it increases. These preparations are mechanically flexible. Preparations of fibrous material with shellac are good insulators, but crack upon bending.

Vulcanized fibers are made by treating paper fiber chemically, and, when dried, they have a fairly high insulation resistance, but they readily absorb moisture, and, upon drying, are liable to warp and twist. They furthermore become brittle when heated.

Sheets of insulation made up from pieces of scrap mica cemented together by linseed oil or preparations of shellac, when carefully constructed with lapped joints, exhibit nearly as good insulating and dielectric properties as sheet mica. While not perfect mechanically, these sheets permit of bending better than pure mica.

Vulcabeston, which is a preparation of asbestos and rubber, exhibits fairly good insulating and mechanical qualities, and is especially fitted for higher temperatures. Its dielectric strength is about T ^ of that of mica.

6. Divided Circuits. — If a current / be flowing through

DYNAMO ELECTRIC MACHINERY.

R, the undivided part of the circuit shown in Fig. I, and if I x and I 2 be the currents flowing in the shunt resistances R x and R 2f then / = I t + f 2 , and, since the pressure E upon each shunt is the same, by Ohm's law,

The currents in the branches of a divided circuit are inversely as the resistances of the branches.

If R e be a /single resistance, that substituted for the shunted resistances R t and R 2 will leave / unchanged, then, by Ohm's law,

The resistance equivalent to a number of shunted resistances is equal to the reciprocal of the sum of the reciprocals of the separate resistances.

Fig. 1.

7. Power of Electric Current. — A difference of potential e between two points requires e ergs of work to bring a unit quantity of electricity from one point to the other.

A unit of quantity is one absolute unit of current flowing

for one second. Hence a current i flowing for t seconds with

a difference of potential e does eit ergs of work. Likewise

a current / flowing / seconds gives // coulombs of quantity,

Eit and with a difference of potential of E volts does — ^ ergs

of work. Hence the work per second or the power is — 7

absolute units. The practical unit of power is the watt, and equals io 7 absolute units. Hence, remembering that by Ohm's law E = IR> the power of a current in

Watts = £1= PR.

For commercial currents and voltages the watt is a needlessly small expression, hence the kilowatt (= 1,000 watts) is generally used as the unit of electrical power. It is represented by the abbreviation k. w. The horse-power is equal to 746 watts, or approximately three-fourths of a k.w.

8. Heat Developed by a Current, — When a current / does work in overcoming a resistance R, the work performed is converted into heat. By the last article the work thus done per second, or the power expended, will be PR watts. Since this rate of production of heat is often of no service, this expenditure of power is generally called the PR loss.

This production of heat causes a rise of temperature in the conductor, and the temperature will continue to rise till the heat generated per second by the PR loss is exactly counterbalanced by the rate of dissipation of heat by conduction, convection, and radiation.

The necessary resistances of electrical machines involve

IO DYNAMO ELECTRIC MACHINERY.

the production of heat in their operation (as does also friction and reversal of magnetism), which causes a rise of temperature. As insulating materials can survive only moderately high temperatures, such machines must be designed to operate without becoming too hot. This is accomplished by decreasing the PR loss, by increasing the radiating surface, and by supplying ventilation.

9. Fuses. — These are devices intended to protect circuits from destruction or damage due to an excessive flow of current through them. They protect them by being themselves destroyed. They are generally made of lead or alloys of lead. Lead is liable to become oxidized after having been installed for some time. It is then liable to form a tube of hard oxide, which is sufficiently strong to hold molten lead in its interior, so as to maintain an electrical contact in the circuit which should be broken. Some alloys are not open to this objection. These alloys, in the form of wires, strips, or ribbons, are fastened at each end to copper terminals which are slotted to fit into fuse receptacles. The wire with its terminals is called a fuse link. Such a link is shown in Fig. 2.

Fig. 2.

Copper wires are sometimes used as fuses on trolley cars, but the high melting point of copper prohibits its use as a protective device on house circuits.

The current which will fuse a wire of lead alloy depends in magnitude upon the length of the wire. Short lengths

ELECTRICAL LAWS AND FACTS. II

of a wire of given cross-section and given material will carry stronger currents than longer lengths. The heat which is generated in the short ones escapes more rapidly, owing to the larger masses of metal commonly forming the terminals of the fuse. Fuses are rated to carry a given amperage, and the rating is stamped upon the copper terminals. According to the national code the fuses must, however, be able to carry indefinitely without melting such a number of amperes that the rated capacity is but 80 per cent of it. This permits the fuse to carry without melting 25 per cent above the rated capacity.

Fig. 3.

For high voltages, and for large amperages, inclosed fuses are sometimes used, in which the fusible conductor is surrounded by a packing of finely divided powder in which borax is included as an element most desirable. Such a fuse is shown in Fig. 3.

Chapter II. Magnetic Laws And Facts

io. Strength of Magnet Pole A unit magnet pole is

one which will repel an equal like pole, when at a distance of one centimeter, with a force of one dyne.

It follows from this definition that a pole m units strong will repel a like unit pole with a force of m dynes. The force exerted between two magnetic poles varies inversely as the square of the distance between them. Hence the force exerted between two magnetic poles of strengths m and w! when ^centimeters apart is defined by the equation d 2

ii. Intensity of Magnetic Field. — A magnetic field is of unit strength or intensity when a unit magnet pole placed therein is acted upon by a force of one dyne, or when a magnet pole m units strong is acted upon by a force of m dynes. The strength of a field is usually represented by 3C.

12. Magnetic Field and Lines of Force. — The space around a magnet where its action is felt is termed the field of that magnet. This field may conveniently be considered as permeated by lines of force. These lines represent the direction of the force exerted by the magnet, and by their closeness to each other show the magnitude of this force.

The student must not get the impression that, because the lines spread apart, a point in the field could be chosen where there would be no line. These lines may well be considered as tubes or pencils of force, filling all the space around the magnet.

The lines of force contained in any plane passed through the magnet pole compose a magnetic spectrum, which can be made visible by the familiar experiment of sprinkling iron filings on a paper, which is laid over a magnet, and by gently tapping it.

By convention one line of force per square centimeter is considered to represent a field of unit strength, the square centimeter being so taken that it is at all points perpendicular to the lines cutting it. Hence the strength or intensity 3C of any field can be expressed by the number of lines of force per square centimeter.

Suppose a sphere of one centimeter radius to be circumscribed about a unit magnet pole. Another unit pole at any point on the surface of this sphere will be acted upon by a force of one dyne. Hence there exists a unit field at any point on this surface. But there are 4 ?r square centimeters on this surface, and each square centimeter will be cut by one line of force. Therefore, there emanate from a unit magnet pole 4 it lines of force. Similarly a magnet pole of strength m sends out 4 it m lines of force.

A magnetic field is said to be uniform when it has the same JC at every point therein, or when the lines of force are parallel.

13. Electro-Magnetic Induction. — In 1831 Faraday and Henry independently discovered that when a conductor was moved in a magnetic field, an electromotive force was set

DYNAMO ELECTRIC MACHINERY.

up in the conductor. This phenomenon is the foundation of all modern electrical engineering.

An absolute unit of E.M.F. is produced when a conductor cuts one line of force per second. If the conductor cuts two lines in the second, or one line in half a second, then two units are produced.

If, in the short interval of time, dt seconds, d<j> lines be cut, then during that interval the value of the induced E.M.F. will be

d<f>

or,

i d<j>

E

10 dt volts.

The negative sign is used because the induced E.M.F. tends to send a current in such a direction as to demagnetize the field. When of no consequence the negative sign will hereafter be omitted.

If a conductor, Fig. 4, / centimeters long moves parallel to itself with a uniform velocity of v centimeters per second across a uniform magnetic field of strength 3C, its path making an angle a with the direction of the lines of force, then the number of lines cut per second is Wlv sin a, and since the rate of cutting is uniform, the E.M.F. at any instant is e = 3Zlv sin a.

If there be a non-uniformity in the rate of cutting lines, due either to an uneven field or an irregular motion, then

T'

Fig. 4- the average value of the induced E.M.F. associated with

the cutting of <£ lines in the time, t seconds, will be e av =— •

For suppose the time / to be divided into / equal and small periods havirg a duration of At seconds. Furthermore, suppose that during these successive periods A<£', A<£", A<£'", etc., lines be cut respectively. Then the induced E.M.F.' s during these periods, which may be represented by /, e'\ e"'> etc., respectively, will be as follows : — d

= e"

=

A*"

At

=

A<f> ,n A/

Adding these / equations, and then dividing by /, gives the equation above, viz.,

*av = j or E av = — ^ volts.

The average value of the induced E.M.F. is therefore independent of the magnitude of the instantaneous values.

If a loop of wire revolve, uniformly or otherwise, in a magnetic field which is uniform or otherwise, its sides cut lines of force at various rates. The instantaneous E.M.F. in the whole loop will be as before.

d$

e = — r > dt

where <£ is the number of lines that links with, or that passes through, the loop. If the loop be of n turns, then i6

DYNAMO ELECTRIC MACHINERY.

the pressure will be n times as great, or during the interval dt,

nd <j>

■fdt

14. Direction of Induced E.M.F. — The direction of flow of a current induced in a closed circuit by moving it in a magnetic field is best represented by drawing the conventional representation of the three dimensions of space. If the flux be directed upwards, and the motion of the conductor be to the right, then the E.M.F. will tend to send a current toward the reader. If any one of these conditions be changed it necessitates the change of one of the others, and conversely the change of any two leaves

Fig. 5*

Motion

Fig. 6.

the third unaltered. About the same idea is represented in Fleming's Rule, which is as follows : —

Let the index finger of the right hand point in the direction of the flux, and the thumb in the direction of the motion. Bend the second finger at right angles with the thumb and index finger, and it will point in the direction of the EM.F.

Another rule is : —

Stand facing a north magnetic pole. Pass a conductor downward. The current tends to flow to the left.

15. Inductance. — Nearly every electrical circuit which has a current flowing in it has lines of force linked with it, due to that current. When the circuit is opened the disappearance of the lines is accompanied by a cutting of the circuit by those lines, and the cutting results in the production of an E.M.F. This is called the E.M.F. of self-induction. Its magnitude is dependent upon the rapidity with which the field disappears, and upon a constant determined by the geometric shape of the circuit and the character of the medium in which it is placed. This constant is called the self-inductance or the coefficient of self-induction of the circuit. It is generally represented by the letter L, and is that coefficient by which the time rate of change of current in the circuit must be multiplied in order to give the E.M.F. induced in the circuit. Its absolute value is numerically represented by the number of lines of force linked with the circuit per absolute unit of current in that circuit. Its practical unit is io 9 times as large as the absolute unit, and is called the henry. In a given circuit it varies as the square of the number of turns of wire. Two circuits may exercise a mutually inductive action upon each other, and an E.M.F. may be induced in one by a change of current in the other. This is called the E.M.F. of mutual induction. In magnitude it depends upon the shape and position of the two circuits, and upon the character of medium in which they are placed. It is also dependent upon a constant which is called the mutual inductance or coefficient of mutual induction of the two circuits. It is generally represented by the letter M. It is that coefficient by which the time rate of change of the current in one of the circuits is multiplied in order to give the E.M.F. induced in the other circuit. Its absolute value is numerically equal to the number of lines of force linked with one of the circuits per absolute unit of current in the other circuit. Its practical unit is the same as the practical unit of self -inductance, that is the henry, and is io 9 times as large as the absolute unit. The coefficient of mutual induction varies directly as the number of turns of wire in either circuit.

16. Quantity of Electricity Traversing a Circuit Due to a Change of Flux Linked with it. — In many dynamo tests, and in many magnetic investigations, it is necessary to measure, generally by means of a ballistic galvanometer, the quantity of electricity traversing a circuit due to a change of flux linked with it. If the circuit have a resistance of r and in dt time the flux linked with n turns changes by dfa then the instantaneous current

nd<f> ._~dt r But the quantity, q = idt, hence

ndd>

which is independent of time. So if the flux change from <t> t to <f>.„ then or Q = -^—^ — - microcoulombs.

17. Work Performed by a Conductor Carrying a Current and Moving in a Magnetic Field. — Let a conductor carrying a constant current i be moved in a direction perpendicular to itself and to the lines of force of a magnetic field. Suppose it to move for dt seconds, and in that time to cut d<f> lines of force. Then the induced E.M.F. e will be

— -f. The quantity of electricity dq that has to traverse dt

the circuit against this E.M.F. during the time dt will be idt. Since potential is a measure of work, the work required to carry dq units of electricity against a difference of potential e is edq ergs. Hence the work in ergs,

d<b dw = edq = idt X —j- = idcf>.

Therefore the current i, in cutting <£ lines of force, performs the work

w — i$ ergs.

From this it is seen that the work done by a conductor carrying a current and cutting lines of force is independent of the time it takes to cut them.

In the above discussion, if the field be not uniform or the motiqn be not uniform, the value of e will not be the same for each instant of time. But since the result obtained is independent of time, it is immaterial how the lines are arranged, and how the rate of cutting varies.

18. Magnetic Potential. — The magnetic potential at any point is measured by the work required to bring a unit magnet pole up to that point from an infinite distance.

The difference of magnetic potential between any two points is measured by the work in ergs required to carry a unit magnet pole from one to the other. The difference of magnetic potential is a measure of the ability to send out lines of force, or to set up a magnetic field.

19. Magnetomotive Force of a Circular Circuit Carrying a Current. — A thin circular conductor carrying a current forms a magnetic shell. If a unit magnet pole be taken from the top side of a shell, and carried around to

the bottom side, work must be done, and this work is a measure / ^ \ ^ of the difference of potential be-

tween the two sides of the shell.

It is immaterial whether the ^K^. /' pole be carried from one side of

%^-j^ the shell to the other, or the

Fig. 7.

shell be turned bottom side up around the pole. In the latter case it is clear that all the lines emanating from the pole will be cut once, and once only, by the conductor, wherefore 4?r lines will have been cut.

If current i flows in the conductor, then, by § 17,

Work in ergs i<f> = 4 tt/.

If there be n turns of the conductor, each line of force will be cut ;/ times, and the work will be ^irni ergs.