(^mmll Winivmit^ p itotg BOUGHT WITH THE INCOME | PROM THE SAGE ENDOWMENT FUND THE GIFT OF SHetirs m. S^ge 189X iy//-^j fS....6.A.kz.^. Cornell University Library arV17293 A^lxt-book on electrcKmag^^^^^^^ 3 1924 031 231 875 olin,anx Cornell University Library The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031231875 Vol. I. ELECTRO-MAGNETISM CONSTRUCTION OF CONTINUOUS CURRENT DYNAMOS. .^^im A TEXT-BOOK ELECTRO-MAGNETISM CONSTRUCTION OF DYNAMOS. Vol. I. BY DUGALD C. JACKSON, B.S„ C.E. Professor of Electrical Engineering in the University of Wisconsin; Member of the American Society of Mechanical Engineers, American Institute of Electrical Engineers, Etc. MACMILLAN AND CO. AND LONDON 1893 All rights reserved Copyright, 1893, By MACMILLAN AND CO. NottoDoU ?5rt3a : J. S. Cushing & Co. — Berwick & Smith. Boston, Mass., U.S.A. PREFACE. This book has been developed from the lectures which the writer has presented to his classes in dynamo construction. No special originality is claimed for the matter presented except in certain details ; but it is hoped that the logical arrangement, and the omission of all unnecessary details, will make the book of so con- venient a form as to lead to its general endorsement as a satisfactory text and reference book. Since the primary object in publishing the book is to supply a satisfactory text-book to be used as the basis of instruc- tion to college classes, certain of the fundamental principles may possibly be more fully presented than would be desirable in a mere reference book. With the same point in view, no cuts or descriptions of typical dynamos are placed in the pages. The student is expected to gain a familiarity with the different com- mercial machines in his work in the college laboratories, and to add to the familiarity by inspection tours made under proper direction. The present volume does not touch upon alternating current machinery nor series arc lighting machinery, vi PREFACE. but in the near future a second volume will be issued treating of these. The time has not yet come when a proper history of the development of the American dynamo can be written ; therefore this book does not touch upon the historical side of the subject. As most of the literature of the subject is of transatlantic origin, comparatively few references can be made to American writers. On the other hand, the book treats the subject from the American standpoint and represents present American practice. It is impossible to mention all the sources from which information has been drawn, but the writer is specially indebted to Professor Merritt's Notes on Dynamo Elec- tric Machinery ; Kapp's Dynamos, Alternators, and Trans- formers ; Thompson's Lectm'es on the Electro-magnet ; Ewing's Magnetic Induction in Iron and Other Metals ; papers by Dr. John Hopkinson and other well-known writers ; and the designers of many of the best Ameri- can machines. Acknowledgment is also due Professor J. P. Jackson of the Pennsylvania State College for his kindness in reading proof. Sept. I, 1893. CONTENTS. Chapter Page I. Primary Definitions and Evaluations .... i II. Simple Electro-Magnets 20 III. The Magnetic Properties of Iron 35 IV. Establishment of Electric Pressures .... 76 V. The Magnetic Circuit of the Dynamo . . . 122 VI. Compensation for Cross-Turns, and the Effect OF Brush Contact 171 VII. Characteristic Curves, and Regulation . . . 195 VIII. Efficiencies 244 IX. Multipolar Dynamos 271 Index 283 vii ELECTRO-MAGNETISM. CHAPTER I. PRIMARY DEFINITIONS AND EVALUATIONS. A Magnetic Field is any space within which a magnet pole is acted upon by magnetic forces. The Strength of Field, at any point in a magnetic field, is measured by the force in dynes exerted upon a unit magnet pole placed at the point. Strength of field is usually represented by the capital letter H. Since force is the rate of change of potential, H evi- dently represents the difference of magnetic potential per unit length. Difference of magnetic potential is frequently called Magneto-Motive Force, or Magnetic Pressure (analogies, the terms electro-motive force, or electric pressure, which are used to designate difference of electric potential). A Unit Magnet Pole is one which acts with a force of one dyne upon an equal pole placed at a distance of one centimeter. A Magnetic Field of Unit Strength is one within which a unit pole experiences a force of one dyne. The total strength of a magnetic field may be conven- iently conceived as the resultant of many unit forces, 2 ELECTRO-MAGNETISM. each of which has its individual Hne of action. These lines of action are called Lines of Force, and the field of unit strength may be defined as having one line of force per square centimeter. Since a unit pole exerts a force of one dyne upon an equal pole placed at one centimeter distance, there is unit field at the latter point. A sphere of one centimeter radius has a sur- face of 47r square centimeters, whence, from the second definition of unit field, 477 lines of force must emanate from a unit pole. The conception of lines of force is very useful and should be thoroughly grasped ; it must always be remembered however that such lines have not a mate- rial existence, but are merely hypothetical. It is evident that a line of force must always join two points of different potentials, and that two lines of force can never intersect. The positive direction along a line of force is from high potential to low potential^ in which direction a free north pole tends to move. When the lines of force in a magnetic field are parallel and of equal number per square centimeter, a magnet pole will experience-the same force at all points of the field, and the field is said to be Uniform. If, as shown above, 4 tt lines of force emanate from a unit pole, it is evident that 4 -Kin lines of force must emanate from a pole of strength m. If, instead of being a mathematical point, the magnet pole of strength m be a sphere of one centimeter radius, m lines of force must emerge per square centimeter of surface. If the radius be r, the number of lines of force per square PRIMARY DEFINITIONS AND EVALUATIONS. 3 centimeter is ^ '"" „ = — ■ A free spherical magnet pole is a physical impossibility, as each pole must be attached by magnetic material to another pole of equal strength but of opposite sign, and the lines of force which emerge from one pole end in the other. However, the definitions given may be applied equally to the physical pole. Suppose that the polar end of an ordi- nary magnet be flat, with an area of A square centi- meters, and pole strength ;« ; then the total number of lines of force emerging from the pole is 4 7r;«, and the number of lines per square centimeter of pole sur- face IS A The ratio — is called Intensity of Magnetization, and A is usually represented by the capital letter /. The magnetic moment of a magnet is ml (where / is the length of the magnet) and the volume of the magnet is Al. It is therefore evident that »«_ Magnetic Moment A Volume and the intensity of magnetization can be defined as the magnetic moment per unit volume. This defini- tion served a very useful purpose in the hands of the early mathematicians, but a more useful definition for practical service is, strength of pole per unit of polar area. From the definition of f it is seen that the strength of field very close to a magnet pole is 4 ttI, ( = ^ "^^ ) , and the total number of lines of force -ATI' emerging from the pole is 4'irIA, { = 4'inn). 4 ELECTRO-MAGNETISM. If a piece of magnetic material be placed in a mag- netic field of strength H, it increases the number of lines of force at the point by acquiring an intensity of magnetization /, which depends upon the magnetic quality of the material. The ratio — in any case is called the Susceptibility of the material and is rep- resented by Greek k. k = -- The susceptibility of iron, H nickel, cobalt, and possibly other less known metals, is very large, and is a function of /. For air and nearly all other materials, whether metal or otherwise, it is zero or a very small negative fraction. With the exception of the magnetic metals named, it can be practically considered as zero for all materials and for a vacuum. The total number of lines of force per square centi- meter, which are induced in and emanate from the poles of a piece of magnetic metal (iron for instance), when placed in a magnetic field, equals H+z^ttI. The first term is the strength of the field (lines of force per square centimeter) before the iron was placed within it, and 47r/ is the increase close to the poles due to the presence of the metal. The introduction of iron in the field some- times changes the numerical value of H, but the general statement remains unaltered. Each one of the H^/^irl lines of force which emerge from or come to the poles can be considered as passing through the iron from south pole to north pole, thus making closed curves with the lines of force which pass from north pole to south pole out- side of the iron. Within the iron these lines are often called by physicists Lines of Magnetization or Lines of Induction ; but the distinction is not necessary or useful PRIMARY DEFINITIONS AND EVALUATIONS. 5 in the practical applications. We will therefore con- sider a line of force as a closed curve which passes from the north to the south pole outside of a magnet, and continues from the south pole to the north pole within the material of the magnet, as shown in Fig. i. CZZZZ D Fig. 1. From what has preceded, it is evident that the total number of lines of force per square centimeter within a magnet is H+^irl. This is usually called the Induc- tion, and is designated by the capital letter B. Hence, B — H^-^-kI. \BdA is usually called the Total Mag- netization, or Total Induction, and is frequently desig- nated by the capital letter N. When B is uniform over the area A, we have N=BA =HA +47r/A =HA +4mn. Since 1=kII, we have B = H^-4'n-KH=H{l +47r«;.). Since a; is a function of / for all magnetic metals, as already stated, therefore i ^-a^itk. is a function of B. I + 4'n-K is called the Magnetic Permeability* of the metal, and is designated by Greek /j,. Thus, /j.= i +4'7rK, whence B = fj.II. * The word permeability was first suggested by Lord Kelvin to repre- sent the mathematical conception of what may be called specific magnetic conductivity, which is in reality the ratio of B to //. 6 ELECTRO-MAGNETISM. For air, and other non-magnetic materials, k is practi- cally equal to zero, and therefore /a=i. Permeability is equivalent to specific "magnetic conductivity"; that is, the permeability of a metal is the same as the mag- netic conductivity of a piece one centimeter in length and one square centimeter in cross-section. Hence, if the value of /n, the summation of H, (= J Hdl), and the length, /, of any magnetic circuit making a complete or nearly complete ring, are known, the induction is given by the formula \Hdl is the total magnetizing force, or magnetic pres- sure, in the circuit, and is often designated by the capital letter M. When B is uniform over an area. A, we have . N=BA = tlEM. We have here a fundamental law of the magnetic cir- cuit that for practical purposes is entirely analagous to Ohm's law for electiic circuits, which is usually represented by the formula C= — If R be replaced in the latter expression by --, the reciprocal of conduc- tivity, we have C=KE. Again, if k be used to repre- sent specific electrical conductivity, the expression becomes ., C=—E, which is exactly similar to the expression for N. As a matter of convenience, the total magnetizing force M may be called Magneto-Motive Force, or Magnetic Pressure PRIMARY DEFINITIONS AND EVALUATIONS. 7 (analogies, electro^motive force, or electric pressure).* The total magnetization N may also be called Magnetic Flux, or Flow (analogy, electric flux, or current). The expression of Ohm's law for the electric circuit, and its counterpart for the magnetic circuit, thus becomes sim- ilar to the expression for the flow of water, gas, etc., through pipes, where the flow in cubic feet per second equals the pressure divided by the resistance to motion, P . ^ =— . The resistance in this case is usually due to F skin friction, and is a function of the velocity of flow ; hence it is not strictly analogous to electric or magnetic resistance, but this does not vitiate the similarity of the general expressions. Another analogy is the stretch of material when under strain. The stretch is equal to the applied stress divided by the elastic force resisting deformation. From the analogies it may be seen that the law of Ohm is a special statement of the results of ordinary observation, and it may be generalized thus : a result is equal to the effort put forth divided by the opposing resistance or opposition. It is advantageous in many cases to use terms signi- fying magnetic resistance instead of magnetic conduc- tivity, and it is convenient to designate the reciprocal of yu. by Greek p. The expression for N then becomes A N= — M, where p represents specific magnetic resistance, Ip and -^ is the actual magnetic resistance of a body / in length and A in cross-section. Magnetic resistance is usually called Reluctance, and may be designated by P. * Compare page I. ELECTRO-MAGNETISM, The ordinary electric and magnetic circuits differ materially in two properties. Thus, a conductor carry- ing an electric current can be readily insulated by various materials, including dry air. On the other hand, as already stated, the magnetic permeability of all non-magnetic materials is practically unity, and, there- fore, thorough magnetic insulation cannot be effected. This leads to the analogy of an electric battery immersed in sea-water, which was first pointed out by Faraday. It is evident that when a battery with attached wires is immersed in sea-water, or other poorly conducting liquid, much of the current will follow the wires through their resistance R, while some of the current will pass through the liquid between the battery poles, as shown by the dotted lines in Fig. 2. The currents passing by the two paths are inversely as the respective resistances. The case of the magnetic circuit is represented by Fig 3, which is an iron ring with a narrow break at R, and a magnetizing coil at C. Many of the lines of force set up in the ring follow the iron all the way and jump the break at R, ^<^ ' \ - — ! ofRi ZZJ Fig- 2. Fig. 3. while others jump across between the magnet limbs or pass directly around the coil. As in the electric PRIMARY DEFINITIONS AND EVALUATIONS. g circuit, tlie total induction in each path is inversely proportional to the reluctance of the path. Thus M M N, = -^ and N^ = ~, where N„ N,, P^ and P, are the total inductions and reluctances through the gap and air respectively. The second essential difference between electric and magnetic circuits is the variation of /x with B for mag- netic metals, while the electric resistance of metals is unchanged by the flow of a current, provided the temperature is not changed. As already stated, /tt is practically constant for all non-magnetic materials, while its variation in magnetic metals is fairly analogous to the change of electric resistance in a circuit which carries an electric current sufficiently large to heat it. In this case the resistance is a more or less complex function of the current. The following rather unsatisfactory representation of the. magnetic field is quoted from Practical Electrical Engineering : "Imagine a magnet represented by a tube, in the centre of which is a screw pump, and let the tube be immersed in water whilst the pump is rotated. The water will issue at one end, flow in curved stream lines and varying velocities about the tube, and enter it again at the other end. The unit exploring pole we replace by a disc of unit surface, which we place in various positions within the space surrounding the tube, an^- thus measure the force of the stream at any point. This analogy is imperfect, because the force exerted by the water varies not as the velocity, but as the square of the velocity. Assuming, however, that the lO ELECTRO-MAGNETISM. former be the case, then such a model can in a some- what crude fashion be made to represent the magnetic field. We may think of the lines of force, not as a definite number of fixed lines threading through the space which separates the two poles of the magnet, but as the stream lines of a kind of magnetic fluid circulating through this space. Near the poles of the magnet the stream is contracted, and the velocity is therefore great. In these places the force of impact of the magnetic fluid upon the exploring pole is a maxi- mum, whilst farther away from the poles where the velocity, consequent upon the expansion of the stream, is less, the force of impact is also less. In this manner can be explained the variation of magnetic force as we move the exploring pole into different parts of the field, and the fact that a magnetic field taken by itself represents a definite amount of stored-up en- ergy." Returning to the ana- logue of a voltaic cell in salt water, the idea of stream lines may be carried farther. Let Zn, Cu, in the figure, represent a cell which has its circuit closed only by the surrounding water ; then the current flowing be- tween the poles of the cell will be distributed in stream lines through the water. These electric stream lines, or lines of flow, can be represented, as in Fig. 4, by lines drawn so that they show the direction of flow (or force) Fig. 4. PRIMARY DEFINITIONS AND EVALUATIONS. n at every point, and by their number indicate the density of the flow or current. The lines thus drawn are similar in form to the liquid stream lines of the mechanical mag- net explained above. They are also exactly similar to the lines of force due to a physical magnet of the same size and shape as the Zn-Cu element. If a good con- ductor, such as a copper rod, be placed at some point, as A, the current will flow through it by preference on account of its higher conductivity, and the stream lines will be deflected. In the same way, a piece of iron in a magnetic field will apparently gather to itself the lines of force, on account of the greater conductivity of the path through it. The close analogy between electric and magnetic cir- cuits is quite useful in understanding the phenomena of the latter, but, as already explained, it is essential that the fundamental differences be carefully remembered. It is also necessary to remember that a magnetic flux cannot be actually treated as a flow of something mate- rial, as is usual in the case of the electric current, because there is nothing in the magnetic circuit analo- gous to the loss of energy caused by friction in a mechanical model, or by the C^R loss when an electric current flows through a resistance. A magnetic field once set up requires no energy to maintain it. It is proved in Thompson's Electricity and Magnetism, Art. 318, etc., that the potential at any point due to a closed electric circuit or magnetic shell, is equal numeri- cally to the product of current strength, turns of the circuit, and the solid angle subtended by the circuit at the point. That is, V=ncw, F being potential, c cur- 12 ELECTRO-M AGNETI SM. rent, « turns, and w solid angle. If the point be taken very close to the plane of the circuit, as in Fig. 5, w becomes 2 tt on one side and — 2 tt on the other side of the plane. Hence the potential changes by 4Trnc in passing from one side of the plane to the other, and therefore 4'7rnc ergs of work must be done in moving a ^'^' ^' unit pole around the circuit from one point to the other. Thus W=4Trnc, where W= work in ergs. If c be used to represent cur- rent in amperes instead of in absolute units, the work becomes W= 4lEIL^ since the ampere is -^-^ the absolute unit of current. As work is equal to force x distance, there follows, W= CHcII, and hence Itt^^ Cjj^i A cylindrical solenoid composed of a uniform layer of wire may be considered as made up of many exceed- ingly thin plane circuits, each acting as a magnetic shell. The force exerted upon a unit pole at a point, such as P in Fig. 6, within the solenoid and between two of the shells, must be the resultant effect due to one side of each of four shells, — the two immediately adjacent to the point, and the two end shells. All other magnetic effects are neutralized by the abutting faces of the various shells. By Thompson's Electricity and Magnetism, Art. 253, it is shown that the force at any point due to an attracting plate is W(t, where w PRIMARY DEFINITIONS AND EVALUATIONS. 13 is the solid angle which the plate subtends at the point, and o- is the density of the attracting matter per unit area of the plate. For a plate with an electric charge, o- signifies the charge per unit area, and in the case of one side of a magnetic shell, a is the magnetic intensity, equal to -•* Since w = 2'jr for the adjacent shells, 10/ ' one of these attracts the unit pole with a force which is parallel to the axis of the solenoid, and equal to ?-2!^ 10/ dynes, while the other shell repels the pole with an equal Fig. 6. force. These two forces are in the same direction, hence the total force on the unit pole due to the adjacent shell faces is - — - dynes. The end shells each exert a force 10/ 1701 ^/* 'Tpt /7/" on the unit pole respectively of — i— and — ? — , one being attraction and the other repulsion. The forces from the end shells are concordant, and their joint effect is there- fore — 1 — + — 2 — , which is opposite in direction to the 10/ 10/ force exerted by the adjacent shells. The total force exerted on a unit pole within the solenoid is thus * Where n is the total number of turns of wire on the solenoid, / is its length, and - can therefore be taken as the number of turns on each shell. 14 ELECTRO-MAGNETISM. dynes. ^^^irnc 10/ w^ic w^fic lol 10/ If the solenoid has an indefinitely great length on either side of the point, w-^ and w^ are zero, and the force becomes ^ = 4^ dynes, and it is uniform 10/ throughout the solenoid. Whence, the work required to carry a unit pole around a path linking the solenoid, is W= CHdl=Hl=^^^^ &rgs. If the solenoid be of finite length, there is no method of exactly measuring the solid angles Wj and w^ unless the point be taken on the axis. In the latter case, if ttj and a^ be the angles subtended at the point by the radii of the end faces, we have by geometry Wi = 2 7r(i— cosa^) and W2=2 7r(i— costtg), whence H = (cos a^ + cos a^ dynes, and H is not uniform. The latter fact makes it impossible to directly compute the work, (= \Hdl),re- quired to carry a unit pole around a path linking the solenoid, but an approximation of considerable exactness can be made in many cases. When the point is taken at the centre of the solenoid, cosa^ + cosaj becomes 2cosa, and cosa=— , D I being the length of the solenoid and D the diagonal. PRIMARY DEFINITIONS AND EVALUATIONS. 15 In any solenoid, H becomes practically uniform and equal to H=^^ — dynes, with an error not exceed- 10/ ing about I'^o '^^ three diameters distant from either end. Hence the work required to carry a unit pole around a path linking any solenoid of greater length than six diameters is approximately W=HI=^^^^— ergs, 10 and // at the middle cross-section is ^^ — dynes. 10/ In the case of a solenoid bent around in the shape of a ring, the end faces neutralize each other, and H = - — - dynes, where / is the length of a circle con- 10/ centric with the ring, and in which the reference point is taken. Since / is different for circles of different radii within the ring, it is evident that H will have dif- ferent numerical values for each point upon any radial line. As the value of / is the least at the inner edge of the ring, H is there the greatest. The work done in carrying a unit pole through the solenoid is, as before, W= Hl= ^ ^^'^ ergs, and is therefore the same for all 10 circles. It is evident that only the end faces of a solenoid affect the potential at any outside point. From the preceding proofs, it is readily seen that the force upon a unit pole outside a solenoid is T7T"'"7^ dynes, in the case of a ring, there are no end faces, and no out- side force is exerted. In each case, it is to be noted that - is equal to the number of turns of wire on the solenoid per centimeter l6 ELECTRO-MAGNETISM. of length, and it might be written j=t, whence for long solenoids J7=4^dynes. lO Returning to the closed electric circuit in-one plane, as given on page ii, the po- /'T^r — 255^ tential V, at any point out- I '"i 1 ^"^T--^-, side of the shell, is ^?^. If I ' — X 9 10 Y J the circuit be in the form of a circle with radius r, and the point be on the axis at a distance x from the plane of the circuit, as in Fig. 7, w becomes 2 7r(l— cosa) = 2 7r( I ^ \ Fig. 7. whence V= 2'jrnc (.. 10 V V^+;l^/ Since force is the rate of change of potential, „ dv* Znri^nc , H= — — = dynes, the current being given in amperes. When the point is at the centre of the circle, x=o, and //= 10 r When such a coil, with a magnetic needle at its cen- tre, is placed with its plane parallel to the magnetic meridian, it becomes a single-coil tangent galvanometer. * The negative sign is used here because force is exerted from high potential to low potential. PRIMARY DEFINITIONS AND EVALUATIONS. 17 The couple exerted by the coil upon the needle is evidently Im cos 6 dynes, where Im is the magnetic moment of the needle, and Q is the angle of deflection measured from the plane of the coil. The earth's mag- netism exerts on the needle a couple of H^lm sin Q dynes, which balances that of the coil when the needle is at rest. Hence 2,'irnc Im cos Q = H.lm sin Q, lor ' ' and therefore \oH.r . a c= — tanp, where c is in amperes. — ^^ is usually called the prin- cipal constant of the galvanometer, and is often desig- nated by G, when the formula is written c=HJG tan Q. A more reliable form of the tangent galvanometer is made with two parallel coils of equal diameter, separated a distance 2x, which is about equal to the radius. The needle is centred upon the common axis midway be- tween the planes of the coils. In this case the force exerted by the two coils upon the deflected needle is '^'"" ^'^ ^ Im cos Q dynes. The earth exerts a force, as before, of HJm sin^ dynes ; i^irr^nc im cos Q = Him sin Q whence and io(;p2 + ^)| __ ioHix'^ + i^^ tang. 1 8 ELECTRO-MAGNETISM. When X equals exactly ^ r, this becomes c=- — — tan Q. These formulas are ordinarily used when currents are measured by the tangent galvanometer, but when ex- tremely refined measurements are to be effected, cer- tain corrections are necessary on account of the finite dimensions of the needle, coils, etc. These, however, need not be considered here. The previous discussion shows that each face of one of the elementary slices or shells of a long solenoid is equivalent to ^!^A unit poles, and that each unit pole in a face has exerted upon it a force of 2 7r-^ 10/ dynes by the shell faces upon each side of it. The total attractive force exerted upon a shell face is, therefore, 2^JE-^2^A =2^(-^Xa dynes. 10/ 10/ \io/y But 2.r^Y^=^. jo// Within a solenoid which has no magnetic core, H= B, hence the force between opposing faces is ^^ dynes. This force acts as though there were a tension alon^ the lines of force equal to _— dynes per square centi- OTT meter. Where B is not uniform over the area A, the i^B^dA force becomes -1—- dynes. The existence of this OTT tension was mathematically demonstrated by Maxwell {vide Electricity and Magnetism, Vol. 2, Art. 642), PRIMARY DEFINITIONS AND EVALUATIONS. 19 and the law was experimentally proved by Bosanquet (;vide Phil. Mag., Dec. 1886, and London Electrician, Vol. 18, p. 83). The evaluation of the tension can also be made by analogy from Thompson's Electric- ity and Magnetism, Art. 261, where the attraction between two charged plates is shown to be — r — 772 D Stt But — , by the analogy between electro-static and electro-magnetic phenomena, can be considered equiva- M^ lent to =B^. Hence the force between the plates is equivalent to dynes. The tension along lines of force is made manifest only where they pass from one material into another of considerably different permea- bility, and the theorem is therefore valuable in calculat- ing the force with which an electro-magnet attracts its keeper. The formula is strictly exact only when the distance between the surfaces of magnet and keeper is small compared to their area, but it can be used with a fair degree of approximation in many useful problems. From an inspection of the formula C&dA F^-^ it is evident that F may be increased by causing an uneven distribution of the induction over the area A, provided- <»>^*^'~ N= CBdA=BA be kept of the same numerical value. 20 ELECTRO-MAGNETISM. CHAPTER II. SIMPLE ELECTRO-MAGNETS. Surround a bar of iron by a coil of wire, through which an electric current flows, and the bar is magni- tized. The arrangement of coil and bar (core) is called an Electro-Magnet, thus distinguishing it from the ordi- nary permanently magnetized steel bars, or Permanent Magnets. The magnetic properties of the electric cur- rent were first announced as recently as 1820, when Oersted published his investigations. Oersted's an- nouncement led to a series of researches by Ampere, Arago, Faraday, Barlow, and their contemporaries (including Joseph Henry of Princeton College), which resulted in many valuable discoveries. Among* the investigators was William Sturgeon, whom we have to thank for the invaluable discovery, made in 1825, that a bar of soft iron becomes magnetic when placed within a solenoid carrying an electric current, and that its mag- netism is lost upon breaking the current. Many electro- magnets were soon made and their effects were carefully studied by enthusiastic physicists, notwithstanding the difficulties to be overcome. At that day the laws of electric circuits were unknown, the common insulated wire of to-day was not made, and the manufacture of an electro-magnet was a matter of much labor. Moreover, SIMPLE ELECTRO-MAGNETS. 2 1 the only sources of current were, at first, plain zinc- copper cells, and later. Grove, Daniel, or similar types of galvanic cells. By the year 1845, the investigators had the great task set before them well in hand, and, overcoming their lack of experimental facilities, had mapped out the laws of magnetic circuits very much as we know them at the present time. This work may be said to have been completed by that marvellous scientist and engineer Joule, who gave his attention to electro-magnetic experiments between the years 1839 and 1850. During later years the mathematical and experimental work of Maxwell, Rowland, Bosanquet, Hopkinson, Kapp, and many others, has expanded and applied the vaguely understood results of the earlier investigators. (Consult Thompson's Electro-Magnets; Enclyclopedia Britannica, Arts. " Electricity," " Elec- tro-Magnetism," and "Magnetism.") It is now well to consider what occurs in a core when it is magnetized. The earliest theories which offered fairly complete explanations of the various phenomena of magnetism were those of Coulomb and Poisson ; these were published before the discovery of the electro-magnet. They were followed by a host of theories which return more or less satisfactory results when put to the test of experiment. Since divided magnets always show two poles on each portion, however minute the division, the molecular nature of magnetism may be considered proven. It is therefore necessary for the theories to be founded upon some basis of molecular polarity, and the physical phenomena resulting therefrom. The theory of Coulomb (about 22 ELECTRO-MAGNETISM. 1785), which was extended and used by Poisson (about 1 821), regarded all molecules as containing equal parts of two magnetic fluids (one "Austral," the other "Boreal"). When under the influence of a magnetic field, the fluids were supposed to separate and occupy opposite halves of the molecules. This hypothesis had many faults and was soon replaced by Ampere's theory (about 1830), (vide Maxwell's Electricity arid Magnetism, Pt. 3, Chaps. 4, 6). In Ampere's theory, each molecule of magnetic material is supposed to be magnetized by an electric current which flows around it. When a bar of magnetic material is not polarized {i.e. is in the neutral state), the molecules are supposed to be arranged hap- hazard, but in such order as to neutralize each other's external effects. When the material is placed in a mag- netic field, the molecules are swung around until their axes are parallel and their like poles are all pointing one way. In regard to this idea. Maxwell says : " If it should ever be experimentally proved that the tem- porary magnetization of any substance first increases, and then diminishes, as the magnetizing force is contin- ually increased, the evidence of the existence of these molecular currents would, I think, be raised almost to the rank of a demonstration." {Electricity artd Magne- tism, Vol. 2, p. 436.) Ewing has shown that the inten- sity of magnetization of iron increases towards a definite maximum, but does not tend to decrease, within the limit of magnetizing powers practically attainable. Therefore the existence of electric currents circulating around the molecules seems to be doubtful. A theory that seems to more nearly approximate the true condition of the SIMPLE ELECTRO-MAGNETS. 23 molecules, was first advanced by Weber (about 1852), and was used by Maxwell in his mathematical investiga- tions. In it, the molecules of magnetic matter are sup- posed to be polarized as an inherent attribute, exactly as gravitation is believed to be inherent in the molecules. That the theory can be made to cover quite satisfac- torily most of the common experimental phenomena of magnetization has been shown by Hughes {vide Proc. Roy. Soc, 1883, ^viA Jour. Soc. Tel. Eng., 1883, p. 374) and by Ewing {^ide Magnetic Induction in Iron and Other Metals). Hughes states the fundamental conclusions of the theory as follows : 1. "That each molecule of a piece of iron, steel, or other magnetic material is a separate and independent magnet, having its two poles and distribution of mag- netic polarity exactly the same as its total evident magnetism when noticed upon a steel bar magnet. 2. "That each molecule, or its polarity, can be rotated in either direction upon its axis by torsion, stress, or by physical forces such as magnetism or elec- tricity. 3. " That the inherent polarity or magnetism of each molecule is a constant quantity like gravity ; that it can neither be augmented nor destroyed. 4. "That when we have external neutrality, or no apparent magnetism, the molecules, or their polarities, arrange themselves so as to satisfy their mutual attrac- tion by the shortest path, and thus form a complete closed circuit of attraction. 5. "That when magnetism becomes evident, the 24 ELECTRO-MAGNETISM. molecules, or their polarities, have all rotated symmet- rically in a given direction, producing a north pole if rotated in that direction as regards the piece of steel, or a south pole if rotated in the opposite direction. Also, that in evident magnetism we have still a sym- metrical arrangement, but one whose circles of attrac- tion are not completed except through an external armature joining both poles. 6. " That we have permanent magnetism when rigid- ity, as in tempered steel, retains them in a given direction, and transient magnetism whenever the mole- cules rotate in comparative freedom, as in soft iron." Granting the hypothesis of Weber, that the molecules are inherently magnets, it is evident that the smallest magnetizing force will swing them all completely around so that their axes are parallel if they are perfectly free to turn. Thus the slightest magnetizing force will develop the highest degree of magnetization. It is a fact, however, that magnetization goes on progres- sively with an increasing magnetizing force, which proves the existence of some force opposing the rotation of the molecules. Weber assumed such a controlling force to exist. Wiedemann and Hughes considered the mole- cules to be retarded in rotation by a sort of frictional resistance, and the latter regarded the resistance be- tween certain narrow limits of rotation as smaller than for large angles of rotation. Weber's conception of a controlling resistance required considerable modification by Maxwell before it covered many of the phenomena of magnetization. The frictional theory served an excellent purpose, but it also could not account for SIMPLE ELECTRO-MAGNETS. 25 certain phenomena. Professor Ewing (about 1890) there- fore replaced the frictional controlling resistance by the mutual reactions of the molecular magnets, and thus- succeeded in explaining virtually all magnetic phe- nomena. He even succeeded in reproducing most of the important phenomena of magnetization by means of a mechanical model composed of many little magnetic needles (representing molecules) set at regular intervals upon a board. The variation in Retentiveness and Coercive Force of different specimens is explained by differences in the grouping of the molecules and in their distances apart. (Compare Ewing, Magnetic In- duction in Iron, etc., Chap. II.) When a piece of magnetic material is magnetized, and the magnetizing force is then withdrawn, the mag- netization of the material does not wholly disappear, but a certain degree of magnetization remains. This is called Residual Magnetism, and its magnitude is a meas- ure of the Retentiveness of the test piece. Residual magnetism is held by different materials with various degrees of stability. In hard steel a large amount of knocking around may be required to materially reduce it, while the least jar will completely destroy it in soft iron. The force which holds the residual magnetism is called Coercive Force and is measured by the strength of the reverse field that is required to exactly remove all magnetization. The softest iron has the greatest retentiveness and the least coercive force, while hard steel with a smaller retentiveness has a very great coercive force. When the coercive force is great, the residual magnetism is called Permanent Magnetism. 26 ELECTRO-MAGNETISM. ^WINDINGS Fig. 8. The magnetism of the molecules has been verified by electro-depositing iron in a weak magnetic field. The iron thus deposite'd shows a considerably larger magnetic moment than would ordina- rily be induced in it by a field of the same strength, making it probable that the molecules were swung into line, while separated from each other under the influ- ence of the electric current. Sylvanus P. Thompson classified the various types of electro-magnets according to their form as follows : 1. Bar magnet. 2. Horseshoe magnet. 3. Ironclad magnet. 4. Coil and plunger. 5. Special forms. The first, second, and fourth types are very common. The first (Fig. 8) consists of a straight bar of iron sur- J-Myyi^^M ■^ARMATURE Fig. 9. A, horseshoe with winding all over, core of one piece ; B, horseshoe with winding on both legs, core of three pieces; C, horseshoe with winding on keeper, core of three pieces. SIMPLE ELECTRO-MAGNETS. 27 rounded by a coil or winding of insulated wire. In the second form (Fig. 9) the iron bar or core is in the form of a' horseshoe. It may be in one piece or be made up of several, properly fastened together. The winding ^ Fig. 10. I i Fig. 11. may cover the entire core, or only a part of it. When the winding is upon only one leg, as in Fig. 10, the magnet is called club-footed. The third form (Fig. 11) is really a modification of the second, in which one leg is divided and is arranged to magnetically and mechanically protect the windings. The fourth type (Fig. 12) is a simple coil without a core, into which a core may be sucked by magnetic action. This is sometimes made in the form of a modi- fied ironclad magnet like a, Fig. 12. Simple electro-magnets are used for a large variety of purposes in various electrical manufactures. Examples : Coil and plunger, or horseshoe attracting armature in arc lamps ; horseshoe attracting armature in telegraph p. i 1 — i J J — i Fig. 12. 28 ELECTRO-MAGNETISM. sounders and electric bells ; bar magnet attracting disc in telephone receivers ; horseshoe supporting load from attached armature ; ironclad magnet in magnetic brake ; and many others. The design for an electro-magnet to be used for most of these purposes is based upon the experience and "eye" of the designer. Thus, the con- ditions under which a telegraph sounder or relay is worked do not permit of exactly determining the total induction necessary to attract the keeper, and the size of the cores, or number of magnetizing turns, cannot be determined from the laws of magnetic circuits. Experi- ence must be relied upon to determine what style of instrument is adapted to each class of work, but the laws of magnetic circuits can be used as a valuable aid in directing improvements {yide " Modern American Telegraph Apparatus," Electrical Engineer, 1892). In the case of a horseshoe magnet of considerable size which is to be used to give a fixed lifting or pulling power, the minimum dimensions can be at once deter- mined from the magnetic laws, and the field magnets of dynamos are now invariably designed in accordance with the laws of magnetic circuits. In every case, the laws may serve an excellent purpose in directing the judgment of the designer. Formerly the lifting power of a magnet was based upon its weight, though it was known that small magnets would support a greater proportional load than larger ones. As early as 1758 Bernouill6 proposed a formula for the lifting power of magnets of similar form as follows : F=A W^, SIMPLE ELECTRO-MAGNETS. 29 where F is the pounds of load supported, W the weight of the magnet in pounds, and A a numerical coefficient, the value of which depends upon the quality of the magnet. This is usually known as Haecker's rule, in honor of the man from whose experiments the rule was deduced. The true formula for the lifting power of a magnet, which has already been developed, is Stt This may be written F=bA, where ^ is a numerical coefficient, the value of which depends upon the quality of the magnet {i.e. the induc- tion per square centimeter). In magnets of similar form, the polar surface A is evidently proportional to 2 W^, whence we have FoobW^. This shows that Haecker's empirical rule, based purely upon experimental investigation, has a proper theoreti- cal foundation, as was first pointed out by S. P. Thompson. The coefficient A was given a value varying from 12.5 to 25 by the early experimenters. For modern horse- shoe electro-magnets having a soft iron core the con- stant would be very much greater; but for present use Haecker's rule is not sufficiently exact on account of the change in the coefficient due to minor changes in the go ELECTRO-MAGNETISM. form of the magnet. We, therefore, now go directly to the formula for tractive force, /JC2 Jn2 F='^^^=- dynes = — grammes, from which the total polar area in square centimeters that is required to enable an electro-magnet to support a load of F grammes upon its keeper, is . 25000F In ordinary electro-magnets with a wrought-iron core of some magnitude, B will usually lie between the limits loooo and 16000 lines per square centimeter. The required polar area being determined, it should be increased by such a factor of safety as seems desirable for the purposes for which the magnet is designed. It remains to determine the length of the core. According to the formula given on page 7, it is evident that an economy of magnetizing power is obtained by using a short core. Hence the core should be no longer than is demanded to accommodate the windings, unless outside mechanical conditions make this impossible. Since the magnetizing power of a coil is proportional to the product nc, the external conditions will usually prescribe the number of turns. Thus in an ordinary arc lamp the current is about ten amperes, and therefore the series regulating magnets must be made with suffi- cient turns to do their work with that amount of current. In the same way the windings on a telegraph instrument must be of such number that the required armature pull SIMPLE ELECTRO-MAGNETS. 31 will be given when the line current circulates. The currents used on telegraph lines are usually to be measured in milli-amperes (seldoni exceeding 200 milli- amperes) ; hence the instrument must be wound with many turns of fine wire. A long telegraph line measures several hundred ohms, and a considerable resistance in the instrument does not entail a great proportional loss. On the other hand, where a coil carries a considerable current, the wire must be of considerable diameter and the windings of the fewest possible turns, to avoid an undue loss of energy in the coils and excessive heating. The area of the windings exposed to the air should not be less than two square inches for each watt lost in the coils if the maximum safe rise of temperature be assumed to be 75° F. This gives the relation hence the maximum current that can be safely used in a coil of given resistance and surface is Where windings have considerable depth, the inner turns become hotter than the outer ones. It is therefore necessary to avoid too deep a winding. S. P. Thomp- son states that in a coil wound to a depth of .5 of one inch, the wire can carry a current density of 3000 amperes per square inch, and where the depth does not exceed .3 of an inch the density can be increased to 4000 amperes per square inch, while the rise in tem- perature does not exceed 75° F. 32 ELECTRO-MAGNETISM. If it be desired to wind two equal coils on bobbins, so that different currents will give the same rise of temper- ature in each, the following relations must be regarded. Since the heating must be the same, C^R^C^R-^. But R = S-- and ^j=.^-i, where p is resistance per mil foot of copper, and /, /j are the lengths of wire on the bobbins given in feet, while D and D-^ are the diameters in mils (thousandths of an inch). The bobbins being equal, the volumes occupied by wire are equal ; hence ^°°7t2 ^^^ ^I'^TTi' ^'^'"" which R^y^ and Ri°^-^. Therefore -^ = -fr\' ^"'' -^ = 7rs which gives If it be desired to wind a given spool to a certain depth and produce a given resistance, the diameter of the wire over the insulation is given in inches by s=y+ 1,2 1 { pniy'-d^) where i is the thickness of the insulation (equal to the total diameter of the wire, minus the diameter of the copper), /the length of the spool, D and d the outer and inner diameter of the spool, all given in inches ; p is the speciiic resistance of copper, and R the required resistance of the coil. The bare diameter of the wire is evidently h — i. The length of wire, in feet, on any coil or spool, is approximately SIMPLE ELECTRO-MAGNETS. 33 where S is the diameter of the wire (insulated). The mean length of a turn on the coil is —{D+d), the num- ber of turns in a layer is -, and the number of layers is ;— . The total number of turns is then -^ — ^^— ^ and the total length is which is approximately as above .8 — (L^ — d"^). On account of the wires bedding into each other so as to increase the number of turns (which is not taken into account in deriving the formula), the approximation is probably as close as it is possible to come. The energy lost in a coil being C^R watts (propor- tional to the heat produced per second) and the magne- tizing power being ^^ — , the energy lost and the rise of temperature is the same for any winding, provided the size of the coil and the product nc be constant* Thus, if n be changed, the cross-section of the wire must be changed in inverse proportion, and the resistance will vary as n^. From the stated conditions, C^ varies inversely as n^, hence C^R-^ = C'^R = z. constant, and the heating effect remains unchanged. For some purposes it is found convenient to use magnetized steel armatures for electro-magnets. These are called Polarized Armatures. Such an armature will 34 ELECTRO-MAGNETISM. evidently be attracted by the magnet when the current passes in one direction, and be repelled when the current passes the other way. Polarized armatures are used in quadruplex telegraph instruments, telephone call-bells (where the ringing current is alternating), etc. MAGNETIC PROPERTIES OF IRON. 35 CHAPTER III. THE MAGNETIC PROPERTIES OF IRON. From the preceding pages it is evident that a full knowledge of the magnetic properties of iron is essen- tial to the successful designing of electro-magnets. This applies with particular force to the design of the field magnets of dynamos, as they contain a consider- able mass of iron, and it is desirable to compute with considerable exactness the windings required for a proposed machine. Unless the quality of the iron to be used is well known, the computations are likely to result in disappointment. In order to predetermine the dimensions and the windings of a magnet designed for a given duty, the most important magnetic constants to know are the relations of fx, to B. It is usual to plot experimental determina- tions of their relations on cross-section paper, and the resulting curve, which is of the general form shown in Fig. 1 3, is called a Permeability Curve. For some purposes a curve, called the Curve of Magnetiza- tion, showing the relation oi B to H is useful. Its char- B Fig. 13. ,5 ELECTRO-MAGNETISM. acteristic form is shown in Fig. 14. For small magne- tizing forces the permeability is small, and the curve of magnetization begins with a short curvature convex to the X axis. As H increases, and /i grows rapidly larger, the curve of magnetiza- tion rises rapidly. When the permeability begins to grow less the curve of magnetization bends, as at A (Fig. 14), and the iron is said to be approach- H(= 1'^"'' ) ing Saturation. From this Fig- 14. point, the curve continues indefinitely in a general direction not far from parallel to the X axis, and slightly concave towards it. S. P. Thompson divides the methods of experimen- tally determining the points on these curves into four classes : 1. Magnetometric class. 2. Balance class. 3. Inductive or Ballistic class. 4. Traction class. The first class covers experiments where the magne- tization of a core is calculated from the deflection of a short magnetic needle placed at a fixed distance from it. This method was used by the early experimenters, such as Miiller, Dub, etc. Professor Ewing also used the method in some of his experiments. On account of the difficulty of exactly determining H in the test piece, the method is not often used for practical tests. In order MAGNETIC PROPERTIES OF IRON. 37 to eliminate the effect of the ends of his test pieces, Professor Ewing was compelled to use wires of a length equal to 300 or more diameters. (See Magnetic Induc- tion in Iron and other Metals^ The second class is, in many respects, similar to the first class ; but the deflection of the needle is balanced by known forces, or the deflection due to the difference between the magnetization of a known bar and of the test piece is taken. This method has been used very little. (See Hughes' " Magnetic Balance," Jour. Soc. Tel. Eng. Vol. 8.; Eickemeyer's "Magnetic Tester," Transactions American Institute of Electrical Engineers, Vol. 9 ; " Edison's Magnetic Bridge," London Electri- cian, Vol. 19.) The third class is the one most used at the present time for determining the magnetic qualities of commer- cial iron. The class can be subdivided into the Ring method, Bar method, and Yoke and Bar method, accord- ing to the form of the test piece. Each of the methods depends upon measuring the transient electric pressure induced in a small test coil wound around the test piece, when the induction in the test piece is changed. This is usually done by a method invented by Weber, in which a Ballistic Galvanometer is used. This is a galvanometer with a rather heavy needle, and therefore a considerable time of vibration. If a current of short duration, compared with the time of vibration of the needle, be passed through the galvanometer, the cou- lombs of electricity which pass will be proportional to twice the sine of one half the angle of the first swing of the needle, as shown below. The first swing is often 38 ELECTRO-MAGNETISM. called the "throw" of the needle. If the angular value of the throw be small the sine is sensibly propor- tional to the arc, and the quantity of electricity passed through the galvanometer is proportional directly to the throw. It is shown by Mechanics that an instantaneous couple which acts upon a torsion pendulum so as to cause rotation, is equal to the acquired angular velocity ( 10/ / while B is found by the throw of the ballistic galva- nometer when the magnetizing current is reversed. It is to be noted that — is the ampere turns per centi- meter of length in the magnetic circuit, and in plotting the curve of magnetization, it is frequently more useful to make use of this term than of H (see page 49). The ring method has been used by many experimen- ters, since Rowland first used it, including Bosanquet, MAGNETIC PROPERTIES OF IRON. 41 Ewing, Nichols, etc. It has the disadvantage, for commercial tests, of requiring a test piece in a form which is not always obtainable, and one of the following methods is therefore more useful. In the bar method the test piece is a straight bar placed in a straight magnetizing solenoid. The value of B is calculated from the throw of a ballistic galvanometer connected to a test coil placed at the middle of the bar. The difficulty encountered in the first class, in the exact determination of H at the middle of the bar, is found here. The method has been used by a number of experimenters in special studies, or for checking the ring method. It is quite convenient for use, as the sole- noid is permanent, and various cores are easily slipped into place. ^E Fig. 16. To avoid the difficulty in determining H, and retain the convenience of the bar method. Dr. John Hopkinson devised the yoke and bar method {Philosophical Trans- actions, 1885, p. 455, and Thompson's Lectures on the Electro-Magnet). The general arrangement of the apparatus is shown in Fig. 16, where ^ is a well 42 ELECTRO-MAGNETISM. annealed, heavy forging, with a rectangular space for the magnetizing coils B, and C is the test piece, which is in two parts, with the abutting faces carefully surfaced. The test piece passes through the ends of the forging with a close fit. One end is fastened rigidly, while the other has a handle H, by means of which it can be with- drawn a short distance. D is the test coil, which is arranged with a spring so as to jump out of the field when one part of the test piece is slightly withdrawn by pulling the handle ; G^ is an amperemeter ; 6' is a reversing switch ; £■ is a source of current ; i? is a variable resistance, and G^ is a ballistic galvanometer. In the apparatus, as used by Hopkinson, the forging, or yoke, was about i8" long, 6J" wide and 2" thick. The test pieces were |-" in diameter, and of the proper length to reach through the yoke. The magnetizing coils contained a total of 2008 'turns, and the test coil contained 350 turns. As the magnetizing current is not reversed in Hopkinson's method, but the test coil is quickly removed from the field, the induced electric pressure is due to N, and the numeral 2 in the denom- inator of the formula for B disappears. It is evident that the value of B can be deduced by observing the swing of the galvanometer, when the magnetizing cur- rent is reversed, as in the ring method, in which case the test piece need not be divided. The test coil used in the Hopkinson method has a considerably larger mean area than the cross-section of the test piece, and the number of lines of force passing through the coil is therefore greater than the number passing through the test piece. The correction which MAGNETIC PROPERTIES OF IRON. 43 must be applied to the indications of the ballistic gal- vanometer, to determine N in the test piece, can be obtained by directly measuring the mean area of the coil, or, better, by indirectly determining its area from the swing of the galvanometer, with a copper or wooden rod in the place of the test piece. The yoke and bar method eliminates the end effect, which is objectionable in the bar method, by completing the magnetic circuit through iron ; but the magnetic circuit is not uniform, and therefore the formula for H is not quite as simple as in the ring method. Let L be the mean length of the lines of force in the test piece ; Zp their mean length in the yoke ; B and By the values of the induction in the test piece and yoke respectively ; fjL and /U.J, the respective permeabilities ; and A and Ay the sectional areas of test piece and yoke. The magnetic circuit formed by the test piece and yoke is so complete that very few lines of force will leak through the air. The total induction in different parts of the circuit can therefore be considered as con- stant, thus : N^BA = B-^A^; and since B =nH, and B^ = yi,^H, there results //" = — = ^^■ Also, ^=4ir^= rHdl=HL+HLy 10 Jo 44 ELECTRO-MAGNETISM. • 71^ BL B-tL-, which gives M= 1 — - — - ^N in which P and P^ are the reluctances of test piece and yoke. If the yoke be sufficiently large compared with the test piece, its reluctance can be considered negligible, and the formula becomes j^_ 4'7rnc _ NL _ BL lO yi,A fjb and --HL, TT 4 ''"'^^ loZ This has the same form as the value of H given for the ring method. The effective length L of the test piece, cannot be measured exactly because the test pieces extend through the yoke, and the exact distribu- tion of the lines of force at the ends is not known. If it be taken as the distance between the ends of the yoke, centre to centre, the ap- proximation is sufficiently close. Mr. Burton has made a modification of the Hopkinson apparatus for some tests in the Univer- sity of Wisconsin labora- tory. The arrangement is similar to one half of the Hopkinson apparatus, with the magnetizing coil on the yoke instead of on the test piece. As shown in Fig. \T, A is a heavy forged Fig. 17. MAGNETIC PROPERTIES OF IRON. 45 yoke of the best Swedish iron, ^ is a magnetizing coil of 1000 turns, and C is an accurately turned test piece. The ends of the test piece are clamped in accurately bored holes as shown, by caps and screws, KM ■ ! ■ Jip nip. as shown in Fig. i8. Here the formula for ' ' ' ZTis the same as in the Hopkinson arrange- ment, provided the reluctance of the yoke is sufficiently small in comparison with that of the test piece. The form of yoke and position of the magnetizing coil cause a considerable leakage between the two legs of the forg- ing, which increases the total induction in the yoke, and makes it necessary in some cases to correct the calcu- lated value of H. The value of the induction in the test piece is found by a test coil and ballistic galvanometer. Instead of using the test coil and ballistic galvanometer, a spiral of Bismuth wire, as made by Hartmann and Braun, may be placed in the magnetic circuit of the yoke, in which case the value of N can be directly determined from the electrical resistance of the spiral. The fourth class covers methods of measuring B by observing the tractive force at a joint in the iron core. Thus, if a ring of iron be divided into two semi-rings, and each half be uniformly wound with a magnetizing coil, the value of B can be calculated from the force required to pull the halves apart. H can be calcu- lated from the current and the windings, in the usual manner. Instead of a ring, a rod divided at the. mid- dle may be used. S. P. Thompson has devised a form of apparatus which he calls a pereameter, for using this method 46 ELECTRO-MAGNETISM. i f y3 ''M\ A! in commercial tests. The arrangement is shown in Fig. 19, where ^ is a heavy forging, .5 is a magnetiz- ing coil within which is a brass tube, and C is a test piece which is slid down the tube. The joint at d, between test piece and yoke, is carefully surfaced. From the force required to pull the test piece loose from the yoke at d, the value of the induction is readily determined. The value of H for any magnetizing current is determined by the same formula as in the Hopkinson ap- paratus. To determine B from the swing of the ballistic gal- vanometer, the constant of the galvanometer i^.e. the instantaneous flow in coulombs required to give a throw of one division) must be known. This can be determined by the following methods : a. By discharge of a standard condenser. If a con- denser of P microfarads capacity be charged by E volts PE pressure, the charge is Q = coulombs. If the '^ 1 000000 charge be passed through a ballistic galvanometer, giving a scale reading of Q divisions, the constant is evidently PE Fig. 19. K I 000000 b. By vibration and deflection. The formula Q — 2irG contains only known or determinable constants in the right hand member. T may be readily determined by timing the vibrations, and — ^ may be determined by MAGNETIC PROPERTIES OF IRON. 47 passing a measured continuous current through the gal- vanometer and noting the steady deflection Oi. From the formula for the tangent galvanometer given on page 16, it is evident that —~ = -^. when ^1 is sufficiently small. Substituting this value of — " in the formula G 2'irG gives K=Q-=^- c. By standard eartii coil (Rowland's method). A coil of area A when lying on a horizontal table encloses V^A lines of force when V, is the vertical component of the earth's magnetism. If the coil be made up of n turns of wire, and it be quickly turned over, the average . 2nA V electric pressure produced is — '. The number of coulombs flowing through any circuit connected to the Et ■ ■ ■ . coil is — , where i is the time occupied in reversing the a coil and i? is the resistance of the circuit. This becomes by substitution — — s— , and hence K= — -— ^— . ■^ 108^ 108 ie6' d. By standard solenoid (probably suggested by Lord Kelvin). In a long solenoid of known con- stants, the total induction caused by a current C is j^^ A.-rrAnC jj ^ gj^^^j secondary (test) coil of n^ turns be wound upon the solenoid, E= — — >■ volts are induced in it upon reversing the current in the solenoid. 48 ELECTRO-MAGNETISM. If the test coil be connected to a ballistic galvanometer, the coulombs are as before, and ^ Et 2 Nn-, j^_ 2Nn^ _ 87rACnKi A direct method of measuring B has just been sug- gested by Siemens and Halske, who manufacture an instrument in which the method is applied, (Fig. 20). AA are two magnetizing coils, into which test pieces CC can be slipped. .5 is a swinging coil connected to the torsion head T. E and E-^ are sources of current connected to the magnetizing and swinging coils respec- tively, and G and 6^1 are amperemeters in the respective circuits. When fixed currents are passed through A and B the latter experiences a certain turning force when no test pieces are in AA and a greater turning MAGNETIC PROPERTIES OF IRON. 49 force when the test pieces are in place. The ratio of the two forces is roughly proportional to — 1 = — = /x, F H F-^ being the force when the test pieces are used. On account of the shortness of the test pieces, this instru- ment is not likely to be a satisfactory one, but it pos- sibly might be modified so as to obtain satisfactory results. The formula giving the value of H in terms of the dimensions of a coil makes it evident that the ampere turns nc, or the ampere turns per centimeter — , may be used instead of H in plotting curves of magnetization. By using proper scales, it is evident that the curves will be exactly alike when plotted with H, nc, or — . The latter is a very convenient constant for practical use. If the ampere turn be taken as the unit of magnetic I 2 Is flC pressure, we have M^^i.it^nc and H=^-f — , where 1.25 is 31^ approximately, and L the length of the mag- netic circuit. It has already been shown that it is necessary to know the permeability curve, or curve of magnetization, of the iron from which an electro-magnet is to be made, before a design can be successfully predetermined. For commercial economy of manufacture, it is also necessary to know the relation between the cost and the quality of the various samples which may be available for use. The magnetic quality of iron depends upon the follow- ing elements : 50 ELECTRO-MAGNETISM. 1. Its physical condition (temper, homogeneity, etc.). 2. Its chemical composition. 3. Some uncertain molecular, or physical conditions, about which little is known. The comparative magnetic qualities of various samples can be determined at once by a comparison of their curves. By a consideration of the magnetic qualities, the comparative cost of working in the shop, and the first cost of metal, the relative commercial economy of different samples is determined. Physical conditions due to the method of manufacture, and to the after treatment of iron, have a marked effect upon the permeability curve ; and it is not unusual to find somewhat different magnetic qualities in two test pieces cut from the same forging, or cast from the same foundry charge. Thus, among several samples of one brand of wrought-iron tested by Bosanquet, the maxi- mum permeability varied from about 19,000 to 25,000. Again, dynamo frames made of cast-iron often show a difference of permeability, although they are apparently produced by uniform treatment of uniform material. In the case of cast-iron frames there may be a differ- ence in the chemical composition due to different tem- peratures at pouring, which partially accounts for their different qualities. Differences in the magnetic quality of two similar samples are likely to be greater near the maximum point of /^ than at the values of B used in common practice. The accompanying curves (Fig. 21) show the effect that can be produced on the permeabil- ity curve by controlling the physical properties. Curves A and A' were taken from a sample of mild steel cast- MAGNETIC PROPERTIES OF IRON. 51 Permeability Curves showing effect of changing Physical Properties. 1400 1200 1000 800 /« 600 400 2G0 3G0O 2500 2000 JX 1500^ 1000 500 2000 4000 6000 8000 10000 12000 14000 16000 18000 B Fig. 21, 52 ELECTRO-MAGNETISM. ing, forgeable but not capable of taking a temper. Curve A shows part of the permeabihty curve for the sample as cast, and A' shows it after the test piece had been thoroughly annealed. Curves B and B' were taken ' from a sample of mild steel capable of taking a temper. B shows part of the permeability curve for the test piece after thorough annealing, and B' after tempering in oil. D and D' are the curves for a soft iron wire, first when carefully annealed, and second when hard- ened by being subjected to sufficient strain to stretch it ten per cent in length. Chilling cast-iron in the mould has an effect similar to that caused by the hardening in the latter sample. The chemical change due to chilling, however, probably plays the most important part in this case. The importance of avoiding all chilling or hardening (by cold rolling, hammering, etc.) during the processes of manufacture, is clearly shown in these examples ; not only is the permeability curve lower for the hardened metal, but its maximum is almost always at a smaller induction. For use in dynamo magnets, it is desirable that the permeability be as great as possible at large inductions, and the maximum should therefore come as late in the curve as possible. The sample from which the curves A, A' were taken, is an admirable example of the mild steel castings that are now used to a considerable extent for dynamo frames. Ordinarily, the use of these castings, in the place of cast or wrought iron, is likely to effect an economy in dynamo construction on account of their excellent magnetic qualities at high inductions, the ease of work- MAGNETIC PROPERTIES OF IRON. S3 ing them in the shop, and their comparatively low cost. They have the disadvantage, to be found in all steel castings at present, that sound metal in large masses is difficult to obtain. How far the process of annealing steel castings can usually be carried with economy, must depend upon local conditions ; but when not annealed the castings possess a permeability for values of B between 14,000 and 20,000, which is fully equal to that of good merchant wrought-iron (see Henrard, La Lumiere Electrique, Vol. 35 ; and Thompson, etc.. Transactions American Institute of Electrical Engineers, Vol. 9). The effect of high temperatures upon the permeabil- ity of iron and steel is remarkable. For small magnet- izations, the permeability increases to a maximum, and then suddenly drops to nearly unity when a certain tem- perature is reached. This temperature is called the Critical Temperature, and seems to vary between the limits of 650° C. and 900° C, the exact value depending upon the nature of the test piece. For magnetizations as large as those used in ordinary practice, the changes in permeability due to changes in temperature are not so rapid ; the permeability does not vary to any marked extent, as the temperature rises beyond the ordinary temperature of the air, until the critical point is ap- proached, when the permeability begins to fall gradually, and finally reaches a value near unity. The curves x, y, and z, Fig. 22, plainly show the change of the perme- ability with temperature changes. They were taken from a test piece of soft iron ; first, when subjected to the very small magnetizing force of three-tenths of a C.G.S. unit (curve x), second, when subjected to a 54 ELECTRO-MAGNETISM. force of 4 C.G.S. units, and third, when subjected to a magnetizing force of 45 units, which is a value within the range of practical use (curve z). ( Vide Hopkinson, Philosophical Transactions, 1889; Ewing, Magnetic In- duction in Iron, etc) The peculiar effect of temperature upon the permeability of steel, containing a considerable percentage of nickel, is reverted to later (page 56). The chemical composition of mild steels has an enormous influence upon their magnetic qualities. Their sensitiveness to differences of treatment may sometimes mask the effects of variations in the compo- sition ; but the following general statements can be tentatively made as covering our present knowledge of the effect of chemical impurities, within the range of inductions used in dynamo magnets : 1. The permeability depends inversely upon the amount of carbon present. 2. The permeability depends inversely upon the amount of manganese present when it much exceeds .15 per cent. Small percentages of manganese seem to have a greater effect for large values of B than for small values. The presence of 3 or 4 per cent of manganese decreases the value of /a for all inductions in a very marked manner. With 12.5 per cent of manganese present, the permea- bility of steel is practically constant at 1.4. Hopkinson says of 12.5 per cent manganese steel, "the induction is strictly proportional to the magnetizing current (j,.e. jx, = constant), and the material shows no loss by hystere- sis. . . . Smaller proportions of manganese reduce the magnetic property in a less degree, the reduction being greater as the quantity of manganese is greater." MAGNETIC PROPERTIES OF IRON. 55 3. The effect of less than .5 percent of silicon does not seem to be marked, but when present in larger percentages it evidently decreases the permeability. 11000 10000 9000 : X 7000 a. ^6000 g 5 Q. 3000 / CURVE Y + i 2000 1000 500 X ~ ^ \ X -^'^' \ cu VE Z ■■ -***-A^ 100 200 300 400 500 TEMPERATURE 600 700 785 800 Fig. 22. When in small quantities and in the presence of manga- nese, it possibly tends to counteract the hurtful effects of the latter. 4. The amount of phosphorus and sulphur present in forgeable steel castings is too small to have any marked effect on the permeability. 5. Nickel, chromium, tungsten, etc., seem to have an injurious effect even when present in small quantities. 56 ELECTRO-MAGNETISM. Tungsten is used to increase the coercive force of per- manent magnets, but the permeability of such magnets is always low. The coercive force of soft wrought iron is usually not much greater than 2 ; in chrome steel, oil tempered, it may reach 40 ; and in tungsten steel it may be greater than 50. Nickel in large percentages has a most peculiar effect on steel. Of 25 per cent nickel steel, Hopkinson says : " It is non-magnetic as it comes from the manufacturers. Cool it, however, a little below 0° C, and it becomes very decidedly mag- netic. But if now the cooled material be allowed to return to the ordinary temperature, it is magnetic. If it be heated, it is still magnetic till a temperature of 580° C. is attained, about which it becomes non-magnetic. Now cool it, and it remains non-magnetic till a temper- ature of a little less than zero is reached, when it becomes magnetic again." 6. Steels cast by an aluminum or silicon process frequently, if not usually, have a high permeability. This may be due to the aluminum or silicon alloying with the iron ; but as these elements do not seeni to remain in the product to any considerable extent, the high permeability is probably due to the greater homo- geneity caused by their fluxing qualities. The effect of carbon on the permeability of steel is plainly shown in the accompanying curves E and F (Fig. 23). E is the curve of a steel casting capable of welding and tempering, and carrying € = .40, Si = .08, Mn = .i8, P=.04, S = .oi7. F '\% the curve of a steel casting capable of welding and tempering, carrying C = i.i3, Si = .09, Mn = .i9, P = .04, S = .oi5. MAGNETIC PROPERTIES OF IRON. 57 Permeability Curves showing the Effect of Various Impurities in Mild Steels and Wrought Iron. MILD STEEL ( G !>^ t^"^\. F \. ^^""^^^'-^^ — -A r r^. i. \ B N 2000 4000 6000 8000 10000 12000 14000 16000 18000 20 Fig. 23. 58 ELECTRO-MAGNETISM. The effect of manganese is shown by curves G and E. It is to be noted that the test piece of curve G carried considerably less carbon than that of curve E, but it shows a lower permeability curve, probably on account of the predominating influence of its greater percentage of manganese. Curve G represents a test piece of Whitworth's mild steel, with € = .32, Si = .64, Mn = .44, P = .035, S = .oi7. The effect of silicon in large percentages is shown by a sample tested by Hopkinson. It carried € = .685, 51 = 3.44, Mn = .69, P = .i3, S = .02, and was carefully annealed before testing. Its permeability, with B a little under 15,000, was about 60. The comparatively large amount of phosphorus in this piece may have aided somewhat in reducing the permeability. Impurities in wrought iron seem to have an effect on its permeability similar to their effect on the permeability of steels. Owing to its greater purity and its excellent physical properties, the permeability of wrought iron has a much higher maximum than is shown by steels. Rowland found the maximum value of /i to be 4600 at .5=5400 in an excellent piece of Norway iron, while fi, was 350 when B was 17,000. Characteristic permea- bility curves for Swedish iron and ordinary wrought iron are shown in //"and / (Fig. 23). Curve H is the average taken from three test pieces carrying approxi- mately C = .o8, Si = .03, Mn = .oi, P = .03, S = .oi. Curve / is the average taken from three test pieces of a good quality of merchant wrought iron, carrying ap- proximately C = .o75, Si = .io, Mn = .25, P=.io, S = .io. The effects of manganese, and possibly of phos- MAGNETIC PROPERTIES OF IRON. ^g phorus and sulphur, are apparent in the smaller maxi- mum permeability exhibited in curve /. The greater permeability shown by curve /for the large values of B makes it seem possible that the effects of Si, P, and S in small quantities is to increase the permeability for large inductions. This may also be true for steels. The cause of this difference in the curves is likely, how- ever, to be due to physical conditions, as soft wrought iron is specially sensitive to differences of treatment. Ewing found that the maximum permeability of a very soft iron rod could be increased by tapping to the enormous value of 20,000, while under ordinary condi- tions it showed a curve similar to that usually given by good wrought iron. Hence, differences in the methods of testing, or some vibrations, may possibly explain the anomalous differences in the forms of curves H and /. As far as our knowledge extends, we may say that it is probable that impurities affect the permeability of wrought iron in the same manner as they affect mild steels. The permeability attains a much greater maxi- mum in wrought iron, and the maximum usually occurs at a materially smaller value- of B. For inductions greater than 15,000, the permeability seems to be fully as great in good forgeable steel castings as in wrought iron. Ewing says : " Speaking generally, the curves of magnetization for steel can be made to closely resemble those for iron by simply altering the scale of H. Under strong magnetic forces, the region of saturation is reached in steel with much the same value of /, or of B, as in iron ; but to reach it or to remove it, requires the application of a stronger force." That the coercive 6o ELECTRO-MAGNETISM. force of mild steel is nearly always greater than that of wrought iron is shown by the complete curves of mag- netization (see page 73). As a finished dynamo frame made of a mild steel casting should ordinarily cost less than one made largely of forged wrought iron, the economy of steel seems unquestionable, provided uniform homogeneous castings can be obtained. Aluminum in wrought iron, as used in the " mitis " casting process, seems to have the simple function of a flux, which is required to make a homogeneous casting. Very little aluminum remains in the product, and the casting has physical and magnetic properties similar to those of ordinary forged wrought iron. Curve K (Fig. 23) shows the permeability of a sample of " mitis " casting. That the small amount of aluminum remain- ing in the iron acts to injure its magnetic quality is shown to be probable by a comparison of curve K with curves H and /, though here again the difference in treatment may be the controlling cause of the differ- ences in the curves. The treatment that cast iron receives in the cupula and in casting may vary its impurities over a wide range of percentages. Very decided variations may exist in the iron poured from a single charge. It is thus doubly important to study the effect of foreign elements upon the permeability of cast iron, in order that both the material used in the foundry, and the treatment it receives, may be of such a nature as to give the best magnetic characteristics to the iron. The frames of continuous current dynamos are not usually MAGNETIC PROPERTIES OF IRON. gi made of cast iron alone, but cast iron is frequently used for pole pieces, bed plates (serving as keeper), etc. ; while the cores (under the windings), or cores and keeper, may be made of wrought iron. Nevertheless, some very excellent continuous-current machines have frames wholly of cast iron, and it is usual to make the frames of alternating-current machines wholly, or largely, of cast iron. The working permeability of cast iron is low under the best conditions, and a poor quality is to be avoided if possible. A poor grade of cast iron used for dynamo magnets must result in machines that have an excessive weight and cost. The effects of impurities upon the permeability of cast iron can only be tentatively stated, although they are better known in this case than in the case of steel and wrought iron. 1. The permeability depends inversely upon the total amount of carbon present. 2. With a fixed percentage of total carbon, the per- meability depends inversely upon the ratio of combined to graphitic carbon. Thus, gray and white iron con- taining the same total constituents will give very differ- ent permeability curves, that for the gray iron being higher. In malleablizing cast iron, the total carbon is decreased towards a limit of less than .i per cent combined carbon, while the other impurities are practi- cally unchanged. The process also serves to thoroughly anneal the material. The marked decrease in carbon and the annealing causes thoroughly malleablized iron to give a permeability curve which is decidedly superior to that given before malleablizing. Chilling in the 62 ELECTRO-MAGNETISM. mould changes graphitic carbon into combined carbon, besides causing changes in the physical structure ; hence it lowers the permeability. Neither malleablizing nor chilling can be fully carried out on the large masses of ordinary dynamo frames, but the softness and homo- geneity of castings produced from a foundry heat depend largely upon care in founding. 3. The presence of manganese has a harmful effect upon the magnetic quality of cast iron. This is probably due mainly to its tendency to cause chilling (i.e. change of graphitic into combined carbon), but it may have an additional effect similar to its influence on wrought iron and steel. 4. Silicon in percentages not exceeding 2.5 per cent seems to be advantageous, as it tends to make the iron soft and prevent chilling. Howe says of silicon: "It diminishes the power of iron to combine with carbon, not only when molten (thus diminishing the total carbon content), but more especially at a white heat, thus favoring the formation of graphite during slow cooling ; it lessens the formation of blow-holes ; it hinders at high temperatures the oxidation of iron and probably of the elements combined with it." 5. Sulphur and phosphorus have a tendency to cause chilling, and thus decrease the permeability of cast iron. 6. Aluminum seems to increase the homogeneity of cast iron, and to affect the contained carbon in much the same manner as does silicon, while in some grades of iron the effect is much more pronounced. The effect of aluminum upon cast iron is greater than upon steel, on account of its direct action in controlling the carbon, MAGNETIC PROPERTIES OF IRON. 63 but its usefulness depends upon the quality of the pig iron used. Thus the addition of aluminum to a soft gray foundry iron results in loss of strength in the product, because the fluxing qualities of the alumi- num are not needed, and it therefore acts merely as an impurity. On the other hand, its addition to certain grades of iron may make a marked improvement in the product. The. effect of varying the carbon is plainly shown in the accompanying permeability curves L to S (Fig. 24). Experimental data are wanting to fully show the effect of silicon, manganese, etc. Curve L is part of the permeability curve of a hard white cast iron, carrying approximately the impurities : Graphitic carbon = 0, combined carbon = 2. 5, Si = .8, Mn = .8, P = .s, S = .3. Curve M shows the average of several test pieces of medium gray iron carrying approximately: Graphitic carbon = 2. 5, combined carbon =1.0, Si = 2.0, Mn = .3, P=.i, S = .o5. Curve iVis the result of a test by Hopkinson of a soft gray iron. It must be very low in carbon and manga- nese. Curve is the average given by a number of test pieces made of malleable cast iron which carried about the same impurities as the test piece of curve M, with the exception of the carbon. The latter probably did not exceed .1 per cent or .2 per cent, all in the combined form. Curve F was taken from a test piece of commercial malleable iron of unknown composition. 64 ELECTRO-MAGNETISM. Permeability Curves showing the Effect of Various Impurities in Cast Iron. 1200 1000 2000 4000 6000 8000 10000 12000 14000 16000 18000 B 300 2000 4000 6000 8000 10000 12000 B Fig. 24. \ MAGNETIC PROPERTIES OF IRON. Miscellaneous Curves. 65 TOO 600 500 JX 400 300 200 100 40000 37000 84000 31000 28000 23&O0 6 2000 4000 6000 8000 10000 12000 14000 16000 18000 20 21? 4 6 8 10 12 14 16 X' 22000 2000 4000 6000 §000 10000 12000 14000 16000 18000 20 21000 THIS LINE REPRESENTS 4-7rl ^ Fig. 25. 66 ELECTRO-MAGNETISM. A good gray cast iron used by one of the large manu- facturers of dynamos gives the curve Q. This carries about .06 per cent of aluminum. The same iron, with an admixture of 1.4 per cent and 6.5 per cent, gives curves R and .S. When the aluminum is increased to 12 per cent, the permeability curve falls below curve S. (See Magnetic Induction in Iron and Other Metals, Hopkinson, Philosophical Transactions, 1885, and Jour- nal Institution of Electrical Engineers, 1890; Henrard, La Lumikre Electrique, 1886; 'Ko^laxid, American Jour- nal of Science, 1873 ; Howe, Metallurgy of Steel.) Curves A, I, and Q are shown together upon the accompanying sheet (Fig. 25). These show very well the characteristic forms of the permeability curves of good mild steel, merchant wrought iron, and good gray cast iron. A curve showing the relation between / and H must evidently be similar in form to the curve of magnetiza- tion, but will fall below it, since ordinates of the I-H curve are In the same way a curve showing the 47r relation of k and B is similar to the permeability curve, but much flatter, for the ordinates are ^~ ■ The 47r curve T (Fig. 25) is a typical one showing the relation of K to H. The rapid increase of « for small values of H is to be remarked, and also the peculiar hyperbolic form of the second branch of the curve with one leg apparently assymptotic to the axis of X. With this form of the susceptibility curve, it is evident that the curve representing the relation between [ and H should MAGNETIC PROPERTIES OF IRON. 67 become parallel or nearly parallel to the axis of X. This has been virtually proven by Ewing's experiments, in which he used magnetizing powers from II=i $00 to //■= 20,000. In summing up the results of his experi- ments, Ewing says : " Under sufficiently strong magne- tizing forces the intensity of magnetization, /, reaches a constant, or very nearly constant, value in wrought iron, cast iron, most steels, nickel, and cobalt. The magnetic force at which f may be said to become practically constant is less than (//■=) 2000 C.G.S. units for wrought iron and nickel, and less than (ff= ) 4000 for cast iron and cobalt. In stronger fields the relation of magnetic induction to magnetic force becomes B=I{+4 7r/=Zi^+ constant." For wrought iron the constant is nearly 477X1700, and for cast iron it is about 477 x 1240. The accompanying curve C/'(Fig. 25) shows the per- meability curve and curve of magnetization for large values of H, in a sample of Swedish Lancashire iron. Figure 26 shows the relation of i//j,=p to H, and is interesting from a scientific point of view. If a neutral piece of iron or other magnetic material be magnetized and the magnetic pressure then removed, a certain proportion of the total induction (already defined as residual magnetism) remains. If a larger magnetic pressure be applied, the magnetization reached will be greater than before, and if the magnetic pressure be reduced to its former value, the total induction will not decrease proportionally, but will continue at a higher value than was previously attained with the same 68 ELECTRO-MAGNETISM. magnetic pressure. It may be generally stated that the total induction attained by any test piece, when subjected to a magnetic pressure, depends upon its previous magnetic state. The ordinates of a curve of magnetization therefore depend, to some degree, upon the method used in testing. If the curve be first taken .0030 .0025 Fig. 26. by measuring the increments of induction due to a step by step increase of H, and then those due to a step by step decrease of H from its maximum value, two curves will be the result, as shown in Fig. 27, where OR is the up (or increasing) curve, and RS the down (or decreasing) curve. This phenomenon, a knowledge of which is of much importance to the designer, was named by Ewing, MAGNETIC PROPERTIES OF IRON. 69 Hysteresis. Ewing also proved that if a certain magnetic pressure be applied to a test piece, the magnetization at once attains nearly its stationary value, but then creeps very slowly to its final value. This he called Viscous Hysteresis. The phenomenon of viscous hysteresis has no practical interest at present. When the number of lines of force passing through a coil is changed, an elec- tric pressure is generated, which is in value B E = ndN ic?dt S. where ^A^and dt are the in- crements of total induction and of time (see page 39). o If a current be flowing in the coil, the work done upon, or by, the lines of force is CEdt, and (from above) nCdN. CEdt = - 10° but N=AB and dN=AdB, while nC = whence dW = CEdt -■ Integrating gives W=CET-- AL loHL J 471" 10^x477 AL 10' X47r*^«2 HdB. HdB, and the energy expended in watts during the duration of the action is AL CE=- 10'' y.^iTT-^'>i HdB. ^o ELECTRO-MAGNETISM. Bs B J ^ y^G> _ \JJ^ AREA ARnf / =Hc!B /f The value of I ' HdB is evidently equal to the area EFGJ (Fig. 28). If the change in the induction be due to a change in the current flowing in the coil, the C of the formula must represent the average current, and according to Lenz's law, work must be done by it against a counter electric pres- sure caused by the increasing induction when the current is increased, and work will be expended by the magnetism when the current is de- creased. The work done against a coun- ter electric pressure as the induction is increased, is stored in the magnetic field, and is returned when the induction dies away. In other words, work must be done upon the magnetic molecules in order to swing them into line when a test piece is magnetized, while work is done by the mole- cules when they swing back upon the withdrawal of the magnetizing force. As no energy is required to maintain a magnetic field when once established, there would be no loss of energy from magnetizing and then demag- netizing a piece of iron, if the curves of magnetiza- tion, ascending and descending, were the same. For, j HdB would be equal and of opposite sign in the two cases. But there is a difference in the two curves, due to hysteresis, and there must be a loss of energy due to Fig. 28. MAGNETIC PROPERTIES OF IRON. 71 the operation, proportional to the area between them. Or, W= AL Hence, W= — 10' X47r AL ^"^ \J^'HdB+ I 'HdB C'HdB. io'X47r' J "^2 HdB HdB is the area ORS. If a piece of iron be carried through a continuous cycle of magnetization, between equal positive and negative values of H, a cyclic curve of magnetization, Fig. 29. Fig. 30. similar to Fig. 30, is given. The integral then becomes AL W= and CE=- 10' X47r AL HdB, HdB. 10" X 477 X T'^B If the cycle be repeated continually, as in the core of 72 ELECTRO-MAGNETISM. an alternating current transformer, or in the revolving armature core of a dynamo, the integral becomes CE= . "^^ ^ — ^HdB where V is the number of cycles, or revolutions, per minute f = -^Y It is to be noted that when the method of reversal (previously discussed) is used for testing, no distinction is made between the ascending and descending curves, and the curve so determined is, presumably, as close to the mean of the two as the physical conditions will per- mit. In regulating a dynamo, the field magnets are as likely to be brought to any definite induction from a slightly higher one as from a lower one, and the mean curve of magnetization or permeability is therefore of most use in designing field magnets. In dynamo arma- tures, or alternating current transformers, the iron is subjected to continuous cycles of magnetization, and a careful study of the area included between the ascending and descending curves is necessary, in order that the loss of energy due to the reversals of magnetism in the iron may be reduced to a minimum. The effect of physical properties and chemical compo- sition upon the area of the cyclic curve of magnetization is very marked. The accompanying figure (31) shows the cyclic curves of magnetization of a soft iron wire ; 1st, after annealing, 2d, after hardening by stretching. This is the same wire previously quoted from Ewing, and for which the permeability curves were given. In MAGNETIC PROPERTIES OF IRON. 71 general it may be said, that apparently anything which tends to reduce the maximum of the permeability curve, also tends to increase the area of the cyclic curve Fig. 31 of magnetization, and hence to increase the energy dissipated per cycle. A careful examination of the relations of the two curves will show this to be true. 74 ELECTRO-MAGNETISM. A much closer experimental study of the effect of chemical impurities, than has yet been made, would be of advantage in pointing towards the best methods of manufacture for mild steel or wrought-iron plates, to be used in alternating current apparatus and in continuous current armature cores. From the formula for the energy dissipated by rever- sals, we may say that the watts of energy wasted is equal to the area of the cyclic curve multiplied by the volume of the iron (in cubic centimeters) times the number of cycles per minute and divided by 7,500,000,000. This energy must evidently be expended in heating the iron. From an inspection of the curves it is evident that the coercive force is equal to OA, and the retentiveness to OS (Fig. 30) ; also, that the area of the curve is approximately equal to that of a parallelogram, with a height which is twice the maximum induction, and a base equal to twice the coercive force. Hence, anything that decreases the coercive force will also decrease the energy lost through hysteresis. The coercive force is not a constant for any sample, but increases directly with B. Ewing found the coercive force in very soft iron to be i.i when B was 3700, and 1.7 when B was 14,000. The propor- tional increase is greater in hard iron. Steinmetz found the coercive force of cast iron to be 10 and 15 when B was respectively 6100 and 10,000, while the coercive force of soft machine steel was 9 and 1 1 when B was 14,000 and 18,800 respectively. Steinmetz has further shown that the waste of energy by hysteresis can be represented by the formula [/= v VB^, where U is the energy in watts lost per cycle and per cubic centimeter MAGNETIC PROPERTIES OF IRON. 75 of iron, Fis the number of cycles per minute, and 1/ is a constant depending upon the quality of the iron for its numerical value. (See Transactions American Institute of Electrical Engineers, Vol. 9.) The value of v has been found to vary from 33 x io~^' to 14 x lO"" for dif- ferent samples of iron and steel. For the sheet-iron used in a certain commercial transformer, Steinmetz found a value i/=40Xio"'^ Since 2^ = 3, it is evident from the formula, that doubling the induction trebles the waste due to hysteresis. The loss due to hysteresis can be calculated from the area of the cyclic curve showing the relation between H and /, as well as from the cyclic curve of magnetization. For, B = H+ 4 tt/ and dB = dH+ 4 Trdl. Hence HdB = Hdff+ 4 TrHdl, but HdJI must disappear for a complete cycle, with equal maximum positive and negative values of . H. Therefore HdB =4 irHdl, and by substitution we have IQlJl ■je ELECTRO-MAGNETISM. CHAPTER IV. ESTABLISHMENT OF ELECTRIC PRESSURES. If two metal rails, as A and B in Fig. 32, be placed perpendicular to the lines of force in a magnetic field, and a metal slider C be moved along them, an electro- motive force or electric pressure will be set up in the slider and rails. If the circuit be closed, a current will flow while the slider moves, and it may be measured by B Fig. 32. a galvanometer, as at G. From Thompson's Electricity and Magnetism, Arts. 363 and 394, we have lO^^ where e is the electric pressure in volts, and iVj and N^ are respectively the number of lines of force passing through or linking the electric circuit (composed of slider, rails, and connections) before the motion begins ESTABLISHMENT OF ELECTRIC PRESSURES. "jj and after time t. This is equivalent to \&e= dt With a closed circuit having a resistance of R ohms, the current flowing is C= -|-= x — -^ The nega- ^ R dt lo^xR ^ tive sign is used to signify that the magnetic field, generated by the induced current, is opposite to the inducing field; or, in other words, the current set up tends to oppose the motion according to Lenz's law. In this case work must be done upon the slider to keep it in motion. If the galvanometer be replaced by a battery or other source of current, giving an electric pressure of e' volts, the slider will tend to move, if not obstructed, at such a velocity that — = loV. In this dt case the slider will do work. If "a" be the perpen- dicular distance between the rails, and B the induction measured in the plane of the rails, then dN=Badl, where /is the length of the rails. Hence ---=Ba--- '^^ — is evidently the velocity of the slider in centimeters dt per second, and it may be replaced by the letter v\ whence e=——-- av\% evidently the area between the rails swept over by the slider in each second, and the value of e is therefore — - times the numder of /ines of force cut through by the slider per second. Also, if a current be passed through an unobstructed slider, it will tend to move at such a velocity as to cut through a number of lines of force per second numerically equal to the impressed electric pressure multiplied by lO*. A wire hung from the pole of a magnet, with its ends 78 ELECTRO-MAGNETISM. dipping in mercury cups at the pole and at the waist of the magnet, as shown in Fig. 33, is practically a con- tinuous slider. When the wire revolves about the mag- net, the electric pressure generated is dN e= \o^dt = -NV= -^irmV, where V is the velocity in revolutions per second, and ^irm is evidently equal to N, the total number of lines of force emanating from the pole. n ^ 't I. / > A . |B ; ( A' > Fig. 42. attention. If the coils of each pair be moved so as to be side by side and with their centre in the axis of revolution, it is evident that double the preceding formulas represents the electric pressure, and \& X 60 For the total number of lines of force (equal to A^'jcosct) now pass through both coils of each pair at any moment, giving the effect due to N^ lines of force for ESTABLISHMENT OF ELECTRIC PRESSURES. 93 each coil, while in the general case the number of lines of force at any moment passing through each coil of a pair is | N^cos a, giving the effect due to | N2 lines of force for each coil. The general case is evidently a ring wound with 2 a coils uniformly spaced, and arranged to revolve about its true axis. The modified case consists of a cylinder upon which 2 a coils are wound longitudinally, and which is arranged to revolve about its axis. In the case of the ring, the number of wires (or conductors) upon its outer surface is evidently equal to n, while in the case of the cylinder the number of conductors on the surface is 2 n. Whence, writing 5 for the number of conductors on the surface in either case, the general formula for the electric pressure becomes 10^x60 This can be formulated as a rule thus : The commutated electric pressure developed in any armature, composed of a set of coils wound on a ring or drum and revolved about their common axis, is equal to the number of lines of force cut per second, multiplied by the number of external conductors on the ring or drum, and divided by 10^. It can now be seen that the development of electric pressure, by the movement of wires in a magnetic field, can be classified under three divisions : I. Where a wire cuts the lines of force by moving across them ; as in the case of a slider or of a wire moving around a magnet pole. 94 ELECTRO-MAGNETISM. 2. Where a coil, or set of, coils, is moved parallel to itself, or nearly so, between points of different strength in a magnetic field. 3. Where a coil, or set of coils, is wound on a ring or drum and given a rotary motion in a fixed magnetic field. The pressure developed by the first division is often spoken of as caused by Unipolar Induction. This term is erroneous, if strictly interpreted, as induction due to one pole (unipolar) cannot exist. The term can be satisfactorily applied, however, to distinguish the first division if its meaning be not literally construed. The first division has been shown to cover the fundamental case, and the second and third divisions can be con- sidered as special cases. On account of the commercial importance of the latter, they will be given separate treatment. It is to be remembered that electrical pressures produced under the conditions defined as belonging to the first division, are rigorously contin- uous, provided V be inversely proportional to B, while the practical conditions of the second and third divisions produce either alternating or rectified pressures. The rectified pressures approximate more or less closely to rigorous continuity only as " a " approaches a large numerical value. In commercial machines intended to produce elec- trical pressures by induction, i.e. Dynamos, the parts of the machines in which the pressures are produced are called Armatures. In considering the requirements to be met in dynamo armatures, it is well to make a classi- fication upon less scientific but more practical lines ESTABLISHMENT OF ELECTRIC PRESSURES. 95 than the division already made. Here again the classes are three in number, but the division is based upon the results produced by the machines, mstead of the manner in which the results are produced. The three classes of armatures are : 1. Rigorously continuous current armatures. These belong in the first division, as already enumerated. 2. Alternating current armatures. A majority of these belong to the third division, and the remainder to the second division, as already enumerated. 3. Ordinary continuous current armatures. These belong for the most part to the third division of the previous classification. The second class given here has no place in the present volume, and the first class will receive only a hasty consideration on account of its small commercial usefulness. The third class covers nearly all armatures of commercial continuous current machines. This class, or the rotating coil armatures, must be again divided, for convenience, into three types : 1. Gramme or ring armatures. 2. Siemens or drum armatures. 3. Open coil armatures. The Gramme and Siemens armatures are often called Closed Coil armatures to distinguish them from the third type- When the ring armature carries its conductors in grooves, it is often called a Paccinotti armature, after its first inventor, who described it in 1864. The drum type is often called after Hefner von Alteneck, who 96 ELECTRO-M AGN ETI SM . designed the first one with multiple coils in 1873. The ring armature of Paccinotti was reinvented and first put into commercial form by Gramme in 1871. In Gramme's form, the ring was not toothed and the coils were wound uniformly over its surface. The first practical armature approaching the drum type in form had a single coil and a two-part commutator. The core was PACCINOTTI CORE. Coils wound in groves. GRAMME CORE. Coil wound uniformly. Fig. 43. CROSS-SECTION OF SHUTTLE ARMATURE. Windings shown by hatchings. a cylinder with two longitudinal grooves, in which the windings were laid. This was invented by Werner Siemens before 1856. It is often called the Shuttle Wound or H armature, on account of its form.* Since the armatures of all commercial machines of the class under consideration have iron cores, the number of lines of force useful in producing pressure is the total number cut by the external conductors, both in the ring and drum armatures. ^'S- 44. This is evident in the case of * See Thompson's Dynamo-Electric Machinery, Chap. 2 ; Urquhaet's Dynamo Construction, Introduction; Kapp's Electric Transmission of Energy, Chap. 2; etc. ESTABLISHMENT OF ELECTRIC PRESSURES. 97 the drum armature, and requires no further comment. In the ring, the iron core provides a path of low reluc- tance for the lines of force, and therefore few lines pass directly across the central space. These few qan be considered negligible, or a correction made for them, as the case may demand, when N is taken as the total number of lines cut by the external conductors (Fig. 44). Armature Winding for Two-pole Magnets. A. Gramme Type. As shown in the preceding dis- cussion, the Gramme armature may be looked upon essentially as a series of 2« coils uniformly spaced around an iron ring, upon which they are wound. Each coil has its terminals connected to adjoining segments Fig. 45. or divisions of a commutator, containing 2 a divisions. This arrangement gives a continuous closed electric circuit in the windings around the ring, exactly as would be given by a continuous helix (Fig. 45). If brushes be 98 ELECT RO-M AGNETI SM . placed upon the commutator at opposite ends of a diame- ter and a current is passed from one to the other, it must divide between two paths composed of the two halves of the armature. In a discussion of the action of the armature conductors as they cut lines of force, and the resulting electric pressure, drawings are very convenient. For convenience of reference to the figures given here- after, it is necessary to make a conventional arrange- ment for the purpose of denoting the direction of currents in conductors shown in cross-section. Indi- vidual conductors to be seen in cross-section will be denoted by small circles. When such wires carry a current, the direction of which is to be shown, they will be marked with a -1- or — sign, respectively, according as the current flows out of the plane of the paper towards the reader, or into the plane of the paper from the reader. With the assistance of this convention, and the well-known modification of Ampere's rule,* the figures show the principles of Gramme armature wind- ings very simply. Two-pole mafchines only will be discussed at present, the modifications required for Multipolar machines being taken up later. Instead of a series of insulated coils on a ring, the Gramme armature may be looked upon as a continuous helix (as already stated) of copper wire wound on an iron core, the whole being arranged with * If a conductor, in which a man is lying so as to loolc " down " along the lines of force, tends to move towards his left, the man is swimming with the current. In a dynamo armature, a current is caused to flow when the conductors are moved against this tendency (Lenz's law); that is, when the conductors are moved towards the man's right hand. In a motor, the armature conductors are caused to move towards the left by the action of the magnetic field when a current flows. ESTABLISHMENT OF ELECTRIC PRESSURES. 99 proper insulation, and mechanical devices for rotation between magnet poles and for collection of the current. For the latter purpose the brushes are usually made of thin copper sheets or wires. Each segment or division of the commutator is connected to a point on the helix, and the winding is thus divided into 2 a equal parts. The helix can be either right-handed or left-handed. When revolved towards the right hand in a right- handed field, as looked upon from the front or commu- tator end of the armature, the lower brush will be -f-, and the upper — , in a ring which is wound right-handed. In a left-handed ring, under the same conditions, the upper brush will be positive. This is shown in Figs. 46 and 47. In the winding of a Gramme armature, the wire is sometimes actually wound on continuously, taps being attached at proper points for connection to the commu- tator. But it is usual to wind the coils separately side lOO ELECTRO-MAGNETISM. by side. In this case tiie ends are led to the respective commutator divisions. Thus the beginning of coil i and the end of coil 2« goes to the first division, the end of coil i and the beginning of coil 2 to the second division, etc., making the effect of a continuous helix, as before. Economy Df construction usually does not allow an armature to be sufficiently large to generate commercial pressures with a single layer of wire, unless the capacity of the machine is great, or the desired pressure is small. The coils, therefore, are usually wound with several layers of wire, one on top of the other. In arc-light dynamos or other machines built for high pressures, the depth of winding sometimes reaches ten or twelve layers on the outer surface of the ring. As the length of the inner circumference of the ring is less than that of the outer, it is evident that the depth must be greater on the inner sur- face. Thus a case might occur where each coil contained six turns placed upon the outer surface in two layers of three conductors, while it would be necessary to put them in three layers of Fig. 48. t"^° each on the inner side of the ring, as in. Fig. 48. When a Gramme armature is of great radial depth as compared with its length, it is usually called a Disc Armature. In such armatures the pole pieces are so placed that the conductors on the sides of the disc cut lines of force, instead of the conductors upon the circumference, as in the ordinary ring armatures. ESTABLISHMENT OF ELECTRIC PRESSURES. loi B. Siemens Type. The winding of Siemens arma- tures is not as simple as is that of Gramme armatures. As in the latter, the coils of the Siemens armatures are DTHECTION OF LINES OF. FORCE 1 ■ ' J i Fig. 49. connected to the commutator so that the winding is equivalent to a winding made with a single wire. The winding may also be either right-handed or left-handed, and the position of the positive brush is determined as in a Gramme armature. The end of coil 2 a and the beginning of coil i are connected to the first division of the commutator ; the Fig. 49 a. end of coil 2 and the beginning of coil 3 to the third division, etc. Figures 49 and 50 show a single turn I02 ELECTRO-MAGNETISM . winding both left-hand and right-hand, and Figs. 490: and 50 a show a three turn winding. In the single turn winding coils between whose number there is a differ- DIRECTION OF LINES OF FORCEi. Fig. 50. ence of "«" or of a±\, lie side by side; the value of the difference depending on the winding, and varying at different parts of the circumference of an armature. If each coil consists of several turns, they may all lie side by side provided the circumference of the armature OIRECTION OF LINES OF FORCE^ Fig. 50 a. be sufificiently large. This is not usually the case, except in machines of large size or specially low press- ures. The windings must therefore usually be made ESTABLISHMENT OF ELECTRIC PRESSURES.- 103 in more than one layer, and the layers may be arranged either in vertical or horizontal order (Figs. 51 and 52). In the former case the coils are wound side by side in the same way as the single layer coils, and the order of winding may be coil number i, coil number «+i, coil number 2, coil number « + 2, etc. In the latter case the first half of the coils are wound in numerical order around the drum, and in such a number of layers as will exactly fill the circumference of the drum. The a+l a+3 Fig. 51. Fig. 52. second half of the coils are wound in numerical order over those already wound, and in an equal number of layers. In horizontal windings, the number of an outer coil is usually "a" plus the number of the coil under it. The figures show vertical and horizontal windings for two-turn coils, where the circumference accommo- dates one half the total number of conductors, and the winding is therefore in two layers. They make evident the fitness of the terms " vertical " and " horizontal." In certain types of windings, the coils are wound upon forming frames, and after a thorough insulating 104 ELECTRO-MAGNETISM. process, they are placed on the core. Figure 53 shows a single coil and a complete armature of the Eickemeyer type, in which the coils are made on exactly similar formers. Sometimes straight coils wound on formers are used, but the formers must then be of different sizes. Before the windings are put on an armature core it is usual to insulate it with two or more layers of shellacked canvas, oiled paper, rubber tape, or similar insulating material, and the whole usually receives a good coat of Fig. 53. Japan or shellac varnish. Where coils cross each other at the ends of drum armatures, or lie alongside of each other on drum or ring armatures, they are separated by thin vulcanized fibre, oiled paper, canvas, mica, etc. Gramme armatures can be more readily insulated than Siemens armatures, as the coils lie smoothly side by side, and thus can be effectually separated. In Siemens arma- tures, the coils cross over each other in passing across the ends, or heads, and satisfactory insulation becomes a more difficult matter. By liberal use of canvas, oiled ESTABLISHMENT OF ELECTRIC PRESSURES. 105 paper, mica, and japan, the insulation can be made satisfactory except for high pressures. The horizontal form of winding causes less difficulty on account of coils crossing on the heads, than does the vertical winding, but it introduces a lack of equality in the coils, which is a compensating disadvantage. The wire that is used in winding armatures is usually covered with two layers of raw cotton thread, the layers being wrapped in opposite directions. It is thoroughly impregnated with japan or shellac when placed on the armature. In some types of windings bare wires are used. In this case the wires are separated by strips of fibre, or similar insulation, and the core insulation is depended upon to prevent ground- ing. In other cases, bare copper strips compose the windings of toothed armature cores, and the insulation is effected by a sheathing of fibre or shellacked canvas, which is placed around each strip. In order that the production of eddy currents may be avoided in the iron cores of armatures, the cores must be subdivided by planes of subdivision perpendicular to the axis of rotation and parallel to the lines of force. Hence it is usual to build up the cores from discs of annealed sheet iron insulated from each other. The cores of Gramme armatures are sometimes made of annealed iron wire or tape coiled on a spider. On page 3 1 is given a relation between the external surface of a coil and the C^R loss which can safely be allowed in the coil. In that case 75" F. was assumed as the maximum allowable rise of temperature, and in armatures it is not permissible to allow a rise of tetnper- ature of much more than about 40° C, or 75° F., above I06 ELECTRO-MAGNETISM. that of the surrounding air. The air of an engine room on a hot summer's evening sometimes exceeds ioo° F., which brings an armature, in which the internal heating causes a rise of 75°, to a greater temperature than 175° F. This cannot be much exceeded without affecting the insulation prejudicially. When an armature is ex- posed to high temperature, the varnish or japan is soft- ened and runs out, and the canvas and oiled paper become slowly charred. This finally results in the current breaking through the damaged insulation, and consequent injury to, or destruction of, the armature. Excessive heating also injures an armature and its com- mutator, through the warping effect of the expansion and contraction. The machines of many manufacturers are permitted to heat to a limit much higher than that here given, some even reaching 80° C, but in the best practice the temperature limit is being reduced. In the case of a fixed coil, as already cited, it is found that the continuous loss of one half a watt in its windings for each square inch of surface will ordinarily cause a rise in temperature of about 75° F. A revolving armature acts to some extent as a fan, causing a current of air to cir- culate about it, with the effect of carrying the heat off from the surface quite rapidly. It is found that under average conditions of construction and operation, from 2 to 2^ watts can be dissipated (by radiation and con- vection) from each square inch of external surface of an armature, without causing its temperature to exceed the temperature of the surrounding air by more than about 40° C. The arrangements made for internal ventilation of the armature vary the allowable loss per square inch ESTABLISHMENT OF ELECTRIC PRESSURES. 107 of surface between wide limits, and the constant given here can only be considered as approximately covering average conditions, where little ventilation is attempted. The heat produced in an armature is due to three causes : 1. The C^R loss in the armature conductors caused by the useful current. 2. Hysteresis in the iron core. 3. Eddy, or foucault, currents in the core, and some- times in the conductors. It is found in average practice that from i to i^ watts for each square inch of external surface is lost in the cores of armatures as they are usually built, due to the effect of hysteresis and eddy currents in the iron discs. When the radiation of the heat thus developed has been taken care of, a margin of one watt per square inch remains for the allowable loss of energy due to the useful current flowing through the copper conductors. In order that the required area for the external surface of any projected armature may be determined, it is neces- sary to know how many watts due to the C'^'R loss are allowable. The loss must be determined from consid- erations of economy in construction. On the one hand, a reduction of the efficiency and an increase in the size of the armature core are required on account of increas- ing the C^R loss, but it results in a saving of copper ; on the other hand, an increased amount of copper must be used as R is decreased, with a consequent increase in cost of manufacture. The best results for dynamos designed for ordinary use, probably, can be gained by an examination of the machines of standard makers. io8 ELECTRO-MAGNETISM. The accompanying table gives the average C^R losses in armatures of various outputs, as allowed by a number of the best American manufacturers. The losses are given in percentages of the total output, and are based on the cold resistance of the armatures. The actual losses at full load will be greater than those tabulated by an amount proportional to the increase of R due to the rise of temperature (=i per cent of its value for each 2\ per cent C. rise of temperature). Table of C^R Loss in Armatures according to Average American Practice. R is taken as Cold Resistance at about 25° C. (75° F.). Capacity OF Dynamo. Loss IN Per Cent. S Kilowatt 4.0 10 " 3-4 IS ** 2.9 20 (( 2.7 25 (C 2-5 30 « 2.4 35 " 2-3 SO (( 2.2 7S " 2.1 ICX3 ** 2.0 R, and therefore the loss, increases i per cent of its value for each 2\ C. rise in temperature. The table is based upon the assumption of a periphery (circumferential) velocity of 3000' per minute. A veloc- ity as great as 4000' per minute is sometimes used, but for mechanical reasons the tendency is towards smaller ESTABLISHMENT OF ELECTRIC PRESSURES. 109 velocities. Where dynamos are designed to do special duty requiring extra mechanical stability, or low speed, or both, a velocity as low as 1600' or 1700' per minute is sometimes used. Three thousand feet per minute can be considered as a fair average for ordinary conditions. It is evidently desirable to make the velocity as great as mechanical or other limiting conditions will permit, as the output for a given armature varies in direct propor- tion to its speed. The C^R loss in an armature varies inversely with the speed, if the output be kept constant. Thus, in the case of a lo-kilowatt (10 K.W.) armature, running at 3000' periphery velocity, 3.4 per cent loss is good practice. If the same armature be run at 1000' additional velocity and the output not increased, either the current, and the size of the conductors in a proportional degree, or the number of armature conduc- tors, must be reduced. By either operation the C^R loss is reduced in proportion to the increase of the speed, and becomes 2.55 per cent. If the armature conductors are not changed, but the output is allowed to vary with the speed, evidently the actual watts in C^R loss remains constant, and the per cent varies inversely with the speed, as before. The value of the periphery speed seems to have no marked effect upon the allowable C^R loss per square inch of armature surface. Thus, in machines without special ventilation, experimented on by Rechnieski, small changes of the periphery speed made no apparent difference in the cooling effect. The increased cooling effect of faster rotation therefore probably compensates, in such machines, for increased eddy current and hysteresis no ELECTRO-MAGNETISM. losses. When special ventilation is arranged, the effect is still less marked. Special ventilation makes a large difference in the heating of armatures. Thus, Rechnieski found the rise of temperature in a ventilated armature to be only about 75 per cent of the rise in a similar but unventilated one. In order that the current may be safely carried by the armature conductors, experience shows that the density of the current should not be greater than about 2500 amperes per square inch of conductor cross-sec- tion. This is equivalent to about 525 cir. mils per ampere : 600 cir. mils is a better and quite usual con- stant, and 650 cir. mils per ampere is frequently used in designing the armatures of large dynamos or machines for special purposes. In special cases, the current den- sity in armature conductors may be made as great as 4000 amperes per square inch or about 325 cir. mils per ampere, but average conditions demand lower densities. The loss of energy due to hysteresis has already been shown to vary as B^-^, and also as the number of cycles per second. It is thus evident that a limiting value of B in armatures, may be reached, which cannot be exceeded without causing excessive heating. This is accentuated by the increase of eddy currents, which are in direct proportion to B, and the heating caused by them is, therefore, proportional to B^- In some dyna- mos running at a low speed the value of B in the armature is as great as 15,000 or 16,000 C.G.S. units. With so high a value of B, a careful selection of the quality of the iron is particularly important. Under ordinary circumstances, the value of B is likely to vary ESTABLISHMENT OF ELECTRIC PRESSURES, m from 6000 to 1 2,000 lines per square centimeter ; the value chosen in any case is determined by such con- ditions as the quality of iron to be used, diameter of armature, method of manufacture, speed, etc. For the average Siemens armature, 10,000 lines per square cen- timeter may be considered as a fair value, while the induction usually runs about 12,000 in Gramme arma- tures. All data necessary to determine the size of an armature for a given duty is now at hand. The determination of the ratio of length to diameter depends upon the mechanical conditions to be met. It is evident from the formula 10^x60 Wx 10^x60 that when a fixed periphery velocity of 3000 feet per minute is determined upon, IVand d may be changed pro- portionally, and E will remain constant. If B remains constant, the sectional area of the core is constant, and h (the length) therefore varies inversely with d. Hence,, in drum armatures, when d is less than h, if it is decreased while the cross-section is kept constant, the number of conductors will be decreased proportionally and the length of one turn of the winding will be increased in a less proportion. Hence the length of wire will be decreased in some degree, but the revolutions per minute must be changed in inverse ratio with d. This is too great a mechanical sacrifice to allow for the purpose of saving a small percentage in the copper. When d is greater than h, if it is increased, the num- ber of conductors is increased proportionally, and the 112 ELECTRO-MAGNETISM. length of wire is increased in a somewhat less ratio. Hence the total length of the windings increases more rapidly than the revolutions per minute decrease, and the extra cost for a reduction of speed is excessive. It is thus shown that the most satisfactory ratio of h length to diameter for general purposes is about -=i. d Special conditions, however, are often met which make a considerable alteration of this ratio advisable. In some cases h has been made as great as 3 ^ in Siemens armatures. For Gramme armatures, the case is more complex, and convenience of construction usually dic- tates the relative dimensions. The ratios are usually between -,=-, -, = 2, and -, = -, -;=-, ^ being the radial d 2 d d i) d 2i depth of the core. The choice of ratios in any case depends upon the capacity of the machine and the ser- vice for which it is designed. The number of segments or divisions in the commu- tator requires careful consideration. A large number of divisions makes a commutator which is expensive to build ; but if the number be too small, unsatisfactory results, due to sparking and consequent burning, are obtained. The number of divisions must be governed in some degree by the pressure generated. Where an arc is started, as by the spark at the commutator, it becomes destructive in proportion to the pressure between the bars. Hence, for dynamos generating 125 volts or less, the average pressure between adjacent commutator bars should not exceed 6 volts, 5 volts being good practice. In machines generating pressures as high as 1200 volts, too great a number of divisions is required by the limit ESTABLISHMENT OF ELECTRIC PRESSURES. 113 of 6 volts between bars, and as much as 25 or 30 volts is sometimes allowed. Since each half of an armature generates the full pressure, a 125 volt armature should have at least 42 coils and an equal number of commu- tator divisions. Not less than 50 coils would be better. Commutator bars are usually made of cast or drop- forged copper, and are preferably insulated from each other, and from the armature shaft, by mica. The following example will show the procedure to be followed in designing an armature. Example of Armature Calculations. In the case of a 25 K.W. dynamo, the table shows C^7? = 2.5 percent of the output =625 watts. Hence the armature should have an external surface of 625 square inches. With no special mechanical condition to meet, the best cross-section for a Siemens armature core is square; hence ^=11.5 and ^ = 132. The in- sulating material between the plates and the space occupied by the shaft compose about 20 per cent of the core in the average armature, leaving 80 per cent of iron; hence the effective area of this core is 132 x. 80 = 106 sq. in. = 684 sq. cm. If ^„= 10,000 C.G.S. lines per square centimeter, iV„ is 6,840,000 C.G.S. lines. At a periphery speed of 3000' per minute, the number of revolutions per minute is V= 1000. From the formula 6oy.Ey.\& "6,840,000 X 1000 is derived at once the number of conductors on the periphery of the armature. If 125 volts be desired at 114 ELECTRO-MAGNETISM. the brushes, 5=110 — , or there must be a total of 55 turns on the armature. On account of the loss of pressure in the armature, etc., it is desirable to add a few extra conductors, and for the best forms of winding an even number of turns is desirable. Fifty-six turns may therefore be chosen, and these can be wound on the core as 56 coils of i turn each, 28 coils of 2 turns each, etc. Choice must rest upon the conditions likely to give the least commutator sparking and the most compact winding. The armature under consideration should therefore be wound with 56 coils of i turn each. The circumference of the armature core is 36.13 inches, in which space must be wound 112 wires insu- lated with cotton, and sufficient space be allowed for fibre insulation between the coils. The latter may be from .02 to .05 inch in thickness, and in the first calcula- tion of the diameter of wires, .04 inch is a fair value to use. The cotton insulation on the wires consists of two opposite windings of cotton thread measuring about .016 inch in total thickness on medium sized wires. Fifty-six coils of i turn, i layer deep, use 112 fibre insulations, or in the circumference 112 x.04=4".48. One hundred and twelve wires wrapped with cotton .016 inch thick require for the cotton 112 X.Qi6=i".79, making a total of 6". 27 occupied by insulation, and leav- ing 29".86 for copper, or 1 12 wires of 267 mils diameter. The nearest wires drawn by American makers are num- ber 2 B. and S. gauge (diameter 258 mils, section 66,400 cir. mils), and number 4 B.W.G. (diameter 238 mils, section 56,600 cir. mils). The dynamo under considera- tion has an output of 200 amperes, or 100 amperes in ESTABLISHMENT OF ELECTRIC PRESSURES. 115 each conductor, which at 600 cir. mils per ampere re- quires a conductor of 60,000 cir. mils. The number 2 B. and S. wire is therefore of proper cross-section, and it may be used if the thickness of the fibre is properly cor- rected so as to exactly fill the circumference of the drum. It is to be remembered that the circumference to be filled has a diameter equal to that of the drum with insulation plus the diameter of the insulated wire. A large wire of circular section is uneconomical of space and hard to wind. Therefore some manufacturers divide the wire into two or more wires wound in parallel, each usually not exceeding in size a number 8 B. and S. gauge wire. In this case, in order to determine the exact size of wire and thickness of fibre to be used, the circum- ference on which it is to be wound must be determined. The diameter of the armature body is 11.5 inches. The body must be properly insulated, before winding, by a covering of shellacked canvas, rubber tape, oiled paper, and japan, or something similar. This may be esti- mated to average .025 inch in thickness, in other words ; .05 inch is added to the diameter of the body. The diameter of the wire may be approximated as .2 of an inch. Hence the diameter of the circumference on which the wire is wound is 1 1.50 + .05 -)- .20 = 11.75 inches, and the circumference is 36".9i. Of this, 4". 48 is used for fibre, leaving 32". 43 for conductor, or 290 mils per conductor. When this is divided into two wires laid side by side, it gives 145 mils per wire, of which 129 mils may be copper. Number 8 B. and S. gauge wire has a diameter of 128.5 mils, and a cross- section containing 16,509 cir. mils. To make the cross- Il6 ELECTRO-MAGNETISM. section required, demands 4 of the number 8 wires, and they can be wound two wide and two deep, thus ||o8llo8ll- Four number 8 B. and S. wires give a cross-section con- taining 66,000 cir. mils = 660 cir. mils per ampere. The external diameter of a finished armature must include the thickness of the binding wires with insula- tion under them, in addition to the insulated diameter of the core and the wires. The size of the binding wires depends to some extent upon the size of the arma- ture. They are usually made of hard drawn brass or german silver. For a 25 K.W. armature the size of binding wires can be taken as number 18 B. and S. gauge, which has a diameter of 40 mils. Four or five bands from f" to i" wide must be put upon the arma- ture. The insulation under the bands is usually made up of mica strips, oiled paper, or fibre, and probably averages in thickness about .020. Thus the 25 K.W. armature of the example will finish to a diameter of, say, 11.5004-. 050 + . 578 + . 120= 12^ inches. To determine whether the C^R^ loss is approximately that assumed, it is necessary to find the length of wire on the armature. The length of a turn equals approximately the perimeter of the armature -j- 15 per cent allowance for piling on heads, connections to commutator, etc. This gives 53" per turn, and 56 turns = about 250'. 250' of number 8 B. and S. wire measures .157 ohms. There are 4 wires in parallel in each turn ; hence the total resistance is one fourth of . 1 57 ohms. As the two halves of the arma- ture are in parallel, this is quartered again, and the cold resistance is ^^ =.010 ohms: and when the armature 16 is heated to 40° C. above ordinary air temperature, the ESTABLISHMENT OF ELECTRIC PRESSURES. 117 resistance becomes .012 ohms. With 200 amperes flow- ing C'^Ra=2.o per cent of total output with the hot resistance, which is less than the allowable loss for a 25 K.W. armature given in the table. The following additional examples will show how far the constants are likely to vary in actual machines. The first example is a Phoenix dynamo designed by Mr. W. B. Esson, who is a believer in excessively high periphery velocities. This accounts for the high veloc- ity (3950 feet per minute). The data for this machine is taken from Thompson's Dynamo-Electric Machinery. The other examples are standard dynamos built by dif- ferent American makers of high standing. I. Phoenix (English) dynamo : capacity, 9J K.W. ; normal pressure, 105 volts; normal maximum current, 90 amperes ; Gramme armature ; external diameter of arma- ture core, d= io|" = io".625 ; internal diameter of core, rf'=8".o; radial depth of core, ^=i^5g"= i".3i2; length of core, ^ = 9".o; net length of iron in core, 8".3i2; effective area of core, A=22 sq. in. = 142.26 sq. cm. ; rev- olutions per minute, V= 1420, giving a periphery velocity of 3950' per minute; external area of core =377 sq. in. ; cold C^i?„=324 watts = 3.4 per cent, giving i^ square inches per watt dissipated. Number of commutator divis- ions, 2^=36 ; each coil consists of 5 turns, making num- ber of conductors on surface, 5 =180; windings made, with square wire 0.180 square inches, making an area equivalent to 28,640 cir. mils ; cir. mils per ampere , „ T^T 10^x60x105 „ -. ^ ^ nnc T = 637; iVl = 2 = 2,645,000 C.G.S. hnes. \r 180x1420 B^ = — ^=17,400 C.G.S. lines per square centimeter. The large value of B^ in this dynamo is to be noted. Il8 ELECTRO-MAGNETISM. It is usual to make B^ slightly greater in Gramme arma- tures than in Siemens armatures (see page 1 1 1), but so large a value is likely to cause excessive heating, unless special care is taken in the selection of the iron for the core and in the arrangements for ventilation. 2. American dynamo: capacity, 22.5 K.W. ; normal pressure, 125 volts ; normal maximum current, 180 amperes ; Siemens armature ; diameter of armature core, (/=io^"=io".438; length of core, A=ii."5; effective area of core, .^=96.4 sq. in. =621 sq. cm.; revolutions per minute, V= 1 300, giving a periphery velocity of 3550 feet per minute ; external area of core = 508 sq. in; cold C^R^=2ii<:) watts=i.i5 per cent, giving 2 jlg- square inches per watt dissipated ; number of armature coils = number of commutator divisions, 2« = 40; each coil consists of two turns, making num- ber of conductors on surface, .S"=i6o; windings made with two number 6 B. and S. wires (.162— .178) in par- allel, giving an area of 52,500 cir. mils ; cir. mils per ampere = s83; N,= ^°^ ^ ^°^ '^^ =3,600,000 C.G.S. ^ 160 X 1300 hnes ; 5^=— ^=j8oo C.G.S. lines per square centi- meter. 3. American dynamo : capacity, 10 K.W. ; normal pressure, 125 volts ; normal maximum current, 80 am- peres ; Siemens armature ; diameter of armature core, ^=6".2S ; length of core, ^ = i2".o; effective area of core, .^=60 sq. in. =387 sq. cm.; revolutions per min- ute, V= 1600, giving a periphery velocity of 2620' per minute ; external area of core, 296 square inches ; cold C2i?„=384 watts = 3.8 per cent, giving | square inch ESTABLISHMENT OF ELECTRIC PRESSURES. 119 per watt dissipated ; number of armature coils = num- ber of commutator divisions, 2«=5o; each coil consists of 2 turns, making the number of conductors on the surface, 5 = 200; windings made with number 9 B. and S. wire (.148 — .164), giving an area of 21,900 cir. mils ; cir. mils per ampere = 548; N,= ^°^ x 6° x 1^5 ^ 2,345,000 j^ 200x1600 C.G.S. lines; B^ = — ^ = 9000 C.G.S. lines per square centimeter. ^ A somewhat different method of predetermining the constants of an armature is given by Monnier. Start- ing with the formula E= — , the resistance of the lo^ X 60 armature is assumed. If the length and diameter of the armature core (using a Siemens armature, for example) be represented by k and d, then the lengths of a turn can be taken as 2h-\-Tid, and the following equation is derived : where A is the cross-section of the wire in cir. mils, and 6 the resistance of a milfoot. If 8 be the diameter of the wire of which the winding is composed, and mh its insulated diameter, then Sm^ = 'Kd. Since the C^R loss in the armature is transformed into heat, the following conditions exist. In any length of the armature conductor, as X, the resistance is — , and the heating, when the armature current is C, is I20 ELECTRO-MAGNETISM. . 24 X — X — for each layer of wire. If the armature 4 A be wound with q layers, the total heat developed in a portion of the windings of length X, and of width mS, is 4A If i be the maximum safe rise of temperature above the surrounding air, and j the amount of heat dissipated per unit surface and per degree difference of tempera- ture, the following relation exists : 4A - -^ Letting 7 represent the density of current in the armature conductors in cir. mils per ampere, there results C= — , whence ^—- — -^^ = K=a. constant. 7 lyfno . 24 d If for g there be substituted the depth of winding in mils,/, divided by mBli.e. g=—], there results {1 „ = -^„ = K. ^, 4.- Z7/- SNVC The equation EC= — r ■ lO** X 60 then becomes EC={2uBmhK)hd, where u is the periphery velocity, and 7 These equations may be written hd= O, {2k + 2>d)d=P, ESTABLISHMENT OF ELECTRIC PRESSURES. 12 1 in which O and P are Icnown quantities when the values of E, C, -/?„, u, B, K, m, 7 and S are given by the con- ditions, or have been assigned such values as experience warrants. Solving gives h = -\S — , and d— =aP^ P-lO A similar solution may be made for the Gramme ring, resulting thus : hb=0, {k + b)d=P, requiring a solution by approximation to find the values of the unknown quantities. This is an unwieldy method of determining the relations of b, h, and d, and would usually give results of little value, since they must almost always be adjusted to conform to such conditions as may arise in the course of a design. 122 ELECTRO-MAGNETISM. CHAPTER V. THE MAGNETIC CIRCUIT OF THE DYNAMO. With the calculations for the armature of a dynamo completed, the calculation and design of the field mag- nets can be at once entered upon. The object of the field magnets is to afford a magnetic circuit in which a mag- netic pressure may be placed for the development of the lines of force which are required to pass through the armature. The total magnetic circuit, or path, of the lines of force may be considered as made up of three parts : the field magnets or frame, the air space or gap, the armature core. The reluctance of the air gap is always a large percentage of the total reluctance of the circuit. It sometimes amounts to more than 90 per cent of the total reluctance. Since the specific reluc- tance of air is unity, there must be considerable leakage of magnetic lines of force directly across from pole- piece to pole-piece, and therefore around the air gap and armature (see Fig. 54 and compare page 10). The leakage paths are in parallel with the useful path for the lines through the armature, and the number of lines of force in each path is inversely as the reluc- tances and directly as the magnetic pressure (compare page 8). The laws of parallel circuits can therefore be applied to the paths for lines of force exactly as they are applied MAGNETIC CIRCUIT OF THE DYNAMO. 123 to electric circuits. The conditions to be met in the two cases are usually quite different, however. Thus, electric circuits are usually in the form of wires, the dimensions of which are readily measured, and the currents are con- fined to them ; while leakage circuits for mag- netic lines of force usu- ally terminate in two surfaces of more or less indefinite form, and the exact areas of the paths are quite indeterminate. Fig. 54. The great area of the surfaces in which the leakage paths terminate reduces the total leakage reluctance to a magnitude directly comparable to that of the useful path through the air gap and armature. To know the number of leakage lines is therefore a matter of moment in determining the reluctance of the frame, and hence in calculating the field windings. The forms of leak- age paths, as ordinarily met with in dynamos, may be reduced by approximation to a comparatively few simple ones, and the total leakage reluctance can be calculated with some degree of approximation. Leakage Reluctance (P^.* The average lengths of the paths of the leakage lines are readily determined in most cases in practice, with a ♦ See Vol. 15, your. Soc. Tel. Eng., Forbes's discussion on Kapp's paper; Picou, Machines Dynamo-Electrique, p. 135; Kapp, Electric 'I'ransmission of Energy. 124 ELECTRO-MAGNETISM. fair degree of accuracy, consequently it is necessary to make limiting assumptions regarding only the areas of the paths. Conceive two surfaces facing each other in air, and a mean distance apart /, and divided into elementary areas dA. The magnetic conductivity of each tube between dA opposite elements is — —, and the magnetic conductivity between the surfaces is % —-, or P -Iff Fig. 55. Fig. 57. If the surfaces are equal planes opposite to each other (Fig. 55), this evidently becomes I A r, I P = 1'''''^^A When the surfaces are unequal planes opposite each other (Fig. 56), it is evident that L = 4l±Asi or P= ^^ . P 2/ A^ + A^ When the surfaces are in the same plane and close together, as shown in Fig. 57, the lines of force may be assumed to be confined between the cylindrical surfaces described with radii ^j and r^. MAGNETIC CIRCUIT OF THE DYNAMO. 125 or From the figure, dA = adr, and /= irr. 1-363 p P-- «log 10: When the surfaces in the last case are a considerable distance apart, it is necessary to change the assumed boundaries of the path of the lines of force. One may be taken to be a plane of width b, placed between the edges of the surfaces, and the other as made up of two quarter-cylinders joined by a plane of width b. If r be the width of the ^'^- ^^• surfaces, the quarter-cylinders will have a radius of r. From Fig. 58, dA=adr, and l=b + 'irr. But dr= — d{b + -Kr). I _a r^+-<"- d{b + 7rr) _ a , b + irr P^ttJi. b + 'rrr ".434 tt ^" b = -734« log; b + Trr 10" orP = - 1-363 a log b + irr 10" With these formulae for the value of P under various conditions, and that giving the value of P between two cylinders (page 131), nearly all examples arising in 126 ELECTRO-MAGNETISM. practice can be approximately solved. The total leak- age resistance is frequently formed of several paths in parallel, P for each path being separately calculable. An example is shown in Fig. 5.9, which is a combination of case 2 and case 3. Fig. 59. The figure shows a cross-section through the legs of a magnet, the dimensions being, height or length a; width w; thickness y^^ — y^; and distance apart 2r^ = b. The average width of the path between the opposite surfaces is 'W-\-{'w-\-7.r) , /I I ■ \ J I (w + r)a — L-^^ ^=w + r. ..A = {'w-\-r)a ana — =:^ — —'—, where P^ is the resistance of the path between the oppo- site surfaces. For the path on each side lying between the semi- circles -^ = .734«log^. For the total magnetic conductivity of the leakage path we take the sum of the several conductivities, or I 1,1,1 1,2 -vr J r, I MAGNETIC CIRCUIT OF THE DYNAMO. I2jr If the legs had been a considerable distance apart, this example would have become a combination of case I and case 4. ' To determine the reluctance between two cylinders of radius r, which are parallel and at a distance apart, centre to centre, b, it is most convenient to first find the reluctance of the path between two infinitesimal elements of length. The total reluctance is then readily found by summing up for the whole length of the cylinders. Figure 60 shows the cross-section of two cylinders A and B with centres at c and c' . A \ B/ — <^\3v "^ Fhy \ ''' A- ll " J 4 — ^/^^ ^/ Fig. 60. • Assuming the cylinder A to be at a magnetic poten- tial M^, and the cylinder B to be at a magnetic potential Mb, then the lines in the figure joining the cylinders show the form of the magnetic lines of force and the other lines show the form of the equi-potential surfaces in cross-section. The cross-section and length of the 128 ELECTRO-MAGNETISM. average path of the lines of force cannot be directly approximated, as in the simpler problems already passed over ; it is therefore necessary to find some expression which represents the magnetic potential ^at any point outside of the cylinders, and then by proper substitu- tions and integrations to solve for P. At a point of magnetic potential M, the rate of change of potential, or the magnetic force, measured along the direction of the axis of x, is evidently . dx At a little distance from the first point measured par- allel to the axis of x, the magnetic force is — — If the dx distance between the first and second points be infini- . • 1 -i, y^ dM dM' d'^M ™ , tesimal, there results = The number dx , dx dx of lines of force passing thi^ough a plane area of infini- tesimal dimensions, dyds, and perpendicular to the axis of X at the first point is evidently dyds, and the dx number passing through an equal area at the second point is dy dz. The difference in the number of dx lines of force passing through the two areas is therefore fdM-dM'\ , , d^M , , , \dydz = — — dxdydz. If this reasoning be applied to an infinitesimal cube with its edges parallel to rectangular axes, along which the total magnetic force is resolved, there is shown to be a difference in the number of lines of force passing through opposite faces of the cube as follows : MAGNETIC CIRCUIT OF THE DYNAMO. 129 d^M df d^M dxdydziox the faces parallel to the FandZaxes. dxdydz for the faces parallel to the ^ and Z axes. dxdyds for the faces parallel to the Xand Faxes. dz Unless the cube be a magnet, an equal number of lines of force must enter and leave it, hence — dxdydz -\ dxdydz -\ -—dxdydz = 0, dx^ dy^ dz^ ^M dm dm^^* dx^ dy^ dz''' If the magnetic field in which the cube is located be uniform, d'^'M is o, and the number of lines of force passing through opposite faces must be equal. If the cube be a magnet of pole strength "w," 477-^ lines of force must emanate from it (compare page 2), hence there is a difference of 4 vm lines of force between the number entering and the number leaving the cube, or d^M d'^M d'^M^ _^ t dx'' dy^ dz'^ In the solution at hand, each line of force may be assumed to be a curve lying entirely in a plane which is perpendicular to the axes of the cylinders. If the axis of z be taken parallel to the axes of the cylinders ^L-M. dxdydz is equal to zero, for there is no change of dz^ potential in that direction, and there results d^M , d^M 1 = o. dx'^ dy"^ * Often called Laplace's formula, t Often called Poisson's formula. I30 ELECTRO-MAGNETISM. Any ejrtjression for the potential M that will satisfy this equation will serve in the desired solution for P. In Fig. 6i, if two points be taken within the circles which represent the cross-section of the cylinders, and Fig. 61. on the line joining their centres, so that the ratio of the distances of these points from the circumference of either circle, ^, is a constant for all points on the circle taken, then the expression M=—A\og^—-^C fulfils ^2 the conditions. A and C are constants fixed by the conditions of the problem. The number of lines of force passing through an element of the surface of either cylinder is evidently ^iV=/i——(:/j. The total dr number of lines of force passing between the cylinders is therefore iV=/tt I ——(/.f, the integration being ex- •/ dr tended around the boundary of a cylinder. From M=-A\Qg^^C, and dM=- -A rda^ da^ a J' "<&! da^ dM dr~ -A dr dr «2 J MAGNETIC CIRCUIT OF THE DYNAMO. 131 ' dr , c dr hence N= -Ay, ds may be written rdldd, where dl is the thickness of the layer under consideration. The integral of the first term is therefore evidently dl times the summation of the angles subtended by the infinitesimal elements of a circumference at a point within it, and is equal to 2 Trdl. The integral of the second term is, in the same manner, dl times the summation of the angles subtended by a circumference at a point without, and is equal to zero. M —M Hence N=-2irAy,dl= ^ ' \ and therefore P= — M.-Mr, ^'«. ^log.^-^log,^2 'B 2 'KAfi dl 2 ivAfx, dl = 7/^°S« For any other length of cylinder, a summation of dl may be taken to the length desired. For leakage paths in air /A = I and I a ■737logioJ Before this formula is available for use, the value of J H must be given in terms of the diameter of the cylinders, and their distance apart (centre to centre). This value is £^_ d a~ b-^ip.-d'^' where d is the diameter and b the distance apart. 132 ELECTRO-M AGNETI SM . The term d : does not lend itself to easy com- putations, but its numerical value is constant for all diameters of the cylinders, as long as the ratio -is kept constant. Hence the reluctance between any two parallel cylinders can be readily found by the assistance of a table giving the reluctances between unit lengths of two cyl- inders for various ratios of -• A table quite similar to d the accompanying one was first given by S. P. Thomp- son in his lectures on the electro-magnet. Table showing the magnetic reluctance in C.G.S. units between unit lengths of two equal parallel cylinders surrounded by air, and hav- ing various values of the ratio -■ b b b ~d P PER CM. d i'PER CM. d P PER CM. 1.25 .19 4- .65s 7^5 .86 1.50 •30 4-5 .67 8. .88 1-75 •337 5- •73 8.5 .90 2. .42 5-5 .76 9- .92 2-5 ■5° 6. •79 9^S •94 3- •556 6.5 .815 lO- .96 3-5 .61 7- .84 To determine the reluctance between any two cylin- ders, find the value of - from their dimensions. d Take from the table the appropriate value of the reluctance per centimeter, and divide by the length of the cylinders in centimeters. MAGNETIC CIRCUIT OF THE DYNAMO. 133 The application of the leakage formulas may be seen from what follows. Fig. 62 a represents the outline of a dynamo frame, the windings of which are on the keeper. In a well-designed and efficient dynamo the reluctance of the portion of the limbs between the keeper and the pole-pieces is usually a quite small fraction of the total reluctance in the magnetic circuit. Hence the total magnetic pressure {M= 1.25 wc) can, with sufficient accu- racy, be looked upon as acting directly between the Fig. 62 a. leakage surfaces. It can also be approximately consid- ered as acting directly between the pole-pieces to generate the useful lines through the armature. With the lim- itations in accuracy due to these approximations, the following relations are now established. The total leak- age lines are, approximately, Ni=MXi=—, where X^ and Pi represent respectively the magnetic conductivity and reluctance of all the leakage paths in parallel. The useful lines are also approximately N^ — — — , where P„+„ 134 ELECTRO-MAGNETISM. is the reluctance through air gap and armature. The total number of lines in the frame is therefore approxi- mately N,=Na+Ni, and the ratio between the total lines passing through the frame and the number pass- ing through the armature is X^+„+Xi Pa+a + Pl This ratio, the importance of which was first pointed out by Dr. Hopkinson, is often represented by the letter v, and is called the Leakage Coefficient. Fig. 62 A. In dynamos where the windings are divided so that one-half the magnetic pressure is developed by a coil on each limb, the number of leakage lines cannot be regarded as directly proportional to Xi. This is evident from Fig. 62 b, which shows that only one-half the total magnetic pressure tends to send leakage lines across the space between the limbs ; because the difference of magnetic pressure between A and B can be taken as MAGNETIC CIRCUIT OF THE DYNAMO. 135 approximately zero, and that between C and D as approximately equal to M; hence, the average difference of magnetic pressure between the limbs can be taken as equal to \M. The necessary correction may be made in calculating Xi, giving a value that we will call X\. This can be directly combined with X^j^^ to find v as before. If the reluctance of the magnet frame is not compara- tively small, as assumed, the magnetic pressure causing leakage through the various paths is sensibly less than M, and must be different for the different paths. The difference of magnetic pressure between the pole-pieces is also sensibly less than M. Hence corrections must be applied to both X„+„ and X,. Errors in estimating the magnetic pressures at various points are evidently elimi- nated to a large extent from the value of v, for they are likely to affect both numerator and denominator X -VX of the fraction °+° — •' in about the same proportion. Moreover, the calculated value of v cannot be expected, and is not required, to be brought to an accuracy closer than 15 to 20 per cent of its true value in the finished machine. The surfaces terminating the leakage paths of actual dynamos are frequently irregularly curved and stand in various planes. It therefore is necessary, in such cases, to assume an average surface to be used in calculating. The windings of the field magnets of dynamos are usually classified according to their arrangement in cir- cuit. The principal divisions are two : separately excited 136 ELECTRO-M AGNETI SM . and self-excited, so called, respectively, when the mag- netizing current is supplied froni an external source or from the armature of the machine under consideration. Self-excited dynamos are again divided into series FIELD WINDINGS EXCITER a BR. EXTERNAL CIRCUIT SEPARATELV EXCITED Fig. 63. wound, shunt wound', and compound wound, depending upon whether : first, the whole current is led through a comparatively few turns around the field magnets ; FIELD WINDINGS A ARMATURE ^BR. EXTERNAL CIRCUIT 1 jTHiirTrinnr^ SERIES WOUND Fig.' 64. /Tfnnnnmrrn FIELD WINDINGS EXTERNAL CIRCUIT SHUNT WOUND Fig. 65. second, only a portion of the current is led, through a shunt circuit, many times around the magnets ; or thirds MAGNETIC CIRCUIT OF THE DYNAMO. 137 a combination of the first two. The third division, or compound winding, cSil be further subdivided according to the arrangenrent of the shunt winding. If this is connected around the series coil, as in Fig. 66, the compound winding is said to be long shunt, and it is short shunt, when the winding is connected directly from brush to brush, as in Fig. 67. The purposes to which the different forms of winding are usually applied will be discussed later (Chaps. VII. and VIII.). FIELD WINDINGS A ARMATURE l^n EXTERNAL CIRCUIT LONG SHUNT Fig. 66. FIELD WINDINGS / ARMATURE |feR EXTERNAL CIRCUIT SHORT SHUNT Fig. 67. The forms of two-pole field magnets are numberless, but in the standard machines they may be reduced to two principal classes : first, single horseshoe type ; second, double horseshoe type. Each of these may be subdivided into three typical forms, depending upon the position of the windings or coils : first, coils on limbs ; second, coil on keeper ; third, coils on both. The third division is not as often used as the others. In designing the windings of field magnets, a good foundation from which to start is the limit of C^R loss 138 ELECTRO-MAGNETISM. and of heating, as in the case of an armature ; hence, a table of C^R losses allowable in good practice follows. This is made up in the same manner as the table of armature C^R losses given on page io8. Table of C^R Loss in Field Windings of Shunt and Series Dynamos. R being taken as Cold Resistance at about 25° C. (75° F.). Per cent of Full Load according to Average American Practice. Capacity of Dynamo. Loss IN Per Cent. 5 Kilowatts 4-5 10 " 3-6 15 " 3-1 20 " 2.8 25 " 2-5 30 " 2-3 35 " 2.1 40 " 1-9 50 " '•7 60 " 1-5 75 " 1-3 100 " I.I R, and therefore the loss, increases i per cent of its value for each 2j° C. rise in temperature. The armature for a given machine having been fully determined, the area of the iron in the field magnet is fixed by the fraction —^ For wrought iron, in the best practice, ^^ varies from 15,000 to 18,000 lines per square centimeter, depending upon the quality of the iron and the conditions for which the dynamo is designed. For average commercial machines, 16,000 lines per MAGNETIC CIRCUIT OF THE DYNAMO. 139 square centimeter can be taken as a satisfactory value. For cast iron Bf varies in the best practice from 6000 to 8000 lines per square centimeter, and sometimes reaches 10,000 lines per square centimeter. For average com- mercial machines, 8000 lines per square centimeter can be taken as a satisfactory value. It is evident that the value of B in the field magnets is determined by considerations of economy of manufacture. Thus, to decrease B, it is necessary to increase the cross-section, and therefore the weight of the iron, of the fields. At the same time, the reluctance is decreased, which decreases nc, though the length of each of the turns in the windings is made greater. Hence, to decrease B, requires an increase in the amount of iron but effects a saving in copper. On the other hand, to increase B effects a saving in iron but causes an increased use of copper. A balance, which depends upon the relative cost of iron and copper in the finished machine, is sought. The value of v evidently depends upon the form of the frame and the value of /'„+„. As the reluctance of the air space is the major part of P^+^, v evidently depends upon the dimensions of the air space and of the leakage paths. Hence, if v be determined for one machine of a given type, it will have practically the same value for all other machines of the same type whatever their dimensions, provided the linear dimen- sions of the individual machines are always in the same proportion. In plain single horseshoe fields, v usually lies between 1.25 to 1.4 for the most efficient machines. In inverted single horseshoe (Edison) and plain double 140 ELECTRO-M AGNETI SM . horseshoe fields, v usually lies between 1.5 and 1.75. In making a first estimate of the size of cores, 1.3 and 1.6 are satisfactory values of v to use for the respective types of fields. Since the reluctance of the air space P^ is a large portion of P^j^^, it is evident that v will be a practical constant for a particular dynamo, over the whole range of saturation in practical working. The following table gives leakage tests made on two machines at various magnetizations. 10 K.W. Machine. 20 K.W. Machine. Magnetizing Power. ■0. Magnetizing Power. V. [ 2 3 4 "•59 1-59 1-57 1.S6 '•57 I 2 3 4 5 1.26 I-3I '•33 1.36 1-33 The range of magnetizing power used in the tests from which these tables are drawn, starts considerably below the normal magnetization and passes consider- ably above it. With a fixed sectional area of core and a fixed num- ber of turns in the winding, a cylindrical core will evidently require the shortest length of wire in the windings, and therefore the least weight of copper. Where economy in manufacture is important, a cylin- drical core is advantageous, as it lends itself readily to machine-shop practice. For these reasons, single horse- shoe magnets usually have cylindrical cores. Exam- MAGNETIC CIRCUIT OF THE DYNAMO. 141 pies : Edison dynamo, Thomson-Houston motor type dynamo, National dynamo. When the cores and pole pieces are forged from one piece, it is more economical to make the cores square with rounded corners. Exam- ple : Edison-Hopkinson dynamo (English). Consequent pole machines with the windings on vertical cores usually have cylindrical cores. Examples : Sprague motor, Rae dynamo, Manchester dynamo (English). When the winding of consequent pole frames is on horizontal cores, the cores are usually elliptical in section for mechanical reasons. Examples : Weston dynamo, Westinghouse horizontal type dynamo. Besides the general cases given above, there are numerous unclassed forms of dynamo fields with either cylindrical or elliptical cores. Examples of cylindrical cores : Gramme dynamos of certain types, Giilcher dynamo, Deprez dynamo, United States motor, etc. Examples of elliptical cores : Mather dynamo, Brush dynamo, various street railway motors, etc. In other dynamos the magnet cores are made from slabs or bars cut from merchant stock. Examples : some Siemens and Crompton dynamos. In the best dynamos, the form of core and frame is dictated by the required mechanical or electrical duty, economy of manufacture being con- sidered at the same time. In some instances the form has been due to a whim of the designer, but whimsical dynamos cannot succeed in commercial work, on account of economical considerations. Dynamos must be de- signed with due consideration for economy of manu- facture and for the conditions of their service. Dynamo designing is as much a science as steam engine designing, 142 ELECTRO-MAGNETISM. and it is as fully dependent on sound theoretical princi- ples. As in the case of the engine, theory must be guided by judgment and experience. For the determination of field windings, we have 1. A = ^^ Experience shows that .35 to .40 watts radiated per square inch of outer surface raises the temperature of the field coils from 30° to 40° C. (70° F.), which is as high as the temperature should go in good practice. Thirty-five to forty hundredths of a watt per square inch of outer surface of the coils is about equal to one-half of a watt per square inch of core surface on which the wire is wound. Hence we have 2. Length of core is such that one-half a watt (at loss given in table, page 138) will be radiated for each square inch of surface on which wire is wound. r, _ output X per cen t loss (table) 3- K, ^=1 = — X per cent loss. For series dynamos. Rj= — , and C}=Cxper cent loss, making Rf= — — For shunt dynamos. ox per cent loss The number of ampere turns is determined from the values of N and P, as already demonstrated, and the number of turns of wire is directly deduced. The mean MAGNETIC CIRCUIT OF THE DYNAMO. 143 length of a turn being determined, the diameter of the conductor can be deduced. The depth of wire on a core can be taken approxi- mately as ^ r, r being the mean radius of the core. On some machines this becomes as great as \r, and on dynamos of capacity less than 5 K.W. it is still larger. If the depth of winding is assumed to be \ r, the mean length of a turn is l=%Trr=%'rvd. Total length of wire TQ L = tl, where t= number of turns. Since R = -^ir . where cm 6 is the specific electric resistance and cm is the sec- ra tional area of the conductor, we have cm = —-- As cm is desired in circular mils, while L is in feet, and R in ohms, it is necessary for 6 to be the resistance of a wire one foot long and one circular mil in area, i.e. the resis- tance of one "mil foot," =9.6 ohms, hence cm= 2^— — R From wire tables, the gauge number and diameter of the conductor are at once determined when cm is known. As a check upon the magnetic determinations, it is best to calculate the value of B in the air space. This should usually be within the limits of 3000 to 6000 C.G.S. Hnes per square centimeter. Example in Determination of Field Winding. Let it be required to wind fields for the armature of the previous example, the fields to be of the Edison type, and v=\.6. Nf=N^ X 1.6=6,840,000 X 1.6= 10,944,000. 144 ELECTRO-MAGNETISM. Use 10,950,000. .5/ = 16,000. .-. A=68s sq. cm., and Df = 2g.$ cm. 29.5 cm.= ii".62S (ii|"). The cores of the Edison type are cylindrical, and in this machine should be iif" diameter of wrought iron. The table shows that a 25 K.W. machine may have a loss of 2.5 per cent in the field windings = 625 watts. Each core therefore should have 625 square inches external surface, making its length bf= — 4 = i7i". The ends of the winding should be protected by a fibre ring from ^^g-" to J" thick. \" is a good average thick- ness ; and as there is a ring at each end, J" in length is occupied by fibre, leaving i6|^" (i6".6) for winding space. The mean length of a turn /=|^7rx ii|" = 4i". i = 3'-42. We will assume that the frame is laid out on the drawing board and the value of v checked by application of the leakage formulae. The ampere turns required on the field must next be calculated by the methods given on pages 7, 43, etc. Thus the magnetic press- ure required to force N^ lines of force through the reluctance of the armature core and air space is M^ = N^Pa+a- The magnetic pressure required to force Nf lines through the frame is Mf=NjPj. Hence the total magnetic pressure is M^ + Mf=N-^P^^^ + NfPf=i.2t, nc, _ N,P^^^ + N,P, and hence nc= — ihe values of the various reluctances are calculated from the estimated cross- sections and average lengths of the paths of the lines of force. The lengths of the paths are most readily found MAGNETIC CIRCUIT OF THE DYNAMO. 145 by direct measurement from the drawing board. The average length of the lines through the armature is greater than the diameter of a Siemens armature, as the lines are required to spread on account of the shaft hole in the discs. It is therefore well to take the length as equal to the line e in Fig. 68. This is likely to be larger than the actual average length, but it errs on the safe side, and /"„ is always small in comparison with P^ so that errors in it do not greatly influence the result. The length of the air space is evidently the difference between the diameter of the armature core and the bore of the pole pieces. Its cross-section is found by taking the product of the length of the armature core times the length of the arc of the pole pieces. To this should be added about 10 per cent to allow for the "fringing" of the lines of force at the corners of the pole pieces. The reluctance of the frame is made up of the reluc- tances of the pole pieces, cores, and yoke. These are not often of the same cross-section or quality of iron, and hence their reluctances must be calculated sepa- rately. Thus Pf=Pj.-\-P^-\-P^. The lengths of the aver- age paths in the parts of the frame are readily taken from the drawing board, and the cross-sections are found from the known values of N^ and Bf. If the quality of iron differs in different parts of the frame, B, must vary accordingly. Evidently f'p^V /^«^« Z**-^* and p^ = _A^ + _^^_4„. /^p^j, ii-Ac i^Au 146 ELECTRO-MAGNETISM. In the example under consideration, we will assume the determination of M to be completed, giving «c= 17,500. The output in current of the dynamo being 200 amperes, the field current is 5 amperes (=2.5 per cent of 200) for a shunt dynamo, and therefore a total of 3500 turns is required, or 1750 turns is required per core. Therefore Z = 3.42 X 3500= 1 1,970 feet, Rf= — ^= 25 ohms, — 11,970x9.6 „ ^ ■ -1 cm = — '-^ 2_ = 45g6 cir. mils, 25 which is about the mean between the area of a number 14 B. and S. and a number 13 B. and S, wire. The "covered diameter" of the former is 80 mils when d.c.c. (double cotton covered). 208 turns of this wire will wind in one layer i6f" long, and 1750 turns require between 8 and 9 layers = 0". 70 depth. It is usual to allow a 10 per cent margin in the field resistance of shunt machines to allow for connections and the insertion of a variable resistance or "hand regula- tor." Making this allow- ance, 7? = 22.5, cm= "'97°X9o ^gioy which is a little 22.5 less than the area of a number 13 B. and S. wire, and the windings can be made with it. Number 13 B. and S. wire has a covered diameter of 88 mils d.c.c, and MAGNETIC CIRCUIT OF THE DYNAMO. 147 189 turns will wind in a layer i6|^" long, while 1750 turns require 9 layers and 49 turns over. The extra turns may be dropped, and the depth of winding be- comes o".79. The mean length of the winding per turn is 3'.25, and the total length is 11,060'. The total resistance is, therefore, 22.18 ohms, which is very close to that assumed, and is therefore satisfactory. It is usual to use a practical check, as in armature wire, based upon the current in the field wire per unit cross-section. On account of the cooling influence of rotation on the armature, the current density in arma- ture conductors can safely be more than double that in field conductors, therefore about 900 to 1000 cir- cular mils per ampere is a good limit in field wind- ings. The area of a number 13 B. and S. wire is 51,780 circular mils, which equals 1036 circular mils per ampere. We are therefore allowing ample cross-section when number 13 B. and S. wire is used. There is a disadvantage, however, in using too small a density of current in the wire, as it requires an increased total amount of copper in the windings. (Compare later pages.) A series winding is determined as follows : The total turns = -^ — = 88, or 44 per core. The approxi- 200 mate length of the mean turn is 3'. 25, and total length of wire 286'. R,= 125 x.025 ^^^^g ^^^^ cm = ^ = 1 76,000 circular mils, and the con- .0156 ductor is therefore 2 number i B. and S. wires wound in parallel, or better, 3 number 3 B. and S. wires wound in parallel. Number 3 B. and S. wire has a covered 148 ELECTRO-MAGNETISM. diameter of about 280 mils d.cc, and 59 turns will wind in a layer i6|-" long. There are 132 turns required per core, which make 2 layers and 14 turns over, per core. Three layers deep is .84 inch, which is practically the depth assumed. Number 3 B. and S. wire contains 67,000 circular mills in its section, hence 201,000 circu- lar mils carries 200 amperes = 1030 cir. mils per ampere, which is satisfactory. In all these calculations the results have not been corrected in order to provide for the pressure or current lost in the armature and fields. In a shunt wound machine, the speed can be increased two or three per cent if necessary to make up the armature loss, and the field loss merely serves to place a small additional burden upon the carrying capacity of the armature conductors. In a series machine the armature and field losses are both provided for by increasing the speed the requisite amount. It would be more scientific, but frequently less convenient, to exactly allow for these losses in mak- ing the original calculations. Where the field cores are divided as in conse- quent pole machines, it is evident that the ampere turns on each divided core must equal the number required on an undivided core used for the same work. If the armature and air space be the same in the two forms of field shown in Figs. 69 and 70, it is evident that P^^ is the same. To do the same work with the armatures, N^ must be equal for the two. Omitting a consideration of leakage, the same number of lines {—Nf) must pass through the total section of the cores and JiV, will then pass through MAGNETIC CIRCUIT OF THE DYNAMO. 149 each core of Fig. 69. As Bf is alike in the two cases, and Nf is the same, the area of each core in Fig. 69 must become half as great as the area of the core in Fig. 70. Hence Pf. = 2Pf, where Pj. is the reluctance Fig. 69. from A^ X.0 B' through either core, and Pf is reluctance from A "lo B through the core. But ampere turns reluctance X lines P.N, P,\N, ^. . ., ^ ^u ^ = = -i-^ = ^l2__/. It IS evident that 1.25 1.25 1.25 the weight of iron can be made alike in the two forms, while the length of wire re- quired is in the ratio of 2 : V2. The value of Rf should be the same in the two types, if the field loss be the same, hence the area of the wire must be directly as its length, and the weight of the copper is in the ratio „. ^^ of 2 : I. In this discussion leakage has been neglected, but 1 50 ELECTRO-MAGNETISM. evidently the same ratios are true if v be equal in the two cases, as for the Edison type and the consequent pole type. Where v is greater, as when the consequent pole type is compared with machines using the keeper for a bed-plate, the consequent pole machine is likely to prove of proportionally greater weight, and the ratio of the weights of copper is also larger. If one pound of copper costs eight times as much as one pound of iron in the completed machine, each pound of copper displaced by the use of less than eight pounds additional iron, effects an economy in the cost of the dynamo. Iron added to a machine frame dis- places copper when it reduces the magnetic resistance of the machine. Iron which is not useful in reducing mag- netic resistance, or in contributing mechanical strength or stability, is a positive disadvantage. It adds to the weight of the machine, and therefore to its cost in manu- facture and handling, without making compensation. It also increases the surface from which leakage lines can emerge. Where iron is properly disposed, and therefore displaces an equivalent amount of copper, economy is also effected, because the iron can usually be handled during the processes of manufacture at less cost than can the copper. These facts lead to machines with magnetic circuits which are carefully designed to make proper use of a maximum weight of iron. In the best types of ordinary commercial machines, the development of the magnetic circuit has reduced the magnetic resistance of the iron part of the circuit to from 10 to 30 per cent of that of the air space. Further increase of iron can therefore MAGNETIC CIRCUIT OF THE DYNAMO. 151 give little economy. For this reason there can be little advantage in increasing the comparative weight of consequent pole machines even when compared with forms in which v is considerably smaller. To bring the single and double horseshoe types to an industrial equality, copper must be economized in the double horseshoe type. The ratio of exposed surface of field core in the double and single type is evidently greater than unity. If the total watts lost in the field windings is the same in each case, the exposed surface per watt is greater in the double horseshoe field, and the density of current in the windings can therefore be safely greater. This decreases the weight of copper in the same ratio as the increase of density, but if carried to its ultimate safe limit, the ratio of weights of copper still remains considerably greater than unity. In order that the ratio may be reduced still further, the watts lost in the field must be increased. By a judicious increase in both the C^R loss and the density of current in the field windings, as compared with the single horse- shoe type, the consequent pole machine can be made commercially satisfactory without injury to the useful- ness of the machine. It has been frequently stated that the effect of joints in the iron of the magnetic circuit is to cause a material increase in the reluctance, but this has been disproved by Ewing's experiments, which show that the effect of a scraped joint is equivalent to the intro- duction of an air gap with a length of from three to four thousandths of a cen,timeter. As the joints in dynamo frames are usually smooth planed or turned, 152 ELECTRO-MAGNETISM. their equivalent air gap probably does not exceed five thousandths of a centimeter, when the joints are clean and bolted tightly together. Four joints in the mag- netic circuit, therefore, may make an equivalent gap of two hundredths of a centimeter, which is not within the limit of error in measuring the armature air space. The weight ,of copper on any machine can evidently be varied by changing the density of current in the wire. In the example above, if number 15 B.W.G. wire were used on the field, the dynamo would be more satisfactory in some respects, but the depth of winding would be increased, and therefore the volume or weight of copper would be greater. As the best machines are near the limit of economy in the proportions of the iron part of the magnetic circuit, it is evident that the air space should hereafter receive the careful and particular attention of designers. In attacking the problem of the air space, it is necessary to consider the question of armature reac- tions. This brings into consideration the forms of pole pieces, magnetic and electric balance of armatures, and the prevention of sparking. On the whole, the influence of the air space on armature reactions and on output is quite obscure. Deprez, Swinburne, and Ryan have endeavored to show that the magnitude of the air space should be dependent on the armature winding and the strength of field. On the other hand, Mordey, Kapp, C. E. L. Brown, Crocker, Anthony, and others, have successfully decreased the air space to a very small magnitude. The first point to be discussed covers the methods of decreasing the air space and the MAGNETIC CIRCUIT OF THE DYNAMO. 153 effect produced on the capacity of dynamos. The first armature, made by Pacinotti, was toothed, each coil lying in a notch ; but when large machines were built, it was found that the Pacinotti teeth caused trouble from sparking, and, therefore, smooth armature cores have been generally used. The toothed cores have two decided advantages : 1. The coils are protected from mechanical injury by the teeth between which they lie, and the direct mechanical bearing of the coils against the teeth mate- rially decreases the class of armature troubles that are primarily due to the armature wires chafing against each other, during the rapid changes of "magnetic drag" through which they pass. 2. The clearance between the armature teeth (iron) and the pole pieces (iron) can be reduced to the least distance compatible with mechanical safety. Hence the magnetic resistance P„^„ is materially reduced. Improperly designed teeth are likely to cause vicious sparking, and excessive heating in the armature core and the pole pieces, hence their disrepute with the earlier designers. If the teeth do not cover a large part of the armature surface, the lines of force become tufted in front of each tooth, as shown in Fig. 71. The passage of these tufts across the face and through the body of the pole piece evidently must cause foucault currents, which are dissipated as heat. The heating of the armature core and the sparking at the brushes are prob- '^' ably due to the sudden formation and disruption of the 154 ELECTRO-MAGNETISM. tufts, when teeth approach, and recede from, the edges of the pole pieces. The heating of the pole pieces can be prevented by making them laminated. Examples : Perrett motor. United States motor. In small motors, the sparking is so small that it may be overlooked to a large extent, and a satisfactory machine may therefore be obtained without additional precautions. In larger machines, the causes of irregular action must be removed in order to obtain satisfaction. This can be done by making the magnetic surface of the armature continuous, provided the pole pieces are properly formed. In old machines with toothed armatures, which are apparently incurably addicted to the vice of bad sparking, a more or less complete reform can frequently be effected by banding the armature with thin iron wire. This band serves to give a fairly uniform magnetic surface, and thus suppresses tufting. In designing a new armature, a practically continuous magnetic surface can be gained by. three methods : 1. Radial teeth very close together. 2. Trapezoidal or T-shaped teeth. 3. Armature conductors embedded below surface in holes or filled slots. Each of these constructions has been used with excellent results. Toothing or embedding evidently increases the mag- netic conductivity from pole face to pole face, but it is evident that the total cross-section of the teeth under a pole face at one time cannot be equab to the full cross- section of the armature core. The teeth are therefore likely to be quite highly saturated, and'the gain in mag- MAGNETIC CIRCUIT OF THE DYNAMO. 155 netic conductivity is not proportional to the reduction of the air space. For instance, if the outside diameter (over the bands) of the 25 K.W. armature referred to on page 113, be 12^", and the mechanical clearance ^", the bore of the pole piece will thus be 12^" in diameter, and the double length of the air space i". If the wires be placed in slots, 4 wires deep and 2 wires wide (Fig. 72), one-half the armature surface would be occupied by slots, leaving the other half for teeth. The air space can now be reduced, as far as mechanical safety will admit, to, say, ^g" (,31), includ- ing bands, and the depth of the ^^s- 72. slots may be about o"./. The reluctance between pole face and armature core is made up of o". 155 of air and o".7, which is one-half air and one-half iron. If it be assumed that all the lines of force pass through the teeth, then B in the teeth is about 20,000 (.5„= 10,000), and /u, for the teeth is about 30. Hence the reluctance of the air space becomes less than 0.4 of its value for the smooth core. When the conductors are dimensioned with special reference to a reduction of the space occupied by wire, the value of Pa+a ^^^ ^ toothed arma- ture can be reduced to a value as small as one-fourth its value when the armature core is smooth. If the arma- ture is worked at a lower magnetization, toothing has a more marked effect. Thus, if B^ be 8000 in the case above, B for the teeth is about 16,000, fi becomes 300, and the total air space reluctance is less than J its value for the smooth core. As the air space reluctance of properly designed two- 1 56 ELECTRO-M AGNETI SM . pole dynamos with smooth armature cores must be from 70 to 90 per cent of the total reluctance of the magnetic circuit, the reduction of reluctance by tooth- ing produces a marked economy in magnetizing force, and therefore in copper. Examples : Crocker-Wheeler motor, United States motor. Since all wires in which a current flows are linked by lines of force of their own, the current in the con- ductors of an armature sets up a magnetization which is distinct from the field magnetization, and the number of effective ampere turns on an armature is equal to ^ the current multiplied by the number of conductors on 1^ the armature (^Cx^S=^SC). When the commu- tating* plane coincides with the normal* plane of a dynamo, the magnetizations due to the field magnets and to the armature current, tend to set up poles in the arma- ture 90° apart. This is the condition of a stationary armature to which a current is given on the normal plane, as shown in Fig. 73. As lines of force of like direction tend to crowd together, a resultant magnetiza- tion of the armature is caused, which lies between the two components. Assuming the two impressed mag- netizations to be proportional to the ampere turns, respectively, on field and armature (which is not greatly in error, see Chap. VI.), they may be represented as two * The neutral plane may be defined as a plane which passes through the centre line of the armature perpendicular to the lines of force. The normal plane is one which is perpendicular to the line joining the centres of the pole pieces. The commutating plane is a plane which passes through the centre line of the armature and cuts the commutator at the points of contact of the brushes. MAGNETIC CIRCUIT OF THE DYNAMO. 157 Fig. 73. 158 ELECTRO-MAGNETISM. forces subject to the triangle of forces, and their resultant will be represented in magnitude and direction by the diagonal of a parallelogram, the two adjacent sides of which represent the two forces. Suppose OF in Fig. 74 is the magnetization due to the field when there is no current in the armature. If a current be passed through the armature, the magneti- zation due to it may be represented by OA, and the resultant of OA and OF by OR. The increase in the total num- ber of lines of force which pass through the armature and air space, due to the armature magnetization, makes it neces- sary to increase the magnetizing force O A in order that the field may be kept constant, i.e. the field ampere turns must be increased from OF to OR. This relation is not exactly true on account of the different values of the reluctance in the path of the lines of force set up by the two windings OA and OF (see Chap. VI.), and also on account of the bend in the curve of magnetiza- tion, but it is sufficiently exact to be of material use in the practical design of many types of dynamos. When the brushes have a positive or forward Lead* (see Fig. 73), which is true to a greater or less extent in all dynamos, the ampere turns on the armature can be considered as causing two magnetizations which are at right angles to each other. Those turns within * When the commutating plane does not coincide with the normal plane the brushes are said to have a lead, which may be either positive or negative when measured in the direction of the armature rotation. MAGNETIC CIRCUIT OF THE DYNAMO. 159 the double angle of lead a, are directly opposed to the impressed field magnetization, and the rest act to skew the field lines, as explained above. In a motor the same relation exists. The relative direction of field and armature magnetizations is reversed for a given direc- tion of rotation, but the lead is negative or trailing, and the turns within the double angle of lead oppose the field magnetization as before. The turns opposing the field magnetizations may be called the Back turns, and the others the Cross turns. The parallelogram of forces previously explained should be taken between the field ampere turns, calculated with an open external cir- cuit, and the cross turns. In an ordi- nary machine, when the current caus- ing OC cross turns (Fig. 75) flows through the armature, the field ampere turns must be approximately propor- '^' tional to OR -f- the back turns, in order to give constant pressure at constant speed. The following examples show the application of this reasoning to dynamos and motors of various forms. Double horseshoe type, 1 10 volts, 80 amperes. Shunt field ampere turns =7800; series field ampere turns at full load = 720, making the total field ampere turns at full load =8520. Armature ampere turns at full load = 5760, a=i5°, back turns =480, cross turns =5280. To compensate for the loss of pressure due to arma- ture and series field resistance, about 400 ampere -turns are needed. By calculation, OR = 7800. Adding 400 ampere turns and 480 ampere turns to coiiipensate i6o ELECTRO-MAGNETISM. the loss of pressure and the back turns, makes the total calculated ampere turns on field, at full load, 8680 and the increase required for compensating the effect of the- load 880, which is not wide of the mark. Single horseshoe type, 125 volts, 80 amperes. Shunt field ampere turns at no load =9470, at full load = 13,440. Armature ampere turns, full load 8000. a = o. Fig. 76 s. Calculated field ampere turns, full load, 12,400. Tx> compensate the loss of volts due to the armature resist- ance requires, at full load, an additional 600 ampere turns, more or less ; making the total calculated ampere turns, at full load, 13,000, which is very close to the number experimentally determined. Inverted single horseshoe type, 112 volts, 24 amperes. Shunt field ampere turns at no load = 2600. Shunt field ampere turns at full load =3200, of which 200 are MAGNETIC CIRCUIT OF THE DYNAMO. i6l required to compensate losa of pressure due to armature resistance. a = o. Armature ampere turns at full load = 2300. Calculated increase in ampere turns at full load, allowing for the C^R loss, is 1000. Double horseshoe type, 400 volts, 150 amperes. Shunt field ampere turns =32,700. Series field ampere turns at full load = 1950. Ampere turns required to com- pensate C^R loss in armature at full load = about 700. a = o. Armature ampere turns at full load = 14,500. Calculated increase in ampere turns at full load, allow- ing for C^R loss, is 3800. Single horseshoe type, 500 volts, 100 amperes. Shunt field ampere turns =21,800. Series field ampere turns at full load =4450. Armature ampere turns at full load =8700. a=is°. Back turns =700, and cross turns =8000. Compensation for armature C^R loss and over-compounding = about 2000. Calculated series field ampere turns at full load, allowing for C^R loss and over- compounding = 4100. Inverted single horseshoe type, 1 10 volts, 30 amperes. Shunt field ampere turns =5200. Series field ampere turns at full load = 2400. Armature ampere turns at full load =5400. a. = o. Compensation for armature C^R loss = about 1000. Calculated series field ampere turns at full load, allowing for C^R loss, =3300. It will be noticed that the calculated increase of field turns required to compensate the effect of armature reaction is usually greater than the actual operation of the machine required. In other words, the armature reactions have a smaller effect than is assumed in the application of the parallelogram of forces. This plan l62 ELECTRO-MAGNETISM seems to have been originally applied by Dobrowolsky to dynamos in which the armature wires were embedded in the iron of the core, which therefore had a magnetic circuit for the hnes of force due to the armature wires, of comparatively small reluctance. In such armatures the reactions are large. For ordinary armatures, where the wires are on the surface of a drum, if OC is taken as from J to f of the cross turns, as suggested by Kapp, the result comes closer to the truth. Seven-tenths may A Fig. 76. Lines of force due to field coils; no current in armature. be taken to represent a fair average to be used in general designing. For example, in the case of the last machine given above, if the resultant of the field ampere turns at no load, and 0.7 of the armature ampere turns at full load, be calculated, the number of additional field ampere turns at full load is shown to be practically 2350, which is almost exactly the number shown by experiment to be necessary in maintaining a constant pressure. Designers of some types of machines often calculate the series field ampere turns MAGNETIC CIRCUIT OF THE DYNAMO. 163 Ns /'• Lines of force due to armature; no current in field coils; current brought to armature on neutral plane JVS. Lines of force due to the resultant effect of current in armature and field windings; current brought to armature on neutral plane J\^S. 164 ELECTRO-MAGNETISM. as a fixed ratio of thp ampere turns on the armature. Esson gives the ratio which the compensating or series ampere turns should bear to the total armature ampere turns as two-thirds. The cross-turns on the armature tend to change the distribution of lines of force on the pole faces, skewing them over from the entering tip to the trailing tip of the pole pieces in the case of a generator, and in the opposite direction in the case of a motor. In order Fig. 783. that a machine may give a maximum output with the least sparking, it is necessary for the brushes to be set at the points where the coils do not cut the lines of force of a strong field. Hence, when the resultant direction of the lines of force passing through the arma- ture is changed, the commutating plane must also be changed. Each advance of the commutating plane evi- dently causes an advance in the position of the poles in the core due to the cross-turns on the armature, and causes a greater skewing of the lines of force (see Figs. 76 to 79). MAGNETIC CIRCUIT OF THE DYNAMO. I6S If no other action came into play, it would be impos- sible for the forward movement of the brushes to catch up with the neutral plane, but in practice, as the commutating position is advanced, the lines of force are crowded, or piled up, in the trailing pole tips, until further skewing of their path through the armature is impossible, and the commutating plane overtakes the Fig. 79. The effect on resultant lines of force caused by moving poles in arma- ture through bringing current to it on commutating plane CD. neutral plane. The result of the lines of force skew- ing or piling up in the trailing pole tips is to give a sensitive commutating plane, and therefore a lead which must be varied with all changes of load. It is also likely to cause sparking, which cannot be entirely suppressed. It therefore is desirable to so form the pole pieces that the piling up of lines of force cannot 1 66 ELECTRO-MAGNETISM. occur. The first point to be gained is a stiff field, i.e. one which in itself has considerable stability. This requires a strong field, with a uniform distribution over the pole faces. By a proper design of the magnetic circuit and of the magnetizing coils it is easy to gain a strong field. To get a fairly uniform distribution over the pole faces, even when the armature is at rest, requires careful designing of the pole pieces. All corners on the pole pieces that are presented to the armature must be care- fully rounded off, and the ends of the pole pieces must be bell mouthed, as shown in Fig. 80. To avoid the piling up of lines of force at the tip, it is necessary to in- crease the magnetic resist- ance of the air space (or its equivalent) at the sides of the pole pieces, and under the tips. This can be done 'either by thinning down the pole pieces or by increasing the air space under the corners. The latter plan, which is shown at the left hand of Fig. 81, is usually most sat- isfactory, as the corners can be well rounded off, and the reluctance toward the sides is not dependent upon the saturation of the pole tips. The form shown in the right hand of Fig. 81, even with the armature idle, is likely to give a distribution that is thinnest at the middle of the face and strongest at the tips. It is evidently dependent MAGNETIC CIRCUIT OF THE DYNAMO. 167 upon the saturation of the trailing tips "a" to hold the magnetic lines in position, and the field is not stiff, but it may be entirely satisfactory when the leakage between the pole tips is sufficient to keep them always saturated. The first form causes the lines of force to be thinnest near the edges, when the armature is idle, on account of the increased air space under the tips. The field is there- fore more likely to be stiff. The stability of the field and the value of v also depend on the angular embrace (angle /3, Fig. 81) of the pole pieces. A large embrace brings the tips close together and increases v to an ex- cessive value, while a small embrace decreases the cross- section of the air space and thus increases its reluctance. In the best dynamos the an- gular embrace usually varies from 120° to 140°, and its exact value must be determined by the judgment of the designer. The form. of the pole tips has a decided influence on the lead, and the obtaining of sparkless commutation. While an armature coil approaches the positive brush, for instance, one-half the total current flows through it towards the brush. When the coil reaches the brush, it is short-circuited by the toe of the brush resting across the "two commutator strips to which the coil is connected. When the coil has passed beyond the brush, half the total current again flows through it towards the brush, but the direction of the current through the coil is reversed. 1 68 ELECTRO-MAGNETISM. If commutation be effected in a field which tends to uphold the current in the short-circuited coil, a large current may flow, with the result of excessive heating in the armature. This current must be forcibly reversed as the coil leaves the brush, and therefore to prevent sparking, the commutating plane must be in angular advance (negative for a motor) of the neutral plane, an amount which is sufficient for the short-circuited coil to be influenced by the field of the entering pole tip. This field can be made of such strength that, during short circuit, the current in the coil is reduced to zero, reversed, and brought up to its normal value. There can then be no undue heating, or sparking when the coil is again introduced into the circuit. In order that the current in the short-circuited coil may be influenced by a weak field, thus making a small lead possible, the self-induction, and therefore the number of turns in each coil, must be small. To easily effect the proper reversal of current in the short-circuited coil, the pole tips are often extended in the middle (Fig. 82). The extension should be rather thin on the edge, so that the field under it is small and fairly uniform. The brushes may then have considerable range of position under a given load, without causing sparking. To avoid a large lead, and consequent back turns, the elongated tips probably should come within 15° or 20° of the normal plane, while the polar embrace measured to the points A probably should not exceed 130°. (Compare Transactions American Institute of Electrical Engineers, Vol. 7, p. 218.) It must always be remembered that sparking can be MAGNETIC CIRCUIT OF THE DYNAMO. 169 entirely suppressed only when the armature is in good magnetic and electric balance. An armature is in mag- netic balance when coils at the same angular distance from the com mutating plane, but on opposite sides of it, are threaded by the same number of lines of force, and when the coils short-circuited by the two brushes have the same angular position with reference to the neutral plane. An armature is in electric balance when all the coils have the same electrical resistance. A Gramme armature is usually in good electric bal- ance, but is likely to be out of magnetic balance when Fig. 82. used in single horseshoe fields, unless the latter are very carefully designed. A horizontally wound Siemens armature is usually out of electric balance, but in mag- netic balance. A vertically wound Siemens armature may be so wound that it is exactly in both magnetic and electric balance. The form and cross-section of the pole pieces have another element requiring attention in the case of sin- gle horseshoe frames. If the pole pieces are tapered at the ends, as at CC in Fig. 83, considerably more than one-half of the lines of force may enter and leave the armature upon the keeper side of the line AB. In this case there will be a resultant pull, due to the tension I70 ELECTRO-MAGNETISM. of the lines of force, which will crowd the armature against the keeper side of the bearings and may cause severe heating. In the in- verted single horseshoe the weight of the armature will partially or wholly counteract this pull, and in the ordinary type the armature may be placed eccentrically in the bore of the pole pieces, so that the air space is longer below. Other devices for making the reluctance symmetrical have also been used, but the best plan is to make the ends of the pole pieces of a suffi- ciently large cross-section to cause the field to be natu- rally symmetrical with regard to the plane AB. Fig. 83. COMPENSATION FOR CROSS-TURNS. 171 CHAPTER VI. COMPENSATION FOR CROSS-TURNS, AND THE EFFECT OF BRUSH CONTACT. With the magnetic effect of the armature coils com- pensated, the difficulties encountered in obtaining a sparkless collection on a plane of commutation which is stationary at all loads, would almost vanish. Many plans for effecting the compensation have been ad- vanced,, but they have usually been of an impracticable nature. Consequently the methods, already discussed (Chap, v.), for reducing the effect of the evil to a minimum, have been generally adopted to the practical exclusion of schemes for its eradication. The latest device for compensating the effect of cross-magneti- zation has been brought to apparent success by Pro- fessor H. J. Ryan, though little practical experience in the use of his device has yet been had. If each armature coil were paralleled by an equal coil which carried an equal current in the opposite direction, it is evident that the magnetic effect of the armature coils would be neutralized. Such a neutralizing layer of coils exists in a motor generator when the motor and dynamo armature wires are wound side by side on the same core, as is sometimes done, but in an ordinary machine the neutralizing coils cannot be placed on the 172 ELECTRO-MAGNETISM. armature, nor can they be placed in the air space unless the depth of the gap be increased unduly. However, a series of coils may be arranged to embrace the arma- ture in the general plane of the lines of force, by pass- Fig. 84. ing wires through holes or grooves made in the faces of the pole pieces (Figs. 84 and 85). If the turns of wire in the coils be equal in number to one-half the number of cross-turns and be connected in series with the external circuit of the dynamo, their magnetic effect can doubt- less be made to practically neutralize the effect of the COMPENSATION FOR CROSS-TURNS. 173 cross-turns. If the neutralizing layer in the faces of the pole pieces be uniform over the whole of the faces, and the commutating plane remain stationary under Fig. 85. the entering corners of the pole pieces, the neutraliza- tion ought to be quite exact. With a lead either greater or less, a portion of the cross-turns must remain to a certain extent uncompensated, and if the lead be vari- I-. ELECTRO-MAGNETISM. able, the compensation may be fairly exact at one load and less exact at others. Professor Ryan says, regard- ing- one of the dynamos built according to his designs : " In the performance of this machine, as well as in that of the first one that we constructed, we find that by the use of the balancing coils all cross-induction may be avoided or it may even be reversed in its effects. In the first machine the number of balancing turns was variable and it was found entirely possible to over- compensate the armature reactive effects so as to get the strong pole corners where we ordinarily would get the weakened ones. We find with the use of the balancing coils that the magnetization through the poles, air gap, and armature do not undergo a redis- tribution under any load ; that the armature current does not alter the total magnetization through the armature at'any value; that the neutral point remains constant ; that the diameter of commutation with metal- lic brushes changes only by the small amount necessary to balance the self-induction of the commutated section by the field in which it is moving ; that regulation for constant current may be effected without change of the diameter of commutation by varying the magne- tization through any limits ; that by proper designing, the output for a given weight of the completed machine may be quite largely increased over that which is realized in the common practice of to-day ; and that the air gap may be made as small as mechanical require- ments will permit without changing the performance of the machine, thus enabling one to realize practically the advantages of differential excitation that is utilized COMPENSATION FOR CROSS-TURNS. I7S SO successfully in the modern alternate current trans- former." Figure 84 shows a half-elevation and half-section of a small four-pole machine arranged for Ryan coils, and Fig. 85 shows the elevation of a two-pole machine similarly arranged. The first machine is a shunt wound dynamo of 16,000 watts capacity designed to run at 400 revolutions per minute; the second machine is a series motor designed to run at i960 revolutions per minute under a constant pressure of no volts and to develop two horse-power. The effect of the compen- sating coils is excellently shown in the series of figures 86 to 92, which represent magnetic dilStribution curves f-^ EXPLORATION 1 CURVE, AT NO LOAD.I 100 / \ EXCITING CURRENT 10.7 AMP. T / \ OPERATED AS A MOTOR, 80 / \ / \ 00 rr- '/ N / \ 40 ■/ z \ ^^ / :3 S, £0 i^ / (r cc 20 s . / / a . Q. i s. A / / V •* V 8 2 2 ! a 4 2 a a 3 ) 3 ! 3 1 S nh i 4 \ 1 1 ! 1 I 1 > 1 sT 1 , inn Fig. 86. taken by the pilot-brush method (page 209), while the machine of Fig. 85 was operated under various con- ditions. The effect of the compensating coil is made so evident by the figures that comment is unnecessary. 176 ELECTRO-MAGNETISM. ^ -^ ~. \ EXF Sf .0„U,0 < CURVE fulI load 100 / V=114; C = 26. / "w SPEED, 1*800, 80 J ^ L wiTHnuT rn.i / \ GO s> 1 1 \ ^ 10 <■/ y s *? '/ CO y' \ 20 l< y " /^ ffl ^> 0. / V 1 ,■; / 3 y / \ M y i ^ s / L L Fig. 87. ^ ■s E {PloratIon £3^ ^ 'ULlJ Loio. 1 y / \ - IB. C=25. mNG-CliRRENT ED ERATED AS A MOTOR, — / / "N s SPE OP J / \ ,>^ / \ "/ s, ,■* P> S, 10 t^ \ 4 / 3 \ 1 / % X 01 / ^ 0. 1 / \ \ * 4 \ ^ T 8 2 2 2 S 1 £ G 9r 1 3 J ; 2 a , ! /» S i 1 , '■ 1 1 1 \\ I 1 iT L / X . " 7?^ on ■^ _ ~ Fig. 88. COMPENSATION FOR CROSS-TURNS. 177 100 ~ /^ s —' EXPLORATION cORVE FULL LOAD.] / \ V=105 C=24 5 80 / \ EXCITING CURRENT, 2600 TwC / r \ OPERATED AS A DYNAMO L WITH COfL. 1 M 60 .\V / ^ "/ 1/ \ ^10 ,-^° y CO \, ^C [y £ s. 3 < f^ 1? — -i. ^ m "" / 3i / \ N S V] ( y / /7 V ^Y, 1 ^1 S i 2 ! 2 1 2 > 2 i 3 1 3 >, a M i 1 1 M Mc 1? ',^ ^ri \ \ M; R" Sti2 atic . Fig. 89. im ^~ ■^ — — — EXPLORATIOfJ curve', fJll'lOa'd. V=97 C=24 EXCITING CURRENT, 2600-TwC- ePEED, 1800 - ^ "" > 80 ..■'^ / \ OPERATED AS A DYNATMO , P > \ WITHOUT COI I • ■ ' ,*' / \ § ^ ;/ \ 1 ■A \ - / CD / "S. N s. CD D 20 / ■s V % / ^ V \ * % J / ^ \ s N "if \ oTi 8 2 1 2 2 a 1 2 5 2S 3b 3 1 ^ a/^! L 31 d'a t i J f 8 1 S'i Ci s^^ 8 V <^ (> \ ^ SC^ if-' \ ^ ^^ <~ .#' X Fig. 90. 178 ELECTRO-MAGNETISM. ^ N EXPLORATION CUHVE 1 — 1 — 1 — ! FULl. LOAD. 10 I* s EXCITING fiURRENT, rB0.T^yO / \ s SPEED, 1B00 .30 t f V V i«'<" =P"- p '' A / N s §20 •/ I \ 3 •A y 3 cr § 10 ID \( •:> a; V A m * «. "> 8: ^ \ J it!; i / S' \ ..'1 1 f> q 82 a i 2(> 2 8 ! 3 2 3 1 3 li/s 8 i » fj ^ J J _ Fig. 91. 6a ~ n ~ n — 1 EX ' V= ■loratIon curve, ra Ll.!oac - so z' — ^ =36. C=20. y f s s SPEED, 1800 4ft / \ OPERATED A3 A OYNA MO 5/ \ J 30 20 / \ / \ ^n= \ \ \ / / .'/ ^ \ 3 1 1 A i 10 / / r 7 s »,., (D \ / a, (r / / / 1^ / \ > o! \ / / / i \ 1 i / 1 2 1 i 1 (il 8 2 ) 2 I 2 1 2 > 2 1 3 1 3 i 3 p's i 1 1 \ ( } on the pole face at a distance a from the centre, we find that the induction within the air space at / is due to the action of all the current elements to the right and left of the point, the integration being extended to the edges of the polar face. A current * Kapp, on dynamos in Practical Electrical Engineering. COMPENSATION FOR CROSS-TURNS. I8S element ^dy at the distance j from p produces a magne- tizing force H= Lli^^ and this integrated over all the elements to the right of p gives the induction through / due to the part of the current sheet that lies to the right of /. Neglecting the comparatively very small magnetic resistance of the iron part of the path of lines, this induction is ^^^|^(^-^)- ^^ ^ similar manner we TTi— ~ iP pole Piece Developed. ! ' I I " find the induction due to that part of the current sheet which Hes to the left of /, or — ^— |-^f- + <7J. This is obviously of the opposite sign, and the resultant induction is the algebraical sum of these two values ; namely, ■ • ^'^ 2 a. For rt = o (i.e. for the centre of the pole piece), 2S ^ the induction is zero, for «= - ij.e. for the edges of the pole piece) it is a maximum, being positive for 1 86 ELECTRO-MAGNETISM. one and negative for the other edge, as shown by the sloping line BB. Its value is 1.25 7X 2h 1.2; X 20 ird This is the induction due to the armature cross-turns only, but in addition there is the induction due to the exciting coils of the field magnets, and to find the true induction within the air space we add these two values. Fig. 101. In Fig. loi is shown the curve B^B'B"B^, represent- ing the induction due to the cross-turns (also Fig. 100), and also the curve B-^^F'F"B^ representing the induction due to the field magnets. The curve B-Ji' WB^ repre- sents the resultant magnetism. The figure shows plainly that any construction which increases the reluctance in the path of the lines of force due to the cross-turns, and thus decreases the height of Q B' and Q" B" , must de- crease the, distortion of the normal field. This increase COMPENSATION FOR CROSS-TURNS. 187 of reluctance may be gained by uniformly increasing the depth of the air space ; by making a single slot across the middle of the pole piece, as shown by the dotted lines in Fig. 100; by placing slots at intervals all the way across the face of the pole piece, as in the Ryan device (Figs 84 and 85) ; by arranging the pole corners so that they are continuously saturated by magnetic leak- age ; or by making the bore of the pole pieces elliptical, as explained on page 162. By the last two methods the reluctance in the path of the lines due to the cross- turns is materially increased without an equivalent increase of reluctance in the path of the effective lines, and since the expense of this construction is small in many types of machines, it is particularly advantageous. That any change in the depth of the air space has a marked influence on the number of lines of force developed by the cross-turns on an armature, is a matter of common observation. A maximum effect is observed in machines where the armature conductors are embed- ded in the iron of the armature core, when the mechanical clearance, and consequently the air space, is small. It has become a common practice to simply increase the air space of such machines by boring out the pole pieces, in order that the evil results of a variable lead and severe sparking may be reduced. This increases the reluctance of the path of useful lines of force (as well as that of the lines of force from armature turns), and necessitates an additional expenditure of energy for excitation, which in turn requires additional cost for the copper in the field magnet windings. It may be safely said that this construction simply reduces the 1 88 ELECTRO-MAGNETISM. effect of the evil instead of striking at its root, and it causes the loss of much of the advantage of embed- ded armature conductors. The lamination of the pole pieces in planes parallel to the armature shaft has been tried with excellent results. The lamination required for this purpose is at right angles to that mentioned on page 151, but it might serve to reduce foucault cur- rents in the pole pieces equally well. It would seem, as already stated, that the mutual magnetic effect of the two windings on the double arm- ature of a motor-generator with one armature should be zero. It is found in practice, however, that vicious sparking is a common habit of motor-generators of any considerable capacity which have the motor and dy- namo windings on the same armature core, and that the commutating plane of both commutators is very sensi- tive. The difficulty seems to be caused by the mutual induction between the two windings, on account of which the two currents mutually interfere at commuta- tion with the proper reversal of current in the coils which are short-circuited. On account of this difficulty it is now usual to make each motor-generator with two sets of fields and two armatures, so that it virtually consists of a separate motor and generator with their shafts coupled. Instead of neutralizing or balancing the magnetic effect of armature cross-turns, an entirely different scheme may be used to effect commutation without sparking. If a counter-electric pressure be introduced in the short-circuited coil by external means, of such strength and during such an interval that the current in COMPENSATION FOR CROSS-TURNS. 189 the coil is reversed and brought up to the proper value for introduction into the circuit, commutation may be effected when the short-circuited coil is in any position, regardless of the influence of the field. The electric pressure introduced must evidently vary with the load, in order that the current in the short-circuited coil may always have the proper value when the coil comes into circuit. A very simple and apparently useful device for introducing the electric pressure in the short-cir- Fig. 102. cuited coil has been proposed by W. B. Sayers. (See Journal Institution of Electrical Engineers, 1893 ; Lon- don Electrician, Vol. 31, etc.) Figures 102 to 104 show the arrangement plainly. The armature winding may be any of the usual types, but the ends of the coils are connected together without bringing them to the commutator. The commutator connections are made through what Mr. Sayers calls -Commutator Coils. The commutator coils, which are shown by the heavy lines in the figures, each connect a commutator seg- ment with one of the main coils which has an angular I go ELECTRO-MAGNETISM. position ahead of its commutator coil about equal to one-half of the distance between the tips of the pole pieces. There are thus as many commutator- coils as commutator segments and main coils, but current is flowing only through those connected to the commu- tator segments which are at any instant in contact with the brushes. The relative angular positions of the commutator coils and their respective main coils place the main coil in the neutral position when its Fig. 103. commutator coil is directly under the trailing or strong pole corner. The figures, 102 to 104, show by means of arrows the direction of the induced electric pressure in the coils, and the action of the commutator coils in controlling the current in the short-circuited coils is made plain. By controlling the number of turns in the commutator coils and varying their angular position with reference to the main coils, the commutation can doubtless be made practically sparkless without regard to the position in the field of the short-circuited coil. COMPENSATION FOR CROSS-TURNS. igt Mr. Sayers has even gone farther than this in making a dynamo which operated satisfactorily with a consider- able backward lead so that the armature magnetized the fields and no field winding was required. The operation of an ordinary machine with sufficient back- ward lead to magnetize the fields from the back turns of the armature causes vicious and destructive spark- ing and severe heating, because the short-circuited coil is placed in a strong direct field which tends to uphold Fig. 104. or even increase its current, while satisfactory operation requires that the current be reversed. It is evident that more turns are required in the commutator coils to effect their purpose when the machine is operated with a backward lead than when the commutating plane coincides with or leads the neutral plane. A constant pressure machine may be caused to regu- late with an astonishing precision by the use of the Sayers device. The accompanying table shows some observations taken by Mr. Sayers upon the operation of 192 ELECTRO-MAGNETISM. a double horseshoe machine with embedded armature conductors, but without field windings. The backward leaJ of the brushes was kept constant. Speed. Pressure. Current. Speed. Pressure. Current. 918 lOI 916 100 S8 920 100 940 100 57 928 lOI 34 966 lOI 62 942 103 35 964 100 80 906 100 58 964 99 78 Little practical experience has been had as yet with the Sayers device, but it seems to offer a satisfactory construction for some cases. In modified form it may possibly serve to reduce the evils due to armature cross- turns to a practical minimum if applied to the ordinary types of machines, thus making it easy to utilize fully the advantages of machines with embedded armature conductors and small air spaces, though its general adoption is doubtful. While armature reactions is the fundamental cause of a variable lead, and its resulting sparking, yet the evil effect may be attacked with some success from an entirely external position. Thus any device which makes a considerable lead possible on light loads, ena- bles a machine to operate with little or no change of lead under varying loads. Placing an extra resistance in the circuit of the short-circuited coil serves the purpose. There are several methods of doing this, the most convenient of which are : using a high resistance brush, such as carbon ; and connecting the armature coils to the COMPENSATION FOR CROSS-TURNS. 193 commutator divisions by wires of considerable resistance, such as fine German silver wires. The carbon brush has come into very general use for machines designed to operate on a pressure of not less than 200 volts, and gives excellent satisfaction. It is not so satisfactory for lower pressures on account of the great cross-section of the brushes and size of the commutator required to prevent undue heating. Thus, satisfaction is given by copper brushes when carrying 100 to 250 and even up to 500 amperes per square inch of contact between brushes and commutator, while carbon brushes cannot carry sat- isfactorily much more than 50 to 60 amperes per square inch. The immediate effect of increasing the resistance in the circuit of the short-circuited coil is very simple, though it doubtless is accompanied by more complex phenomena. When working at full load the short-cir- cuited coil must be in a field of considerable strength in order that its current be properly reversed. If the load falls off and the lead is not reduced, the field tends to cause an excessive flow of current through the short- circuited coil. The extra resistance checks the excessive current and thus reduces sparking and heating. When constant pressure dynamos are operated under fairly constant loads and receive careful attention, the high resistance brush or its equivalent is unnecessary ; but where the loads vary rapidly or the machine is neg- lected, the high resistance brush is invaluable. This explains the popularity of the carbon brush for use on street railway generators and motors and for general power service. Evidently a comparatively large extra resistance for the electric pressure of the short-circuited ig4 ELECTRO-MAGNETISM. coil to overcome will cause comparatively little loss in the total pressure due to the main current passing through it. The currents are as i to 2 in ordinary constructions, while the ratio of the electric pressures is likely to be smaller than i to 50. The width of the brush itself may have a marked influence on sparking. The effect in most cases is doubtless a complex one, in which the length of the interval of short circuit, and the self-induction, mutual induction, and resistance of the short-circuited coils all play a part. That self-induction and resistance play a considerable part is shown by dividing the brushes of a machine (Fig. 105), and placing the two portions of each brush several commutator segments apart. In this case commutation can be satisfactorily effected in a stronger field than when single brushes are used, and to gain sparkless commuta- '^' ■ tion in a field of fixed strength the. number of segments included between the brush parts must be increased as the load decreases. The effect of self-induction is also shown to some degree by the pro- pensity of ring armatures to spark with less apparent reason than drum armatures. An illustration of the effect of mutual induction has already been suggested in explaining the action of motor-generators (page 188). A complete study of the effect of self-induction or of the width of brush contact has never been made, but that sparking may be considerably affected by changing the width of the brushes is well known (^ide Weymouth, " Sparking at Commutators,'' London Electrician, Vol. 30). CHARACTERISTIC CURVES. 195 CHAPTER VII. CHARACTERISTIC CURVES, AND REGULATION. Four curves which represent relations between E, N, nc, etc., are usually called characteristics, a name first applied to one of them by Deprez. They are : 1 . The Curve of Magnetization, or Hopkinson s curve. 2. The External characteristic. 3. The Loss line. 4. The Magnetic distribution curve. The Curve of Magnetization is essential to a proper study of the economical performance of a dynamo, and it is a valuable check upon the calculation of the mag- netic circuit. The practical determination of the curve is simple, and it should be carried out by builders, for each new size or type of dynamo constructed. The dynamo to be examined is run at a convenient constant speed, and the field is magnetized from an external source of current, which is variable at will. The magnetizing current is measured by an amperemeter, the pressure at the dynamo brushes by a voltmeter, and the speed is taken by a convenient counter. The readings of the voltmeter should be corrected to a con- stant speed, if this varies, and the amperemeter and 196 ELECTRO-M AGNETI SM . corrected voltmeter readings should be plotted on rec- tangular axes with such a scale that nc and N^ can be directly read off. The curve of magnetization of a dynamo should not be regarded merely as a curve rep- resenting the relation between amperes in the field and volts at the brushes. The curve is of much value in determining, by comparison, the relative performance of dynamos, and for this purpose it must be plotted with such scales that it represents at once the relation between nc and N^. It is usually plotted with nc on the X, or horizontal, axis, and N^ on the Y, or vertical, axis. The ratio of the scales upon which 71c and N^ are plotted makes a decided, difference in the appear- ance of the curve, and a uniform ratio should be adopted. When 100 magnetic lines of force are plotted to the same length as one ampere turn, the curve usu- ally takes a convenient form, but this depends somewhat on the type of the machine to which the curve belongs. By applying a proper series of scales to a curve of mag- netization, the same curve can evidently be used to rep- represent the pressure at the brushes, as a function of «?; or, when a constant pressure is maintained, it may represent the speed, as well as the total magnetization passing through the armature, as a function of ik. The effect of hysteresis is plainly marked by a difference in the curves of magnetization, which are determined with increasing and decreasing currents. In the actual working of dynamos, the magnetization for any load falls in the descending or ascending branch of the curve, depending upon whether the load has previously been greater or less. In any case, the differences in CHARACTERISTIC CURVES. 197 magnetization due to this cause are not great, and the average of the branches is taken as practically repre- senting the curve of magnetization. The curve of magnetization starts from the Faxis, at a distance above the origin which is proportional to the residual magnetism. Since, when B is small the value of jti increases rapidly as B increases, the iirst part of the curve is convex to the X axis. After the first curvature, the curve of magnetization tends to the direc- tion of a straight line, which it follows until B has become some thousands of lines per square centimeter, when /A begins to decrease rapidly, as B increases farther. The curve then deviates from the direction of the straight line, making a more or less abrupt bend, which is concave to the X axis. A little distance beyond the bend, or knee, the curve again approximates to a straight line, this time more nearly parallel to the X axis. The value of nc at each point of the curve can be divided into three portions : first, the number of ampere turns required to force the lines of force through the air space ; second, the number required to force the lines through the field magnets ; third, the number required to force the lines through the armature core. These component values can be plotted with N^, giving par- tial curves of magnetization for the air space, magnet frame, and armature core. For any value of the ordi- nates, the sum of the abscissas of the partial curves is equal to the abscissa of the curve of magnetization. The partial curve representing the air space is a straight line passing through the origin, since the permeability of air is constant and the retentiveness is zero. It is 1 98 ELEGTRO-MAGNETISM. this line which the total curve approximately follows in the lower part of its course (between the two bends). The partial curves for the field magnets and the arma- Fig. 106.* ture are evidently curves of magnetization, representing the quality of the iron used in these parts of the dynamo (see page 35). Figure 106 shows the curves of * Adapted from Transactions American Institute of Electrical Engi- neers, Vol. 5, p. 150, "The relation between the cross-section of the iron in armature and field of the Gramme dynamo." CHARACTERISTIC CURVES. 199 magnetization of a dynamo where two different ring armatures were used with the same field magnets. The armatures were made with different radial depths, so that one had 2.4 times as great a cross-section as the other. Their external diameter was the same, so that the air space was constant. The line OA, in the figure, is the partial curve for the air space, OD represents the magnet frame, OB^ and (95^ represent respectively the small and large armature cores. Curves OC^ and OC2 are the total curves taken with the different armatures. The lower parts of both the total curves follow the air space line very closely, while OC^ deviates from the line much earlier than OC^. That this is due to the satura- tion of the armature core is made evident by curve OB^. The curves of magnetization show the output of the large armature to be 26 per cent greater than that of the small one, when the ampere turns on the field num- ber 3750, while the difference in the weight of the machine, due to difference in the armatures, is only about 7|- per cent. The difference in weight of arma- ture copper is inappreciable. For more stable working the machine might be magnetized by 5000 ampere turns, in which case the large armature gives 33 per cent greater output than the small one. The increase of the magnetizing force from 3750 to 5000 ampere turns, increases the output of the small armature only 3 per cent, while the output of the large armature is increased 9 per cent. In the original design of the machine these results should be obtained with a fair degree of accuracy by calculation, but the curves which are taken after the 200 electro-magnetism: machine is built evidently give the designer an excellent check upon his work. The partial curves can be made useful in determining wrhether excessive saturation exists in any part of the magnetic circuit, which may have been overlooked in- making the design. The small armature in the example given was saturated at 3750 ampere turns, to a value of ^=17,500. ^ in the large armature, for the same number of ampere turns, was about 10,000. In the field cores, B was respectively about 12,500 and 16,000. Other things being equal, no other comment than these curves is required to establish the commercial economy of the larger armature. The External Characteristic has different forms for series, shunt, and compound wound dynamos. To experi- mentally determine the external characteristic of any dynamo, it is made to excite itself, while the volts at its terminals, and its current, are measured with different resistances in the external circuit. The observations may be plotted in a curve using volts as ordinates and amperes as abscissas. In a series dynamo, the total current from the armature magnetizes the fields, the volts increase with the current, and the curve is very similar to the curve of magnetization. It always falls below the curve of magnetization, however, the differ- ence of the ordinates being equal to the loss of pres- sure due to the armature reactions and the resistance of the windings of the machine. With a constant lead, according to the previous discussion of armature reac- tions, the difference in the ordinates of the two curveii is practically proportional to the current, and can be CHARACTERISTIC CURVES. 201 represented by a straight line. This line is the third form of characteristic curves, or the Loss Line. When the lead varies with the current, the back turns vary as a function of both the lead and the current, and the loss line may become considerably convex toward the X axis. Figures 107 and 108 show characteristic curves exper- imentally determined from dynamos while the lead was kept constant. In Fig. 107, A and B are respectively Fig. 107. the external characteristic and curve of magnetization of a series dynamo. OL is the loss line, which rep- resents the mean direction of the points marked O. These points have ordinates equal to the difference between the ordinates of the two curves, and their positions show no tendency to uniform curvature con- 202 ELECTRO-MAGNETISM. vex toward the X axis, which is according to the theory of armature reactions already developed. In Fig. io8, A and B are the external characteristic and curve of magnetization of a shunt dynamo without lead. The points marked O are points on the loss line determined by a construction which is given later. By the theory of armature reactions, the lead being constant, these points should be located upon the line of loss due to Fig. 108. armature resistance. OL is such a line and the points are located upon it within the limits of error in the determination of their position. The curve A in Fig. 107 shows that for a certain value of the current, a series machine will give a maximum pressure at the poles. For larger or smaller currents the pressure at the poles will be less. The CHARACTERISTIC CURVES. 203 pressure is evidently at its maximum when the loss line is parallel to the curve of magnetization, since the total pressure increases faster than the internal losses up to that point, and beyond that point the losses increase more rapidly than the total pressure. As already said, the loss line of a shunt dynamo can also be derived from the curve of magnetization and the external characteristic, and if the curve of magnetization and loss line be known, the characteristic can be directly derived; but, as shown in Fig. 108, its form is very different from that of the external characteristic of a series dynamo. Suppose that the curve M in Fig. 109 represents the curve of magnetization of a machine and OL the loss line. For convenience the curves are plotted on opposite sides of the Faxis, but the abscissas of both are measured from O. With a current c=Oc in the shunt field coils, the pressure E{=OE) is devel- I* k. ■fc-Sfjp ■ifSs