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250 PROCEEDINGS OF THEIEEE, VOL. 63, NO. 2, FEBRUARY 1975 linear Electric Machines- A Personal View ERIC R. LAITHWAITE, FELLOW, IEEE Invited Paper Abrtmct-The history of linear motors is P history of stupe. Once Mi departed from the cylindrial geometry of rotating machines, 1 duction motors dominate the field of linear drives to the same extent as does the rotary induction machine in relation to more complicated rdjustrble-speed motors. It is thexefae thought appmpriite to devote only one section to linear motors other than induction. A f8iriy full treatment of electromagnetic levitation is also included to@er with 8 treatment of oscillating machines. Perhaps the most important featured are the division of electrial mLchines into two cksses which are termed “magnetic” and ‘‘electromagnetic” and the ‘‘topological ex- plo9ion”whichIsrtpresenttrldnsp~inlineumotordesign. Some linea machines ne already well established on 8 commercirl basis but the vast bulk of recent inventions still remain to be exploited. w i k wodd Of tfiree;dimensiorul design becoma posa’ble. Lineu in- I. INTRODUCTION A. What Is a Linear Motor? T HE HUMAN MIND has an urge to classify. The fascina- tion of his practice is almost as preoccupying as our delight in observing spheres in motion, which latter satisfaction results in millions of man days being spent annually in the worship of ball games. Having defined a class of some- thing, the next natural urge is t o f i d out when it was first done or who made it and hence to write a history! Often however, it is difficult t o know where to begin, simply because the subject is not well defined. Who, for example, made the fmt wheel? Was it the result of observation of lumps of rock hurtling down a hiilside, or of the rolling of a twig under a human foot? Onething is certain,onemust define a begin- ning, or one cannot proceed t o write. In the case of linear electric motors the defition is fairly clear. A linear motor can be defined as being the result of a cylindrical rotary machine which has been mentally split along a radial plane and unrolled, as is the induction machine shown inFig. 1. This does not in itself imply that there can be no linear machines which do not have analready-manufactured rotary counterpart, as we shall see, but the definition does not include electrostatic machines, nor is the subject of magneto- hydrodynamics (MHD) included. So much has been written on MHD, and most of this recently, that it is relatively easy to obtain and its inclusion here is thought to be beyond the scope of a paper of this length. One other physical arrangement which may, at first sight, be thought to constitute a motor, is also omitted. Fig. 2 illustratesone such system. The row of dc-fed electromagnets are moved mechanically relative to a sheet of conductor, such as aluminium, thereby imparting force to the latter. This, and other similar systems, including those containing permanent magnets, are considered t o be clutches,and not motors. If the coils of the system shown Manuscript received August 10, 1974; revised October 9, 1974. The author is with the Department of Electrical Engineering, Imperial College of Science and Technology, London SW7 ZBT, England. n 1 J Fig. 1. Imaginary process of splitting and unrolling a rotary machine to produce a linear motor. I Fig. 2. A row of magnets (permanent or dc-fed electromagnets) which are moved mechanically to impart force to a secondary conductor do not, within the scope of this article, constitute alinear motor. in Fig. 2 are stationary, and the current in them is switched on and off in sequence, so as to induce currents in, and produce force on, secondary conductor, only then is this a linear motor. In other words, a linear motor must comply with the alterna- tive name for an electrical machine-an “electromechanical energy converter.” There are however, some exceptions to this apparently all- embracing rule. Firstly, there are many applications for linear machines in which there is no mechanical output, because there is no motion. If electrical energy is fed to a machine in order to produce force alone, this machine is considered to fall within the defition of a linear motor. It will be seen at once that this includes the subject of electromagnetic levitation, a subject which has recently become very important in relation t o the suspension of high speed vehicles. Secondly, in view of the importance of the latter subject, it is necessary to make an exception to the definition of a “clutch,” for one of the levitation systems presently being investigated on a large scale consists of a superconducting magnet which, when moving, induces current into a secondary member and thereby pro- ducesaforce of repulsion betweenprimaryandsecondary. Although this lifting force is produced only as the result of mechanical thrust in a horizontal direction, the story of elec- tromagnetic levitation would be incomplete without it.
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Page 1: Linear Electric Machines- A Personal View

250 PROCEEDINGS OF THE IEEE, VOL. 63, NO. 2, FEBRUARY 1975

linear Electric Machines- A Personal View

ERIC R. LAITHWAITE, FELLOW, IEEE

Invited Paper

Abrtmct-The history of linear motors is P history of stupe. Once M i departed from the cylindrial geometry of rotating machines, 1

duction motors dominate the field of linear drives to the same extent as does the rotary induction machine in relation to more complicated rdjustrble-speed motors. It is thexefae thought appmpriite to devote only one section to linear motors other than induction. A f8iriy full treatment of electromagnetic levitation is also included to@er with 8 treatment of oscillating machines. Perhaps the most important featured are the division of electrial mLchines into two cksses which are termed “magnetic” and ‘‘electromagnetic” and the ‘‘topological ex- plo9ion”whichIsrtpresenttrldnsp~inlineumotordesign. Some linea machines ne already well established on 8 commercirl basis but the vast bulk of recent inventions still remain to be exploited.

wik wodd Of tfiree;dimensiorul design becoma posa’ble. Lineu in-

I. INTRODUCTION A . What Is a Linear Motor?

T HE HUMAN MIND has an urge to classify. The fascina- tion of his practice is almost as preoccupying as our delight in observing spheres in motion, which latter

satisfaction results in millions of man days being spent annually in the worship of ball games. Having defined a class of some- thing, the next natural urge is t o f i d out when it was first done or who made it and hence to write a history! Often however, it is difficult t o know where to begin, simply because the subject is not well defined. Who, for example, made the fmt wheel? Was it the result of observation of lumps of rock hurtling down a hiilside, or of the rolling of a twig under a human foot? One thing is certain, one must define a begin- ning, or one cannot proceed to write.

In the case of linear electric motors the d e f i t i o n is fairly clear. A linear motor can be defined as being the result of a cylindrical rotary machine which has been mentally split along a radial plane and unrolled, as is the induction machine shown in Fig. 1. This does not in itself imply that there can be no linear machines which do not have an already-manufactured rotary counterpart, as we shall see, but the definition does not include electrostatic machines, nor is the subject of magneto- hydrodynamics (MHD) included. So much has been written on MHD, and most of this recently, that it is relatively easy to obtain and its inclusion here is thought to be beyond the scope of a paper of this length. One other physical arrangement which may, at first sight, be thought to constitute a motor, is also omitted. Fig. 2 illustrates one such system. The row of dc-fed electromagnets are moved mechanically relative to a sheet of conductor, such as aluminium, thereby imparting force to the latter. This, and other similar systems, including those containing permanent magnets, are considered to be clutches, and not motors. If the coils of the system shown

Manuscript received August 10, 1974; revised October 9 , 1974. The author is with the Department of Electrical Engineering, Imperial

College of Science and Technology, London SW7 ZBT, England.

n

1 J

Fig. 1. Imaginary process of splitting and unrolling a rotary machine to produce a linear motor.

I Fig. 2. A row of magnets (permanent or dc-fed electromagnets) which

are moved mechanically to impart force to a secondary conductor do not, within the scope of this article, constitute a linear motor.

in Fig. 2 are stationary, and the current in them is switched on and off in sequence, so as to induce currents in, and produce force on, secondary conductor, only then is this a linear motor. In other words, a linear motor must comply with the alterna- tive name for an electrical machine-an “electromechanical energy converter.”

There are however, some exceptions to this apparently all- embracing rule. Firstly, there are many applications for linear machines in which there is no mechanical output, because there is no motion. If electrical energy is fed to a machine in order to produce force alone, this machine is considered to fall within the d e f i t i o n of a linear motor. It will be seen at once that this includes the subject of electromagnetic levitation, a subject which has recently become very important in relation to the suspension of high speed vehicles. Secondly, in view of the importance of the latter subject, it is necessary to make an exception to the definition of a “clutch,” for one of the levitation systems presently being investigated on a large scale consists of a superconducting magnet which, when moving, induces current into a secondary member and thereby pro- duces a force of repulsion between primary and secondary. Although this lifting force is produced only as the result of mechanical thrust in a horizontal direction, the story of elec- tromagnetic levitation would be incomplete without it.

Page 2: Linear Electric Machines- A Personal View

LAITHWAITE: LINEAR ELECTRIC MACHINES 251

B. The Pioneers of the Nineteenth Century Following Faraday’s discovery of the Laws of Induction in

183 1, engineers were not slow to exploit the phenomena and in particular Hippolyte Pixii, in 1832, produced an ac generator which was undoubtedly the forerunner of our modem power station alternators, having the secondary (output) coils sta- tionary, with a rotating set of magnets to induce the electro- motive force (EMF). This was a particularly notable contri; bution, for in the early 1830’s the only “engines” known were of the piston and cylinder type and ingenious linear-to-rotary converters such as the Scotch Yoke were invented to convert the linearly generated power into a form which could make use of the much-beloved wheel. In the 1830-1850 period much of the ingenuity in electric motor and generator inven- tion was restricted by the overriding thought that “an engine should look like an engine.” Even when quite good rotary electric motors were designed their inventors still retained words such as “the stroke” to define a double pole pitch. One magnetic engine in particular due to Allan (circa 1850) did indeed have magnetic keepers arranged like pistons with an overhead canshaft and four “cylinders.”

Another feature (or perhaps “fashion” is a better. word) of the period which placed considerable constraint on innovation was the emphasis which was placed on efficiency. A machine had to work “well” and consideration of overall economics (now perhaps called “total technology”) was a century away. One cannot read a history of nineteenth century electric motor development without having the greatest admiration for the sheer ingenuity of the inventors. From about 1850 until about the turn of the century, designers of “dynamoelectric machinery” (as it was often termed in early patents) con- centrated much of their effort to the subject of shape. The dc machines came first, largely because of the discovery of elec- troplating and of carbon-arc lamps, and there was a dominating duty to manufacture “battery-like” current. It is no exaggera- tion to say that the future of ac generation and certainly of polyphase ac was not by any means assured until Tesla’s invention of the induction machine in 1888 which was to dominate the world of electric drives. It is of historic interest to note that a physicist named Bailey demonstrated a simple twephase induction motor at a Royal Institution Discourse in London, England, in 1882 and ended with the words “but it will never be of any practical value.”

It is probably true that the greater part of the population today assumes that highly sophisticated machinery such as electric drills, forging hammers, and lawnmowers have been designed. The sad fact is that technology advances in a similar manner to that of life forms, evolution-the elimination of the unprofitable, being the heart of the process.

Unfortunately, the human technology process retains one facet which Nature does not. This rather expensive ingredient is called tradition. It appears in many forms. A recent design of a teapot manufactured in Germany was streamlined like a racing car-perfectly functional and perfectly balanced. Cir- cular in plan view, many people did not like it because it re- minded them of a bedpan-an article often associated with pain and suffering. Tradition dictates in large part to the way in which we travel. The country which developed the steam locomotive was slower to use air travel as a result. For a time, tradition dictated how a high jumper should approach his task and not until the Western Roll, the Eastern cutoff, and the

‘ O H

1890 1 9 4 0 TI ME

I990

Fig. 3. World “activity” in linear electrical machines, defined as money spent on the subject, plotted as a function of time.

Fosbury “flop” had f i t been seen to be successful did the fashion change.

Much is written about brainwashing. The most highly developed form of this activity is that in which we brainwash ourselves. Even the man who invents a new method of analysis is liable to become obsessed with trying to apply it to more and more situations. Nature is not at all affected by tradition, although its rate of killing off the unprofitable is much slower than that of the managing director. Another way of expressing the sentiments of the previous paragraph is to say that what is obviously progressive to nature gets done. This is not neces- sarily the case with engineering, for humans, quite apart from any vested interest, have an inbuilt objection to change and it is this which called for the excuse we call “tradition.”

The exciting things in science and engineering occur when there is a breakthrough and a whole new technology is bow. Although linear motors date back to Wheatstone in 184 1, the engineering profession as a whole was so convinced of the “correctness” of rotary motion, and the high efficiencies ob- tainable with cylindrical machines with tiny clearances between rotor and stator that it put aside linear motors, virtually until the Westinghouse Electropult [ 11. In the meantime the whole field of engineering economics had gone through a reappraisal, one might even say “revolution.” First, power-to-weight ratio and cost and later, reliability, low maintenance, and absence of pollution had overridden efficiency and power factor as criteria of quality. The linear motor, with its inherent reliability, reborn in 1946, was here to stay.

One can represent the interest in linear motors as a graph of “activity” plotted as a function of time and this is done in Fig. 3. The little activity which existed in pre-Electropult days was largely carried out by textile engineers-amateurs in the electromagnetic skills-but ingenious men who, as history showed subsequently, would have succeeded but for the cheapness of the Lancashire Loom and the mistaken belief in efficiency as the expression of all that was good in a device.

The vertical (logarithmic) scale is based on an estimate of the rate at which money is spent on the building and testing of linear motors rather than on the quantity sold, for develop- ment costs often dominate the early stages of a technology. At such time it is legitimate to estimate the expenditure in terms of the rate at which papers on the subject are produced. As an example of the evidence supporting the graph of Fig. 3, a survey of linear motors undertaken in 1967 revealed a total

Page 3: Linear Electric Machines- A Personal View

252 PROCEEDINGS OF THE IEEE, FEBRUARY 1975

of just over 700 papers. In that year, an average of seven papers per month were being published. By 1970 the number has risen to 12 and by 1972 to 18. It is concluded that the rate of rise at the extreme right of the graph is not an over- estimate of the degree of activity.

C. Topology is the Key A view of a landscape reveals at once which parts of it have

been made by man and which are “natural.” The manufactured articles reveal their origin almost entirely as the result of their shape [2]. Nature’s colors we can reproduce and in some cases (fluorescent paints for example) even surpass. But we cannot afford to develop the elaborate shapes of leaves, trees, flowers, feathers, and living tissue. We are dominated by the circle and the straight line, and in our primitive way have developed both of these fundamental shapes in some detail. So far as the subject of electrical machines is concerned, the circular exercises have resulted- in all the varieties of rotating machines which we have come to regard as “conventional” (simply because they were developed first’). The straight line, on the other hand, is the younger of the two shapes and did not produce “fashionable” electrical machines until the 1960’s. This has not been a lack of willingness to try direct generation of linear motion so much as a disenchantment with early applications. The reason for the lack of success of such ven- tures is, however, twofold.

Firstly, there are changing fashions as regards what is eco- nomically profitable, but perhaps more important, there are definite limits to the extent to which the phenomena of electromagnetism can be exploited. Within these limits how- ever there is much scope for inventive ingenuity, particularly as regards the shape of a machine. Indeed it would not be an exaggeration to say that inventions could be achieved by re- versing the process which is traditionally said to be the “mother of invention” and could be described as: “Find a problem- solve it.” The reverse process could be stated in similar terms as: “Get yourself a new shape of motor-find out what it can do.”

This latter process at once reveals itself as being very close to the subject we call “biology”-for in the study of nature’s almost infinitely varying shapes and the speculation about their functions we find enough brain-taxing material to make a whole discipline. The engineer has all such problems with which to contend, plus the fact that he is free to create his own shapes in the fmt instance! Little wonder, therefore, that he largely uses simple shapes and simple materials (mostly nearly pure metals) in contrast to nature, in which we find no pure metal.

Only recently has man discovered what is regarded as the fundamental building block of life itself-the DNA molecule. It could be said (without modesty) that it is also only com- paratively recently that the fundamental building block of an electromagnetic device has been isolated and as a result has

‘ A recent paper on the subject of linear motors with moving primary described such motors as “Rotating machines with the planet Earth as rotor.’’ Whilst this is an obvious stretching of the topological imagina- tion it is interesting to reflect that whilst “planet Earth” is a good conductor for some purposes, such as the “earthing” of electrical equipment and even power transmission, it is an insulator in induction motor language and must be covered with, at least, a sheet of con- ducting material before motors of reasonable proportior& may be made to work successfully. Section I1 takes up this point again in relation to the size of motors and its relationship to the secondary member.

made the profitable applications of electric machines stand out in every contrast to those which are unprofitable [ 3 ] . In particular, the progress of linear machine development has been aided considerably by the isolation of such a basic building block.

It can be argued that this approach to electromagnetic theory is oversimplified, that it is only one man’s viewpoint, one of a number of different analogies which can be applied to the study of a four-dimensional problem, the basis of which none of us can truly understand, and this is not denied. The defense of this approach is F i t ly , that the theory is indeed simple and secondly, that it has pointed the way to m&y successful inventions. The new fashion in linear motors could be said to have sprung virtually from the abandonment of analysis, and this is all the more surprising in that it occurred at the very time when the universal digital computer was making its bid to dominate the world.

The fault with a large part of analysis is that whilst it can predict the performance of almost any given structure to great accuracy, it rarely points the way to make a better structure. So far as the linear motor game is concerned, making better machines is, at this time, what the game is all about!

An example of the use of the goodness factor in the context of modem linear motor developments concerns the proposal to increase the supply frequency to high speed motors so as to avoid the use of very long pole pitches which, at f i i t sight, inevitably result in excessive weight of motor, excessive leak- age flux (and therefore low power factor) and extra end winding losses leading to low efficiency. The goodness factor has pole pitch p , frequency f , and airgap clearance g among its ingredients and with other quantities considered constant could be written:’

P’f G = K - g

whilst the synchronous (field) velocity

us = 2 p f .

If a designer hopes to make a “better” motor by increasing f , he is right, provided all other factors remain constant. But if he is constrained by a fixed speed requirement, (1) applies, and he will make a better machine fundamentally by reducing f and increasing p for the latter term is the only squared quantity in the goodness factor. Detailed design will trim bits off the factor here and there but G is such a basic quality of an electromagnetic device that to ignore its simple messages is to court disaster. It is interesting to note that Russian engineers developed its concept separately and pro- duced an equivalent factor, which, to give it the emphasis it deserves, was named “magnetic Reynold’s number.”

11. DIFFERENT TYPES OF LINEAR ELECTRIC MOTOR A . The “Great Divide ’’

By the simple topological exercise of splitting and unrolling shown in Fig. 1, it is clear that every type of rotating machine can be “linearized.” It does not follow that having done so, the linear version will be as useful as its rotary ancestor. Nor are successful linear machine types limited only to those which

a The value of K is derived in Section 11-E (2).

Page 4: Linear Electric Machines- A Personal View

LAITHWAITE: LINEAR ELECTRIC MACHINES 253

A

(b) Fig. 4. (a) A “drag-cup” rotary motor carries no winding on its

stationary steel core. The dotted lines indicate the greatly reduced available dot area due to a contracting geometry. (b) In a “linearized” drag-cup motor it is more profitable to have windmgs on both sides of the airgap. This is the “double-sided sandwich” or “sheet-rotor” motor.

have proved their worth as rotary drives. For example, the small drag-cup servo motor carries a stationary cylindrical iron core in the rotating form, as shown in Fig. 4(a), but it does not generally carry a winding. The reason for this is the con- straint placed upon rotor slot sizes, should such a machine be contemplated, by the reduction in available perimeter for the slot bottoms imposed by a geometry which is essentially shrinking towards the center. The linear counterpart of the drag-cup machine, shown in Fig. 4(b), is the well-known “double-sided sandwich” or “sheet rotor” motor which has been much used because of the simplicity of the secondary structure and the fact that a double-primary winding halves the primary ohmic loss compared with a winding on one side only [41.

It is possible, however, to divide both linear and rotary machines into two quite distinct gioups which are almost as fundamentally different as positive and negative ,numbers. This distinction is never .disclosed in textbooks on electrical machines nor in industry, where the uninitiated learn from their elders what machines are profitable and what are not, and the whole question of skill in assessment of performance is resolved by what is generally called “experience.” Yet the inquiring mind of the schoolchild may legitimately ask ques- tions such as: “Why are hysteresis motors never made in 1000-hp sizes?” and “Why is it not good engineering to make 1-hp induction motors with 60 poles, yet most profitable to make 5000-hp induction machines with over 100 poles?”

The arguments in the following subsections provide the complete answer to these and many other similar questions, which would, in the case of new types of linear machine,

require much labor and money to answer on a purely trial and error basis-the method described as “experience.” The basis of the division into two groups requires some initial definitions.

B. A Definition of “Airgap” All linear motors which are required to produce relative

motion between primary and secondary members (or are at least capable of doing so, in the case of machines normally operated at standstill) have an interface between the two members which usually consists of a thin wafer of air. In a rotating machine this is normally referred to as the “airgap,” but such description is not accurate for at least one class of linear machine in which the secondary conducting material is located in this air space. In such cases the length of the “effec- tive” airgap is the distance between the two ferromagnetic faces. In such cases the French description of the airgap, even of rotary motors, the “entrefer,” is a much better description and a loose translation such as the “air interface” might be more appropriate. However, since there are many useful linear motors in service in which only the primary member contains ferromagnetic material, the words “equivalent airgap” will be used everywhere to describe the magnetic length which must be used in magnetic circuit calculations in cases where the airgap is not readily observable. This technique is merely an extension of that used in conventional design where the effect of the slot openings in the rotor and stator steel are taken account of by the use of Carter’s coefficient [SI which multiplies the physical gap by a number greater than unity to give an effective airgap length.

C. Definitions of “Magnetic” and “Electromagnetic ’’ Machines

With the concept of a primary-secondary interface estab- lished it is now possible to define completely which motors fall on one or other sides of the great divide. If there exists during operation of a machine, a magnetomotive force (MMF) on each side of the airgap interface, that machine is an elec- tromagnetic device. In this context, a permanent magnet is to be regarded as a source of MMF, and it matters not whether an MMF on one side is induced from the other, or whether it is supplied directly. On the other hand, if there is MMF on one side only of the interface, then such a machine is merely magnetic.

The importance of the distinction is perhaps best emphasized in simple terms which are therefore somewhat unscientific, for the term “better” is not yet defined. The facts are:

1) electromagnetic machines get better as they are made

2) magnetic machines get better as they are made smaller.

The following two sections will explain the significance of the

bigger; and

word “better” and will deal with statement 1).

D. The Basic Building Block It is possible to visualize every kind of machine (either

rotary or linear) as the interlinking of magnetic and electric circuits, a first attempt at such representation being shown in Fig. 5(a). A and B are primary coils which assist each other in driving the flux around the magnetic circuit, during which it may cross the airgap twice. C and D are secondary coils which are short circuited in the case of induction motors and consist effectively of a single turn in many cases.

Page 5: Linear Electric Machines- A Personal View

254 PROCEEDINGS OF THE IEEE, FEBRUARY 1975

( 4 ( 4 Fig. 5. A topological “journey” to discover the most basic form of

electromagnetic device. (a) Two ahgaps with both “go” and “return” primary coils. (b) Reduction to a single gap and coil system. (c) The gap is absorbed into the whole of the magnetic circuit. (d) After “lumping” the coils of (c) together, the result is the most primitive machine.

Clearly there is no loss of generality by considering only coils such as A and C and a single airgap, as shown in Fig. 5(b), together with a circuit which is completed as shown. What is more, this structure can be a pictorial representation of the actual physical construction of some types of linear machine. In practice, the ferromagnetic part sf the magnetic circuit contributes to the reluctance as well as the airgap itself and the system may be further simplified, for theoretical purposes, to the system shown in Fig. 5(c). This is a suitable point on the topological “journey,” depicted

in Fig. 5, to point out the principal departure from reality, for whilst an electric circuit is clearly defined in practice, the magnetic circuit cannot strictly be treated in the same manner, for there exists no insulating varnish which will prevent magnetic flux from “leaking” between all points of differing magnetic potential. Fig. 6 illustrates the leakage fluxes which have been neglected in this simplified approach towards a fundamental “electromagnetic molecule.”

Fig. 5(c) resembles very closely the physical structure of a transformer. In transformer theory it is often convenient to combine the two electric circuits into a single circuit by the process known as “lumping,” provided the leakage impedance of the resultant coil is the sum of that of one of the coils, as measured physically, and of that of the other multiplied or divided by the square of the turns ratio between the two coils, as appropriate. When this is done, the basic structure of a machine is seen to be that shown in Fig. 5(d).

No further reduction is profitable and the simple interlinking of magnetic and electric circuits is the basic building Mock from which all electromagnetic machines are developed. Each real machine is capable of being represented by such a simple linkage and from this abstraction an overall estimate of its properties may rapidly be made. The basic linkage shown in Fig. 5(d) may be taken to a f i i t stage of quantization by

Fig. 6. Leakage flux, which is neglected in simple theory, relating to Fig. 5.

t MAGNET’C M.M.F. = FLUX X CIRCUIT

Fig. 7. A representation of electromagnetic action. Items in the center column are desirable. Items in the last column are “the enemy.” The two desirable quantities mutually self-generrte.

evaluating the principal qualities of the two circuits, and for this purpose use is made of Fig. 7.

E. The Factor of Goodness Horizontally, the two rows of quantities describe the linear

relationship between EMF and current in the electric loop, and between MMF and flux in the magnetic lmp. The product of flux and current gives rise to the force, which commodity it is the purpose of the linkage to produce. Current in the electric circuit however, itself generates MMF in the magnetic, whilst the rate of change of flux in the magnetic generates EMF in the electric. Thus the desirable quantities could self-reproduce to infinite size were it not for the constraints of resistance and reluctance. The product of these two quantities may therefore be taken to represent the “badness” of the machine. Evaluat- ing resistance and reluctance in terms of the lengths, areas and conductivities of the two circuits ( I , Ae u, I , A , p, respec- tively) results in the expression:

Badness a le Irn uPAe-4,

The dimensions of this quantity may be shown to be time and to proceed to an overall factor of “goodness,” we may write

k Badness X time

G =

Page 6: Linear Electric Machines- A Personal View

LAITHWAITE: LINEAR ELECTRIC MACHINES 2 5 5

(a) (b) I 10 1 0 0 loo0 Fig. 9. Two primitive machines illustrate the essential difference be-

GOODNESS FACTOR (G) tween “electromagnetic” and “magnetic” machines. (a) A machine

Fig. 8. Effect of the factor on efficiency with other with magnetomotive force on both sides of the &gap. (b) The =me properties assumed constant. basic machine with MMF only on the stator.

It has been shown [ 6 ] that for an ac machine the quantity kltime is equal to the angular frequency of the supply a. Hence,

Equation (2) is a simplified guide to all electrical machine design, but especially so in the case of linear machines since it points the way to the successful design of machines which, by the nature of their application, are required to have large airgaps in their magnetic circuit. The same equation also illustrates at once that electromagnetic devices become more effective as they are scaled up in size, for the second bracket alone contains the physical dimensions of the machine and a machine which is increased in size by a factor of two in every linear dimension must increase its goodness factor by four. The quantities in the first bracket of (2) are concerned with the nature of the materials of which the machine is made ( p generally being virtually equal to po in linear machines in which the airgap contribution dominates the magnetic circuit reluctance) and the supply frequency. The second bracket amazingly contains all possible designs and sizes of machine and it is therefore within this bracket that the designer must use his skill, the inventor his ingenuity, in attempting always to increase the value of C.

The term goodness was deliberately chosen so as not to con- fine its usefulness to specific properties of machines such as efficiency, power/weight ratio or power factor, for every designer knows that any one or more of these quantities may be increased at will at the expense of the rest. It is instructive, however, to examine the effect of C on one particular quantity (the example chosen here is efficiency) assuming that no con- cessions are made in any other property of a machine of given size and output. Fig. 8 shows this effect and at once the region around G = 1 appears to be especially noteworthy, for machines having G greater than, say 3, are generally acceptable whilst motors with G < 113 usually have little chance of successful commercialization, except in very special circumstances.

Overall, the slogan for the designer of an electromagnetic machine is clearly: the bigger, the better! Such machines in- clude synchronous and induction motors, all types of com- mutator motor, both single and polyphase, and dc machines.

F. Effect of Size in Reluctance Machines Whilst the scaling rule for electromagnetic machines has been

proved rigorously for all shapes of machine ever made or yet to come, an equally general proof has not so far been possible for magnetic machines, yet proof of the rule “the smaller, the

Fig. 10. Waveforms of the flux linking the stator coil for the machines shown in Fig. 9.

better” can be achieved for any shape of magnetic machine yet invented. As example, the case of a simple reluctance machine will now be worked, since this alone goes a long way towards a general proof for all reluctance machines.

Fig. 9 shows two machines which are intended to be used as reluctance alternators. Both have precisely the same dimen- sions of magnetic circuit, the same number of turns of the same diameter of wire on the output coil. The permanent magnet has the same strength in each case but the difference lies only in the fact that the magnet (primary MMF source) is situated on the rotor in machine (Fig. 9(a)) and on the stator, i.e., the same side of the airgap interface, in machine (Fig. 9(b)). Since both machines have identical electric circuits which can dissipate their losses at exactly the same rate, the maximum current from each is the same. Thus the power output from each machine depends only on the voltage which each can generate when rotated at the designed speed.

Fig. 10 shows the time variation of magnetic flux through the output coil of each machine. In both cases, the flu can rise to the same maximum value, as dictated by the magnetic circuit design, for in the position shown in Fig. 9, the machines are electromagnetically indistinguishable. After a half revolu- tion of the rotor however, the core flux in machine (a) will have completely reversed, whilst that in Fig. 9(b) will have gone through a complete cycle of events and the machine is returned to an identical position to that in Fig. 9(b), because its rotor is not polarized. Thus the frequency of the alternating flux in machine (b) is twice that of machine (a).

When the flux waveforms of Fig. 10 are differentiated to determine the voltages, machine (b) would realize precisely the same peak-to-peak voltage as that of (a), provided its flux value in the quadrature position fell to zero, for the loss of a factor of 2 in peak-tepeak flux due to nonpolarization would be exactly compensated by a 2 : 1 increase in frequency. In such a case the output of machine (b) would take the form of the dotted curve in Fig. 1 1.

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256

machine (b) mpchine (bl i d e a l i d

PROCEEDINGS OF THE IEEE, FEBRUARY 1975

Fix. 11. Waveforms of the EMF generated in the stator coil of machines shown in Fig. 9.

n

W Fig. 12. The magnetic situation of the machine in Fig. 9(b) a quarter of

revolution later than that shown in the earlier f m e .

Fig. 12, however, shows that in the quadrature position of the rotor the flux is far from zero, for the reluctance of the magnetic circuit can never be infinite. Thus the output of machine (b) falls below that of (a) by the precise amount that its minimum flux fails to reach zero in the quadrature position, i.e., by a simple measure of the magnetic reluctance in that position. If now the dimensions of both machines are doubled, the reluctance of (b) in the quadrature position will have been halved (being proportional to length/area) as will the reluc- tance in the in-line position. The designer cannot, therefore, look to increase in size to reduce his “enemy” (as can the designer of an induction motor where the “enemy” can be identified as magnetizing current). The fact that iron saturates implies that the output of a magnetic machine only increases as & X area whilst its weight is increasing in proportion to (length)3.

111. LINEAR INDUCTION MOTORS A. Some Facts Concerning AI1 Types of Induction Motor

The rotary induction motor dominates the world of electric drives. The reason is simple to appreciate. It requires neither electrical, nor in the ultimate designs, physical contact between primary and secondary members. The inherent robust nature of the secondary member makes it an obvious choice and its dominance would be complete, were it not for its one disad- vantage-that of being essentially a fmed speed machine.

For an induction motor to develop torque, there must be relative speed between its traveling magnetic field and its secondary, and, therefore, there must be secondary current and Z2R loss. For every unit of torque, there is an appropriate fraction of a unit of loss, and if speed control is sought by the process of allowing greater relative speed between field and rotor, the efficiency unavoidably falls in proportion to the amount of speed reduction.

The speed w of the field of a rotary machine is generally quoted as w = f / P where f is the supply frequency and P is the

(b) Fig. 13. Linear motors divided into two classes simply by the fact of

whether the primary or the secondary is the longer member. (a) “Short primary.” (b) “Short secondary.”

number of pairs of poles. It is thus possible to change the speed of the driving mechanism, i.e., the rotating field, either by changing f or by changing P. Either alternative produces high efficiency running, but each carries a penalty clause. To change frequency using solid-state devices is “expensive” in the sheer bulk of such equipment, its first cost, its weight, and its reliability. To change P at first sight looks as if the motor winding must be replaced, but this is not so, for to a limited extent, a given winding can be reconnected by a simple 6- contact switch to give two or three different speeds. Prior to the 1950’s only two speeds in the ratio 2 : 1 were possible, but the work of Rawcliffe [7] , [8 ] using pole-amplitude modula- tion (PAM) and Eastham [9] using phase modulation made possible almost any two or three speeds within the range which are acceptable on the basis of their Goodness factors. In addition, continuous “pole stretching” is possible using phase shifting regulators provided the energized section of the pri- mary does not extend completely around the periphery in the case of a rotary motor [ 101.

B. Essential Differences between Linear and Rotary Machines The unrolling process depicted in Fig. 1 introduces many

new features not normally considered in conventional rotating machines. The most obvious of these is that if primary and secondary are of equal length and linear motion is allowed to proceed, a piece of the primary member at one end at once loses its secondary counterpart whilst a portion of the second- ary hangs freely from the other end. If motion is sustained even for a short period, the two parts of the motor will part company entirely! Thus for continued motion one or other member must be lengthened. Whether this member be the primary or the secondary is usually a vital choice in the design of a linear motor for any specific application, for clearly linear motors may be divided into two main groups as shown in Fig. 13:

1) “short primary” machines in which the secondary is

2) “short secondary” machines with elongated primaries. elongated; and

In either group, either the primary or the secondary may be made the moving member.

C. Edge Effects The behavior of linear motors in the two groups is different

from each other and both are different from that of a rotary machine. A large part of these differences is due to the fact that either the primary or the secondary member of the flat machines has a “start” and a “ f i i h ” in the direction of motion. These front and back edges set up transient currents in the opposing member which affect the characteristics of the machine to a greater or lesser extent depending on the number

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LAITHWAITE: LINEAR ELECTRIC MACHINES 257

I . . I . . I I , I . . I 1 1.0 0 7 5 05 0.25 0

SLIP

Fig. 14. Effect of the exit edge loss on the speed-thrust curve of a linear motor.

I s N S

t 1 ’ I I -Actual kngth of motor - 1 I I I r- Maqnetic --I

length

Fig. 15. Effect of a very large airgap is seen to make a linear motor ap- pear longer than it really is, due to flux spreading at the ends.

of poles which are contained in the total length of the machine. Summarizing these additional effects, those associated with a short secondary are generally less detrimental than those of a short primary, for the same number of poles. A short-secondary machine is practically indistinguishable from an equivalent conventional machine when its length is greater than two poles. A short-primary motor, however, may remain sensitive to edge effects (depending on which type is being considered) for up to 8-poles length, or even greater numbers.

The nature of these edge effects may also be summarized as follows with respect to short primary machines.

1) There is secondary current and secondary Z2R loss which is not associated with a corresponding amount of useful thrust, as is the case in a motor with no edges, i.e., a rotary motor.

2) There are reactive volt-amperes drawn from the supply which cannot be accounted for either as being due to magne- tization or to leakage reactance. The physical nature of this phenomenon is thought to be due .Lo the continual removal of magnetic energy at the exit edge of a machine, this in turn being due to the fact that short circuited loops on the second- ary member prevent an instantaneous reduction to zero of flux which threads them at the instant they leave the active zone of the machine. (It is possible that when the nature of this “consumer” of reactive volt-amperes is fully understood, it may lead to the invention of the unity power factor induc- tion motor, for rarely in nature is an effect restricted to one side or other of a zero.)

3) The exit edge effect also produces a backward thrust on the secondary which subtracts from the thrust performance in the region of a speed-thrust curve as shown in Fig. 14. This action is still present at synchronous speed and therefore a short primary motor does not normally run “light” at the speed indicated by the formula us = 2pf. Generally, the run- ning light speed is lower than this value.

4) If, however, the airgap is large, flux spreading at the edges, as shown in Fig. 15 creates a situation in which the physical length of the machine appears to have been increased and such

Fig. 16. Standing waves are set up in the core of a linear motor as the result of the “splitting” process which imposes impenetrable bound- aries at the resulting edges. (a) Flux pattern in rotFry machine at one ifstant of time. (b) Result of splitting along A A . (c) Flux pattern r cycle later than that shown in (b).

motors can run light at speeds in excess of those calculated in terms of the winding pitch.

5 ) In a rotary machine, as shown in Fig. 16(a), the flux from each pole divides equally left and right as it enters the core region, so that the core depth d is only required to be large enough to accommodate the flux from the teeth in h,alf a pole pitch. If, however, the machine is split along A A and un- rolled, as in Fig. 16(b), there appears to be no change in the situation with regard to the core flux. Fig. 16(b) however represents a particularly fortuitous instant of time in a cycle of events and 4 cycle later in time the situation is as shown in Fig. 16(c). The ends of the machine are now to be seen as virtually impenetrable barriers to the emanation of flux for- wards or backwards in the direction of motion and the whole of the flux from the teeth of one pole pitch must pass longi- tudinally through the core.

An alternative way of describing this phenomenon (and this explanation emerges naturally from a mathematical treatment of the boundary effects) is to say that the front and back edges set up, in addition to the traveling magnetic field, super- imposed standing waves which may in the worst case neces- sitate doubling the core depth of a short primary machine in relation to the core depth of an equivalent rotary motor.

Short secondary machine edge phenomena, whilst none the less complicated if a rigorous mathematical calculation is attempted, are easier to summarize. If the secondary member is the equivalent of a cage rotor or is in the form of continuous sheet conductor where the current in it is entirely free to choose its own paths, then secondary current density tends to increase towards the edges and externally the secondary ap- pears to have been constructed from material which has a higher resistivity than that which is known to have been used.

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258 PROCEEDINGS OF THE IEEE. FEBRUARY 1975

D. Series and Parallel Connection The foregoing summarization of the behavior of short pri-

mary and short secondary linear induction motors was at one time in the late 1950’s thought to be the sum total of all there was to know about the edge effects of these machines. It is now realized that such knowledge represents but a small frac- tion of what there is to know. The old-fashioned approach has been used here simply because one has to make a beginning somehow, and the subject if treated as a whole would be almost entirely unpalatable. (This is true of many aspects of science and leads to the almost inevitable result that the various aspects tend to be taught historically [ 1 11 .)

Section I I I C is a reasonable summary only for very special classes of machine, namely: 1) those which result from the splitting and unrolling of a conventional rotary motor, whose primary coils 2) are connected in series. In this paragraph, only alterations to 2) will be dealt with for

the possibilities of departing from the topology dictated by 1) are semi-infite and the history of linear motors can be said without exaggeration “to have only just begun!” Topological considerations however are developed more fully in Section V.

The basic properties of a conventional motor are scarcely af- fected by the method of connection of the primary coils. Voltage and current ratings can be interchanged at will by the designer simply by changing the number of turns per primary coil and reconnecting coil groups in series or parallel as desired. The efficiency, power factor, weight, power output, and cost are scarcely affected by these manipulations. What is not generally realized is that this is entirely due to the cylindrical symmetry which exists (or should exist) in a rotary machine. The fact that unbalanced magnetic pull (a magnetic rather than an electromagnetic effect), which occurs when there is some slight departure from symmetry, is affected by the choice of series or parallel primary connections can be compared to the first few drops of rain of a thunderstorm, for after linearization takes place, a seriesconnected primary linear motor is as dif- ferent from a parallel-connected machine as the proverbial “chalk from cheese.”

Basic physics teaches us that it is electric current which sets up magnetic flux. The ac machine designer may, however, more profitably regard the voltage as the originator and con- troller of flux, for the following reason. If a magnetic circuit be surrounded by a coil of N turns connected to a source of EMF E of angular frequency w , the flux through the coil is determined absolutely (in the absence of coil resistance), for the only voltage which can and must oppose E is that produced by a rate of change of flux. Expressed mathematically in terms of the reluctance 61 of the magnetic circuit:

inductance of a coil of N turns = N 2 / R reactance at frequency w = N 2 w/61

rms current supplied from rms voltage E = E61/N2w MMF of coil is therefore N(E61/N2w) = E611Nw.

Flux threading coil is thus

Equation (3) shows that it is possible to change the parameters of the magnetic circuit (length, area, permeability) in any way whatsoever, without changing the total flux through the coil (in the absence of leakage).

(b) Fig. 17. Mean flux and current distributions in a short-primary linear

motor. (a) With primary coils connected in series-primary current fued. (b) With primary coils connected in parallel-gap flux density fured. Current density is indicated by the size of cross-sectioned “conductors.’’

As an example of the way in which a change from series t o parallel affects the performance of linear induction motors, a short primary motor is shown in Fig. 17(a) connected in series, Fig. 17(b) in parallel. In Fig. 17(a), short-circuited loops of the secondary entering the active zone are reluctant t o tolerate rapid changes of flux and hence tend to “wipe” the flux towards the back end of the machine. The secondary MMF at the entry edge, will, in the absence of magnetising current, i.e., assuming in the first instance a perfect magnetic circuit, be equal and opposite to that of the primary and the resultant flux just inside the entry edge will be zero. The primary coils, being in series are all required to pass the same current and the coils further down the primary are unable to assist the first coil at the entry edge in “imposing its will“ upon the secondary.

The flux distribution in a series, short primary machine is always distorted and pushed largely towards the exit end of the machine.

If, however, all coils of the same phase are connected in parallel, as in Fig. 17(b), each coil will demand a flux, as dic- tated by (3) and the rms flux density will be uniform as shown.3 The secondary conductors now receive enormous current pulses as they enter and leave the active (primary) zone, currents which reflect in equally large primary currents. It is at once apparent that these primary currents exist at this level continuously whilst those in the secondary are merely transient. It is for this reason alone that seriesconnected short primary machines have been virtually the only machines to be studied and manufactured to date. Much theoretical study is required on possible series-parallel hybrid connections.

In short secondary machines, however, parallel connection is generally preferred, otherwise the short-circuited secondary will reduce the flux in the active zone to a very low level, as shown in Fig. 18, and the bulk of the primary volt-amperes will be wasted in setting up useless flux, resulting in a very low power factor indeed.

It is interesting, however, at this point, to introduce another rule of thumb which can be most useful for the linear-motor designer. In this case it has no mathematical standing, rather it is a result of the size of useful electric devices and the size of

tributions in the airgaps shown in Fig. 17 will be cyclically distributed. ’It must be emphasized that the instantaneous flux and cursent dis-

The flux lines shown represent the envelopes of the flux and current waves only.

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LAITHWAITE: LINEAR ELECTRIC MACHINES 259

Fig. 18. Mean flux distribution in a seriecconnected short-secondary motor.

men-a coincidence in fact. This rule might be phrased “short- circuited iron is equivalent to air.” The interpretation of this rule in practice can be illustrated by measuring the input im- pedance of a short-circuited transformer and comparing it with the measured impedance of the primary coil alone, if removed entirely from the rest of the apparatus!

Applying this to the case of the parallel-connected short sec- ondary machine is a means of demonstrating (although not proving) the rule, for the flux in the zone occupied by the sec- ondary is still dictated by (3) and hence a uniform flux distri- bution obtains from end-toend of the motor. Langsdorf [ 121 in his excellent book of ac machines makes reference also to the rule in connection with the measurement of zero-sequence reactance of alternators in which, having specified that the test be carried out with a spinning, short-circuited rotor, he con- cludes delightfully and enigmatically “almost the same result will be obtained with the rotor stationary or removed entirely!”

E. Magnetic Pull The forces which are used in electrical machines can be de-

scribed in mechanical terms as “shearing stresses” for they take place tangentially in rotary machines, perpendicular to the main airgap flux direction (which is true of both rotary and linear types). Engineers since Boucherot (1905) have lamented the fact that in rotary motors there are radial magnetic forces of the order of 20 times those which the designer seeks to ex- ploit. Boucherot made a very serious and very nearly success- ful attempt to harness these radial forces by arguing that “To assume that rotary motion is natural motion is begging the question,” and he proposed reciprocating motion (mechanical spring-turned) and produced a rotary version oscillating tor- sionally. The only mistake he made was to be unaware of the “great divide” and that changes of reluctance can only be ex- ploited in small-sized devices.

The rotary machine designer womes about the radial pull only because of its nuisance in making such severe demands on the accuracy of cylindrical symmetry required. In the linear machine, the magnetic pull is able to exert its entire effect all over the pole surface and such force must be opposed by mechanical means. This facet of linear motor design played a big part in the development of the double-sided sandwich motor, for the ferromagnetic parts of the primary and secon- dary are designed to have no relative velocity and can therefore be rigidly separated by struts. In single-sided motors, the whole magnetic pull requires to be contained by a rolling fric- tion device. In the early days of linear motors this fact in- hibited development, and for most engineers, ruled out all of its possibilities.

Having discussed the differences between magnetic and elec- tromagnetic machines it would now appear as if the phenomena of both exist in a machine of the latter kind although essen- tially in different axes. In the former class, magnetic forces

occur in two axes, only the less potent of which can be used. Such appears to be the ultimate frustration of the machine designer. The fact that magnetic mechanisms improve with reduction in size suggests, however, that in large electromag- netic devices the radial pull (in the case of rotary motors) might present less of a problem, and this is indeed the case.

It is more profitable however to evaluate magnetic pull in terms of the relative values of flux density B and current loading J , because it is a feature of all induction motors that when the goodness factor is high the pattern of primary cur- rents is very largely mirrored in the secondary, the slight tan- gential displacement between them being responsible for the electromagnetic torque or force which it is the object of the designer to maximize. But currents flowing in opposite sense in a pair of parallel conductors cause the conductors to repel each other, so there exist also in rotary machines repulsive radial forces between J (stator) and J ‘ (rotor), J and J’ differ- ing only by the nearly negligible (for high G ) magnetizing current [ 131. The radial pull F, can therefore be evaluated as

F, = (& - 7) per unit area Po J2

perhaps, therefore, better described as a pressure, for such is its dimension.

Examination of typical values of B and J reveals that in con- ventional designs it is not uncommon to have values of gap flux density as high as 1.0 T, whilst typical values of J are of the order of 20 000 A/m. The ratio of B i and k J z is thus of the order of 1500 and magnetic pull can safely be calculated simply as B i / 2 ~ o per unit area. The value of BJ obtained using these numbers is also seen to be of the order of one twentieth that of B 2 / 2 h , as suggested earlier.

With linear motors, however, the situation may be quite dif- ferent. When a designer tackles the problem of making a highly efficient induction motor with a large airgap he finds, almost inevitably, that if his machine is of the type obtainable by simple splitting and unrolling of a rotary design, he must use wide slots and narrow teeth. This fact tempts us to look at all types of induction machine, both linear and rotary for the pa- rameters which fix the ratio of slot pitch to slot width in the primary member and the result of such investigation is so potent that a shortened form of the proof from the original paper is quoted here [ 141.

An efficient induction motor is essentially required to oper- ate at low values of slip. This requirement is also reflected in the goodness factor approach and it is usually found that successful commercial induction motors run at slip s where 3/G > s > 1/G. The goodness factor relates the magnetizing component of the primary current to the total current and these two quantities can be translated into current loadings Jm and J , so that J, = J m d m . The relationship be- tween airgap flux density Bg‘and magnetizing current loading has been shown to be [ 61

Bg = pI.6 Jm / W where g is the airgap length and p the pole pitch of the machine.

Combining these equations and representing the slip con- straint as a restricted number k

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2 60 PROCEEDINGS OF THE IEEE, FEBRUARY 1975

In a conventional rotary machine the value of g is usually so small that Bg/J, has a high value (of the order of 1/20 000). In very small drag-cup servo motors the evidence supporting (5) is to be found in the fact of stator slots occupying 80 per- cent or more of a slot pitch. The same is true of linearized rotary designs where the airgap must of necessity be much larger than in its rotary counterpart. In addition, the full speed working slip is governed by edge effects rather than by the other dictates of conventional machine design which lead to the empirical formula 3/C > s > 1/G. For a short primary machine the designer will normally aim at a full load slip at least as great as l/(n + 1) where n is the number of poles on the primary [ 151. Taking a value of C of 10 (a reasonable value for a large airgap machine, although low by rotating machine standards) and n = 4:

J~ = J , ~ I + [ G / ( n + 1)12 =&J,

whence (5) becomes

J, . \ /ST I.6 ( 7 g which is an intermediate value of Bg/J, between the limits of (5) set by a value of k. Thus to a f i t order of approxima- tion (5) is not, for a linear motor, substantially different from the corresponding design criterion for rotary motors.

This being so the formula for the so-called “magnetic pull” may indicate a net value which is negative, i.e., a push. This is especially true of designs in which primary teeth are not used, the whole winding being contained in the large airgap [ 161, for in such designs current loadings of 20 times those used in con- ventional rotary designs are not excessive. At once a factor of 400 is injected into the ratio Bi/p iJ: and if the designer so chooses he can reduce the value of Bg to 0.2 T, resulting in a further factor of 25 when the repulsion force is some six times greater than the force of attraction.

F. A New Technique in Megnetic Circuit Design Enough evidence has already been presented that linear

motors offer the possibility of completely new shapes of mag- netic circuit. There is no fundamental reason, for example, why the magnetic circuit (or indeed the electric) need lie in a plane. In particular it becomes necessary to design machines having magnetic circuits which operate in parallel. Such situa- tions are rare in rotating machines, the shaded pole motor being the almost unique example. Where both electric and magnetic circuits are interwoven in series-parallel combina- tions, analysis and prediction of performance becomes difficult, not because a computing machine’s storage capacity is insuffi- cient, but because the programmer is never really sure that he has properly expressed the problem correctly in respect of the (usually artificial) boundary conditions which he has chosen. The electric equivalent circuit technique is much used in ma- chine problems because it removes the process of arranging the inevitable simultaneous equations in the easiest form for solu- tion and presents the designer with a physical picture of the machine as well as enabling solution, usually by means of a simple p or j operator. The electric equivalent circuit, among other things, seeks to obscure the magnetic circuit’s reality,

‘This equation cannot be justified absdurely for a linear machine displaying marked front and back edge effects but for n > 4 it will be found to be sufficiently accurate for most general design purposes.

(b) Fig. 19. (a) Representation of an electromagnetic arrangement. (b) Ar-

rangement by means of a magnetic equivalent circuit. The magnetic inductances N : / R , , etc., are new quantities (“transferances”) which are the magnetic analog of inductances in electric circuits.

replacing its imperfections by series inductors (in the case of leakage flux) and by parallel inductors and resistors (in the case of reluctance and loss components).

A complete dual of the electric equivalent circuit has recently been developed to meet the new situation introduced by linear motor development. lust as the electric equivalent network is extremely useful in conventional machine studies where all machines are to be run from a fixed voltage, i.e., in parallel, so the magnetic equivalent circuit is best suited to solve problems involving parallel magnetic circuits. The technique [ 17 1 con- sists of representing all reluctances, whether as the result of ferromagnetic limbs or physical airgaps as “in-phase” elements of a circuit (cf. resistors in electric circuits), connecting to- gether the various circuit components in precisely the same way as are the limbs and gaps of the actual machine. Where a coil surrounds a limb and is itself connected to a resistor, the magnetic circuit is considered to have been broken at that section and a “90” lag” element inserted whose value is N 2 / R where N is the number of t u r n s on the coil and R the total re- sistance in the coil and its external circuit (cf. inductors in electric circuits where L = N 2 / @ and a is the reluctance of the external magnetic circuit). If the coil surrounding the mag- netic limb is entirely inductive and carries an all-inductive load (total inductance L ) , the element to be introduced into the magnetic circuit is an in-phase component-a fictitious reluc- tance of value N 2 / L . If two elements in the electric circuit are in series they are to be connected as magnetic circuit elements in parallel and vice versa. Fig. 19 shows an example of mag- netic circuit building which illustrates all these points in the technique.

The analog has more recently been extended by Carpenter [ 181 to enable it to be used in problems involving distributed circuits.

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LAITHWAITE: LINEAR ELECTRIC MACHINES 261

IV. ELECTROMAGNETIC LEVITATION A. A Brief History

Historically, the fact that horizontal airgap single-sided linear motors can be designed to produce lifting forces even though both primary and secondary members contain ferromagnetic cores was probably discovered as recently as 1964 [ 131. Equation (4) in the previous section states the conditions nec- essary for such net lifting force to exist. From 188 1, when Fleming demonstrated his famous “jumping-ring” experiment, until the 1960’s, all levitation experiments had consisted of a primary coil system, with or without a steel core, operating into a conducting but necessarily nonferromagnetic secondary.

In 19 14, Bachelet proposed that a levitation and propulsion system should be applied both to the propulsion of shuttles across weaving looms and to guided transport systems. He set up separate companies to handle these projects but both seem to have been swallowed up in the World War I. By coincidence it was in the year in which World War I1 began, 1939, that Bedford et al. [ 191 used a double-concentric coil system shown in cross section in Fig. 20. The dotted lines indicate how such a system may be improved by the addition of an outer wall of steel. This arrangement set an early fashion for levitators. It is usual to arrange for the inner coil current to lag in phase behind that of the outer to produce an inward-traveling field, although it was later established that in large levitators where the secondary goodness factor is high, the two coils can be connected in series opposition for successful stable suspension.

Aside from Bachelet, the early experiments on levitation were conducted in a spirit of curiosity, even those in the late 1950’s which were to be the forerunners of much more serious experiments directed to high speed transport applications. The Fist application to be commercially successful was that of sus- pending small quantities of molten metal so that melting and mixing could be performed in controlled atmospheres without the necessity for a contaminating crucible. A small team of U.S. scientists produced a series of valuable papers on such devices [ 201 -[22], a typical arrangement being shown in Fig. 2 1. In order to heat the metal t o melting point rapidly, high frequency supplies (tens of kilohertzs) were used in the pri- mary coils which, because of skin effect were conveniently made of copper tubing through which cooling water could be pumped to enable high primary currents to be used. The upper coil above the specimen assists the repulsive forces from the c o n i c a l coil below and has become known as the “attractor.” When melted, most metals formed into the characteristic pear shape shown in Fig. 21, although some metals dripped when molten and it was thought that those which did not achieved their stability through a restraining, self-forming skin of oxide. It is interesting to note that for small quantities of metal it was found difficult to prevent the temperature of the specimen from rising to an excessive value but this is now seen as a par- ticular manifestation of the rule “the bigger, the better” for electromagnetic devices. This, and another similar phenome- non can be conveniently fitted into the linear motor story at this point, as an introduction to the all-important applications described in Sections VI11 and IX.

B. The Law of Size Lovell [23] experimenting with a 2-coil power-frequency

levitator of the type shown in Fig. 22, discovered that near the center .of the top surface of the primary coil system small pieces of conductor were attracted downwards t o the coils, in

- --- I I I I I

I - -2

Outer Coil

Fig. 20. Early electromagnetic levitator (in cross section) developed by Bedford, Peer, and Tonks in 1939.

-01 a0-

W

Fig. 2 1. Cross section through a levitator for liquid metal.

,- cone of attraction

Fig. 22. Lovell’s attractor for nonferrous metal. It was hoped to we such a device for removing metal particles from human eyes.

4 Cone of

attraction ! j j h +4?J;A/$(+dk14 f 4 f f!..; t + + J . 4 {*.! f I +

lxiw IX‘IXI Fig. 23. The “cone of attraction” over a double circular coil system

within which cone, small nonferrous metal pieces are attracted towards the coils. Outside of the cone similar pieces are repelled.

fact he defined a “cone of attraction” as shown in section in Fig. 23 within which conductors were attracted and outside of which they were repelled. Lovell tried to use such a system for the removal of particles of metal from human eyes but failed and it was the nature of the failure which stimulated the author to deduce, in a paper on electromagnetic levitation [ 241 , the more all-embracing rule for induction forces which is expressed mathematically as

a T p t -- - k (L)-” F l m

(6 )

where T is the instantaneous temperature of the secondary ujnductor, and a T p t the rate of temperature increase. The force F on the mass m of the secondary produced its accelera- tion in free flight and the ratio of the rate of temperature in-

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262 PROCEEDINGS OF THE IEEE, FEBRUARY 1975

( 4 (dl Fig. 24. Experiments concerned with the flotation level of conducting

rings of various thicknesses in a “jumping-ring” apparatus.

crease to available acceleration is seen to increase with reduc- tion in linear dimension L , for n is a positive number greater than unity and k is simply a constant of proportionality.

Equation (6) expressed as a slogan may be written: “AS electromagnetic propulsion devices are made smaller the sec- ondary must ultimately melt before it moves” (since it is con- strained at least by friction). Lovell’s experiment did not, therefore, fail for lack of primary MMF. It appeared to fail on what the late Bragg described so beautifully as “the nature of things,” [25 1 .

Yet we must take care at all stages of development lest we blind ourselves to the next step. In this case, impossible as it seems to improve on Lovell’s device, a recent experiment with a simple jumping ring apparatus has suggested that this may not necessarily be so. The experiment [26] is illustrated in Fig. 24.

If a thick aluminum ring “floats” in the position shown in Fig. 26(a), thinner and thinner rings will be found to float at lower and lower levels for the same excitation (Fig. 24(b)) until a ring of aluminum foil fails to lift at all (Fig. 24(c)). If now the thick ring is reintroduced from above as at Fig. 24(d) the thin ring at once moves upwards and it has been established through a refined experiment that in this last condition the levitated foil ring is carrying a smaller current than it is in position (Fig. 24(c)). What the thick ring does is to cause the primary to take more current which is in phase with the foil current, for quadrature currents, however large, produce no net uplift. This simple experiment suggests that a low value of goodness in a primary/secondary system can be improved by the addition of a quite separate tertiary electric circuit, acting analogously to a catalyst in a chemical action. There may yet be hope for the small electromagnetic device?

The second example of constraint imposed upon the induc- tion motor designer, particularly he who would seek to gen- erate kinetic energy in a secondary mass, rather than power, is provided by the identity that in accelerating such a secondary from rest to the synchronous speed against no restraint except its own inertia, the heat loss in the secondary is equal to the kinetic energy at the synchronous speed [6] . Since the mass of the secondary can only absorb this heat in proportion to the cube of its linear dimension or radiate it in proportion to the square of that linear dimension, projectiles moving faster re- quire to be larger if they are not to melt before attaining full speed. This law which may be summarized as “the faster the

bigger” is supported by the experimental work of Thorn and Norwood who tried to attain “hypervelocities” of the order of 50 000 km/h by electromagnetic means, in order to test the ef- fects of possible impact by meteorites on space capsules [27].

C. The Levitation of Noncircuhr Shapes Double-concentric coil systems can support spherical objects

easily. Circular plates are almost as easy to stabilize although in both cases it appeared, until recently, that Lovell’s require- ment that at least a part of the suspended object must cut the cone of attraction must be upheld. It also appeared from ex- perimental results that the apical angle of the cone of attrac- tion was essentially large (> 120’) and therefore possible sus- pension heights were limited to a few centimetres at most.

The next shape of conducting object to be levitated was a rectangular sheet. The development stages are shown in Fig. 25. In Fig. 25(a) the double-concentric seriesapposing coil system represents the starting point. In Fig. 25(b) the system has lost its circular symmetry but remains essentially the same in that it consists of two “concentric” coils in series opposi- tion. It is also found to be electromagnetically the same as Fig. 25(a) in that in the presence of the rectangular conducting sheet, inwardly traveling fields can be detected in the vicinity of the plate edges as indicated by the arrows and these fields are undoubtedly a part of the stability mechanism. Examina- tion of Fig. 25(c) shows that for a large part of the central (working) region the system is identical to Fig. 25(b), for it is difficult to see how the levitated plate can be aware of the presence of end connections which can be made semi-infiitely remote.

In such a system, the two coils can now be spaced apart to accommodate plates of a large range of different widths, for it is found that the only condition for stability is that the side edges of the plate should lie over the region of the central ferromagnetic core of each coil.

Whilst this apparatus was in use at Manchester University in 1962 a new phenomenon was observed when the two coils were accidentally connected so that the current in the two innermost longitudinal members flowed instantaneously in the same direction. In other words, one coil had been reversed in respect of the arrangement shown in Fig. 25(a). This recon- nection was seen to make virtually no difference to the stable levitation ability for rectangular conducting sheets and was later t o be of great importance in the further developments for high-speed transport applications.

D. Development o f the “Magnetic River” Calculation of the performance of levitators is extremely dif-

ficult and laborious. The analysis is essentially three dimen- sional and, where successful, it only enables a given construc- tion to be assessed. If it be found that the performance is poor, numerical analysis rarely tells the investigator how it can be improved. But this is an engineering study and not merely a physical one and engineers often ascribe to currents and fluxes a reality to which they are not entitled and to pieces of steel and copper a “personality,” the concept of which would cause the average physicist to throw up his arms in horror! Nevertheless it was by means of such intuitive processes that the next sequence of developments was achieved, ending with a combined ”propulsion and levitation system so simple to con- struct, yet so ideally suited to the solution of transport prob- lems as to seem to have achieved the impossible, for the levita-

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LAITHWAITE: LINEAR ELECTRIC MACHINES 263

v x-x I,

Fs. 25. Stages in the development of a rectangular-plate levitator. (a) A concentric coil system. (b) Elongation of the concentric coil system along an axis which becomes an axis of free movement. (c) A rearrangement of coils gives the same result as (b).

tion and stabilizing forces are obtained for zero power input, for laterally and vertically, there is no relative motion between primary and secondary members, and, therefore, the output power in these axes is zero.

The physical arguments which led to this invention are illus- trated in Fig. 26(a) which shows a cross section through the levitator shown in Fig. 25(c). It was argued that the edges (XX) of the plate were too remote to “see,” i.e., to be seriously affected by, the outermost edges ( Y Y ) of the steel, so the outer steel members are redundant and the system is reducible to that shown in Fig. 26(b). This is not surprising since the latter is only a linearized version of the levitator of Bedford et al. [ 191. Since this first argument holds it is certain that removal of the steel situated below the outer current-carrying conductors (shaded in Fig. 26(b)), can also be removed.

Next, it was argued that since in electromagnetic systems only the linkages between electric and magnetic circuits are meaningful, the outer conductors of each coil can be moved to the positions shown in Fig. 26(c) without losing any of the vital linkages. When this system was tried in practice however, it was found to be essentially unstable, but remembering the Manchester accidental misconnection, it was reconnected with the currents in the two slots connected to give instantaneous flow in the same direction, as shown in Fig. 27(a),-and found to be stable. It was then pointed out by Eastham that if the levitator were not constructed as continuous lengths of con- ductor-filled ferromagnetic channel, but were to be divided into separate “C” cores and coils, as shown in Fig. 27(b), the

Fig. 26. First stages in the development of a magnetic river. (a) Cross- section through the levitator shown in Fig. 25. (b) Removal of the outer teeth is found to make no difference to the lift and stability. (c) Repositioning of the return currents again makes no difference?

(a)

-t

(b)

Fig. 27. Further stages in magnetic river development. (a) Plan view of levitator shown in Fig. 26(c) with currents in one coil reversed. (b) Subdivision of the excitation coils and the introduction of poly. phase supplies produces both levitation and thrust.

system would propel longitudinally as well as levitate a rec- tangular plate of approximately the same width as the overall core dimension in Fig. 27(b). Thus began the concept of a magnetic river [ 281 in which an invisible fluid appeared to float and propel pieces of conductor in much the same way as a river of water floats and propels pieces of wood. What is more, if an observer attempts to push the metal plate sideways from its support system, it is seen first t o rise as if hitting an embankment and the electromagnetic “river banks” at once assume a reality to which, of course, they are not entitled.

One limitation which was found to exist in the system shown in Fig. 27(b) was that the dimension x separating the two rows of “C” cores could not be reduced below a value roughly equal to the slot width. The reason for this was discovered not whilst attempting to “explain” the mechanism of the magnetic- river system but whilst endeavoring to make a circular version which it was hoped might support and rotate simultaneously a

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264 PROCEEDINGS OF THE IEEE, FEBRUARY 1975

/

U

(b) Fig. 28. An attempt to make an annular magnetic river. A plan view of

the machine of Fig. 27(b) is “rolled up” about an axis normal to the plane of the diagram. (a) Circular current flow gives lateral instability.

of the annulus produce stability. (b) Return currents forced to return around the inner and outer edges

Fig. 29. Magnetic river produced by a single row of “C” cores laid in a line perpendicular to the cross section shown.

conducting annulus. The primary arrangement is shown in Fig. 28. This system proved to be unstable and Eastham dis- covered that only if the coils were reconnected so that the instantaneous current flow in the annulus is not circular and self-contained, as in Fig. 28(a), but is forced to break and return, as shown in Fig. 28(b), is stability achieved. The return currents were now clearly the means by which stability was achieved and the reason why the gap x was necessary in Fig. 27(b). There had to be lateral space for the &-important return currents.

The next important development came with the realization that a single row of “C” cores would themselves produce a magnetic river, a cross section through such a system being shown in Fig. 29. This was clearly advantageous, for being an electromagnetic device, its characteristics improved as it was made bigger and therefore a single “C” core, scaled up to oc- cupy the same track width as a double “C” core, had a much higher goodness factor. This result could be phrased in

‘mi lL-x

Fig. 30. The necessary geometry of a plate levitator and supported sheet is an expanding one. Provided the sheet is of such a width as t e fit be- tween the dotted lines at the levitated height, the same degree of stability will obtain. As height is increased, appropriately more power is, of course, required from the primary (currents Z4 > 13 > Z2 > ZI).

another way by saying that the development of the single row of cores corresponded to a change in lateral pole number from four poles to two.

One such system built was found to be stable in the five axes required (pitch, roll, yaw, lateral displacement, and vertical bounce) and propelled in the sixth. What is more, critical damping to disturbances was observed in four of the five stable axes. The roll axis was found to be underdamped and in an effort to improve the damping, wider secondary plates were tried. Beyond a certain width, lateral stability was lost. How- ever, a plate too wide to be stable when levitated at height h was seen to become stable as the primary current was raised so as to levitate at a height greater than h. At-once it was clear that the cone of attraction rule was broken and that there was no limit, in theory, to the height at which a conducting object could be supported, for the system is seen to work on an ex- panding rather than a restricting conical geometry, as shown in Fig. 30. So long as more current is available in the primary, a wide plate can be supported at a greater height, with the same lateral stability. Supported heights greater than 0.3 m have already been achieved in practice.

E. Magnets for Nonferrous Metals This is not to say that the cone of attraction no longer exists

in such systems. The breakout is the fact that the secondary conductor need not cut such a cone in order to be stable. Re- turning to the doublecoil system of Fig. 26, it has been shown that a lagging current is desirable for the inner coil and, there- fore, a short-circuited inner coil makes a successful levitator for the shorted coil acts as a “shading ring” in a single-phase sys- tem. So potent is the attraction and lateral guidance within the cone in certain circumstances, for example where a con- ducting ladder is fitted into the top portion of the primary slots of a linear motor, as shown in Fig. 31, that a strip of aluminum, approximately the same width as that of the ladder, can be made to adhere to the primary pole surface and simul- taneously be propelled longitudinally, when the pole surface is vertical, as in Fig. 32(a), or even wheR the pole surface is below the motor, as in Fig. 32(b).

Similarly a single ac coil surrounding an extended laminated core is capable of picking up pieces of nonferrous metal of a p propriate size (an interesting size being that of coins), provided a short-circuited ring is sunk into the operative pole face [29].

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LAITHWAITE: LINEAR ELECTRIC MACHINES 265

n

Fig. 31. A conducting ladder fitted into the top of the slots of a linear motor but restricted to cover only the central region by the use of two additional longitudinal slots will produce forces which cause a secondary conducting strip to adhere to the surface and to be laterally centered.

t (b)

Fig. 32. The conducting ladder shown in Fig. 31 produces sufficient forces to support the weight of the secondary strip. (a) Laterally. (b) Vertically.

Another example of the same phenomenon is the fact that the central conducting plate of a double-sided sandwich motor is laterally unstable, and if free to move will be attracted quite strongly to whichever primary unit should be the nearer. One attempt at an explanation of this phenomenon and of the cone of attraction phenomenon in general is now attempted.

F. Constant Phase-Line Plotting It-is often customary to plot lines of flux or lines of mag-

netic equipotential in order to give a visual aid to the action of a static electromagnetic system. In this case the magnetic fields are moving, i.e., different parts of the space around the excited region carry fluxes of different phase. Since phase alone is sufficient to indicate the direction of travel of a field system it is proposed to plot lines of constant phase in the region of interest and subsequently to regard such lines as if they were height contour lines on a geographical map. If the convention adopted is such that a more lagging phase line is given a lower number, pieces of conductor wiU be seen to conform to the simple rule that they move “downhill.”

If .a pair of oppositely magnetized pole surfaces energized from a single-phase supply, as shown in Fig. 33, is now con-

( 4 ( 4 g. 33. mots of lines of constant phase for fields due to ac magnets. The l i e s arc numbered 50 that they may be regarded as height con- tours on a geographical map. (a) Flat plane. (b) The “shading” effect of a secondary conductor, producing inward-traveling fields. (c) and (d) show why a displaced conductor is attracted to the nearer pole.

dered, the phase plot is a blank sheet, as shown in Fig. 33(a), e., the system is analogous to a level plane. If now a small

--ab of conductor is inserted, as in Fig. 33(b), its effect is to cause the field passing through it to lag and the resulting phase plot, as measured experimentally, is of the form shown. Smaller pieces of conductor placed in positions such as that shown dotted will in fact be found to move downhill, i.e., inwards.

Having established the technique it can now be used to argue the case of the double-sided sandwich motor, for the condi- tions at any lateral section of such a motor are precisely those shown in Fig. 33 if the propelled sheet considered (for sim- plicity in this first example) is narrower than the primary. When the secondary conductor is displaced to the position shown at Fig. 33(c), it can be argued that the absence of con- ductor on, or near to, the lower pole has the tendency of al- lowing the surface flux to return to a nearly “flat plane,” whilst the greater proximity of the conductor to the upper face allows increased electromagnetic coupling, i.e., higher goodness factor, in this region and hence a steeper array of contour lines along the face. Constant phase lines, like isobars, isotherms, height contours, etc., must be continuous throughout the region so the only possible contour configuration is that which is shown at Fig. 33(d), from which it is at once obvious that there is a vertical force pressing the conductor to the pole face as well as laterally stabilizing it. This experimental technique [30] , whilst only qualitative, is of use in the consideration of high-speed motors for vehicle traction discussed in a later section.

V. LINEAR MOTOR TOPOLOGY A. A Brief History

The essential differences between manufactured articles and living things have been seen to be largely differences in shape. The curves which men produce have a simplicity which is commendable only perhaps when production methods have shown their use to benefit the community or some section of it. If it were not so, artists and sculptors would be virtually nonexistent, for we regard the shapes of nature as something to be worshipped and often ascribed to the ability of God to bring pleasure to men!

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266 PROCEEDINGS OF THE IEEE, FEBRUARY 1975

(a)

Fig. 34. (a) Conventional rotary machine. (b) Flat linear motor, which can be regarded as the intermediate class. (c) Tubular linear motor. Topological relationship between (a) and (c) is apparent here.

Wheatstone, stretching his imagination beyond the confiies of tradition, in 1841 to 1845 produced a series of electric motors with eccentric rotors [ 3 1 ] and in the process suggested the splitting and unrolling exercise with which it is now almost traditional to begin a first explanation of a linear motor to the uninitiated, whether by pen or by word of mouth.

But how inhibiting is such an approach! It implies at once that the linear machine can never be better than its “ancestor.” Wheatstone copied one of his rotary machines, but there was no shame in that for the electrical engineers of the next hun- dred years did precisely the same. What is more interesting however, is that the few useful and unconventional topological changes which were made during the same period were made by textile engineers who were not so indoctrinated as to copy existing motors. Thus Jasicek and Polnauer [32] invented the double-sided sandwich motor. Tubular motors were also built by the textile machine maker Forman 1331. This latter inven- tion is perhaps the next logical step in a process which begins with the splitting and unrolling of a cylinder for it simply in- volves a rerolling about a different axis, as shown in Fig. 34. Certainly it will suit our purpose here to elaborate on the tubular motor at this stage, for its topology is simple, its ad- vantages few and obvious. It will, therefore, serve as a prelude to the topological explosion which was to occur in the late 1960’s and early 1970’s.

B. Tubular Motors The feature of tubular motors which severely limits their

application is the fact that the primary windings do not merely link the fictitious flux path, but are inextricably linked with the real secondary structure, access to which can only be made via. the ends of the tubular primary. This necessity virtually implies that short-primary machines are much more likely to find application than are the short-secondary type.

The principal advantages of tubular motors, on the other hand are all centered 6n the simplicity of the stator construc- tion, in particular the fact that a tubular motor need have no wasteful “end winding” in either primary or secondary. How this arises is illustrated in Fig. 35 in which a plan of the primary windings of a flat linear motor is drawn (Fig. 35(a)) and divided into three distinct regions by the dotted lines. The portion between the dotted lines is usually regarded as the “active region” of the machine, the two regions outside being regarded in part as a necessary evil, especially by the designer of conventional rotary motors. It is customary, in the rotary world to restrict the insertion of magnetic material to the center region only, and, therefore, all linear motors up to the 1970’s were designed in the same way.

C. The Question of End Windinns The orthodox view of end-windings is that they have two

disadvantages and one advantage which are as follows.

And wlnding

Fig. 35. (a) End windings of a flat linear motor. (b) When rolled into a tube each active part of a coil joins onto itself and the end windings are made redundant.

Fig. 36. A tubular motor primary is no more than a row of simple coils.

Disadvantages: a) They produce 12R loss over and above that which is necessary in the “active” conductors alone, thus re- ducing efficiency and’ power-to-weight ratio. b) They drive a flux pattern of their own which does not link with the second- ary, tending to result in low power factor.

Advantage: They represent the only exposed portion of the primary winding where effective forced cooling can take place. The heat produced in the stator slots is. largely conducted laterally by the conductors themselves to the end windings. Conduction through the insulating layers inside the slots is relatively small.

When the diagram of Fig. 35(a) is rolled up to form a tubular motor (Fig. 35(b)), it is at once apparent that the whole of the end-winding regions is superfluous for A falls on B and the conductor A B in Fig. 35(b) is entirely self-sufficient, as are all similar conductors. The motor winding may thus consist of a row of simple coils, as shown in Fig. 36, suitably phased and spaced to give the desired synchronous speed. The technique of “phase mixing” [ 101 so commonly employed in rotary ma- chines with a view to space harmonic reduction may also be employed in simple tubular windings as shown in Fig. 37. Whilst Fig. 37(a) shows a cross section through a tubular primary in which only simple coils are used, two-layer coils, as in Fig. 37(b) give some degree of phase mixing but a com- pletely different manufacturing approach is shown in Fig. 37(c), in which each phase is constrained to a single continuous layer. The winding of such a machine in practice is as simple as that of winding individual bobbin coils, a single layer being

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I 4

I I I

l a I a I n I ! ,

(C) Fig. 37. (a) Cross section through the tubular motor shown in Fig. 36.

(b) A tubular motor primary wound in two layers to produce “phase mixing.” (c) Continuous winding technique for a layered primary.

Fig. 38. A physical picture of one layer of the machine shown in Fig. 37(c).

shown in Fig. 38 in which the direction of wind is reversed every pole pitch.

D. Magnetic Circuits o f Tubular Motors The magnetic circuit of a tubular motor is of particular

interest in the development of the most recent forms of linear motor, for whilst tubular motors themselves are not much used, a study of their magnetic circuits points a new way to electromagnetic machine design. Fig. 39(a) shows a rotary motor with its rotor removed. The idea of using only a thin- walled copper cylinder as rotor of such machine (as in a “drag- cup” design) without a rotor iron core is almost unthinkable, for it is obvious that the effective airgap is very large, its area severely restricted by a rapidly contracting geometry which is inherent in the adoption of cylindrical topology.

When the motor is unrolled, as in Fig. 39(b), however, the flux path area is no longer so constricted and the flux can literally spread to infinity, albeit the further it spreads the longer is the path. Nevertheless, the effective airgap of such machines is not as large as might, at first sight, be imagined. It has been shown [6] that, to a first approximation, magnetic circuit calculations for flat open-sided machines may be made on the assumption that the effective airgap is p / n where p is the pole pitch.

When the motor primary is rerolled into a tube, it must be done in such a way that the iron core emerges as the inner

I I (b)

- Fig. 39. Magnetic flux paths in space. (a) From a conventional motor

with rotor removed. (b) From an open-sided linear motor.

Y

Fig. 40. The effective airgap of tubular motors of bore radius a and pole pitch p .

member, whether or not the primary winding is still contained in it, or whether it is transferred to the outer shell, for two major changes have been made by this last topological step. On the outside, the ,flux is able to spread to infinity in two dimensions, the one as already discussed with reference to Fig. 39(b) and the other in the fact of an ever-widening circle at greater distances from the winding. The benefits of this last effect clearly depend on the ratio of winding radius to pole pitch. Fig. 40 shows the reduction in effective airgap below the p/n value for flat machines, plotted as a function of the ratio of radius to pole pitch (alp) . Good designs of tubular motor are, therefore, possible with no primary steel whatso- ever. Nevertheless, some of the earliest liquid metal pumps which were of tubular form, incorporated steel in the stator core and avoided the awkward tapered laminations which would appear to be required by dividing the core into 6 or 8

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C

CORE

Fig. 41. A practical arrangement of adding a ferromagnetic structure to the primary of a tubular motor.

Fig. 42. Cross section through a tubular motor shows constriction of flux paths along the bore (small area), and low reluctance paths out- side the primary (large area).

rectangular-section slabs, as shown in Fig. 41. This form of construction is seen to involve very little more complication than that of a rotary motor, provided the stator slots are open slots with parallel sides, and the windings which ultimately occupy them can be wound in position first, so that the steel slabs can subsequently be dropped over them.

Within the bore of the tube, however, the magnetic situation is reversed and a much more constricted flux path even than that shown in Fig. 39(a) obtains, as shown in a longitudinal cross section of a tubular motor, Fig. 42. It is, therefore, not usually possible to make successful tubular motors devoid of iron cores.

E. Manufacturing Techniques for Tubular Motors However ingenious a technological invention, if it is not in

step with progress in materials science and with manufacturing methods, it is a failure, at least temporarily. Babbage’s calcu- lating machine of 1838 had to wait over 100 years for the development of triodes and pentodes before the modem com- puter was seen to be profitable. In tubular motors, industry has already produced several designs which may sacrifice some part of their ability in order to make them easier t o fabricate.

Fig. 43 shows a cross-sectional view of a commercial tubular motor in which the following advantage’s of the new topology and of new materials have been exploited.

1) The low flux density of a low-speed actuator (low speed implies small pole pitch and (5) illustrates the subsequent re- quirement for wide slots and narrow teeth) allows the teeth to be constructed of solid steel plate which can be prepunched with all the necessary bolt holes and central hole to accommo- date the secondary cylinder.

2) The same plates are used as cooling fins for carrying away the heat from the secondary and from the primary windings.

3) Yet again, these same plates provide a large area path for flux return outside the stator windings. So potent is this area,

Fig. 43. Cross section through one type of commercial. tubular motor requiring only 3 simple basic components-coils A , punched steel plates E , and “C” cores C.

Fig. 44. Alternative commercial tubular primary. Slotted punchings are stacked and cemented together, after which a hole is drilled, in the position shown dotted, to accommodate the secondary rod.

that despite the large gaps between successive plates, removal of the “C” cores which are, at f i t sight, the usual cores which connect adjacent poles magnetically, increases the input power per unit thrust by less than 10 percent. The “C” cores are thus to be seen as little more than mechanical protection for the primary windings, whose connections are brought out through the splits in the “C” cores.

Fig. 44 shows an alternative form of construction in which slotted punchings are stacked and encapsulated in resin, after which a hole is drilled from end-to-end to provide space for the moving secondary rod. The primary coils are then inserted and located in the slots and the construction is complete.

F. Gramme-Ring Winding In modern rotating machines of all types it is customary to

use only “surface windings” in either rotor or stator. A surface winding is one in which the active conductors are contained in slots in the ferromagnetic material which faces the airgap and in which all active conductors are connected together by end connections which are laid in a generally circumferential direc- tion. Early machine pioneers did not appreciate the advantages in terms of savings in copper, in power input and in leakage flux and returned their coils around the core of the machine as shown in Fig. 45(a). Such windings became known as “Gramme-ring” windings although they were, in fact, invented by Pacinotti.

Linear versions of such windings are illustrated at Fig. 45(b), (d). The theoretical analysis of such machines is very different from that of surface-wound machines, for in the case of the latter each conductor which crosses the width of the machine must have a corresponding conductor to return that current, and the investigator can write one of his constraints as the following integration:

where J is the current loading at distance s from one end of the

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( 4 r e . 45. Examples of Gramme-ring primary windings. (a) In a rotating

machine. (b) In a single-sided linear motor. (c) In a double-sided sandwich motor. (d) In a “Mock Tubular” motor in which like poles oppose each other from the two outside primary members.

machine, whose total length is 1. A glance at Fig. 45(b) how- ever, suffices to show that this constraint no longer applies, and sufficient equations to provide an analytical performance to be calculated must be sought from other boundaries. “The choice of boundary conditions is as skilled an art as any in the scientific world,” [6].

A double-sided linear motor with each side of the primary wound may be one of two typ 3s. Either the two windings may assist one another in driving flux across the airgap, in which case the secondary may contain ferromagnetic material, or may consist simply of a sheet of conductor as in Fig. 4 % ~ ) . If however the windings in the two halves are so arranged that instantaneously “N”-pole faces “N”-pole and the flux is driven axially along the central secondary member as in Fig. 45(d), the latter must contain ferromagnetic material or the motor will draw a prohibitively large magnetizing current due to the constriction of the magnetic circuit between the primary blocks, just as in the case of the tubular motor illustrated in Fig. 42. Indeed such machines have been labelled “mock tubular style” [34] for their relationship to the tubular motor is seen to be no more than making the cylindrical cross section of the latter into a square, as shown in Figs. 46(a) and (b),

(b) ( 4 Fig. 46. Tubular motors and “mock tubular” motors. (a) A cross-

section through a tubular motor similar to that in Fig. 41 but having only 4 primary blocks instead of 6. (a) A square geometry is funda- mentally no different from the circular geometry of (a). (c) The primary of (b) is Gramme-ring wound. (d) Removal of 2 blocks makes the square into a rectangle having certain benefits.

Gramme-ring winding it, as in Fig. 46(c) and using only two opposite sides of the Gramme-ring winding, as in (d).’ It will be apparent however that the Gramme-ring tubular motor is much more wasteful of copper than its surface wound counter- part shown in Fig. 46(b). The advantageous features of the mock tubular motor are first that the secondary is accessible all along its length, which is certainly not the case with a tubular motor proper. In short secondary machines the ques- tion of rotor accessibility could be vital. Secondly, the tubular motor proper demands two-dimensional lamination of its secondary, the mock tubular can be made from lamina which is more economical.

It is also clear however, that the primary windings of double- sided mock tubular motors need not be of the Gramme-ring type but could be surface windings. At the same time, the secondary of such machines could also be either surface or Gramme ring.

Discussion in this section so far is enough to show the enormously greater variety of shapes of linear motor which are possible by comparison with rotating machines, and this is true for every type of machine, i.e., induction, reluctance, dc, hysteresis, etc. There is sufficient development work to be done on linear motors t o occupy research workers all over the world for at least several decades.

G. The Problems of Long Pole Pitches

velocity u of the traveling field, for u = 2pf. Hence The goodness equation (1) may be rewritten in terms of the

5 The motor shown in Fig. 4 1 is no more than a hexagonal section machine with bored out interior. Flat and tubular constructions are thus seen to merge topologically.

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270 PROCEEDINGS OF THE IEEE, FEBRUARY 1975

This rearrangement is useful in illustrating two points, one of which was discussed in Section I€.

1) “The bigger the better” slogan is translatable into “the faster the better.”

2 ) For a given velocity it is apparently always preferable to increase the pole pitch and reduce the frequency, for this will lead to higher values of G for fixed speed and given secondary structure.

Equation (7) represents, of course, a highly simplified view of an induction machine. In practice, the f i t modification to demand serious attention is the impedance of the end windings.

In the exact linear counterpart of a rotating machine, the primary coils are considered in the same way as are those of their cylindrical ancestors in that the portions of the coils located in the slots and usually approximately at right angles to the direction of motion are regarded as “useful,” whilst the portions outside the ends of the ferromagnetic core are re- garded as “wasteful” end winding, wasteful in three ways: 1) the actual conductor is wasted; 2 ) extra 12R loss is incurred; and 3) extra leakage reactance is added. Ingenious topology however has enabled all these wastages to be minimized, and it is interesting to note that at this stage in the linear motor story only the end windings have exploited a truly three-dimensional

Linear motor design, much more than that of rotary ma- chines, indicates that a designer may regard the pole surface of a machine in much the same way as does a tailor his cloth. The “quality” of the cloth can be assessed in terms of the goodness factor alone. The designer knows that for any given set of values of p , f, and p he may evaluate such quantities as efficiency, power factor, and most important, the force per unit area, t o a first approximation. He is then required to “measure the customer for his suit” in that restrictions are placed on him by the application for which the motor is in- tended, e.g., the speed, the total power, the cost.

The total power divided by the speed will give him the total force needed, hence at once the area of “cloth.” He then has a free choice in respect of the linear dimensions of that area, i.e., he can make a rotary motor with an axial length 1 and radius r or axial length 21 and radius r / 2 . In linear machines, he is less restricted in that he may make the length of the rectangle in the direction of motion such as to give a fractional pole number.

One of the main problems which is highlighted by such a technique is that of designing a linear induction motor for high speeds, e.g., of the order of 400 km/h. The equation u = 2pf reveals at once that if the motor is t o be run directly from 6 0 - H ~ mains, p is at least 1 m (allowing for slip). sup pose the total thrust required is 3 tonnes requiring a total area of pole surface of 2 mz . It would appear reasonable to try for a square pole on the grounds of reducing end-winding waste to a reasonable figure, but the side of the square wodd then be only a m , i.e., the motor would be only 1.4 poles long and edge losses prohibitively high. Furthermore, if used as a moving short primary motor over a long track (as in high-speed transport applications) increase in track width is very expen- sive and the designer is forced to the conclusion that on track dimensions alone, his rectangle should be more of the order of 6 m X i m . This makes the “useful” conductor 3 m long and the wasted length three times greater. Only d of the copper is useful. It would appear that our high-speed customer is a very odd shape!

topology.

Fig. 47. Flux paths in a single-sided motor with a large pole pitch show why both primary and secondary core depths must be excessively large if saturation is to be avoided.

Nor do the designer’s problems end with the end-winding considerations. The magnetic circuit design is an even bigger problem, for the whole of the flux from the end pole must be conveyed to the next pole through the core of the machine, as illustrated in Fig. 47. Even though (5) has shown that for large airgap motors the slot width is likely to be of the order of 3 of the slot pitch the core depth must still be of the order of p/4, if the steel is not to be run into saturation. A core 25 cm deep is certainly not viable for a single-sided motor of the form shown in Fig. 47, and even a double-sided sandwich motor would require a very heavy primary.

H. Transverse Flux Machines The topological solution6 to the problem .of the long pole

pitch came in 1969 with the realization that the electric circuit had “broader shoulders” than the magnetic circuit and could more readily bear the strain of an excessively extended pole pitch. This philosophy is based on three virtually inescapable facts.

1) There is no magnetic insulator comparable to the splendid varnishes and plastic materials that can be used to contain electric current within its boundaries. Electric circuits can, therefore, be multiturn, long and narrow, whilst magnetic circuits must be essentially single-turn, short, and fat. Super- conductors behave as would a magnetic insulator but are, as yet, far too expensive for most applications.

2 ) The conductivity of copper is “better” than the magnetic conductivity (ccl.~~).’ The two are not directly comparable, for one is essentially an ac phenomenon, frequency dependent, whilst the other can be simply a dc phenomenon. However, in transmission lines, each 1 cm2 in cross section, an electric line of copper sustains an undesirable volt drop per amp per metre of 1.6 X whilst a 50-Hz ac line in laminated steel of the same cross section o( = 1000) suffers an MMF penalty of nearly 4.0 X lo4 A/M/V. Taken in the context of the third ingredient, it is hoped that the interpretation of the word “better” is understood.

3) Both magnetic and electric circuits have effective satura- tion levels for flux density B and current density J , although the latter, being fixed by the heat transfer from the conductor surface is not inherently fixed by the nature of the circuit, as in B , for a better cooling system can raise J almost indefinitely (at a price). Taking values of 2 T for the maximum flux density and 1000 A/cm2 as a reasonable target for maximum J , transmission lines of 1 .O cm2 cross section, when the materials

supply is “processed” to a higher frequency to allow reduction o f pole 6as opposed to the dimensional solution in which the mains 60-Hz

pitch. ‘See (2) for the logic which allows permeability to be regarded as

magnetic conductivity.

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LAITHWAITE: LINEAR ELECTRIC MACHINES 271

are worked to their limit, sustain voltage drop and MMF con- sumption respectively of 0.16 V/m and 1660 A/m.

It is not surprising that magnetic circuits have remained short, fat, and consisting of a single turn throughout the history of electric motors.

The reason why these considerations are important in linear motor designs, and in particular to the problem of the long pole pitch is that the f i t attempts to resolve the problem con- sisted of the use of Gramme-ring windings to eliminate the enormous bunch of end windings which inevitably accrues when a surface winding is used, giving rise in particular to ex- cessive primary leakage. This change had been seen to be a simple rotation of the plane of the electric circuit through 90°, and experiments had shown that the change led to an even greater reduction in power factor (the return conductors over the sides and back of the iron core, being nearer to the core than those of a surface winding, give rise to even more leakage flux), the change was seen as comparable to the physician who had attempted to heal the healthy and left the sick to die! The transverse flux technique was born in this manner 1351.

When the flux path is turned into the plane which is normal to the direction of motion, the reluctance of the magnetic circuit is seen to reduce with increase in pole pitch and it be- comes obvious that what might now be called the “conven- tional” linear motor, i.e., the machine which results from the simple unrolling of a conventional rotary motor, takes the worst .of both worlds in a long pole pitch design, for then both electric and magnetic circuits are stretched out in the direction of motion with disastrous results.

It is now clear that the transverse flux motor is both a simple concept and at the same time .a profound one. It is simple in that it implies that instead of employing one row of long poles, two rows are placed side-by-side as shown in Fig. 48, so that an N pole in the one is always opposite an S pole in the other and there is never a necessity for flux to pass in the direction of motion. It is profound in that it is not merely one new motor, it is a new technique of designing-a new way of life for the electrical machine man. It is recogni- tion of the existence of the lateral dimension in a linear motor, which can be utilized in ways which are not normally possible in rotating machines because of’the difficulty of manufacturing curvatures in two dimensions simultaneously. Now one should consider the number and arrangement of the lateral pole array as well as the longitudinal. Now linear motor windings might be designed on the basis of a chessboard matrix of teeth and slots as shown in Fig. 49 in which the lateral conductor distri- bution was as important as has been the longitudinal in rotat- ing machine design for over a century. The phrase “linomat” has been coined for machine designs based on the technique illustrated in Fig. 49 in which the motor members are thin and of large area (like tablemats). Among the new concepts is that of reducing undesirable end-winding effects by virtually elimi- nating end windings entirely.

I. Built-in End Windings The f i t manifestation of the advantages of using end wind-

ings as active conductors instead of unavoidable waste occurred during attempts to obtain a power balance for forces in the direction of motion of a double-sided sandwich motor. I t was repeatedly found that the measured propulsive force was greater than the measured value of B X J multiplied by the area of the pole face. Even though the explanation for this result

Fig. 48. The primary of a simple transverse flux motor (TFM) may consist of 2 conventional motors placed side by side with provision for a backing core to transmit flux laterally all along the machine.

Fig. 49. The “linomat” concept of a matrix of lateral and longitudinal slots to be f h d with primary conductors so as to shape the field pat- tern in two dimensions.

I ‘ \ J * ’ I I ’ I \

I , ‘ \‘ I ‘ \

\ \

Fig. 50. The partial utilization of so-called “end-winding leakage flux” in a double-sided sandwich motor suggests the possible total utiliza- tion of this flux by embedding the end winding in steel.

was soon found in the fact that the end windings of the primary were loosely coupled to the extensions of the plate by what had hitherto been regarded as end-winding leakage flux, as shown in Fig. 50, the idea of utilizing end winding MMF to the full was not conceived until the problem of the large pole pitch machine was solved. It is never easy to see the “general” from the “particular,” but alwuys simple in reverse.

Some early practical arrangements of transverse flux motor are shown in Fig. 5 1. The transversely laminated primary cores are separated into a series of blocks to discourage longi- tudinal flux. At once each block can be identified as a trans- former core and as such there are “C” cores and “E” cores as shown in Fig. 51(a) and (b), respectively. Theoretically all limbs could be made to carry windings at the pole face, as shown in Fig. 52(a) and (b). In the case of the “C” core

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272 PROCEEDINGS OF THE IEEE, FEBRUARY 1975

Fa. 51. Early practical arrangements of transverse flux motor. (a) “C” core. (b) “E” core.

E 0..

I

(4 (dl Fig. 52. Cross sections through TF”s. (a) “C” core primary. (b) “E”

core, fully wound primary. (c) “E” core partially wound primary. (d) “E” core as in (c) applied to single-sided system.

(Fig. 52(a)), the inner end windings are enclosed by steel core and are, therefore, tightly coupled electromagnetically whereas the conductors on the outsides of the cores contribute leakage flux and this is inherent in the “C” core design. In the “E” core, however, a greater proportion of the end windings are enclosed in steel, but a further arrangement in which the out-

Fig. 53. An attempt to reduce leakage flux from a Gramme-ring wind- ing by copper screening. The figure is a lateral cross section through a motor primary with the screening material shaded.

side coils are omitted (Fig. 52(c)) embeds all the end winding in steel and the proportion of leakage flux in such a machine is very small. Furthermore, when used in a singlesided system as shown in Fig. 52(d) the airgaps in the return part of the magnetic circuit can be reduced for the conducting sheet need extend no further than the outer edges of the slots, as shown, provided there is sufficient thickness of secondary conductor to provide adequate “end-ring” conduction, for in long pole pitch machines the longitudinal current density is likely to be many times that of the lateral.

The question of secondary conductor width in relation to the primary poles has been studied in depth, first by Russell and Norsworthy [ 361, who produced a formula for the effec- tive increase in surface resistivity due to end currents in a plate projecting a distance c on either side of a motor of width w having a pole pitch p . Thus the effective resistivity p’ is equal to the calculated resistivity p (assuming zero end resistance) divided by a factor ( 1 - k), where

tanh (y) k =

This result assumes transverse current flow everywhere in the active zone of the sheet secondary. Only outside this zone, i.e., in the overhanging conductor, does the current have freedom of two-dimensional distribution. Extensions of this work have now taken account of complete freedom over the whole secondary and more refined formulas for the calculation of equivalent resistivity are now available [37], [38].

One further point concerning the use of Gramme-ring wind- ings is worthy of note here because it has possible applications in other aspects of motors. It has been suggested that the leakage flux from the return conductors on three sides of the iron core can be reduced considerably by screening these sides with conducting sheet, as shown in Fig. 53.’ This technique is tantamount to producing a short-circuited secondary in an induction system whereby it becomes difficult for alternating flux to penetrate the conducting layer. Whilst it has been a p plied successfully the problem of commutation in commuta- tor motors (the armature slots in this case are lined with conducting sheet) the technique is not, in general, profitable for linear motors because of the extent of the leakage phe- nomenon. The use of conductive screening effectively replaces an impedance jX by the “residue of the imperfections” [6] of the transformer system, i.e., by R + j x , where x << X but R represents the heat loss produced in the shorted secondary. In the case of linear motors it is not the ratio x / X which is not small enough to be profitable, but the size of R ,which is intolerable.

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LAITHWAITE: LINEAR ELECTRIC MACHINES 273

. . , LATTICE-SLOTTED CONVENTIONALLY

LAMINATED LAMINATED CORE Fig. 57. The topology of a tubular TFM. (a) A flat TFM. (b) A tube

rolled up from (a). It is now Seen that flux passes diametrically across

Fig. 54. A transverse flux machine with built-in end windings and a a of and lon@tudind producing a the central core rather than along it. Outside the flux may return in CORE

crossover center section. very low external reluctance.

Fig. 58. One layer of a polyphase tubular TFM winding. The pitch of the helix is 2 pole pitches measured axially, so that after passing diametrically across the end of the tube the return helix fits between the outgoing helix at intervals of one pole pitch.

ogy is relatively simple, as shown in Fig. 57. Since all the flux within the bore may pow pass diametrically, the core may consist of a stack of discs instead of the bundle of wires r e quired in previous tubular motors. In other words, two-

Fig. 55. Cutaway view of a hybrid TFM in which the central part of the dimensional lamination, which was an inhibiting factor in the commercial manufacture of tubular motors (most manufac- turers being content to restrict the maximum size of tubular motors so as to allow a solid steel core to be used) is now re-

F placed by onedimensional lamination of precisely the same form as if a conventional rotary motor were being constructed.

H F Also, the possibility of coreless motors now exists for the re- Fig. 56. The shape of a single punching of the lateral ferromagnetic luctance aCTOSS a diameter i~ not large. Outside the primary

system of the machine shown in Fig. 55. winding the flux may spread in all directions giving rise to a

“E” core has conventional longitudinal laminations which slot into the lateral transverse laminations.

very small exterior reluctance.

Two examples of transverse flux motors (TFM’s) employing built-in end windings are shown in Figs. 54 and 55. Fig. 54 shows a double array of conventional windings in slots each with a conventional winding on the outside but with a cross- over winding between the rows which saves two extra rows of end-winding “noses.” Fig. 55 shows a hybrid arrangement in which conventional slotted punchirtgs are used to construct the center of an “E” core TFM, but the core depth is minimal and only used to give mechanical support to the teeth in this region. This block of punchings slots into a set of transverse punchings, one of which is shown in Fig. 56, between the points C and D , in the position shown dotted. The longitudinal slots ABCG and HDEF accommodate the end windings from the conductors in the conventional punching slots.

J . Transverse Flux Tubular Motors When the TFM had been established as the solution to the

high-speed motor design problem the same technique was tried out on a tubular machine [ 391 to see 1) what configuration re- sulted, 2) what advantages, if any, it had to offer. The topol-

Tubular TFM windings may be constructed by winding spiral coils, as shown in Fig. 58, in a double layer, the second layer being of opposite-handed helical shape to counter the rotating field component produced by the first layer. Alter- natively, the use of a tubular TFM having only one layer may be used with advantage in such applications as liquid metal stirrers where the agitation produced by the rotary component assists in mixing in the additives and new material to be melted. In such applications, of course, the primary is the inside member of the motor, the liquid secondary surrounding it entirely.

K. Skewed Slot Motors for Lateral Guidance The use of the helix as a winding shape rather than attempt-

ing to build poles individually suggests that the same technique might be used with advantage in flat machines, i.e., in the form of Fig. 57 before rolling up. This is indeed so and represents the ultimate refinement of a linomat in which short inter- spersed progressions, first in the direction of field motion (a bit of end winding) then in the lateral direction (a bit of

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274 PROCEEDINGS OF THE IEEE, FEBRUARY 1975

U m

o n CIU 00

(b) Fig. 59. (a) A stepped winding on a linomat construction. (b) Simple

skewed conductor. (a) may be replaced by (b).

useful conductor) become a smooth skewed conductor as shown in Fig. 59. This technique has already been effectively employed in the end winding and crossover regions of the motor shown in Fig. 54. What is now being suggested is that the “conventional” sections of that motor be reduced to zero width and that the resulting motor winding (known as the “waffle” type) consists simply of diamond-shaped coils laid one upon the other to give a two-layer winding, just as con- ventionally wound machines have their primary coils over- lapped in two layers. The waffle winding is shown in Fig. 60.

One interesting variation on the same theme involves the use of “herring-bone” windings which produce, in addition to forward thrust, components of traveling field which move to- wards the center of the pole area and, therefore, guide the secondary laterally. A first attempt at such a machine (not a TFM) is shown in Fig. 61. However, the TFM techniques just described may be extended to contain at least a section of herring-bone-wound pole face, as shown in Fig. 62. It should also be noted however, that both the herring-bone and waffle techniques can be used with longitudinal flux motors as well as with TFM’s.

In machines with large airgaps which demand wide slots and narrow teeth, the skewed slot waffle design is difficult to achieve in practice since the teeth are virtually reduced to zero. But the interesting possibility which emerges from such con- siderations is whether or not a slotless machine might be profitable [ 161. Experiments so far indicate that provided the pole pitch is large enough to give a high value of C in the absence of teeth, the slotless waffle arrangement is likely to

Fig. 60. A “waffle-type” winding in which useful conductor and end- winding become indistinguishable and, therefore, all “useful.”

Fig. 61. A herring-bone motor produces lateral guidance 8s well aa forward thrust.

Fig. 62. A waffle motor primary with the outer edges as part herring- bone to guide the secondary.

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LAITHWAITE: LINEAR ELECTRIC MACHINES 21 5

L I N E A R lNDU,CTlON MOTOR

short :primary shortlsecondary moving Primary moving ’ secondary

Iongittdinal m r s e

Prima? flux Primary flux

FLFT T U B ~ L A R surface’primary gramme-ring maqnetlcally steel

Open Outside outslde secondary secondary

magnetically singld-sided doublei-sided

I - magnetically magnqtically

single-sided likerpoles unlik; Poles single t sided double’sided orib d l y magnotically opposite opposite electrically electrically inner outer

s h i e t I I I I woupd w y n d

secondary i

steel both

--1 comp’osite *et

seco dar secondary primary double-sided double sided singe-sided

1

comksite electrically electrically electrically secondary

one side of secondary W n

- surface

secondary pramme-ring

secondary currents magnetically I c u r r i 1

Fig. 63. A table containing a description of every type of linear induction motor so far known. A journey from the top of the table to the bottom which involves making a choice at each “junction” is sufficient to describe completely a particular machine, topologically.

prove extremely attractive, having the potential of very high values of J , low leakage reactance (and therefore high power factor1and being readily adaptable to transverse flux techniques.

The subject of linear motor topology is expanding so rapidly that it is already almost too big a subject for an article of this length. As recently as 1970 an attempt was made to classify linear induction motors by a dichotomous table derived from purely topological considerations [40]. By 1971, this had be- come out of date as the result of the discovery of TFM’s. A revised table was compiled in 1971 [41 I which was almost im- mediately put out of date by the invention of tubular TFM’s. A new table is included here (Fig. 63) in the belief that this, too, will survive for but a few years but also, therefore, in the hope that it may, of itself, trigger off some new departure in shape and a new invention for a reader.

VI. LINEAR MOTORS OTHER THAN THE INDUCTION TYPE A. Some Will Succeed, Some Never Will

Historically, the f i rs t rotating machines were dc machines. The incentive to produce “battery-like current”’ was centered in the then new technique of electroplating and in the carbon arc lamp. Linear motors did not follow the same pattern, for Wheatstone’s eccentric engines led directly to reluctance mo- tors in which a steel cylinder was attracted successively to a row of dc-fed magnets which were switched on in turn, as required. Fig. 64 illustrates the system. It is interesting to note that if the cylinder be replaced by a flat sheet of con- ductor, the latter will be propelled in the opposite direction for it can be shown that a switched field has its principal com- ponent of traveling field in the opposite direction to that in

fit a commutator to the latter’s alternator of 1832, which was an axial 8 A phrase attributed t o Ampere when advising Hippolyte Rxii how to

flux version of the modem alternator.

which it appears to go [421. Like their rotary counterparts, hysteresis and reluctance motors are profitable in small sizes whereas dc and ac commutator motors, together with syn- chronous motors are all more profitable when large.

For short-stroke actuators the design of linear machines which require MMF to be supplied by physical contact to both sides of the airgap presents no insurmountable problem, but where an application demands that the stationary member be hundreds of times the length of the moving one (as in trans- port applications) the use of commutator machines with dc field excitation becomes extremely expensive. Whilst dc ma- chines of this type (generally misnamed “synchronous motor^"^ ) are being developed quite extensively at the present time by several teams in different parts of the world, it seems highly improbable that anyone will seriously contemplate linear versions of the Schrage motor, N-S motor or any of the more sophisticated ac commutator motors, purely on economic grounds.

Synchronous motors proper are as yet an enigma. On the face of it, it would seem an obviously simple structure to build, but it would not escape the end effects which beset a linear induction machine, end effects which are still regarded by some authors as formidable [43] , although it should be added that transverse flux machines are, by their very nature, able to contain fractional or odd numbers of poles along their length without generating any standing waves of core flux

A rotary dc machine could be called a synchronous motor in that its armature coils are switched so as to synchronize at all times the arma- ture field with the dc-fed poles. The fact that the ordinary commutator

quite different from the synchronous motor proper, the latter being, in performs this feat automatically is the feature which makes the machine

large sizes, incapable of self-starting. The replacement of the commuta- tor of the dc motor by electronic switches which are triggered by pulses generated by the rotating armature does not, in the opinion of the author, change their class from dc moton to synchronous motors.

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276 PROCEEDINGS OF THE IEEE, FEBRUARY 1975

F?Lo ARMATURE

Fig. 64. The very fmt linear motor, built by Wheatstone between 1841 and 1845.

whatsoever, and experimental evidence suggests that they exhiiit less entry and exit edge losses than do longitudinal flux machines. It would appear that workers who are already having success with electronically controlled synchronous mo- tors might care to take a shortcut in the light of the evidence provided by those who have labored long with linear induction machines, and go for transverse flux synchronous motors be- fore end effects have a chance to raise their ugly heads.

8. Linear DC Machines One of the earliest dc machines was proposed as the driving

mechanism of an electric hammer [44], this will be dealt more fully in Section VII. It is sufficient to say here that both moving armature and moving field types were considered and the date was 1922.

An important machine was built at the Royal Aircraft Es- tablishment in the early 1950’s [45]. The stationary field system was fed from 1200 lead-acid accumulators (an aircraft hangar full!) which delivered 260 000 A at 96 V. The moving armature, weighing just over 1 lb, was fed through slip tracks and brushes and began its 46 ft run carrying a current of 81 000 A at 52 V. The maximum speed attained was over 1500 ft/s and this machine remains, to date, the fastest, most highly powered (25-MVA field, 4-MVA armature) linear motor of any type.

Much more recent work on a similarly arranged system is aimed at utilizing the dc field from a superconducting magnet mounted on the moving member as excitation and supplying track conductors with dc to form the armature member. The greatly increased flux density obtainable from superconductor enables a 50-ton vehicle to be driven from a continuous track wire laid in the form of a rectangular wave pattern in the track and carrying perhaps no more than 300 A. Work on this sys- tem at the University of Toronto, Toronto, Canada, by Prof. Slemon’s team has reached an advanced stage. A design study, well-supported by experimental data has suggested that the ‘‘wiggly wire” track could be laid in lengths as large as 10 km with an overall efficiency as high as 70 percent. Only one supply processing unit per 10 km could be economically ac- ceptable and the levitation and guidance of the vehicle could be provided by separate cryogenic magnets on each side of the driving magnets and appropriate track conductor.

Fig. 65. A tubular dc actuator having a 2-pole armature and single-coil field system (due to Green and Paul of Bangor, Wales, 1969).

Dc motors with liquid armatures have been used as pumps for liquid sodium and potassium mixtures (461 (see also Section VIII).

A new series of ideas on linear machines began in the late 1960’s at the Interuniversity Institute of Engineering Control at Bangor, Wales. The first paper [47] describes a tubular arrangement of poles and armature as shown in Fig. 65. The construction is essentially simple to manufacture and can be extended to include any number of poles (including odd numbers). The inventors point out that for limited displace- ment the main disadvantage of the dc motor, i.e., the extended commutator, is eliminated.

C. Reluctance Machines The second and fourth papers of this series [48], [49] de-

scribe a helical screw arrangement in which a cylindrical stator had a two-start thread of square cross section cut on the inside surface of the stator bore. The mild steel armature is in the form of a cylinder with annular grooves cut in its surface. The stator grooves cany windings whose phases can be controlled. Linear motion is achieved by controlling the phase in relation to the points of minimum reluctance. Although the tubular version was invented f i t , the mechanism is perhaps easier to appreciate in an openedaut flat version as described in the third paper [SO] and illustrated in Fig. 66. In terms of the topology classification, these machines are transverse flux motors.

Historically these machines represent the most recent and sophisticated of a long line of reluctance devices which include some other machines of interest. In 19 14, Bachelet extended the jumping ring arrangement of Fleming to produce a levi- tated track along which he could propel a vehicle. His propul- sion system was a crude reluctance device in which the ferro- magnetic body of the vehicle was pulled towards a circular coil with horizontal axis through which the vehicle moves, when a pulse of current was passed through the coil.

A multiplicity of such coils was used by Birkeland in 1901 in an attempt to make an electromagnetic gun, but the inventor did not realize that his essentially magnetic machine lay on the wrong side of the “great divide” ever to succeed as a weapon of war.

One further example of ingenious topology finds its outlet in another form of reluctance device. Stepping motors are much used in rotary form and linear versions of these have also been used for position control. The vernier progression, best known as a measuring instrument, has also been applied to reluctance motors as shown in Fig. 67. As the left-hand end of one mem- ber moves through one tooth pitch in relation to the other member, a traveling wave of low reluctance path (the region A in Fig. 67) travels from one end of the array to the other. Thus when a rapidly traveling field is applied by feeding the coils of the primary with phased ac, the resulting linear speed

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LAITHWAITE: LINEAR ELECTRIC MACHINES 211

I I I

A secondary / small anale L slots at a

-carving conductors Lv lateral

prirnay slots parallel to XX’

(b) Fig. 66. (a) A flat skewed-slot reluctance motor carrying a primary

polyphase winding whose phases are adjusted to provide position con- trol by arranging for the minimum reluctance pattern to occur at a de- sired position. (b) The minimum reluctance area is clearly seen in a plan view and is seen to be analogous to Moiri fringes in optical systems.

Fig. 67. A vernier reluctance motor in which the low reluctance path A travels 9 times as fast as the secondary. Currents in the primary slots produce a traveling field which locks on to the low reluctance zone at all times.

Fig. 68. Instantaneous flux pattern over the surface of a linear motor primary. This figure can be used as an animated cartoon to indicate the rotating nature of this traveling field. Cut a hole the size of the circle A in a piece of card and draw the diagram across the back of the card to reveal the changing direction of the field between the dotted lines as the pattern progresses.

of the secondary member is divided by the number of teeth per “pole.” The phased ac may be replaced by a supply from pulse generators so as to register position of the secondary.

D. Hysteresis Motors The only known application of the hysteresis motor princi-

ple in linear motors is contained in a hybrid arrangement of linear and rotary members. Above the surface of an open- sided flat linear motor the instantaneous flux distribution is as shown in Fig. 68. If a piece of card has a hole cut in it of the same size as the circle A and the diagram of Fig. 68 is placed, first with A opposite the hole, and then the diagram is moved so that the strip shown dotted passes slowly across the hole, the instantaneous direction of the field will be seen to change in the sequence “up,” “right,” “down,” “left,” “up,” etc. indicating that there exists, in addition to a linearly traveling field, a rotating component which tends to roll metallic ob- jects within the field in such a direction that if placed on the primary surface, they will tend to roll backwards, i.e., against the natural forward flow of the field. Highly conducting ob- jects, such as copper cylinders, roll as the secondaries of induc- tion motors by induced current. Small ferromagnetic objects, being of higher resistivity and naturally lower goodness factor due to their size, roll by hysteresis action alone, and the smaller the object, the greater its acceleration in accordance with “the smaller the better” rule. Masses of iron f i g s placed in a nonmetallic tray on the stator surface behave in a manner which is beautiful, fascinating, and highly instructive. It is as if nature herself were pointing the way to make better machines. The filings pile up in a series of parallel vertical walls whose shape is generally changing continuously, a typical side view being shown in Fig. 69(a) and a plan view in Fig. 69(b). The separation between adjacent walls increases with increase in their height and thus indicates the natural preference of the system to shape itself so as to present a minimum reluctance to the flux emanating from the stator surface. Increase of wall area allows the stator flux to bend Zaterally so as to enter the wall faces. Once again a three- dimensional flux pattern is seen to triumph over a one- or two- dimensional pattern for if the secondary of such a system be a cylindrical rotor, modeled on the filing pattern, i.e., it con- sists of a row of thin discs of highly hysteretic steel mounted on a common lateral shaft, as shown in Fig. 70, the resulting “rack and pinion motor” (for its action suggests precisely that of a mechanical rack and pinion) has a greater acceleration than any cylindrical hysteresis motor of conventional construc- tion (511.

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278 PROCEEDINGS OF THE IEEE, FEBRUARY 1975

V I I . OSCILLATORY MACHINES

A. The Relationship between Rotary and Simple Harmonic Motion

Boucherot protested in 1908 that “to argue that rotary mo- tion is natural motion is begging the question.” Be that as it may, simple harmonic motion in particular is so closely related to rotary motion that almost any property of one system is immediately translatable into an analogous property of the other. For example, the peak velocity of an oscillating particle is a o where a is the amplitude, the linear velocity of a particle rotating in a circle is r u where the radius r is the analog of a in the linear system. In rotating devices a mechanical limit is imposed by centrifugal restrictions. A similar limit exists in oscillatory systems because the continuous transfer of kinetic energy to potential and vice-versa may be very large in com- parison with the available’ power output. This last effect makes it almost imperative that linear oscillating systems be tuned mechanically to relieve the magnetic or electromagnetic mech- anism from the task of pouring in electrical power from the supply just to accelerate the mass, only to have to pour in further power at a later stage in the cycle to decelerate it, all this power being totally converted to heat.

B. Magnetic Machines Fail in Large Sizes Boucherot himself was probably the f i t man to make a

sound engineering job of harnessing the elusive magnetic forces in a machine to produce continuous motion, although it should be recorded that in 1838, Prof. Jacobi succeeded in propelling a boat on the River Neva by means of a double- acting magnetic engine in which the work of two pistons and cylinders in a steam beam engine was replaced by solenoids attracting iron cores. Like generations of engineers who were to follow Boucherot, he himself lamented the fact that the radial magnetic pull in an ordinary induction motor (the [B2/2& - c(0J2/2I term discussed in Section IV) could only be used for short movements, after which the mechanism must be reset before further power output could be realized. Boucherot tuned a cylindrical rotor with torsion springs and

(b)

Fig. 69. Patterns of iron filings over a linear motor. (a) Side view. (b) Plan, indicate that multiple disc rotors are more profitable than thin-walled cylinders for hysteresis motors.

Fig. 70. A multiple disc “rack and pinion” motor has a greater accelera- tion than any other shape of hysteresis motor.

For similar reasons a small helix of hard steel wire can be rotated inside a nonmetallic tube at heights of the order of 15-20 cm above the surface of an open-sided motor, suggesting the possibility of making miniaturized Archimedean pumps for use during surgical operations [ 5 1 1. The rotating part of such a pump is of such a shape that it is almost ideally suited to form the dual purpose of hysteresis motor rotor and rotary Pump.

fixed ferromagnetic pieces to its surface which were alternately attracted by ac-fed coils of the tuned frequency on each side of each iron piece. Alas for Boucherot, he made his experi- mental machine too big for the “magnetic world” and it failed to qualify on power-to-weight ratio. It is however interesting to observe that his idea has recently been revived by two of the author’s excolleagues in Manchester, England, who have developed a transverse flux version of Boucherot’s ma- chine [ 5 2 ] .

C. Induction Oscillators The revival of interest in linear motors which began in

Manchester, England, in 1947, was itself initiated by the de- sire to apply linear motors to the propelling of shuttles in looms, an inherent oscillatory motion although ideally non- sinusoidal in “waveform.” An investigation revealed [ 531 that the “natural” form of the speed-thrust curve of an induction motor made it possible to sustain oscillations along a straight track without the use of any switching mechanism (an impor- tant ingredient in such an invention at a time when there were no thyristors). The mechanism is illustrated in Fig. 71 (a), which shows the track of a pair of open-sided linear motors connected “back-to-back” with their traveling magnetic fields

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LAITHWAITE: LINEAR ELECTRIC MACHINES 279

0 0, I - V V

SPEED (b)

(C) The self-oscillating induction motor principle. (a) The primary

consisting of polyphase coils producing inward-traveling fields. (b) The speed-thrust curve of the motor which ensures self-oscillation only by the fact that it has a peak to the right of the speed zero. (c) The speed-thrust curve with the reverse and forward motion sec- tions superimposed.

directed towards the center. A short rotor starting from rest at a distant x1 from the center is initially acted on by an ac- celerating force ou (Fig. 71(b) shows the speed-thrust curve of the motor from which the values of force are obtained). As it accelerates towards the center the accelerating force increases until it passes the center point at speed v and force o’b. On entering the reversed field the effective speed is now - u and the decelerating forces which act upon the secondary now move along the speed-thrust curve from c t o a and are seen to be everywhere less than the accelerating forces from u to b . Thus the stopping distance x2 is greater than the starting distance xl and each successive traverse will continue to be greater until a point such as d is reached, near to the synchro- nous speed, at which a stable amplitude is reached.

Unfortunately such a system is inherently inefficient. It is a property of an induction machine that the energy lost as heat in the secondary in accelerating a mass m up to synchronous speed us is equal to the kinetic energy at that speed (+mu:). As an accelerator, therefore, the induction machine with fixed pitch has a basic energy efficiency of only 50 percent. The decelerating portion however is, even by this standard, a dis- aster for to stop the missile from speed us incurs a secondary loss of three times the peak kinetic energy. Thus in one traverse, from rest to rest, the heat generated by the secondary mass m is 4(4mu:) [61. The solution, as already indicated, lies in limiting the motion of the secondary with end springs so that, on a diagram Fig. 71(c), similar to that of Fig. 71(b) but which is folded about the vertical axis for simplicity, the un-

il L C .

Fig. 72. A single-phase ferroresonant oscillating ring.

FERF&RESO NAN T ‘2UMPS“

Fig. 73. Diagram indicating that the force cycle is self-sustaining by the reversals which, by the ferroresonant phenomena, are conscious of the past history of the moving secondary.

sprung motion via the characteristics 0 X A B X 0 is replaced by the much more efficient loop C‘ X A’B’ X C . The fact that the line CC’ is not vertical is due to the mechanical imperfec- tion of the springs.

The criterion that such oscillation should be possible is that the natural speed-thrust curve of the motor should have a peak to the right of the vertical axis which implies that for parallel connection the ratio of leakage reactance to resistance should exceed unity-clearly an unprofitable arrangement, but for a series-connected system the criterion is G > 1, which corre- sponds to the condition that the same motsr should be able to run from a single-phase supply [ 6 ] , indeed a single-phase track with end springs is virtually unidentifiable characteristic wise from a back-to-back polyphase system, apart from the former’s inability to self-start.

An ingenious alternative selfascillating system was fiist pro- posed by Centener and is described by Trombetta [44]. A polyphase winding along a linear track carries no star point but is fed at both ends from generators of frequency w1 and w2, respectively. The resulting traveling field direction reverses at frequency (0, - 02)/2n. This system differs from the back- to-back arrangement in that the latter is reversed by theposi- lion of the center of the track, the former by the time interval between reversals only and the resulting oscillation in the presence of varying mechanical resistance has a drifting center of oscillation. A development of this earlier system by West and Jayawant [54] however led t o the more interesting ar- rangement shown in Fig. 72 in which two coils embracing opposite ends of a laminated steel bar are electrically tuned for particular positions of a short-circuited copper loop. The coils are connected to a sufficient voltage to saturate the bar after which oscillation ensues as a direct result of the phenomenon known as “ferroresonance,” whereby, unlike the previously described systems there is a net oscillation-sustaining force on the shorted loop when taken through a cycle of operations virtually at standstill. The variation in force due to such a system is illustrated in Fig. 73.

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2 80 PROCEEDINGS OF THE IEEE, FEBRUARY 1975

Fig. 74. A synchronous oscillating copper loop threaded simultaneously by ac and dc fields and tuned with mechanical springs.

D. Synchronous Oscillators The difficulty of synchronizing a linear synchronous machine

is not at all apparent in an oscillating linear machine of the same type. The basic reason for this feature is that the latter, when run as a motor is not required to reach full amplitude on the first stroke whereas a linear motor is required to attain full speed virtually instantaneously after switch on, and a rotary machine is likewise restricted.

On the grounds that conductor must be carried by the oscil- lating mass and with reduction of recirculating power in mind ($mu*) one form of synchronous oscillator was designed in such a way that the moving part consisted of a conducting loop only (as in a West and Jayawant oscillator). The machine is shown in Fig. 74 in which the paths of the dc exciting flux, driven by coils AA’ and those of the ac flux, driven by coils BB’ are clearly indicated. Such a machine performs 120 strokes/s when the ac supply is at 60 Hz. Four-pole versions for 60 strokes/s have also been built and tested [ 551. The limiting factor on such designs is that at total amplitudes of 10 cm the maximum velocity of a two-pole machine at 60 Hz is only 6n m/s which is slow by comparison with turbo alternator surface speeds and therefore not highly efficient, even when the moving loop is spring tuned. It is however an interesting machine in that it suggests that the self-starting limitations of conventional synchronous machines lie fundamentally in circu- lar motion, for if a crank and shaft are fitted to the machine shown in Fig. 74 it at once becomes incapable of self-starting, being required to commence with a full stroke.

E. Reluctance Oscillators Of the modem machines, one of the first t o founder on the

rock of “the smaller the better” was a French invention aimed at producing an electrical transmission system for automobiles. Basically it converted reciprocating motion to rotary although the output could obviously be obtained as an EMF, by closing the magnetic circuit with a laminated limb, embracing a coil, instead of using the pulsating flux to drive a rotary motor. The system is shown schematically in Fig. 75. This invention lacked nothing in ingenuity, indeed in so far as it converted linear to rotary motion in a magnetic circuit it is probably unique, but the dimensions of the block required to os,cillate between the alternate poles in order 1) to give a reasonably long pole and therefore a high enough speed and 2) to leave a large enough distance between the vacated poles, were, in this example, the dimensions which dashed the hopes of those who might have first made a small model and found it to work most

I

Fig. 75. A magnetic linear-to-rotary convertor using a reluctance oscillator as generator and a repulsion-type commutator motor to utilize its output.

satisfactorily. The insidiousness of “the smaller the better” rule for magnetic machines is that the first step in the develop ment of a new idea is to make a small model. In the case of magnetic machines the first attempt is, therefore, almost in- evitably most encouraging. Only when large s u m s of money have been invested does the manifestation reveal itself in its true colors.

WII. &’PLICATIONS OF LINEAR MOTORS A. General Classification

A few years after the new generation of linear motor inven- tions had begun (during the 1950’s) the applications of linear machines were seen to fall naturally into thre,e groups, each of which has its own particularly advantageous features and each its inherent limitations. These features are obviously of the same importance as the rules of size, for a superficial knowl- edge of them is all that is necessary to enable senior engineers t o assess the probability of success for a new application be- fore the development work is started.

The three groups of application are 1) force machines; 2) en- ergy machines; 3) power machines. The rotary counterparts of these classes are not as clearly defined for it is difficult t o find any commonly used rotary form of class 2). Class 1) which is possibly the most useful of the three in the case of lineax mo- tors finds a rotary counterpart only in the almost miniature world of control systems, where torque motors are much used. In larger sizes it is generally considered that the maximum size of the product B X J , i.e. the shearing stress available at an electromagnetic interface, cannot match the stresses available using hydraulic actuators or torque motors. The high effi- ciency of rotary electric motors on the other hand has long been known and exploited in the counterpart of group 3).

Liquid metal pumps must also be included in the force- machine class for although the pumping speed may be quite high, the effective airgap may be 10 cm or more and the value of G is as low as that in an actuator. Moreover, since the principal application for these machines lies in pumping liquid sodium and potassium from nuclear reactors the fluid must be contained in a stainless steel pipe whose walls also constitute a part of the airgap (stainless steel being virtually paramagnetic only) and incur 1 2 R losses.

Liquid-metal pumps built commercially have included both double-sided flat induction types, tubular induction machines, and linear flat dc motors [56]. The tubular type was soon dis- carded since a burnout involved breaking a pipeline filled with radioactive material whereas replacement of a flat motor primary can be accomplished by remote control without pipe disconnection.

The record for the least efficient high-powered linear motor which is seen to be a commercial success is surely that of the

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LAITHWAITE: LINEAR ELECTRIC MACHINES

open-sided primary which drives liquid steel up a 3’ slope in a Leningrad car factory [57] . The total gap between motor primary surface and liquid steel secondary is over 6 cm, the input power is 60 kW and the mechanical output 50 W. The machine is successful because it reduces the capital cost of transporting the steel by one half that of an alternative system, it reduces running cost by 40 percent. The productivity of labor is multiplied by three and the steel is self-cleaning, the nonconducting slag falling to the bottom of the incline.

B . Force Machines Force machines, more commonly known as “actuators” are

generally called upon to perform tasks at very low speeds, in electromagnetic terms. Often they may be required merely to produce pressure with virtually no linear movement whatever. In such circumstances it is clear that criteria different from those used in assessing conventional rotary motors will have to be applied. For example, at zero speed a motor has zero mechanical output and therefore both its power-to-weight ratio and its efficiency are zero, but this by no means implies that it is not performing a useful job. Other criteria such as force-to-input, force-to-weight, and force-to-cost now replace the more formal nondimensional ratios of efficiency, power factor and even goodness factor, yet some of the new criteria can easily be evaluated in terms of G, especially the ratio of force-to-primary Z2R loss. This last quantity is seen to be intimately connected with all three of the new criteria for the secondary member, usually consisting of a solid piece of un- insulated metal, can withstand much higher temperatures than can the insulated, multiturn primary. The processes by which heat loss is removed from the primary are those which f i x the size of this member and hence, in large part, the weight and cost of the whole machine.

For most low-speed machines it will generally emerge that the best designs are found to have values of C not very differ- ent from unity, a fact which indicates at once that actuators belong to a quite different world from that of “power” ma- chines. The precise values of G which should result from “correct” design procedure have been shown not surprisingly to be dependent upon the number and selection of quantities whose variation is at the discretion of the designer. Table I , taken from [58] shows examples of this principle. The values p1 and p2 are the equivalent surface resistivities of primary and secondary respectively, often most easily evaluated in terms of an “equivalent copper depth” [ 61. In this table p is the pole pitch and f the supply frequency.

If two quantities are available for continuous variation by the designer, other constraints are often necessary to prevent iteration procedures from leading to impossible values of zero or infinity in other quantities. For example, if p and p2 are both capable of change, the value of G would appear to ap- proach inf i i ty as each variable is raised to infinity, but since this would also imply infinite rotor Z2R loss either rotor cool- ing or the limitation on total number of poles necessitated by extra edge losses provide such limits. However the values of G in Table I , in the first and second columns, fimt row, must be identical so that 3pl / (p l + p 2 ) = 1 or p2 = 2pl . Since G = 1,Jl =*J2 sothat therotor loss 3 p 2 J : = 3(2p1)(J:/2) = i p 1 J: and primary and secondary losses are seen to be equal.

The fact that the limit on available thrust per unit of pole area, for a 60-Hz supply, is of the order of 1.0 N/cm2 ( a p proximately 1.2 lb/in2) virtually confines linear motors in

281

TABLE I IDEAL VALUES OF G FOR ACTUATORS

Variables

Values for maximum

force/input, with

fixed value of p2

Values for maAnum

force/input with p2

aesumed proportional to l/p (virtually

constant leakage

factor)

Values for maximum

force/weight or force/cost

low-speed applications to situations in which either the de- manded thrust is relatively low or the time rating is very low for to obtain the desired value of C for best operation, it is rare that the primary pole pitch can be reduced below about 4 cm. This value gives the slowest motors an indicated syn- chronous speed of 4.8 m/s, which means that for every tonne of thrust, some 50 kW of heat loss must somehow be removed from the motor so long as it continues to operate. The high value of loss per unit thrust on the one hand and the low value of shearing stress (which for short-term force-cooled machines can only be increased to about 20 N/cm2) makes large linear motor thrusters poor competitors to hydraulic, or even pneu- matic actuators, unless there are some special reasons why the latter two cannot be used. The fact is that large rotary electric motors can be made most effective through the use of worm gears, rack and pinions, etc. whereas there is no easy linear equivalent of the gear.

The advantages of linear motors as actuators in the low and medium thrust ranges are many, however. Linear motors are silent, consume nonpolluting “fuel” which is readily available in both domestic and industrial situations, they are easily dis- connected and reconnected in a different locality, making them flexible in application. There are no moving parts to wear out, no rubbing contacts to arc, indeed there is no necessity for either electrical or mechanical contact between driving member and load. If more force is demanded than is available, additional units can be added easily. Primary thrust units can be potted in resin, making them waterproof and ready for use in tropical climates and contaminated or explo- sive atmospheres. They are robust and easily handled, clean to operate, noiseless and highly reliable. They win in competition with hydraulic motors on what might therefore broadly be termed “convenience.”

They are even commercially competitive as rotary drives, (which at first seems like Eskimos buying refrigerators!) but the reasons for this are simple once pointed out. If a drive is required for a large aerial turntable, or radio-telescope, or low- speed ventilation fan (where low revolution per minutes are vital if the fan is to be noiseless) the linear speed at the periphery may be quite high, high enough to give a value of G > 1. In such cases the structure which is to be driven itself provides practically the whole rotor structure and only an

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282 PROCEEDINGS OF THE IEEE. FEBRUARY 1975

Fq. 76. Sliding door operated by linear motor unit. The equipment provides complete control throughout the operation and can be adapted to both single and biparting doors. (Courtesy of Herbert Morris Ltd., Loughborough, England.)

Fig. 78. X-ray unit at Westminster Hospital, London, England, is posi- tioned by a linear motor with its primary mounted in the ceiling be- hind an antidust cover. (Courtesy of Herbert Moms Ltd., Lough- borough, England.)

a large gearbox with its inherent backlash and wear has been avoided. The stator is easier t o handle and ship overseas for it effectively “falls t o pieces” at the touch of a spanner and each piece is self-contained, tropicalized, and durable. Extension of the power range is possible with rotary drives, for several con- ducting discs can be mounted on a common shaft when the stator units are fitted between adjacent discs so that each face of the primary block can be used, the flux now passing directly through the intermediate primaries and only the two end motors require a magnetic return core.

At the other end of the scale, miniature linear induction motors have been used for extremely accurate position control and at Imperial College, London, England, an accuracy of f 14 ii was obtained.

Other advantagesinclude the fact that even the magnetic pull between primary and secondary of a single-sided unit can be exploited to advantage, as in crane drives, and primary designs have been produced which allow an existing steel “H” girder alone to act as motor secondary.

A comprehensive paper on the applications of linear motors up to that time was written by Sadler and Davey [ 591. A se-

The joist itself acts as secondary of the singleaided motor. (Courtesy shown in Figi. 76-8 1. Fig. 82 shows a tubular motor manu- of Herbert Morris Ltd, Loughborough, England.) factured by the technique illustrated in Fig. 44. Fig. 83 shows

the component parts of this machine before assembly. Figs. annular ring of aluminium sheet is needed to complete that 84 and 85 show linear motor driven conveyors operating in part of the drive. Stator units can be mounted around the France, whilst Fig. 86 shows a linear motor driven production annulus until sufficient torque has been obtained. The use of line in a Japanese locomotive factory.

77. k t of a roll- conveyor system handling rolled st-] joists. lection from the described in that paper are

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2 84 PROCEEDINGS O F THE IEEE, FEBRUARY 1975

Fig. 87. The moving primary carriage of the Westinghouse aircraft

home Engineers.) launcher “Electropult” on its secondary track. (Courtesy of Wesiing-

Fig. 85. The conveyor with some of its secondary conducting carriers in position. (Courtesy of Merlin Gerin, Grenoble, France.)

Fig. 88. Aircraft being attached by a steel cable loop to the linear motor primary carriage. (Courtesy of Westinghouse Engineers.)

Fig. 86. Linear motor bogie transports a pair of wheels in 8 Japan- locomotive factory.

C. Energy Machines Linear accelerators have been prominent among the mile-

stones of linear motor history. The aircraft launcher Electropult (Figs. 87 and 88) built in 1945 was easily the largest, the fastest, and the highest powered linear motor until

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LAITHWAITE: LINEAR ELECTRIC MACHINES 285

the apparatus can be seen on the right of the picture. (M.0.D; Fig. 93. A emerging from the R.A.E. at 1350 ftls. (P.E.) R.A.E. Farnborough, England, Crown copyright reserved.) Note also the traces made by stray particles of metal which are

clearlv movine much faster than the missile. (M.O.D. (P.E.) R.A.E. Farndorough,kngland, Crown copyright reserved.)

Fig. 91. The circuit breakers at the instant of switchoff. (M.O.D. (P.E.) R.A.E. Farnborough, England, Crown copyright reserved.)

the 1950’s. It developed 10 000 hp and accelerated a 10 000-lb aircraft from rest up to 115 mi/h in 4.2 s. Its synchronous speed was 225 mi/h and it employed dc braking to bring the carriage to rest after ,the aircraft had been launched. This project was the one which first attracted this author to work on these exciting machines.

Previous to the Electropult, Birkeland had patented the electromagnetic gun pictured in Fig. 89. This was only a miniature and the reason why it never became a success is ob- vious when it is known that its mechanism was that of a switched reluctance motor.

Fig. 90 shows the dc motor at the Royal Aircraft Establish- ment at Farnborough, England 1451. Fig. 9 1 shows the six air-

Fig. 94. End view of impact extruding machine built in Manchester, England, in 1963. The central mass is attached t o a pair of aluminum “fins” which constitute the secondaries of parallel, twin, double-sided primaries.

blast circuit breakers switching off the field system after a launch. Fig. 92 shows the storage battery which fed the ma- chine and Fig. 93 shows a missile emerging at a speed of nearly Mach 2.

Fig. 94 shows an end view of an impact extruding machine built at the University of Manchester Institute of Science and Technology in 1963 [ 601 . The central mass was supported

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PROCEEDINGS OF THE IEEE, FEBRUARY 1975

Fig. 95. The running trough for the Linear motor used for crash testing cars at the Motor Industry Research Laboratories at Nuneaton, England. The track is $8 ft long and the terminal speed is 32 mi/h. (Courtesy of Motor Industry Research Association, Nuneaton, England.)

Fig. 96. A tubular accelerator with a graded pole pitch to produce a continuously accelerated magnetic field.

by linear ball races above and below and driven by a twin, double-sided primary operating on aluminum fiis attached to each side of the “hammer.” This was the first parallel- connected machine to be built, (the correct connection for a short-secondary motor). It demonstrated clearly the principal advantages of all linear motor accelerators, they are as follows.

1) The first cost is lower than that of any other system, even including gravity fed machines. The machine illustrated de- veloped 45 ft/s in a distance of 2 ft. The current rating was such as to indicate clearly that reconnection for double speed would enable such speed to be attained within the same dis- tance. A gravity machine with a terminal velocity of 90 ft/s would require a gantry some 130 ft high. The entire machine occupied a space of 36 in X 26 in X 12 in. The accelerated mass was 21.5 lb.

2) The terminal speed is controllable within very close limits.

In the mid 1960’s a car crash test facility was built at the Motor Industry Research Laboratories at Nuneaton, England. Fig. 95 shows the track with the double-sided moving primary sandwich motor running on its central girder sunk into a chan-

nel. When the car was impacted the motor unit was auto- matically detached and brought to rest by aircraft-type arrestor gear. This machine has given continuous service for 8 years and is now being modified to give higher speeds than the 32 mi/h terminal speed for which it was F i t designed.

The basic energy of a linear motor is 50 percent as indicated in Section VII-C. This figure however can be exceeded by ac- celerating the field at almost the same rate as the missile, so that the slip for maximum efficiency obtains at all speeds [ 61. Such a system can be obtained by a graded series of coil pitches and one such machine (a tubular motor) is shown in Fig. 96. The alternative system is to feed the machine from a source of variable frequency. The former method presupposes the performance of the particular secondary used and is peculiar to that secondary. The latter method could be elec- tronically programmed and controlled by signals generated by the missile itself. Both of these systems, however, have now been shown to be costly elaborations and a 3-step speed-varying track achieves almost the Same result [6 1 I . The 3-step system can be compared to a 3-gear automobile where the relative cost of continuous gear changing with a fixed speed engine is also prohibitively costly.

D. Power Machines Several factors delayed the exploitation of linear motors in

general and power machines in particular. When a small device has been invented any commercial organisation interested can afford to make and test one, but when it is an electromagnetic device, a small machine is on the “wrong side of the hill” and the device proves to have very poor characteristics. This was particularly important in the early part of this century when the “fashion” in engineering was to regard efficiency and power factor as all important. To be asked to build an electromag- netic railway such as Zehden proposed in 1905 [621 or Bachelet in 19 14 without any guarantee of success was asking too much. As the century progressed the fashion of “Can it be done at all?” returned and liquid metal pumps were a “must” for the commercial harnessing of nuclear power. Their ef- ficiencies, of the order of 30 percent, only served t o c o n f m what the earlier generation had suspectedhear motors with big airgaps were poor machines. Yet a strange anomaly now existed, for at the same time as liquid metal pumps were being pioneered, highly successful turboalternators with airgaps of several inches were ‘being run as an everyday occurrence. Communication appears to have been the problem, for induc- tion motor designers apparently never talked to alternator de- signers and not until the days of the goodness factor were all electromagnetic machines “made one” and the airgap was seen in its proper background, i.e., related to pole pitch and not a tyrant in its own right.

The power machines may have fewer specific applications than have the other two groups but such as there are, are far more “glamorous.” High-speed ground transport is now per- haps second only to space research in this respect and certainly vast sums of money are now being spent in the development, not only of linear motors for this purpose, but also of methods of levitating the vehicles, so that they float above and are guided along a track. Whilst the countries of the world are not yet agreed on the best system of suspension, there is general agreement about the use of high-powered linear motors as driving units.

First came the double-sided sandwich motor aimed at reduc- ing track costs to an absolute minimum, but soon it was found

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LAITHWAITE: LINEAR ELECTRIC MACHINES 2 8 1

Of VQhlClQ

LIFT

DRAG‘ t . I

Photo-coll’’-

Fig. 97. Schematic layout of attractive Maglev system.

to be unsafe for high speeds, for aluminum plate has not the strength of steel and, therefore, cannot be subjected to the welded rail technique. By 1967, Britain had gone single sided, with the rest of the world following, mostly between 197 1 and 1973. France and Britain were developing air cushion lift and guidance, mainly through the efforts of Bertin .in France and the Tracked Hovercraft Company in Britain. Then came set- backs. ’ In 1973 the British Government closed the Tracked Hovercraft project, despite the fact that a 40 tonne vehicle had attained a speed of 108 mi/h against a 20 mi/h headwind, start- ing and stopping within the only mile of track available, and despite the fact that a further 2 mi of concrete beams had been made and were ready to erect. In 1974, Bertin’s Aerotrain re- ceived a similar Governmental “coup de grace.” Air cushions were out, it seemed.

In their place came two forms of suspension both of which were confusingly called “electromagnetic suspension.” The one, usually called “Maglev” is illustrated in Fig. 97. Amplifier- fed electromagnets are mounted on each side of the vehicle (at a low level) with their pole faces horizontal and upwards, to operate into a pair of solid steel rails, one on each side of the track. A sensing device tells the amplifier to increase or de- crease the magnet current accordingly as the gap between mag- net poles and rail is too large or too small. Such a system is being developed in several countries, including Messerschmitt- Bolkow-Blohm and Krauss-Maffei in Germany, the latter winning a medium-speed contract (80 km/h) in Toronto, Canada. Such systems are quoted as being operative with power inputs as low as 1 .O W/kg lifted [63 1. This statement is no more meaningful than that a crane-operating lifting mag- net can pick up 3 tons of scrap steel for 80 W of input. In the latter case the fallacy is clear. The crane does the actual lifting with its winch motor. The steel simply closes a mag- netic circuit-and a very good closure it is. In the case of high-speed vehicles, the fallacy is less clear. A vertical disturb- ance due to track imperfection or side wind of only 2 mm, oc- curring in a distance of 1 m, requires correction at 400 km/h involving a vertical acceleration of 49.2 m/s2. The peak power required during the correction is, therefore, 22 W/kg, a total power of 1.1 MW being handled by the amplifier on a 50-tonne vehicle. This is of course just one manifestation of “the smaller the better” law for pure magnetics.

The rival scheme, using entirely different techniques, has oc- casionally been referred to as “repulsive Maglev” to distinguish it from the system just described in which the magnets are attracted to the track rail. More usually the second system is known as “cryogenic levitation,” since air-cored superconduct-

(b)

Fig. 98. Basic force diagram. (a) For the currents in primary and secondary of a cryogenic suspension system. (b) For the currents in primary of secondary of a magnetic river. Note the change of direc- tion of induced current shift which results in drag in (a) and propulsion in (b).

ing coils on the vehicle induce current in an aluminum track plate, when the vehicle moves. Above 40-60 (depending on design) the vertical forces between superconducting coil cur- rent and induced track current is sufficient to lift the vehicle clear of the track. The fact that thereafter the vehicle is un- stable in roll can be corrected by vertical track plates and other sets of cryogenic coils. The system, therefore, may in- volve a “U”-shaped aluminum channel as track member [ 64 ] .

It cannot be too strongly emphasised that the attractive Maglev system is a “magnetic” system whereas the cryogenic system is on “the right side of the hill.’’ A recent article dif- ferentiated between the two systems by classifying them as electromagnets with or without iron cores [ 651. This division only applies in the two cases just considered, for iron cored magnets improve with increase in size provided they induce EMF and not flux into the secondary. Nevertheless the finding [65] were sound in that attractive Maglev can only work with clearances of the order of 1-2 cm, whilst inductive repulsive systems could operate with 20-30 cm clearance. So could a magnetic river. The main difference between a “magnetic river” and cryogenic levitation is that the former pushes hori- zontally, as well as lifts, whereas a cryogenic magnet produces drag as well as lift.

Any well-coupled induction device (high6 value) produces an induced secondary current pattern virtually equal and o p posite to that in the primary, the one slightly displaced in the plane of the interface as shown in Fig. 98(a). The opposite currents repel and give, in the case of the cryogenic magnet a lifting force and a drag force in the ratio governed by the dis- placement angle.

The most recent developments in synchronous propulsion using the wiggly wire described earlier could provide the answer to the drag problem of cryogenics [ 661.

Developments in Maglev and cryogenic suspension were be- gun before the demise of air cushion systems so they can be said to have “survived” air-cushion suspension and guidance rather than to have “replaced” them. The cryogenic system began with a levitation and guidance mechanism as an entity in

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itself, linear motor propulsion being a natural partner but not an integral part of those facilities. It is now moving towards an all-in system. The combination of single-sided linear motors and Maglev suspension has been causing trouble to some workers due to the fact that a well designed single-sided linear induction motor (LIM) produces lift and not downward force at standstill and in general the lift force is a function of speed, falling to zero at some value of slip between 1.0 and zero, and for still smaller values of slip changing to a downward force. This feature appeared to make the magnetic river a nonstarter in this high-speed context" until work by Freeman and Lowther showed how a LIM could be designed to give constant lift and @idance forces at speeds, including reversed-cumnt Fig. 99. 6-ft long Tracked Hovercraft exhibited at Hovershow '66 in

braking 1681 - The magnetic river now offers the potential of measuring 7 in X 1 in X 1 in. (Courtesy of Hovercraft Ltd., England.) Portsmouth, England, reached 34 mi/h powered by a linear motor

being able to design a propulsion system which provides levita- tion and guidance for no additional equipment and for no addi- tional equipment and for no additional power input. It can be supplied at mains frequency. It is electromagnetic and, there- fore, scales up advantageously. Perhaps its place in relation to other systems is best indicated by comparing it with the other electromagnetic suspension system, i.e., cryogenics, as shown in Fig. 98(b) where the secondary induced currents are seen to be displaced in the opposite sense from those in Fig. 98(a). The horizontal component of the total force is now propulsive and for the same goodness factor it would appear that the ratio of vertical to horizontal force components is the same in the two cases. In other words, the drag force on a cryogenic sys- tem may, in practice, be of the same order as is the propulsive force of a magnetic river scheme. It can be argued that it is early days yet to pronounce so favorably towards the magnetic Fig. 100. RTV 31 in course of construction. (Photo by Ron Bailey

magnetic river is so potentially advantageous that it wiil cer- tainly receive the full experimental treatment in the months ahead.

It is virtually impossible to stand back, at this time, and present an unbiased summary of the state of power machine development at a time of such fertility in new ideas. Let it suf- fice to illustrate a few examples from the work in various countries, obviously without being aware of the true state of the art in any one of the projects for each inventor will initially protect his device by remaining silent on the latest developments.

Fig. 99 shows a 6-ft model of the Tracked Hovercraft ex- hibited at Portsmouth, England, in 1966. The problem of seal- ing down the electromagnetic propulsion system was solved using a supply of 400 Hz. The shape of the vehicle changed in the process of developing the 25-ton vehicle (RTV 3 1) seen in process of manufacture in Fig. 100 and in Huntingdonshire in 1972 (Fig. 101). Fig. 102 shows the linear motor which

- ~~

river and to condemn the cryogenic levitation system but the Studios, Huntingdon, England, for Tracked Hovercraft Ltd., England.)

propels t h i s vehicle. In Germany several experimental tracks have been built, propulsion and levitation systems differing but propulsive systems now moving in the direction of single- sided motors. Fig. 103 shows a French vehicle carrying a double-sided sandwich motor. French manufacturers of linear motors have now largely withdrawn from the scene. By con- trast Fig. 104 shows the Japanese two-man vehicle on its experimental track. Levitation is provided by cryogenic mag-

Berlin, Germany, is described m a paper by Hochhausler [ 67 ]. This sys- ''A similar system to the magnetic river which was exhibited in

tem was primitive in that the magnetic circuit was only completed laterally through a large airpp, the system as designed consisting of two parallel conventional linear motors with principally longitudinal flux.

Fie. 101. Full-scale Tracked Hovercraft (Research Test Vehicle 31) on its mile of track at Earith, Huntingdon., England. (Photo by Ron Bailey Studios, Huntingdon., England, for Tracked Hovercraft Ltd.. England.)

net on board using the Powell and Danby original type with coils, rather than continuous aluminum sheet being fitted al l along the track. Propulsion of this vehicle is by linear motor primaries, track-mounted at intervals, with secondary member carried on the vehicle (presumably with a view to reducing vehicle weight).

A start has been made on commercial manufacture of trans- verse flux machines and Fig. 105 shows a 1 / 5 scale machine built by Linear Motors Ltd of Loughborough, England for Tracked Hovercraft Ltd.

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LAITHWAITE: LINEAR ELECTRIC MACHINES 2 89

Fig. 102. The single-sided linear motor which propels RTV 31, manu- factured in England by G.E.C. Ltd. (Photo by W. Eaden Lilley & Co. Ltd., Cambridge, England, for Tracked Hovercraft Ltd., England.)

Fig. 103. French test vehicle with double-sided motor manufactured by Merlin Gerin in Grenoble. (Courtesy of Merlin Gerin, Grenoble, France.)

Fig. 104. Japanese twO-man t a t vehicle suspended by cryogenic magg- net system and propelled by linear motors. (Courtesy of Japanese National Railways.)

IX. CONCLUSIONS Enough has been illustrated in this article, to indicate that

novelty in topology, pure invention in fact, has leapt away from the consolidating analysis which usually follows in its

Fig. 105. The fust commercial TFM made by Linear Motors Ltd. of

borough, England.) Loughborough, England. (Courtesy of Linear Motors Ltd., Lough-

wake. There was a time in the 1950’s when it appeared as if the subject of rotating machines had become so stereotyped and dull that educational establishments were scrapping their machine laboratories and resorting to all-theory courses with generalized machine theory as their bedrock. What has been done since has been almost entirely the result of practice, in- genuity and shrewd application of electromechanical analogy.

How long will it be before the theory of a graded pole pitch, transverse flux tubular motor with short secondary, in a state of acceleration, will be sufficiently far advanced that optimum design procedure can be formalized? At the present time the topological explosion begun some 15 years ago shows little sign of abating and the gap between invention and pure theory widens.

Linear motor technology must surely now form part of aca- demic courses if only for the sake of what it can teach about conventional rotary machines, about real motors, the best of which have a measure of symmetry and anisotropy. General- ized theory is no longer “general.”

It is always difficult to look into the “crystal ball” of tech- nology and predict the most likely trends but i t would appear that motor shapes will continue to change and perhaps in the direction of the shapes of living creatures, for the most ad- vanced forms of linear motor are now of the same basic shape as those of some of the most primitive animals on earth, i.e., seashells [691.

ACKNOWLEDGMENT The author is indebted to the Science Museum, South

Kensington, London, England, for the loan of the Wheatstone machine illustrated in Fig. 64.

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