1966, No. I 15

An eddy-current couplingemployed as a variable-speed drive

W. Bähler and W. van der Hoek

538.541 :62-578.3

The idea of the eddy-current coupling is not new; the device was in fact used long ago forthe transmission of high power. In recent years advancing mechanization has stimulatedfresh interest in the eddy-current coupling, particularly in the homopolar type, in view ofitssuitability as a variable-speed drive for low power applications. Electronic controlof thecoupling offers many new possibilities in process control and other industrial controlapplications.

In 1825 Arago discovered that a rotating copper disctends to communicate its motion to a magnetic needlesuspended above it (fig. 1). Arago was unable to ex-plain this phenomenon and called it "rotational mag-netism". Itwas not until 1831, when Faraday discoveredthe phenomena of induction that it was understood

~Fig. I. Arago's experiment. A copper disc rotating in its ownplane tends to communicate its motion to a magnetic needlesuspended above it.

that the field of the magnetic needle generated eddy-currents in the rotating disc. The forces producedbetween these electric currents and the magnetic fieldcaused the needle to rotate with the disc.

These eddy-currents, which always arise in a con-ductor subjected to a varying magnetic field, havebeen intensively studied since electric generators firstcame into use. Such studies were not only directed to-wards limiting the losses caused by the eddy-currents(for example in the iron core of a transformer), butalso towards possible uses. The eddy-current couplingis one of the possible applications, and Arago's ex-periment can be regarded as its first demonstration.

Ir. W. Bähler is with Philips Research Laboratories, Eindhoven;Prof Ir. W. van der Hoek is with the Works MechanizationDepartment of Philips Radio, Gramophone and Television Division,Eindhoven, and an associate professor of Mechanical Engineeringat the Technical University of Eindhoven.

Construction of an eddy-current coupling

Eddy-current couplings, as later developed inmany different designs, always contain two memberswhich can rotate freely with respect to one another(fig· 2). The magnetic field is generated by the induc-tor 1. The second member, the eddy-current cylinder 2(it mayalso be a disc) consists of conducting materialin which the eddy-currents are induced.

Frequently the inductor is provided with one ormore coils, excited by means of slip rings and woundin such a way that opposite poles are alternately pro-duced on the circumference of the inductor. The coilsare excited by d.c. current. When the inductor isdriven the magnetic field rotates with it. The situationshows much resemblance to that found in a three-phase induction motor, where a rotating magneticfield is produced by electrical means. Just as in thethree-phase induction motor, there must, to obtaina torque at the output shaft, be a certain slip betweenthe rotating magnetic field and the eddy-current cylinderof the coupling.

The absence of mechanical contact between inductorand eddy-current cylinder makes the eddy-currentcoupling suitable for transmitting power under irregu-lar or shock loading, such as found in rolling mills

4

Fig. 2. Schematic representation of an eddy-current coupling.1 inductor, 2 eddy-current cylinder. The input shaft 3 and theoutput shaft 4 are supported in bearings in the housing 5.

16 PHILIPS TECHNICAL REVIEW VOLUME 27

Fig. 3. Sketch of a homopolar eddy-current coupling. 1 inductor, here magnetized by a singlestationary exciting coil 6. 2 eddy-current cylinder. The input shaft 3 is supported in bearingsin housing 5, made, like the inductor, of a ferromagnetic material. The output shaft 4 is sup-ported in bearings on the input shaft. 7 "teeth" of the inductor.

(a) and Cb)show the lines of magnetic field. In (c) the eddy current loops are shown.

Q

and cranes. Other advantages are that the coupling canbe controlled by a small direct current and that thetorque is entirely ripple-free, due to the absence ofslots or bars in the eddy-current cylinder.

The eddy-current coupling is called heteropolarwhen the inductor has both north and south poles.The heteropolar type is widely used for the transmis-sion of high power.

The operation ofthe coupling does not depend, how-ever, on reversal of the polarity of the magnetic field.It is sufficient if the field varies between a minimumand a maximum value. A drawback ofthis construction(referred to as "homopolar"), is that for a given maxi-mum amplitude of the magnetic field one can obtainonly a quarter of the torque obtainable with a hetero-polar type; set against this drawback there is theadvantage of certain constructional simplifications.

Some homopolar types, for example, need only onecentral coil which does not rotate with the inductor,and this means that the exciting current can be suppliedby very simple and reliable means. In such couplingsthe local variation of the intensity of the magneticfield is produced by designing the inductor in the formof a disc with "teeth", which rotates in the spacebetween the coil and the cylinder (fig. 3).The homopolar coupling with stationary exciting

coil has proved particularly useful as a low-powervariable-speed drive.

A simplified model

For any given application the eddy-current couplingmust meet specific requirements. In order to produce adesign that meets the requirements, the influence ofcertain factors on the characteristics of the couplinghas to be considered. Typical factors are the relative

angular velocity of the inductor in relation to the eddy-current cylinder, the dimensions, the magnitude of theexciting current and also the choice of material, theyare dealt with here by considering a simplified model.It is assumed that an infinitely large flat plate of thick-

ness (h is situated in a flat air-gap of height <5 (fig. 4).The air-gap is bounded above and below by magneticmaterial which has zero electrical conductivity, a = 0,and infinitely high magnetic permeability, !l = 00.

The conductivity of the plate is a = al and its magneticperrneability z, = !lO, the same as that of free space.

At the plane z = +t<5, which bounds the upper space,there is an infinitely thin layer containing a sinusoidalpattern of currents flowing in the positive and in thenegative y direction. The current does not depend on y.The "pole pitch", i.e. the length of half a period of thissinusoidal pattern, is Af2. The "current layer" moveswith a velocity v in the positive x direction. The plateis stationary.

If we compare this model with the actual eddy-current coupling we see that the inductor is representedby the current layer, and the eddy-current cylinder bythe plate. The velocity v of the current-layer is equiva-lent to the difference in speed between the inductor

z

~x

a=O,f1==

Fig. 4. Simplified representation of an eddy-current coupling,used in deriving the torque equations.

1966, No. 1 EDDY-CURRENT COUPLING 17

and the eddy-current cylinder of a real coupling.Since the currents in the exciting current layer flow

only in the positive and negative y direction, the mag-netic field which they generate in the air-gap has no ycomponent. Since, moreover, the x and Z componentsof the magnetic field are independent of y, the electricalfield in the air-gap contains a y component only.

On the basis of Maxwell's equations we can set downa differential equation for the electrical field strength inthe air-gap, the' "wave equation", which we haveto solve for the steady state.The Ay of the exciting current is given by the ex-

pression

Ay = Ayo exp ~j 2; (vt-x) ~, ... (1)

where Ayo is the amplitude of the current.Because of the periodicity of the moving pattern of

the exciting current the electrical field strength at anygiven point must be given in the steady state by asolution of the wave equation that has the same timedependence as the exciting current. For Ey, the ycomponent of this electrical field, we therefore write:

Ey = Eyo(z) exp ~j2; (vt-X)}, . . (2)

where Eyo(z) is a complex variable which denotes boththe amplitude and the phase shift of the electrical fieldwith respect to the exciting current.If, in the solution (2) of the wave equation, we take

into account the boundary conditions relating to themodel (fig. 4), we find that both in the eddy-currentplate and in the space Eyo(z) is approximately indepen-dent of z and equal to:

!-l0 v AyoEyo(z) = - . . (3)

vO'l(h!-lO - j2n~/).

We therefore have the relation between the electricalfield strength in the plate and the exciting current.What we are particularly interested in, however, is theforce exerted on the stationary plate by the movingmagnetic field.This force can very easily be found with the aid of

theoretical considerations of the energy involved. TheJoule heat, which is generated in the plate by the eddy-currents.averaged over a pole pitch, is equal to the workwhich the tangential force K, averaged over half aperiod, performs per unit area and per unit time.The Joule heat per unit volume element ~ldx isEy20'1~ldx, and therefore:

Substitution ofeq. (2) in eq. (4), together with eq. (3)'-yields after some manipulation:

/-toA~02).K=-----

4n~ (~+VO)Vo v

(5)

where:

2n~vo =---.

).al~l/-tO

For v = Vo the force reaches a maximum equal to:

(6)

/-toAY02).Kmax = --:----:--

8n~

Substitution of eq. (7) in eq. (5) finally yields:

K 2

(7)

--=--- (8)Kmax v Vo-+-

Vo v

Equation (3) is arrived at as follows [1J. In our model a partof the air-gap is taken up by the eddy-current plate. The electricalfield strength in the eddy-current plate is given by the three-dimensional wave equation:

bE'Ç72E-/t(]bi = 0, . . . . (9)

and the electrical field strength in air is given by:

. . . (10)

Substitution of eq. (2) in (9) and (10) gives expressions for Evo(z)ofthe form:

Evo(z) = P exp ~z V (Z;r + k2 ~ +

+ Q exp ~ - z 11(~r+ k2 ( •• (11)

where k2 = j(2:rr,fÄ)v/t(J holds for k. (In air (J = 0, which meansthat k = 0 in eq. 11.)Pand Q are integration constants which differ in each of the

three layers of the air-gap - air, eddy-current plate, air. Theseintegration constants can be found with the aid of the boundaryconditions that apply at the surfaces of the three layers. In thefirst place, the magnetic permeability of the eddy-current plateis equal to that of the air-gap. This means that both at the upperand the lower surface of the eddy-current plate (z = ±t(h) thetangential components and also the normal components of themagnetic field, Hz and Hz, are equal on each side of the bound-aries. Owing to the infinite magnetic permeability of the materialoutside the air-gap, the tangential component of the magneticfield at the lower boundary (z = -!c5) is zero. Because ofthe pre-sence of the current-layer this does not apply to the tipper bound-ary of the air-gap (z = +tc5). Ifwe take the contour integral ofthe magnetic field in the plane of a flat loop perpendicular to they axis and close to the boundary (Maxwell: p 'H.ds = Îtr~e), wefind there Hz = -Av. '

(4) [1) This calculation may be found in: R. Rüdenberg, Energie derWirbelströme in'elektrischen Bremsenund Dynamomaschinen,Enke, Stuttgart 1906.

18 PHILlPS TECHNICAL REVIEW VOLUME 27

Using the boundary conditions we find six equations fromwhich the integration constants can be calculated. Before solv-ing these equations, however, we replace the exponential powerswhich they contain by the first term of the series expansion. Thisis permissible (see eq. 11) when the height r5 of the air-gap issmall both in relation to the pole pitch J..f2 and in relation to theskin depth r5skln [2] of the eddy-current plate.

Solution of the simplified equations results in eq. (3).

The torque-speed characteristic...The relation between K and v, as found for the sim-

plified model, also applies in principle to the actualeddy-current coupling. Instead of the force and velo-city we iJitroduce two other quantities: the torque Mexerted on the output shaft, and the relative speed nof the input shaft with respect to the output shaft.

Corresponding to eq. (8) we can write:

2M. . . . (12)--=-'---,

Mmax n no-+-no n

and equations can be written down for Mmax and nocorresponding to (6) and (7). The curve found when Mis plotted as a function of n is referred to as the torque-speed characteristic (fig. 5).

Whether an eddy-current coupling is suitable for aparticular application depends on the position and

o _nFig. 5. Torque-speed characteristic of an eddy-current coupling.Maximum torque Mm." is reached at a speed 110.

height of the maximum in the torque-speed charac-teristic. In designing an eddy-current coupling it isalso possible, with the aid of the equations for Mmax

and no, to choose the dimensions, exciting current andthe materials in such a way as to produce the requiredcharacteristic. For example, increasing the thickness ofthe plate or its conductivity gives a lower speed formaximum torque.It can also be seen that increasing the gap-width ~

causes the maximum to shift towards a higher speed.Wben ~ is increased, however, it is necessary at thesame time to increase the exciting current in propor-

tion to ~ in order to keep the maximum torque Mmax

constant. Theoretically the required exciting current isat a minimum when the gap-width ~ is equal to the platethickness ~1.

The homopolar type

Fro~ now on we shall be solely concerned with thehomopolar version of the eddy-current coupling.Before applying to this version the results found sofar, it is necessary to consider the effects of the differ-ences between the model and the actual coupling.

In the model we fust assumed a heteropolar versionin which the field distribution was purely sinusoidal. Asa first approximation we can treat the field distributionin the actual homopolar coupling as a sinusoidal fieldsuperimposed on a field which is constant around thewhole circumference. The constant field component hasno influence on the behaviour of the coupling as thepotential difference that it produces between the twoends of the eddy-current cylinder is constant over thewhole circumference, so that no currents can flow.In practice, however, the field differs from that of themodel in a further respect: the alternating compo-nent, as measurements show, is not sinusoidal but has ashape between a sine wave and a square wave. Wecan think of the alternating field as the resultant of asinusoidal field and higher harmonics, whose ampli-tudes can be calculated by means of numerical Fourieranalysis. An investigation has shown that the influenceof the higher harmonics on the shape of the torque-speed characteristic is not negligible. Compared withthe characteristic for the purely sinusoidal field distri-bution, the maximum torque is larger and displaced to-wards a higher speed; and the initial slope of the curvebecomes steeper.

Another difference concerns the gap-width ~. Inthe model this was assumed to be constant. In theversion of the eddy-current coupling which we con-sider (see fig. 3) the inductor is in the form of a discwith teeth around the circumference, so that the gap-width varies. To obtain agreement between the torquespeed characteristic of the coupling and the theoreticalcharacteristic we have to introduce a fictitious gap-width ~/, which is greater than the gap-width at theteeth.In the model we assumed an eddy-current plate of

infinite length in the y direction and a current layerindependent of y. This meant that the eddy-currentsflowed only in the y direction, that is to say perpendi-cular to the direction of motion. In actual eddy-currentcouplings, including the homopolar type, the finite di-mensions of the eddy-current cylinder require that theeddy-currents at both ends of the fingers have to formclosed loops (see fig. 3c). Because of this, extra resist-

1966, No. 1 EDDY·CURRENT COUPLING 19

ance is presented to the eddy-currents, causing a furtherdiscrepancy between the actual torque-speed charac-teristic and the theoretical one. The discrepancy canbe found by estimation and by measurements on actualeddy-current couplings [31.

A variable-speed drive

We have already mentioned that the homopolarversion of the eddy-current coupling has proved par-ticularly useful as a variable-speed drive for low-powertransmission. This is due not only to the simple con-struction of the coupling, but more especially to thepossibility of electronic control of the exciting cur-rent.

Fig. 6 shows schematically a speed-control systemin which the eddy-current coupling is used as a variablespeed drive. The input shaft of the eddy-current coup-ling K is driven by an electric motor M which runsat constant speed. The speed of the output shaft ismeasured by a tachometer which gives a voltage pro-portional to the speed. This voltage is compared with areference voltage which corresponds to the desiredspeed and which can be adjusted with a potentiometerP. An amplifier A energizes the exciting coil of the eddycurrent coupling with a current proportional to thedifference between the two voltages.

Fig. 6. Diagram of a speed-coritrol system employing an eddy-current coupling K. The input shaft of the coupling is driven by amotor M at constant speed. The speed of the input shaft ismeasured by tachometer T, whose output voltage is comparedwith a reference voltage, adjustable by means of potentiometerP. Amplifier A energizes the exciting coil with a current propor-tional to the difference between the two voltages.

As is often the case in control systems the actualvalue of the controlled quantity - in our example thespeed - has to be lower than the desired value beforecurrent can be supplied to the exciting coil. The differ-ence between the two speeds decreases as the gain ofthe amplifier is increased. The magnitude of the gain(amplification factor) has however to be limited to acertain maximum depending on the dynamic charac-teristics of the coupling.

Many variable-speed drives of the type describedabove have been in use at Philips for some years nowin a wide variety of production machines, including

Fig. 7. Exploded view of a Philips eddy-current coupling. Thelarge cylindrical member on the left is the stationary housing,made of ferromagnetic material. To the right can be seen inorder the exciting coil; the inductor, mounted on the input shaft;the copper-eddy-current cylinder, mounted on the output shaft;the cap and the tachometer. At each end bearings are visible.

machines for coiling wire and tape after rolling, draw-ing or lacquering. Recently both the eddy-currentcoupling and the complete drive were put on themarket [41. Fig. 7 shows an exploded view of a Philipseddy-current coupling. The dev ice incorporates a tacho-meter, which indicates the speed of the output shaft.

Torque-current characteristic of the variable-speed drive

For a variable-speed drive it is desirable to be able totransmit the maximum torque in the widest possiblerange of speeds between zero and the speed of the mo-tor. We have stated earlier that the form of the torque-speed characteristic of the eddy-current coupling canbe influenced by the appropriate choice of materialsand dimensions. The choice is not, however, entirelyfree, because the maximum exciting current, the widthof the air-gap and the thickness of the eddy-currentcylinder wall are also governed by constructional andother conditions. Therefore, in a good design the maxi-mum in the torque-speed characteristic does not alwayslie in the speed range employed, as might besupposed.

[2] The skin depth of the materialof the eddy-current plate isgiven by: Óskin = VAjnfloav.At this depth IEl = (lje)IEsurracel .

[3] The discrepancy has been exactly calculated for a situation asin fig. 4, but with a sinusoidal field in both the x and the ydirection. See the article quoted [1].

[4] The electronically controllededdy-current coupling was devel-oped for use in Philips establishments by the Works Mecha-nization Department of the Radio, Gramophone and Tele-vision Division. The further development, production andmarketing have been taken over by Philips Industrial Equip-ment Division.

20 PHILIPS TECHNICAL REVIEW VOLUME 27

20kgcm is stationary and the difference between the speeds ofthe two shafts is at a maximum. For a given speed thecurve gives the maximum torque that can be deliveredto the output shaft.

1-.

/V x

~ ~

/ ~ ~/ ~~

/ ~

IIII

11,

18

16

M

rThe value of n can also be greater than ttm, i.e. the speed of the

output shaft may in certain cases be "negative". This is found forexample in servo systems using two eddy-current couplings whoseoutput shafts are coupled together and whose input shafts aredriven in opposite directions. Compared with the drive describedin this article, a servomotor of such a type has the advantagethat the speed is vari able in two senses of rotation.

A system of this kind is used for driving the radiotelescopes atDwingeloo (Netherlands) and at Malvern (England) - an appli-cation in which an important feature is the exceptionally smoothtorque of the eddy-cu rrent coupling at low revolutions.

Another advantage already mentioned, which the eddy-currentcoupling has when compared with servomotors of other types, isthat it requires only very low driving power.

14

12

10

8

6

4

2

The power delivered by the output shaft is equal tothe product of the torque and the shaft speed. Apartfrom this useful output, there is a certain amount ofpower which is converted into heat in the eddy-currentcylinder: this power is equal to the product of thetorque and the difference between the speeds of theinput and output shafts. The heat is partly dissipatedby the air, due to the fan-like action of the inductor.The transfer of heat to the air is assisted by the strongair currents close to the eddy-current cylinder whichare set up by the teeth on the inductor. In spite of thiseffective heat removal, so much heat can be generatedin the eddy-current cylinder (when the output shaft is

500 1000 1500 2000 2500rp.m,--..n hm

Fig. 8. Measured torque-speed characteristic of a Philips eddy-current coupling type PE 2245. In the hatched area continuousoperation of the coupling is not recommended, as the tempera-ture - particularly at the bearings - then exceeds the maximumpermissible value.

Fig. 8 shows the torque-speed characteristic derivedfrom measurements on the Philips PE 2245 eddy-current coupling. In the figure n is the relative speedof the input shaft with respect to the speed of the out-put shaft of the coupling. At the point n = 0 the speedof the output shaft is thus at a maximum: at the pointn = nm (nm is the speed of the motor) the output shaft

Fig. 9. Demonstration arrange-ment with two eddy-currentcouplings, Coupling 1 drivesdrum 2 at constant speed, sothat the wire is unwound atconstant speed from reel3. Thewire runs from the drum overa dynamometer mechanism 4to the take-up reel 5, which isdriven by eddy-current coupling6. The wire is guided by anumber of rollers in such a waythat the arm 7 of the dynamo-meter is drawn in one directiononly. A spring holds the arm In

balance.

1966,No.'! EDDY-CURRENT COUPLING 21

turning at low revolutions, and is delivering a hightorque), that in places,particularly in the bearings, thetemperature of the drive can become higher than is,strictly permissible.

The hatched area inside the curve in fig. 8 refers tosuch a situation. If the coupling is used continuouslyin this range, the temperature will exceed the maximumpermissible value.

Applications of the variable-speed drive

One application of the coupling as a variable-speeddrive has already been described. A few other examplesare mentioned below.In driving a take-up reel for wire (or tape) it is usually

the speed of the wire, rather than the speed of the reelthat has to be kept constant. Here, instead of a tacho-meter on the output shaft ofthe eddy-current coupling,we can use a tachometer driven directly by the wire.The speed of the wire can also be kept constant by

continuously measuring the diameter of the take-upreel. This can be done by means of an arm, fitted to thereference voltage potentiometer, and which rests onthe wire being wound on to the reel. As the windingbecomes thicker, the potentiometer is turned by thearm so that the angular velocity of the reel is reduced,and the wire speed is kept constant.A further possibility is to drive the wire itself instead

of the take-up reel. Fig. 9 shows a demonstrationarrangement with two eddy-current couplings (fixedhere to the front plate ofthe associated electricmotors),

which winds a wire on to a reel at constant speed andunder constant tension. A few turns of the wire arelooped around the drum 2 which is driven at a con-stant speed by the eddy-current coupling 1. The eddy-current coupling 6 drives the take-up reel 5, and insuch a way that the tension of the wire remains con-stant. This is achieved by passing the wire througha dynamometer mechanism 4 and 7, whose outputvoltage is compared with a reference voltage.In addition to the speed of a shaft, the speed of a

wire and the tension in the wire, other quantities canbe controlled, for example the torque exerted on astationary shaft. The only condition is that it must bepossible to represent the controlled quantity by avoltage, which can be compared with the reference vol-tage in the control amplifier. There is thus a consider-able field of application for variable-speed drives inprocess control, since in many processes performanceis monitored electrically, and very often performance isgoverned by a speed.

Summary. With the aid of a simplified theoretical model of a(heteropolar) eddy-current coupling the relation is derived be-tween the transmitted torque and the relative speed of the inputand output shafts of the coupling. This relation is also valid fora homopolar eddy-current coupling. The homopolar version,the design of which is particularly simple as the .exciting coil isstationary, is finding increasing application as a variable-speed drive for low-power transmission. An important featureis that the exciting current can be electronically controlled, sothat with simple circuits a shaft or other speed or a torque canbe kept constant at a desired value. .