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PATENT

(21) Application No. 44048/71

(52} Index at acceptance

G3T ASXH4] SMS 63 6C2 7K

(72) Inventor DALE ROLAND KOEHLER

SPECIFICATION

(22) Filed 21 Sept. 1971

(44) Complete Specification published 6 Feb. 1974

(5 1) International Classification G04C 3/00//H04R 9/00

(11)

(54) IMPROVEMENTS RELATING TO ELECTROMAGNETICTRANSDUCER AND ELECTRONIC WATCH

(71) We, BULOVA WATCH COM-PANY, INC, a corporation organized underthe laws of the State of New York, one- of theUnited States of America, of 630 FifthAvenue, City and State of New York, UnitedStates of America, do hereby declare theinvention, for Which we pray that a patentmay be granted to us, and the method bywhich it is to be performed, to be particularlydescribed in and by the following state-merit:—

This invention relates generally toelectronically—controlled timepieces whichincorporate electromagnetic transducers forsustaining a tuning fork in vibratory motion,and more particularly to an improved trans-ducer structure that makes possible a sub-stantial reduction in the size of the timepiece.

In the United States Patents t0 Hetzel2,900,786 and 2,971,323, there are disclosedelectronic timepieces including a timekeepingstandard constituted by a tuning fork Whosevibrations are sustained by two electro-magnetic transducers operating in conjunctionwith a battery—energized transistor circuit.The vibratory action of the fork is convertedinto rotary motion to turn the time-indicatinghands of the timepiece.

In timepieces of the type disclosed in theHetzel patents, each electromagnetic trans-ducer is associated with a respective tine ofthe fork, the transducer including a magneticelement attached to the end of the tine andvibrating therewith. The magnetic element onone tine Ieciprocates with respect to astationary main drive coil section, and that onthe other time moves back and forth withrespect to a. stationary minor drive coilsection and a sensing coil. The two drive coilsections are connected in series to the outputcircuit of the transistor, while the sensing coilis connected to the input thereof, wherebyalternating voltage induced in the sensing coilrenders the transistor conductive to producecurrent pulses in the drive coil sections formagnetically actuating the tines.

When a battery-operated timepiece is to beconfined within a small watch casing or in aminiature housing of similar dimensions wherespace is at a premium, it is essential that theelectrical and mechanical efliciency of thesystem be of exceptionally high order. Other-wise any loss of energy, which in a large-scale device may be negligible, can give riseto serious drawbacks in a more compactstructure. It is vital, therefore, that the trans-ducer or transducers which actuate the fork,operate at optimum efficiency, for in this way,even with a battery of small power capacity,it is possible to sustain the vibratory actionof the fork for a prolonged period.

Because the sole source of energy for thetimepiece is a single-cell miniature battery, anyfactor which dissipates energy 01' reducesefliciency not only cuts down the useful batterylife, but also creates operating difliculties. Inorder, therefore, to create a highly compacttimepiece, it is important that maximum usebe made of all available space and that thetransducers which actuate the fork be as smallas possible without, however, requiring anundue amount of power.

In the above—identified Hetzel US. Patents,the transducer includes a magnet elementformed by a cylindrical cup having a circularcross—section, a permanent magnet rod or coreof uniform cross-section being coaxiallymounted within the cylinder to define anannular air gap therein. The stationary driveor sensing coils associated with the magnetelement are received within the annular airgap, whereby in operation, the magnetic ele-ment reciprocates with respect to the coil.These transducers will hereinafter be referredto as being of the cylindrical magnet rod type.

In the prior US Patent to Bennett et :113,221,190, there is disclosed an improved

transducer arrangement for a timepiecegenerally of the type disclosed in said Hetzelpatents. In this Bennett et al U.S. patent,the permanent magnet is not of uniform cross-seetion throughout its length, but is linearly

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tapered to assume a frustoconical form, thecoil received in the annular air gap beingsimilarly tapered in order to realize thegreatest number of turns within the air gapat the position therein of maximum fluxdensity. These transducers will hereinafter bereferred to as being of the frustoconicalmagnetic rod type.

While transducers of the frustoconicalmagnetic rod type are distinctly superior tothose of the cylindrical magnetic rod type,they are not sufficiently efficient to makepossible a reduction in the dimensions of awatch to the point where a truly miniature ora ladies’ size tuning—fork watch movementbecomes feasible.The reason for this is that should one

reduce the existing size of a transducer ofa cylindrical or frustoconical magnetic rodtype, a higher input power would be requiredto drive the same tuning fork to compensatefor the reduction in magnitude of the electro—mechanical coupling (emu) factor. The e.m.c.factor is a direct measure of the amount ofelectrical energy converted to mechanicalenergy at the transducer interface and there-fore the smaller the e.m.c. factor, the largerthe electrical power required for a givenamount of mechanical power. Hence, with asingle—eell battery of the type and sizepresently used in conjunction with electronictimepiece movements, the cell would beexhausted in a relatively short period. On theother hand, if a larger battery ce]l is employed,this would be self—defeating, for the verypurpose of reducing the nansducer size is tomake a smaller watch; hence, if the reductionin transducer size dictates the use of a largercell, then nothing has been gained. It must beborne in mind that battery size is an importantparameter in the over—all size of the timepiece,and that the existing dimensions of electronictimepiece battery cells are a limiting factorin producing a smaller watch movement.

In practice, a power requirement for a tun-ing-fork watch which is in excess of aboutfifteen mierowats cannot be satisfied withinthe limits of a conunercially—acceptable watchvolume. With transducer designs of the typeheretofore known, should the transducer bemade smaller to conserve space, the resultantincrease in power requirement would gobeyond the tolerable limit due to an increasein the fork amplitude. The improvementresulting from the transducer design of thisinvention is manifested in both size andpower whereby the battery volume may bereduced markedly and therefore the size ofthe watch movement.

In view of the foregoing, it is the mainobject of this invention to provide electro-magnetic transducers of exceptional efficiencyfor actuating a tuning fork in an electronicwatch, or for any other appropriate purpose.More specifically, it is an object of the

invention to previde a transducer whosemagnetic element includes a permanentmagnet rod coaxially mounted in a cylindricalcup, the eross-section of the rod diminishingfrom the cup end to the free end in a non-linear manner causing the rod to assume abullet—like shape which gives rise to a sub-stantially uniform magnetic flux density with-in the rod.Among the significant advantages of the

transducer including a bullet—shaped magneticrod ate the following:

(A) Because of its exceptional efficiency, onemay reduce the size of the transducer andthereby reduce the size of the associatedtimepiece movement, and yet operate thetimepiece with a material decrease in thepower requirement of the movement, therebyeffecting a decrease in battery size.

(B) Because the transducer is markedlymore efficient than known transducers, onemay scale down the size of the battery andeffect a further reduction in volume of thetimepiece.

(C) Because the improved transducer makesit feasible to reduce the size of the move-ment, it opens up many new designpossibilities, not only for ladies-model watches,but for other miniaturized timing mechanisms.

(D) Though the transducer permits amarked reduction in the scale of the move-ment, it does so without impairing the tim-ing accuracy thereof.

According to the present invention, there isprovided an electromagnetic transducer com-prising a magnetic element constituted by acylindrical cup of magnetic material having apermanent—magnet rod fixedly supportedcoaxially therein to define an annular air gap,the rod having a cross—section whichdiminishes from the cup end of the rod to thefree end thereof in a nonelinear manner toyield substantially the same flux density atall points in the rod, whereby all of theflux is substantially restricted to the air gap,and a multi—turn coil received within saidannular air gap, said magnetic element beingmovable relative to the coil, the cross—sectionof the coil substantially complementing theradially outer surface of the rod and theradially inner surface of the cup, therebymaking possible the full use of the availablespace within the gap.For a better understanding of the invention

as well as further features thereof, referenceis made to the following detailed descriptionto be read in conjunction with the accompany-ing drawings, wherein like components in theseveral Figures are identified by like referencenumerals. In the drawings:

Fig. 1 is a schematic representation, inperspective, of the basic components of anelectronic timepiece including a transducer inaccordance with the invention;

Fig. 2 is a separate view of the tuning-

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fork structure showing the transducer partlyin section;

Fig. 3 is a side view of the transducer;Fig. 4 is an enlarged sectional view of the

transducer;Fig. 5 is a diagram of an idealized magnet

assembly;Fig. 6 is a diagram of a prior-art magnetic

transducer element of the cylindrical rod type;and

Fig. 7 is a diagram of a prior-art magnetictransducer of the frustoconical rod type.

Referring now to the drawings, and moreparticularly to Fig. 1, the major componentsof a timepiece including a transducer inaccordance with the invention are a time-keeping standard constituted by a tuning fork10 and an electronic drive circuit 11 there-for, a rotary movement of conventional designincluding a gear train 12 for turning the handsof the time piece, and a motion transformerincluding an index wheel 13 operatively coupl-ing the fork 10 and the rotary movement,and acting to convert the vibratory action ofthe fork into rotary motion. The tuning forkhas no pivots or bearings and its timekeepingaction is therefore independent of the eflectsof friction.

All of the electrical components of the drivecircuit are mounted on sub—asseinbly units ormodules F1 and F2 attached to a disc-shapedmetallic pillar plate 14 which may be sup-ported within a watch casing of standarddesign, or within any other type of housing,depending on the use to which the time-piece is put. Electronic circuit 11 is constitutedby a transistor TR having a base, a collectorand an emitter, a resistance—capacitance biasingnetwork R~C, and a by—pass capacitor Cb toprevent parasitic oscillations of the circuit.The electronic circuit 11 is energized by aVoltage source in the form of a battery V.

Tuning fork 10 is provided with a pair offlexible tines 15 and 16 interconnected by arelatively inflexible base 17, the base beingprovided with an upwardly—extending stem 18secured to the pillar plate by suitable screws19 and 20. The cental area of the pillarplate is cut out to permit unobstructed Vibra-tion of the tines.

The tuning fork is actuated by means oftransducers T1 and T2. Transducer T1 isconstituted by a magnetic element 21 securedto the free end of tine 15, the element coatingwith a stationary drive coil 22 and phase-sensing coil 23. These coils are wound on anopen—ended tubular carrier 24 aflixed to thesub-assembly P; which is secured to the pillarplate 14. Coils 22 and 23 may be wound injuxtaposed relation on carrier 24, or the phase-sensing coil 23 may be wound over drive coil

The second transducer T2 is constitutedby a magnetic element 25 secured to the free

end of tine 16, and coacting with a drivecoil 26 wound on a tubular carrier 27.The two transducers T1 and T2 are of

like design, except that an additional coil isprovided in transducer T1. The constructionand behavior of the transducers are similarto that of a dynamic speaker of the permanent-magnet type, save that the moving element isthe magnet, and not the coil.

Figs 2 and 3 show transducer T1 in greaterdetail, and it will be seen that magnetic ele-ment 21 is constituted by a cylindrical cup21a of high permeability magnetic material,such as iron, and a permanent—magnet rod 215coaxially mounted therein. Magnet 216, whichmay be made, for example, of Alnico, issupported on the end wall of the cup to pro-vide a magnetic circuit in which the lines ofmagnetic flux extend across the annular airgap 21c defined by the inner magnet and thesurrounding cylinder. Rod magnet 21!: is ofdiminishing cross-section from the cup end tothe free end thereof, to produce a longitudinalprofile which is continuously curved, forreasons Which will be later explained.As best seen in Fig. 3, cylindrical cup 21a

is cut longitudinally along diametrically-opposed planes to form slots 21d and 219.This eflects a substantial reduction in thetransducer dimension with relatively little fluxleakage. The cut-outs act to reduce the spaceoccupied by the cups in depth within the eas-ing, and make possible a more compact con-struction of the timepiece. The slots also pre-vent so—called “dash-pot” effects resultingfrom air compression by the magnet—and-cupassembly. Such damping is avoided by the slotopenings and also by the openings in thetubular carrier.

It will be seen that fixed carrier 24 forsupporting the drive coils 22 and 23 is hom-shaped and is dimensioned to complement thetapered magnet 2117. Carrier 24 and the drivecoils supported thereon are received withinannular gap 21c and are spaced both fromthe magnet and the surrounding cylinder,whereby the magnetic element is free toreciprocate axially relative to the fixed coil.

In operation, an energizing pulse applied tothe drive coils of transducers T1 and T2 willcause an axial thrust on the associatedmagnetic element in a direction determinedby the polarity of the pulse in relation to thepolarization of the permanent magnet andto an extent depending on the energy of thepulse. Since each magnetic element isattached to a tine of the tuning fork, thethrust on the element acts mechanically toexcite the fork into vibration.The vibratory action of the fork and the

concomitant movement of the magnetic ele-ment induces a back E.M.F. in the drive coil,and in the case of transducer T1, in thephase-sensing coil as well. Since the magneticelement reciprocates in accordance with the

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vibratory action of the tuning fork, the backE.M.F. will take the form of an alternatingvoltage whose frequency coresponds to that ofthe tuning fork.

Three functions are served by the trans-ducers. They drive the tuning fork by convert-ing pulses of cunent delivered to the coilsto mechanical pulses. They control theamplitude of the tuning fork by sensing thealternating voltage induced during each cycle;and they control the instant during the cyclewhen the drive pulse is to be delivered tothe coils.

Referring now to Fig. 4, the transducer inaccordance with the invention is shown inenlarged form to clarify the relationship ofthe components thereof and the factors whichcome into play in optimizing the design.

It will be seen that the permanent magnetrod 216 is coaxially mounted within thecylindrical cup 21a, which acts as a high-permeability return member; an annular gapbeing defined by the interior space betweenthe rod and cup. In order to utilize themagnet to best advantage, there must be auniform flux density within the magnet, andthere must be no leakage flux escaping fromthe magnetic element. In this connection,reference is made to the article of S.Evershed—“Permanent Magnets in Theoryand Practice”-—-J. Institute of ElectricalEngineers, 13 May 1920 (Volume 58, page797).

Since as one progresses from the base orcup end. of the magnet rod to the free endor tip thereof, flux leaks out of the magnetat a rate determined by the reluctance of themagnetic circuit, one must decrease thecross—section of the magnet so that thedecreased amount of flux in the magnetdivided by the decreased cross—sectional area,yields the same flux density at all points inthe magnet to attain optimum magnetic per—formance. Furthermore, the cross-section ofthe rod should diminish to zero at the tip,whereby all of the flux will have beenrestricted to, or will have emanated in theannular air gap within the cylindrical'cup.Thus the configuration of magnet rod 211:

in Fig. 3 is such as to provide a cross-section which diminishes from the cup end tothe free end in a non—linear manner such thatthe longitudinal profile is continuously curvedto produce a rod having a bullet-like shape.The cross-section at the free end or tip iszero, thereby minimizing flux leakage, andthe curvature of the profile is such as to yieldthe same flux density at all points in themagnet.The shape of coils 22, 23 which occupy the

air gap between the rod and the cup comple-ments that of the magnetic element, so thatthe outer boundary of the coils is cylindricalto confonn to the inner surface of the cup,whereas the inner boundary is curved to con-

form to the curvature of the rod. In thisway, full use is made of the available spaceWithin the annular gap, the greatest numberof coil turns being at the mouth of the gap.

Theoretical and Design ConsiderationsIn designing an electromagnetic transducer

of the type in question, with a view tooptimizing its power performance, one mustconsider not only the magnetic flux generatedby the permanent magnet, but also the volumeof available space for the current conductorswhich are subjected to this magnetic flux.

In the electromagnetic transducer, we there-fore encounter an interaction between thefield created by the permanent magnet and thefield developed by the current-carrying con-ductors. Hence the factors to be taken intoaccount in seeking to attain optimum per-formance are the field strength of thepermanent magnet, the field strength of thecoil operating therewith (other factors remain-ing the same) and the mass of the magnet ele-ments.The characteristics of magnetic circuits and

magnetic materials of which they are made,are expressed in terms of certain magneticquantities and units which may be describedas follows:

Magnetornotive Force.In an electromagnet, magnetization is

accomplished by means of electric current inwindings linked with a magnetic circuit. Inan electromagnet of the type in question,the windings are those of the coil placed inthe annular gap of a magnetic circuit definedby a permanent rod coaxially supported with-in a cylindrical cup of high permeability. Thetotal measure of the magnetizing effect ofsuch a coil is called the “magnetomotive forceF”, the units of the force (mmf) being calledthe "gilbe ”.

Magnetic Flux.The total measure of the magnetized con-

ditions of a magnetic circuit, when acted uponby a magnetomotive force, is called the“magnetic flux mp”. It is characterized by thefact that a variation in its magnitude givesrise to an E.M.F. in an electric circuit linkedwith it. The E.M.F. thus induced is at anyinstant, directly proportional to the time rateof variation of the flux.

Magnetic Reluctance.That property of a magnetic circuit which

determines the relationship between themagmtic flux and the corresponding mmf, iscalled the “magnetic reluctance R” of thecircuit. It is defined by the followingequation:

F

"P =—:

R

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where ¢=magnetic flux, maxwells; F=mmf,gilberts; and R=magnetic reluctance in cgsunits.

Magnetizing Force.The mmf acting on a magnetic circuit is

distributed along its length in a manner deter-mined by the distribution of the windingsand the reluctance of the magnetic circuit. Themmf per unit length along the circuit is calledthe “magnetizing force H”, and is defined bythe following equation:

dFH=—,

d1,

where H=magnetizing force, oersteds; F:mmf, gilberts; and l=length, cm.

Magnetic Flux Density.This is the magnetic flux per unit area of a

section normal to the flux direction. The egsunit is called the “gauss”, and is defined by thefollowing equation:

atB: ,

dA

where B=magnetic flux density, gausses; ti):magnetic flux, maxwells; and A=area, sq. cm.

In order to utilize the permanent magnetin the magnetic circuit to best advantage, itis essential that the magnetic flux density Bbe uniform within magnet. It will be shownthat in the present magnetic circuit, whichinvolves a cylindrical cup configuration, adiminishing cross—section of the magnet fromthe cup end to the free end is necessary toattain a uniform flux density. Since as oneprogresses from the cup end to the free endof the magnet, flux emanates from the magnetat a rate determined by the reluctance of themagnetic circuit, one must so decrease thecross-section of the magnet whereby theresultant decreased amount of flux divided bythe decreased cross—sectional area, yields thesame flux density B at all points in themagnet, thereby optimizing the performance ofthe magnet. Moreover, the cross-section mustdecrease to zero at the tip of the magnet sothat all of the flux will have been restrictedto or will have emanated in the annular air

1).We shall begin by considering a transducer

having an ideal magnet which producesmagnetic flux and thereby generates amagnetic field in a working gap. This is doneunder ideal citeumstanccs; that is, withoutany leakage and hence with no loss of flux.In Fig. 5, there are shown two permanentmagnets ML and M2 which are spaced apart

to define an air gap in a magnetic circuitcompleted by a high—penneability, yoke-

shaped return member. The transducer is tooccupy a total volume V0, which is partmagnet, Vm, and part gap, Vg; hence

V0=Vm+VE.

The flux return volume and the wasted airvolume is neglected, a truly ideal situation.The flux conservation statement is as follows:

(1) BmAm=BgAz’

and the conservation of energy statement is:

(2) <DH.dl=05 HmLm=Hng=Bng,

realizing that the permeability of air isapproximately unity. After multiplyingequation (1) by equation (2), we obtain:

BmAm ' HZan=BgAg ' BEL;

01'

(3)

If we multiply this equation on the right byVg, and on the left by its equivalent, Vo—Vm,we obtain:

(4)

Assuming in our ideal system the absenceof flux leakage and that we are able toutilize all of the air gap with ideally placedconductors, then Vg, the volume of the gap,is a measure of the magnetic field generatedby the conductors as a result of a fixed currentflowing therein. On the further assumptionthat the size of the conductors and thereforethe number of turns per unit area is fixed,the quantity, Bng, or (BngY, is therefore theinteraction term that one seeks to maximize.Let us make the definition:

(5)

We can maximize this quantity with respectto magnet volume by differentiating and set-ting the result equal to zero. That is:

dq

BmHme=Bg2Vg

BmHme(Vu_V111):Bgzvzz

q=(Berf=BmHme(Vo_Vm).

=BmHm(_Vm+Vo_ m)=01de

01‘

Vm=VaI2~

With this result substituted in equation (5), weobtain:

Vo2qu=BmHm ' .

4 (5)

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This quantity may be further maximizedwith respect to the operating conditions ofthe magnet by designing for peak energy—product point operation. Of course, it is to berealized that there is no guaranty that thetwo optimization requirements could besimultaneously satisfied. In practice, therefore,the actual design would probably not occur ateither Vm=Vom or BmHm=maximum, for themagnetic material used. With given transducervolume dimensions as a working constraint,however, one would select a magneticmaterial to yield the maximum qu, there-fore achieving the best system possible. Theanalysis thus far has been concerned with anideal system and the results are intended toserve as theoretical guidelines.We shall now proceed to apply these teach—

ings to an electromagnetic transducer systemfor a mechanical vibrator such as a tuningfork or a reed. Practical considerations dictatea circular cross-section for the magnet and

' conductor coil, but this need not be the case.

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The prior-art transducer in Fig. 6, asapplied to a tuning fork, is of the cylindricalmagnet rod type, as shown in the above-identified Hetzel patents, and serves as agood approximation to the ideal system dis-cussed in connection with Fig. 5, in that theannular air gap G between, the centralmagnetic rod Ru and the cylindrical cup Cc,can be considered the working gap. Disposedin the gap is a cylindrical coil 8,.

This also applies to The transducer shownin Fig. 7, which is of the prior-art frusto-

(7)

We view this result as the differential equationprescribing the magnet profile, This formula—tion satisfies the criteria of (1), no flux outthe end of the cylindrical volume, and (2),constant flux density B (and H) in themagnetic material.

Solving this diflerential equation for y, withthe boundary conditions that y=o at z=L,and y=rn at z=0, leads to the algebraic pro-file equation:

22

(8) y2(1+210ge R/y)=32(l_F),

where

a2=r02(1+2 logG R/ru).

Having developed the qualitative shape ofthe magnet, it remains to determine thequantimtive dimensions necessary to maximizethe transducer efliciency. We can re—phrasethe original optimization problem for our par-

t-

d¢=2y2rdyB=mmf - conducmnce=(Hz)

conical or linear tapered type shown in theBennett et a1 patent, for most of the magneticflux spans the volume occupied by the con—ductors, i.e., relatively little leakage flux isgenerated. In the tapered rod construction, rodRt coaxially disposed within cup Cc operatesin conjunction with a similarly tapered coil

n.In discussing the ideal magnet in con-

nection with Fig. 5, no mention was made ofthe shape of the magnet. However, if there isto be no leakage and if a single Bm appliesto the entire magnet, then a constant cross-seetion is implied. But in a magnetic ele-ment having a cup configuration operating inconjunction with a coaxially—mounted magnetrod, a decreasing cross—section is desired inthe rod so that no flux extends out the endof the cylindrical volume. To this extent, thetapered rod in Fig. 7 is an improvement overthe cylindrical rod in Fig. 6.Of greater importance is that there be a

uniform flux density B within the magnet toutilize the magnet material to best advantage.This not only requires a decreasing cross-sectional area, but a rate of decrease whichis proportional to the rate at which flux flowsout of the magnet rod to the wall from theneutral or cup end of the rod to the freeend.

Reverting now to Fig. 4, which discloses thepresent invention, and considering a cylindricalhollow shell in the magnet, we can write theequivalent or Ohm’s Law for the magneticcircuit. The flux in the circuit is:

27rdZ

10%; (R/Y)

ticular application by writing the differentialform of the induced voltage:

do dzdE=dn - —=dn—_ _,

dt dz dtwhere

dn=(R—-A —y)?t2dz,

where A is a mechanical clearance betweenmagnet and conductors and where A2 is thewire density (turns per unit area). New

dz

’dt

(velocity of the coil relative to magnet), and

(1?)

dz

ZfiHZ

—,

logo (R/Y)

whence we have :

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L (R-A—Y)E=vf27A2———HzXdz=kv

5 lags (R/Y)

The quantity 6 is again a mechanical clearanceat the bottom of the cylindrical cup.The maximization problem then reduces to

determining the value for re, the radius ofthe magnet at its base, which will yield amaximum in E. For the case of a transduceras part of a mechanical vibrator, however,there is a further minor refinement necessary.If one examines the equation expressing thepower consumed by the vibrator with trans—ducer,

1 E2 E” m

2, 2R 2:; Qk’

(93

whereR=equivalent resistance of vibrator,E=induced voltage in transducer coil,o)=2w-frequeney of vibrator,n=efliciency of system,Q=quality factor of vibrator,m=mass of transducer and vibrator,k=electromechanical coupling factor; andp=power,

one sees that one should really maximize

k2

m

as opposed to k2. The quantity k has typicallybeen a measure of the quality of the trans-ducer, but one sees that if consumption ofpower is the foremost consideration, as it isin timepiece applications, then the quantitykz/m is the more important measure.A step-by—step variation of to, from a zero

value up to a maximum value dictated by thecylindrical cup dimensions, accompanied bya numerical integration of equation (9) and acalculation of m, will yield a curve for k2/mwhose maximum determines the choice of r,for the optimized transducer for the par-ticular magnetic material chosen.

It is understood that these teachings resultin both the quantitative and qualitative shapeof the magnet and conductor coil to optimizethe transducer efliciency, and further, it isappreciated that approximations to the curveof equation (8) such as mulfi-taper configura-tions in which the cross-seetion of the roddiminishes in a series of tapered steps, wherebythe flux density B is approximately uniform,can yield almost optimum results. Theseteachings therefore make possible the fabrica-tion of very small transducers Which canoperate on a minimum of power.

Comparative ImprovementIt has been determined, for a particular

small transducer size applicable to a ladies’tuning—fork watch movement, that a trans—ducer in accordance With the invention isstrikingly superior in its performance charac-teristics to known types of transducers of thecylindrical magnet rod and the frusto-conical magnet-rod type. The following tableshows the approximate comparison for thesethree types of transducers, having the samemagnetic-element cup sizes but differentmagnet rod shapes for a particular transducersize applicable to a ladies’ watch movementof the type envisaged.

Transducer Magnet Power to Drive ForkIn

Shape — in arbitrary unitsk2

Cylindrical 7.0Frustoconical 2.5Bullet—shaped

(Present Invention) 1.0

This table shows clearly the significance ofthe present invention. It indicates a 7:1reduction in power input required to operate atuning fork as a result of employing theoptimum transducer design of this invention,in comparison with the more conventionalcylindrical magnet shape. This, obviously, per—mits one to design a tuning—fork transducerdrive system with substantially smaller size(which would otherwise require much morepower because of reduced efficiency), yetrequiring less battery power and therefore asmaller battery, resulting in a much smallerwatch movement complete with self—containedbattery.

It should also be approciated that there aremany areas of application for electromagnetictransducers other than the tuning fork utiliza—tion described above, such as loud—spcakers,hearing aids, etc., and that for each applica—tion the electromagnetic transducer of thisinvention more optimally meets the require—ments of minimum electrical energy per unitvolume of transducer than does each of theexisting transducer types. An expression ofthis optimization on a comparative basis isshown in Table II where the electromagneticcoupling factor squared is given for the threetypes of magnet shapes discussed above.Again, the obvious improvement shows thesuperiority of the present invention.

TABLE IITransducer Magnet Relative Effectivity

Shape k2 in arbitrary unitsCylindrical .2Frustoconical .6Bullet—shaped

(Present Invention)

WHAT WE CLAIM IS:—1. An electromagnetic transducer compris-

1.0

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ing a magnetic element constituted by acylindrical cup of magnetic material havinga permanent—magnet rod fixedly supportedcoaxially therein to define an annular air gap,the rod having a cross-section whichdiminishes from the cup end of the rod to thefree end thereof in a non-linear manner toyield substantially the same flux density atall points in the rod, whereby all of theflux is substantially restricted to the air gap,and a multi—tum coil received within saidannular air gap, said magnetic element beingmovable relative to the coil, the cross-sectionof the coil substantially complementing theradially outer surface of the rod and theradially inner surface of the cup, thereby mak-ing possible the full use of the available spacewithin the gap.

2. A transducer according to claim 1, where—in the rod has a longitudinal profile which iscontinuously curved, the free end of the rodhaving a substantially zero eross-section.

3. A transducer according to claim 1 or 2,wherein the rod diminishes in cross—section ina series of tapered steps.

4. A transducer according to any one of thepreceding claims, wherein the coil is stationaryand the magnetic element is mounted on avibratory member to reciprocate the elementrelative to the coil.

5. A transducer according to any one ofthe preceding claims, wherein the cylindricalcup is longitudinally slotted on diametricallyopposed sides.

6. A transducer according to any one of thepreceding claims, wherein the rod is formed of

a material having a high value of residualmagnetic induction and coercive force, andthe cup is formed of a material having highflux permeability.

7. An electromagnetic transducer sub-stantially as hereinbefore described withreference to Figures 1 to 4 of the accompany:ing drawings.

8. An electronic watch provided with a tun-ing fork, means to convert the vibratory actionof the fork into rotary motion to drive thegearworks of the watch, and an electro-magnetic transducer as claimed in any one ofthe preceding claims, wherein the magneticelement of the transducer is mounted on onetine of the fork to vibrate therewith and thecoil is mounted at a stationary position inthe watch, and means to apply electricalpulses to the coil to sustain the fork in vibra—non.

9. An electronic watch including the trans-ducer of claim 7, substantially as herein-before described With reference to Figure 1of the accompanying drawings.

HASELTINE, LAKE & CO.,Chartered Patent Agents,

Hazlitt House,28, Southampton Buildings,

Chancery Lane,London WCZA lAT.

and9 Park Square,Leeds, LSl ZLH,

Yorks.Agents for the Applicants.

Printed for Her Majesty’s Stationery Oflice, by the Courier Press, Leamington Spa, 1974.Published by The Patent. Office, 25 Southampton Buildings, London, WC2A IAY, from

which copies may be obtained.

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1345359 COMPLETE SPECIFICATION

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