U.S. patent number 3,622,819 [Application Number 05/045,326] was granted by the patent office on 1971-11-23 for permanent magnet electromagnetic transducer.
This patent grant is currently assigned to Bulova Watch Company, Inc.. Invention is credited to Dale R. Koehler.
United States Patent |
3,622,819 |
Koehler |
November 23, 1971 |
PERMANENT MAGNET ELECTROMAGNETIC TRANSDUCER
Abstract
An electromagnetic transducer for actuating the tuning fork of
an electronic watch. The transducer is constituted by a magnetic
element secured to a tine of a fork which causes the element to
vibrate relative to a stationary multiturn coil. The magnetic
element is formed by a cylindrical cup having a rodlike permanent
magnet core supported coaxially therein to define an annular
airgap. The core diminishes in cross section from the cup end to
the free end thereof in a nonlinear manner such that the
longitudinal profile of the core is continuously curved or
nonlinearly tapered to produce a substantially uniform magnetic
flux density within the core, the cross section of the coil and its
longitudinal profile complementing that of the core.
Inventors: |
Koehler; Dale R. (Westwood,
NJ) |
Assignee: |
Bulova Watch Company, Inc. (New
York, NY)
|
Family
ID: |
21937237 |
Appl.
No.: |
05/045,326 |
Filed: |
June 11, 1970 |
Current U.S.
Class: |
310/25; 335/255;
968/483 |
Current CPC
Class: |
H02K
33/02 (20130101); G04C 3/102 (20130101) |
Current International
Class: |
H02K
33/02 (20060101); H02K 33/00 (20060101); G04C
3/00 (20060101); G04C 3/10 (20060101); H02k
033/02 () |
Field of
Search: |
;310/65,23,24,30,34,35,14,25 ;335/255,261,229,258,259 ;318/122-134
;58/23,23MV |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Duggan; D. F.
Claims
I claim:
1. An electromagnetic transducer comprising:
a. A magnetic element constituted by a cylindrical cup having a
permanent-magnet rod fixedly supported coaxially therein to define
an annular airgap, said rod having a cross section which diminishes
from the cup end of the rod to the free end thereof in a nonlinear
manner to yield substantially the same flux density at all points
in the rod, and
b. a multiturn coil received within said annular airgap, the cross
section of the coil substantially complementing that of the rod,
said magnetic element being movable relative to said coil.
2. A transducer as set forth in claim 1, wherein said rod has a
longitudinal profile which is continuously curved, the free end of
the rod having an approximately zero cross section.
3. A transducer as set forth in claim 1, wherein said rod
diminishes in cross section in a series of tapered steps.
4. A transducer as set forth in claim 1, wherein said coil is
stationary and said magnetic element is mounted on a vibratory
member to reciprocate the element relative to the coil.
5. A transducer as set forth in claim 1, wherein said cylindrical
cup is longitudinally slotted on diametrically opposed sides.
6. A transducer as set forth in claim 1, wherein said rod is formed
of a material having a high value of residual induction and
coercive force, and said cup is formed of a material having high
flux permeability.
7. An electronic watch provided with a tuning fork, means to
convert the vibratory action of the fork into rotary motion to
drive the gearworks of the watch, and means to sustain the fork in
vibration, said last-named means comprising:
a. an electromagnetic transducer including:
1. a magnetic element constituted by a cylindrical cup having a
permanent-magnet rod fixedly supported coaxially therein to define
an annular airgap, said element being mounted on one tine of the
fork to vibrate therewith, said rod having a cross section which
diminishes from the cup end to the free end thereof in a nonlinear
manner to yield substantially the same flux density at all points
in the rod, and
2. a multiturn drive coil received within said annular airgap, the
cross section of the coil substantially complementing that of the
rod, said coil being mounted at a stationary position in said
watch, and
b. means to apply electrical pulses to said coil to sustain said
fork in vibration.
Description
BACKGROUND OF THE INVENTION
This invention relates generally to electronically controlled
timepieces which incorporate electromagnetic transducers for
sustaining a tuning fork in vibratory motion, and more particularly
to an improved transducer structure that makes possible a
substantial reduction in the size of the timepiece.
In the patents to Hetzel Nos. 2,900,786 and 2,971,323, there are
disclosed electronic timepieces including a self-sufficient
timekeeping standard constituted by a tuning fork whose vibrations
are sustained by two electromagnetic transducers operating in
conjunction with a battery-energized transistor circuit. The
vibratory action of the fork is converted into rotary motion to
turn the time-indicating hands of the timepiece.
In timepieces of the type disclosed in the Hetzel patents, each
electromagnetic transducer is associated with a respective tine of
the fork, the transducer including a magnetic element attached to
the end of the tine and vibrating therewith. The magnetic element
on one tine reciprocates with respect to a stationary main drive
coil section, and that on the other tine moves back and forth with
respect to a stationary minor drive coil section and sensing coil.
The two drive coil sections are connected in series to the output
circuit of the transistor, while the sensing coil is connected to
the input thereof, whereby alternating voltage induced in the
sensing coil renders the transistor conductive to produce current
pulses in the drive coil sections for magnetically actuating the
tines.
When a battery-operated timepiece is to be confined within a small
watch casing or in a miniature housing of similar dimensions where
space is at a premium, it is essential that the electrical and
mechanical efficiency of the system be of exceptionally high order.
Otherwise any loss of energy, which in a large-scale device may be
negligible, can give rise to serious drawbacks in a more compact
structure. It is vital, therefore, that the transducer 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 action of the fork for a
prolonged period.
Because the sole source of energy for the timepiece is a
single-cell miniature battery, any factor which dissipates energy
or reduces efficiency not only cuts down the useful battery life,
but also creates operating difficulties. In order, therefore, to
create a highly compact timepiece, it is important that maximum use
be made of all available space and that the transducers which
actuate the fork be as small as possible without, however,
requiring an undue amount of power.
In the above-identified Hetzel patents, the transducer includes a
magnet element formed by a cylindrical cup having a circular cross
section, a permanent magnet rod or core of uniform cross section
being coaxially mounted within the cylinder to define an annular
airgap therein. The stationary drive or sensing coils associated
with the magnet element are received within the annular airgap,
whereby in operation, the magnetic element reciprocates with
respect to the coil. These transducers will hereinafter be referred
to as being of the cylindrical magnet rod type.
In the prior patent to Bennett et al. No. 3,221,190, there is
disclosed an improved transducer arrangement for a timepiece
generally of the type disclosed in said Hetzel patents. In this
Bennett et al. patent, the permanent magnet is not of uniform cross
section throughout its length, but is linearly tapered to assume a
frustoconical form, the coil received in the annular airgap being
similarly tapered in order to realize the greatest number of turns
within the airgap at the position therein of maximum flux density.
These transducers will hereinafter be referred to as being of the
frustoconical magnetic rod type.
While transducers of the frustoconical magnetic rod type are
distinctly superior to those of the cylindrical magnetic rod type,
they are not sufficiently efficient to make possible a reduction in
the dimensions of a watch to the point where a truly miniature or a
ladies' size tuning-fork watch movement becomes feasible.
The reason for this is that should one reduce the existing size of
a transducer of the cylindrical or frustoconical magnetic rod type,
a higher input power would be required to drive the same tuning
fork to compensate for the reduction in magnitude of the
electromechanical coupling (e.m.c.) factor. The e.m.c. factor is a
direct measure of the amount of electrical energy converted to
mechanical energy at the transducer interface and therefore the
smaller the e.m.c. factor, the larger the electrical power required
for a given amount of mechanical power. Hence, with a single-cell
battery of the type and size presently used in conjunction with
electronic timepiece movements, the cell would be exhausted in a
relatively short period. On the other hand, if a larger battery
cell is employed, this would be self-defeating, for the very
purpose of reducing the transducer size is to make a smaller watch;
hence, if the reduction in transducer size dictates the use of a
larger cell, then nothing has been gained. It must be borne in mind
that battery size is an important parameter in the overall size of
the timepiece, and that the existing dimensions of electronic
timepiece battery cells are a limiting factor in producing a
smaller watch movement.
In practice, a power requirement for a tuning-fork watch which is
in excess of about 15 microwatts cannot be satisfied within the
limits of a commercially acceptable watch volume. With transducer
designs of the type heretofore known, should the transducer be made
smaller to conserve space, the resultant increase in power
requirement would go beyond the tolerable limit due to an increase
in the fork amplitude. The improvement resulting from the
transducer design of this invention is manifested in both size and
power whereby the battery volume may be reduced markedly and
therefore the size of the watch movement.
SUMMARY OF THE INVENTION
In view of the foregoing, it is the main object of this invention
to provide electromagnetic transducers of exceptional efficiency
for actuating a tuning fork in an electronic watch, or for any
other appropriate purpose.
More specifically, it is an object of the invention to provide a
transducer whose magnetic element includes a permanent magnet rod
coaxially mounted in a cylindrical cup, the cross section of the
rod diminishing from the cup end to the free end in a nonlinear
manner causing the rod to assume a bulletlike shape which gives
rise to a substantially uniform magnetic flux density within the
rod.
Among the significant advantages of the transducer including a
bullet-shaped magnetic rod are the following:
A. because of its exceptional efficiency, one may reduce the size
of the transducer and thereby shrink the size of the associated
timepiece movement, and yet operate the timepiece with a material
decrease in the power requirement of the movement, thereby
effecting a decrease in battery size.
B. because the transducer is markedly more efficient than known
transducers, one may scale down the size of the battery and effect
a further reduction in volume of the timepiece without raising the
power requirement therefor beyond a tolerable limit.
c. Because the improved transducer makes it feasible to shrink the
size of the movement, it opens up many new design possibilities,
not only for ladies-model watches, but for other miniaturized
timing mechanisms.
D. though the transducer permits a marked reduction in the scale of
the movement, it does so without impairing the timing accuracy
thereof.
Briefly stated, these objects are attained in a transducer
including a magnetic element formed by a cylindrical cup having a
magnetic rod supported coaxially therein to define an annular
airgap, a multiturn coil being received in the gap. The rod
diminishes in cross section from its cup end to its free end in a
nonlinear manner, such that the longitudinal profile thereof is
continuously curved or otherwise nonlinearly tapered, to produce a
substantially uniform magnetic flux density within the rod, the
coil having a complementary cross section and longitudinal
profile.
OUTLINE OF THE DRAWING
For a better understanding of the invention, as well as other
objects and further features thereof, reference is made to the
following detailed description to be read in conjunction with the
accompanying drawings, wherein like components in the several
Figures are identified by like reference numerals. In the
drawings:
FIG. 1 is a schematic representation, in perspective of the basic
components of an electronic timepiece including a transducer in
accordance with the invention;
FIG. 2 is a separate view of the tuning-fork structure showing the
transducer partly in 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 magnetic transducer of the
frustoconical rod type.
DESCRIPTION OF THE INVENTION
Referring now to the drawings, and more particularly to FIG. 1, the
major components of a timepiece including a transducer in
accordance with the invention are a timekeeping standard
constituted by a tuning fork 10 and an electronic drive circuit 11
therefor, a rotary movement of conventional design including a gear
train 12 for turning the hands of the timepiece, and a motion
transformer including an index wheel 13 operatively intercoupling
fork 10 and the rotary movement, and acting to convert the
vibratory action of the fork into rotary motion. The tuning fork
has no pivots or bearings and its timekeeping action is therefore
independent of the effects of friction.
All of the electrical components of the drive circuit are mounted
on the unitized subassembly units or modules F.sub.1 and F.sub.2
attached to a disc-shaped metallic pillar plate 14 which may be
supported within a watch casing of standard design, or within any
other type of housing, depending on the use to which the timepiece
is put. Electronic circuit 11 is constituted by transistor TR
having a base, a collector and an emitter, a resistance-capacitance
biasing network R-C, and a bypass capacitor C.sub.b to prevent
parasitic oscillations of the circuit. The electronic circuit 11 is
energized by a voltage source in the form of a battery V.
Tuning fork 10 is provided with a pair of flexible tines 15 and 16
interconnected by a relatively inflexible base 17, the base being
provided with an upwardly extending stem 18 secured to the pillar
plate by suitable screws 19 and 20. The central area of the pillar
plate is cut out to permit unobstructed vibration of the tines.
The tuning fork is actuated by means of transducers T.sub.1 and
T.sub.2. Transducer T.sub.1 is constituted by a magnetic element 21
secured to the free end of tine 15, the element coacting with a
stationary drive coil 22 and phase-sensing coil 23. These coils are
wound on an open-ended tubular carrier 24 affixed to a subassembly
mounting from F.sub.1 which is secured to pillar plate 14. Coils 22
and 23 may be wound in juxtaposed relation on carrier 24, or the
phase-sensing coil 23 may be wound over drive coil 22.
The second transducer T.sub.2 is constituted by a magnetic element
25 secured to the free end of tine 16, and coacting with a drive
coil 26 wound on a tubular carrier 27.
The two transducers T.sub.1 T.sub.2 are of like design, except that
an additional coil is provided in transducer T.sub.1. The
construction and behavior of the transducers are similar to that of
a dynamic speaker of the permanent-magnet type, save that the
moving element is the magnet, and not the coil.
FIGS. 2 and 3 show transducer T.sub.1 in greater detail, and it
will be seen that magnetic element 21 is constituted by a
cylindrical cup 21a of magnetic material, such as iron, and a
permanent-magnet rod 21b coaxially mounted therein. Magnet 21b,
which may be made, for example, of Alnico, is supported on the end
wall of the cup to provide a magnetic circuit in which the lines of
magnetic flux extend across the annular airgap 21c defined by the
inner magnet and the surrounding cylinder. Rod magnet 21b is of
diminishing cross section from the cup end to the free end thereof,
to produce a longitudinal profile which is continuously curved, for
reasons which will be later explained.
As best seen in FIG. 3, cylindrical cup 21a is cut out
longitudinally along diametrically opposed planes to form slots 21d
and 21e. This effects a substantial reduction in the transducer
dimension with relatively little flux leakage. The cutouts act to
reduce the space occupied by the cups in depth within the casing,
and make possible a more compact construction of the timepiece. The
slots also prevent so-called "dash-pot" effects resulting from air
compression of the magnet-and-cup assembly. Such damping is avoided
by the slot openings and also by the openings in the tubular
carrier.
It will be seen that fixed carrier 24 for supporting the drive
coils 22 and 23 is horn shaped and is dimensioned to complement the
tapered magnet 21b. Carrier 24 and the drive coils supported
thereon are received within annular gap 21c and are spaced both
from the magnet and the surrounding cylinder, whereby the magnetic
element is free to reciprocate axially relative to the fixed
coil.
In operation, an energizing pulse applied to the drive coils of
transducers T.sub.1 and T.sub.2 will cause an axial thrust on the
associated magnetic element in a direction determined by the
polarity of the pulse in relation to the polarization of the
permanent magnet and to an extent depending on the energy of the
pulse. Since each magnetic element is attached to a tine of the
tuning fork, the thrust on the element acts mechanically to excite
the fork into vibration.
The vibratory action of the fork and the concomitant movement of
the magnetic element includes a back E.M.F. in the drive coil, and
in the case of transducer T.sub.1, in the phase-sensing coil as
well. Since the magnetic element reciprocates in accordance with
the vibratory action of the tuning fork, the back E.M.F. will take
the form of an alternating voltage whose frequency corresponds to
that of the tuning fork.
Three functions are served by the transducers. They drive the
tuning fork by converting pulses of current delivered to the coils
to mechanical pulses. They control the amplitude of the tuning fork
by sensing the alternating voltage induced during each cycle; and
they control the instant during the cycle when the drive pulse is
to be delivered to the coils.
Referring now to FIG. 4, the transducer in accordance with the
invention is shown in enlarged form to clarify the relationship of
the components thereof and the factors which come into play in
optimizing the design.
It will be seen that the permanent magnet rod 21b is coaxially
mounted within the cylindrical cup 21a which acts as a
high-permeability return member; an annular gap being defined by
the interior space between the rod and cup. In order to utilize the
magnet to best advantage, there must be a uniform flux density
within the magnet, and there must be no leakage flux escaping from
the magnetic element. In this connection, reference is made to the
article of S. Evershed--"Permanent Magnets in Theory and
Practice"--J. Institute of Electrical Engineers, 13 May 1920
(Volume 58,page 797).
Since as one progresses from the base or cup end of the magnet rod
to the free end or tip thereof, flux leaks out of the magnet at a
rate determined by the reluctance of the magnetic circuit, one must
decrease the cross section of the magnet so that the decreased
amount of flux in the magnet divided by the decreased
cross-sectional area, yields the same flux density at all points in
the magnet to attain optimum magnetic performance. Furthermore, the
cross section of the rod should diminish to zero at the tip,
whereby all of the flux will have been restricted to, or will have
emanated in the annular airgap within the cylindrical cup.
Thus the configuration of magnet rod 21b in FIG. 3 is such as to
provide a cross section which diminishes from the cup end to the
free end in a nonlinear manner such that the longitudinal profile
is continuously curved to produce a rod having a bullet like shape.
The cross section at the free end or tip is zero, thereby
minimizing flux leakage, and the curvature of the profile is such
as to yield the same flux density at all points in the magnet.
The shape of coils 22, 23 which occupy the airgap, complements that
of the magnetic element, so that the outer boundary of the coils is
cylindrical to conform to the inner surface of the cup, whereas the
inner boundary is curved to conform to the curvature of the rod. In
this way, full use is made of the available space within the
annular gap, the greatest number of coil turns being at the mouth
of the gap.
THEORETICAL AND DESIGN CONSIDERATIONS
In designing an electromagnetic transducer of the type in question,
with a view to optimizing its power performance, one must consider
not only the magnetic flux generated by the permanent magnet, but
also the volume of available space for the current conductors which
are subjected to this magnetic flux.
In the electromagnetic transducer, we therefore encounter an
interaction between the field created by the permanent magnet and
the field developed by the current-carrying conductors. Hence the
factors to be taken into account in seeking to attain optimum
performance are the field strength of the permanent magnet, the
field strength of the coil operating therewith (other factors
remaining the same) and the mass of the magnet elements.
The characteristics of magnetic circuits and magnetic materials of
which they are made, are expressed in terms of certain magnetic
quantities and units which may be described as follows:
Magnetomotive Force.
In an electromagnet, magnetization is accomplished by means of
electric current in windings linked with a magnetic circuit. In an
electromagnet of the type in question, the windings are those of
the coil placed in the annular gap of a magnetic circuit defined by
a permanent rod coaxially supported within a cylindrical cup of
high permeability. The total measure of the magnetizing effect of
such a coil is called "magnetomotive force F," the units of the
force (m.m.f.) being called the "gilbert."
Magnetic Flux.
The total measure of the magnetized conditions of a magnetic
circuit when acted upon by a magnetomotive force, is called the
"magnetic flux .phi.." It is characterized by the fact that a
variation in its magnitude gives rise to an E.M.F. in an electric
circuit linked with it. The E.M.F. thus induced is at any instant,
directly proportional to the time rate of variation of the
flux.
Magnetic Reluctance
That property of a magnetic circuit which determines the
relationship between the magnetic flux and the corresponding
m.m.f., is called the "magnetic reluctance R" of the circuit. It is
defined by the following equation:
.phi.=E/R,
where .phi. = magnetic flux, maxwells; F=m.m.f., gilberts;
and R = magnetic reluctance in c.g.s. units.
Magnetizing Force.
The m.m.f. acting on a magnetic circuit is distributed along its
length in a manner determined by the distribution of the windings
and the reluctance of the magnetic circuit. The m.m.f. per unit
length along the circuit is called the "magnetizing force H, " and
is defined by the following equation:
H=DF/dl,
where H = magnetizing force, oersteds; F -m.m.f. gilberts; and 1 =
length, cm.
Magnetic Flux Density.
This is the magnetic flux per unit area of a section normal to the
flux direction. The c.g.s. unit is called the "gauss," and is
defined by the following equation:
B=d.phi./dA,
where B = magnetic flux density, gausses; .phi. = magnetic flux,
maxwells; and A=area, sq. cm.
In order to utilize the permanent magnet in the magnetic circuit to
best advantage, it is essential that the magnetic flux density B be
uniform within the magnet. It will be shown that in the present
magnetic circuit, which involves a cylindrical cup configuration, a
diminishing cross section of the magnet from the cup end to the
free end is necessary to attain uniform flux density. Since as one
progresses from the cup end to the free end of the magnet, flux
emanates from the magnet at a rate determined by the reluctance of
the magnetic circuit, one must so decrease the cross section of the
magnet whereby the resultant decreased amount of flux divided by
the decreased cross-sectional area, yields the same flux density B
at all points in the magnet, thereby optimizing the performance of
the magnet. Moreover, the cross section must decrease to zero at
the tip of the magnet so that all of the flux will have been
restricted to or will have emanated in the annular airgap.
We shall begin by considering a transducer having an ideal magnet
which produces magnetic flux and thereby generates a magnetic field
in a working gap. This is done under ideal circumstances; that is,
without any leakage and hence with no loss of flux. In FIG. 5,
there are shown two permanent magnets M.sub.1 and M.sub.2, which
are spaced apart to define an airgap in a magnetic circuit
completed by a high-permeability, yoke-shaped return member. The
transducer is to occupy a total volume V.sub.0, which is part
magnet, V.sub.m, and part gap, V.sub.g ; hence
V.sub.0 =V.sub.m +V.sub.g.
The flux return volume and the wasted air volume is neglected, a
truly ideal situation. The flux conservation statement is as
follows:
(1) B.sub.m H.sub.m =B.sub.g A.sub.g, and
the conservation of energy statement is:
(2) .phi.H.sup.. dl= O; H.sub. m L.sub.m =H.sub.g L.sub.g =B.sub.g
L.sub.g,
realizing that the permeability of air is approximately unity.
After multiplying equation (1) by equation (2), we obtain:
B.sub.m A.sub. m .sup.. H.sub.m L.sub.m =B.sub.g A.sub.g .sup..
B.sub. g L.sub. g
or
(3) B.sub. m H.sub. m V.sub. m =B.sub. g .sup.2 V.sub..sub.g
If we multiply this equation on the right by V.sub. g, and on the
left by its equivalent, V.sub. o -V.sub. m, we obtain:
(4) B.sub. m H.sub. m V.sub. m (V.sub. o -V.sub. m)= B.sub. g
.sup.2 V.sub. g .sup.2
Assuming in our ideal system the absence of flux leakage and that
we are able to utilize all of the airgap with ideally placed
conductors, then V.sub.g, the volume of the gap, is a measure of
the magnetic field generated by the conductors as a result of a
fixed current flowing therein. On the further assumption that the
size of the conductors and therefore the number of turns per unit
area is fixed, the quantity, B.sub.g V.sub.g, or (B.sub.g
V.sub.g).sup..sup.2 , is therefore the interaction term that one
seeks to maximize. Let us make the definition.:
(5) q=(B.sub.g V.sub.g).sup.2 =B.sub.m H.sub.m V.sub.m (V.sub.o
-V.sub.m).
We can maximize this quantity with respect to magnet volume by
differentiating and setting the result equal to zero That is:
dq/dv.sub. m =B.sub.m H.sub.m (-V.sub.m +V.sub.o -V.sub.m )=O,
or
V.sub.m =V.sub. o/2.
With this result substituted in equation (5), we obtain:
(6) q.sub.max =B.sub.m H.sub.m .sup.. Vo.sup. 2 /4.
This quantity may be further maximized with respect to the
operating conditions of the magnet by designing for peak
energy-product point operation. Of course, it is to be realized
that there is no guaranty that the two optimization requirements
could be simultaneously satisfied. In practice, therefore, the
actual design would probably not occur at either V.sub.m =V.sub.0/2
, or B.sub.m H.sub.m = maximum, for the magnetic material used.
With given transducer volume dimensions as a working constraint,
however, one would select a magnetic material to yield the maximum
q.sub.max, therefore achieving the best system possible. The
analysis thus far has been concerned with an ideal system and the
results are intended to serve as theoretical guidelines.
We shall now proceed to apply these teachings to an electromagnetic
transducer system for a mechanical vibrator such as a tuning fork
or a reed. Practical considerations dictate a circular cross
section for the magnet and conductor coil, but this need not be the
case.
The prior art transducer in FIG. 6 as applied to a tuning fork, is
of the cylindrical magnet rod type, as shown in the
above-identified Hetzel patents, and serves as a good approximation
to the ideal system discussed in connection with FIG. 5, in that
the annular airgap G between the central magnetic rod R.sub.c and
the cylindrical cup C.sub.c, can be considered the working gap.
Disposed in the gap is a cylindrical coil S.sub.c.
This also applies to the transducer shown in FIG. 7, which is of
the prior art frustoconical or linear tapered type shown in the
Bennett et al. patent, for most of the magnetic flux spans the
volume occupied by the conductors, i.e., relatively little leakage
flux is generated. In the tapered rod construction, rod R.sub.t
coaxially disposed within cup C.sub.c operates in conjunction with
a similarly tapered coil S.sub.t.
In discussing the ideal magnet in connection with FIG. 5, no
mention was made of the shape of the magnet. However, if there is
to be no leakage and if a single B.sub.m applies to the entire
magnet, then a constant cross section is implied. But in a magnetic
element having a cup configuration operating in conjunction with a
coaxially mounted magnet rod, a decreasing cross section is desired
in the rod so that no flux extends out the end of the cylindrical
volume. To this extent, the tapered rod in FIG. 7 is an improvement
over the cylindrical rod in FIG. 6.
Of greater importance is that there be a uniform flux density B
within the magnet to utilize the magnet material to best advantage.
This not only requires a decreasing cross-sectional area, but a
rate of decrease which is proportional to the rate at which flux
flows out of the magnet rod to the wall from the neutral or cup end
of the rod to the free end.
Reverting now to FIG. 3, which discloses the present invention, and
considering a cylindrical hollow shell in the magnet, we can write
the equivalent of Ohm's Law for this magnetic circuit. The flux in
the circuit is:
We view this result as the differential equation prescribing the
magnet profile. This formulation satisfies the criteria of (1), no
flux out the end of the cylindrical volume, and (2), constant flux
density B (and H) in the magnetic material.
Solving this differential equation for y, with the boundary
conditions that y=o at z=L, and y=r.sub.o at z=0, leads to the
algebraic profile equation:
(8) y.sup.2 (1+2 log.sub.e R/y= a.sup.2 (1-Z.sup.2 / L.sup.2),
where
a.sup.2 =r.sub.o.sup.2 (1=2log.sub.e R/.sub.r ).
Having developed the qualitative shape of the magnet, it remains to
determine the quantitative dimensions necessary to maximize the
transducer efficiency. We can rephrase the original optimization
problem for our particular application by writing the differential
form of the induced voltage:
dE=dn.sup. . d.phi./dt =dn d.phi./dz dz/dt,
where
dn=(R-.DELTA.-y) .lambda..sup.2 dz,
where .DELTA. is a mechanical clearance between magnet and
conductors and where .lambda..sup.2 is the wire density (turns per
unit area). Now dz/dt= v (velocity of the coil relative to magnet),
and
whence we have,
The quantity .epsilon. is again a mechanical clearance at the
bottom of the cylindrical cup.
The maximization problem then reduces to determining the value for
r.sub.0, the radius of the magnet at its base, which will yield a
maximum in E. For the case of a transducer as part of a mechanical
vibrator, however, there is a further minor refinement necessary.
If one examines the equation expressing the power consumed by the
vibrator with transducer,
where R = equivalent resistance of vibrator,
E = induced voltage in transducer coil
.omega. = 2.pi. .sup.. frequency of vibrator,
.eta. = efficiency of system,
Q = quality factor of vibrator,
m = mass of transducer and vibrator,
k = electromechanical coupling factor; and
P = power,
one sees that one should really maximize k.sup.2 / m as opposed to
k.sup.2. The quantity k has typically been a measure of the quality
of the transducer, but one sees that if consumption of power is the
foremost consideration, as it is in timepiece applications, then
the quantity k.sup.2 /m is the more important measure.
A step-by-step variation of r.sub.o, from a zero value up to a
maximum value dictated by the cylindrical cup dimensions,
accompanied by a numerical integration of equation (9) and a
calculation of m, will yield a curve for k.sup.2 / m whose maximum
determines the choice of r.sub.o for the optimized transducer for
the particular magnetic material chosen.
It is understood that these teachings result in both the
quantitative and qualitative shape of the magnet and conductor coil
to optimize the transducer efficiency, and further, it is
appreciated that approximations to the curve of equation (8) such
as multitaper configurations in which the cross section of the rod
diminishes in a series of tapered steps, whereby the flux density
Bis approximately uniform, can yield almost optimum results. These
teachings therefore make possible the fabrication of very
physically small transducers which can operate on a minimum of
power.
COMPARATIVE IMPROVEMENT
It has been determined, for a particular small transducer size
applicable to a ladies' tuning-fork watch movement, that a
transducer in accordance with the invention is strikingly superior
in its performance characteristics to known types of transducers of
the cylindrical magnet rod and the frustoconical magnetic rod type.
The following table shows the approximate comparison for these
three types of transducers, having the same magnetic-element cup
sizes but different magnet rod shapes for a particular transducer
size applicable to a ladies' watch movement of the type
envisioned.
Transducer Magnet Shape Power to Drive Fork m/k .sup.2 in arbitrary
units Cylindrical 7.0 Frustoconical 2.5 Bullet-shaped (Present
Invention) 1.0
This table shows clearly the significance of the present invention.
It indicates a 7:1 reduction in power input required to operate a
tuning fork as a result of employing the optimum transducer design
of this invention, in comparison with the more conventional
cylindrical magnet shape. This, obviously, permits one to design a
tuning-fork transducer drive system with substantially smaller size
(which would otherwise require much more power because of reduced
efficiency), yet requiring less battery power and therefore a
smaller battery, resulting in a much smaller watch movement
complete with self-contained battery.
It should also be appreciated that there are many areas of
application for electromagnetic transducers other than the tuning
fork utilization described above, such as loud speakers, hearing
aids, etc., and that for each application the electromagnetic
transducer of this invention more optimally meets the requirements
of minimum electrical energy per unit volume of transducer than
does each of the existing transducer types. An expression of this
optimization on a comparative basis is shown in table II where the
electromagnetic coupling factor squared is delineated for the three
types of magnet shapes discussed above. Again, the obvious
improvement speaks to the superiority of the present invention.
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Table II
Relative Effectivity Transducer Magnet Shape k.sup.2 in arbitrary
units
__________________________________________________________________________
Cylindrical 0.2 Frustoconical 0.6 Bullet-shaped 1.0 (Present
Invention)
While there has been shown and described a preferred embodiment of
electromagnetic transducer in accordance with the invention, it
will be appreciated that many changes and modifications may be made
therein, without, however, departing from the essential spirit of
the invention.
* * * * *