[0001] The invention relates to underwater electroacoustic transducers, and more particularly
to improvements in flexural-bar type acoustic sources for use in sonar systems. The
present invention is concerned with improvements in the design of a modified "free-free"
flexure bar transducer element, a vibratile element that thereafter sometimes is called
"FLEXBAR" to distinguish it from the common "bender-bar" sonar projector element.
BACKGROUND OF THE INVENTION
[0002] Past efforts were concentrated to a very large extent on the so-called "bender-bar"
transducer, which is a flexural-bar with "hinged-hinged" end conditions. In spite
of those efforts, a number of inherent, generic problems remain. The bender-bar mountings,
for example, inevitably result in loss of power due to structure-borne vibration and
can create a severe ship or submarine habitability problem for hull-mounted transducer
arrays. In addition, for hull-mounted, deployable, and towable sonar projector arrays,
the bender-bar coupling through its mounting results in complex, spurious modal response
that aggravates the array mutual impedance problems, severely limits the acoustic
power output, and often results in unwanted back radiation.
[0003] The theoretical end conditions for an ideal hinged-hinged flexure bar (the bender-bar)
are: (1) the end deflections must be zero (y = 0 for x = 0 and x = L), and (2) the
end bending moments must be zero (d²y/dx² = 0 for x = 0 and x = L). The extensive
prior art has evolved three principal mounting designs for bender-bars: viz: (1) the
pin-hinge; (2) the flange-hinge; and (3) the leaf-hinge. To some degree all three
design approaches can be made to yield end bending moments that are small, but none
of these can achieve the other requirement of end deflections being small, without
adding excessive mass to the mounts. Attempts have also been made to cancel the reaction
of the bender-bar on its mounting by utilizing a second bender-bar vibrating in opposite
(180°) phase. This is an expensive solution, since it doubles the number of bender-bars,
and of course, doubles the weight. Furthermore, it is of limited value since it is
virtually impossible to match bender-bars so as to have equal amplitude and opposite
phase (180°) over the required frequency band pass. This crowded prior art is set
forth in some detail in a book "The Flexural Bar Transducer" written by R. S. Wollett
and published by the Naval Underwater System Center, New London, CT, in 1986.
SUMMARY OF THE INVENTION
[0004] The conventional wisdom of the sonar community has been that, "The free-free bar
is free of external applied forces or reaction forces ... such a bar has no useful
applications as an underwater transducer". (R. S. Woollett,
The Flexural Bar Transducer, 1986, p. 203). This viewpoint presumeably has its origins in the fact that, unmodified,
the free-free flexure bar radiates as an acoustic dipole with the concomitant poor
radiation loading. The present invention relates to a method and means for modifying
the free-free bar so that it radiates as a monopole, with greatly improved radiation
loading. At the same time, the modified free-free bar retains the unique properties
of being (a) nodally mounted and (b) dynamically balanced. As a direct result of these
properties, the modified free-free bar has substantially zero mechanical reaction
on its mounts, and exhibits essentially no structure-borne vibration. These characteristics,
together with high efficiency, relatively low cost and other related properties, make
this transducer element demonstrably superior to the bender-bar in virtually all sonar
projector applications. To distinguish this innovative modified free-free flexure
bar from the conventional hinged-hinged "bender-bar". The name "FLEXBAR" will be used
throughout the remaining portions of this patent specification.
OBJECTS OF THE INVENTION
[0005] It is a principal object of the invention to provide a flexure bar sonar projector
element that overcomes the inherent, generic problems of the bender-bar element; viz,
problems associated with mechanical reaction on its mountings. This object is achieved
by the invention as characterized in the independent claims. This invention prevents
acoustic radiation from said outer portions which would be out of phase with said
acoustic radiation from said central portion; and thus allowing the said underwater
acoustic transducer to radiate acoustic energy into the water essentially as a monopol,
rather than a dipole.
[0006] Further objects of the invention are to provide a flexure bar sonar projector element
that:
- has true nodal mounts ("keep your nodes clean"),
- has a simple, fundamental free-free bar flexure resonant mode ("keep your modes clean"),
- is dynamically balanced (virtually no reactive forces on its mountings),
- has a high electromechanical coupling coefficient ( 0.3 to 0.6)
- has a high electroacoustic efficiency ( 70%),
- can be effectively mechanically biased (for high-power applications),
- is mechanically tunable (over ∼1 octave),
- is suitable for almost any acoustic array configuration plane, cylindrical, spherical,
conformal, etc.),
- is suitable for low-frequency arrays (over a range, 20 Hz to 2000 Hz),
- is suitable for high-power array, (e.g., 0.5 mega watts acoustic output),
- is suitable for broad-band arrays (∼1 octave),
- can be utilized in surface ship or submarine sonar projector arrays (either sonar
dome arrays or conformal arrays),
- can be designed for use as an acoustic source for towed sonars or deployable sonars
(e.g., active sonobuoys),
- is capable of high acoustic power-to-weight ratios typically 20 to 30 watts/pound,
in water),
- exhibits unilateral acoustic radiation (one face only) with a high front-to-back radiation
ratio (∼60 dB),
- has excellent heat dissipation (a direct thermal path to the ocean), and
- is both easy to fabricate and easy to maintain quality control (individual elements
can be readily mechanically tuned to within ∼1 Hertz).
[0007] Preferred details and embodiments of the invention are described in the dependent
claims.
[0008] Other objects and advantages of the invention will become apparent by perusal of
the following detailed description and the attendant figures and claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] The present invention is illustrated by the accompanying drawings of which:
- Fig. 1
- is a schematic sketch of a free-free bar vibrating in flexure at its lowest mode;
- Fig. 2
- is a schematic sketch of a free-free bar nodally mounted in a water-tight housing
and radiating underwater as an acoustic "dipole";
- Fig. 3
- is a schematic sketch of a modified free-free bar vibrating in its lowest mode;
- Fig. 4
- is a schematic sketch of a modified free-free bar nodally mounted in a water-tight
housing and radiating underwater as an acoustic "monopole";
- Fig. 5
- is an isometric sketch showing a preferred embodiment of a piezoceramic FLEXBAR;
- Fig. 6-A
- is a top view of the "wedge" method of applying a precompression mechanical bias to
the piezoelectric stacks of the FLEXBAR;
- Fig. 6-B
- is a side-view section of the "wedge" method shown in Fig. 6-A;
- Fig. 7
- is a sketch showing the "taper-pin" method of applying a precompression mechanical
bias to the piezoceramic stacks of the FLEXBAR;
- Fig. 8
- is a sketch showing the "taper-threaded plug" method of applying a precompression
mechanical bias to the piezoceramic stacks of the FLEXBAR;
- Fig. 9-A
- is a top-view of a FLEXBAR designed for a resonant frequency of ∼1 KHz;
- Fig. 9-B
- is a side-view of the FLEXBAR of Fig. 9-A;
- Fig. 9-C
- is an end-view of the FLEXBAR of Fig. 9-A;
- Fig. 10
- is a curve showing the relative displacement of the center of the FLEXBAR of Fig.
9-B measured in air, as a function of frequency;
- Fig. 11
- is a curve showing the relative displacement along the FLEXBAR of the FLEXBAR of Fig.
9-B, measured in air, as a function of distance along the bar;
- Fig. 12
- is a curve showing the total impedance of the FLEXBAR of Fig. 9-B measured in air,
as a function of frequency;
- Fig. 13
- is a curve showing the resonant frequency and the location of the nodes for the FLEXBAR
of Fig. 9-B as a function of total added mass;
- Fig. 14
- is a curve showing the electromechanical coupling coefficients of the FLEXBAR design
of Fig. 9-B as a function of total added mass for both k₃₃ and k₃₁ construction;
- Fig. 15
- is an exploded sketch showing the principal components of a sonar transducer module
comprised of a plurality of FLEXBARs and termed a "FLEXDUCER" module;
- Fig. 16-A
- is a top view of a FLEXDUCER module comprised of 5 FLEXBARS of the design of 9-B;
- Fig. 16-B
- is an end view of the FLEXDUCER module of Fig. 16-A;
- Fig. 16-C
- is a side view of the FLEXDUCER module of Fig. 16-A;
- Fig. 17-A
- is a top-view sectional sketch showing design details of a FLEXBAR mounting;
- Fig. 17-B
- is a side-view sectional sketch showing design details of a FLEXBAR mounting;
- Fig. 17-C
- is an end-view sketch showing design details of FLEXBAR mountings;
- Fig. 18
- is an equivalent circuit representation of the FLEXDUCER module of Fig. 16-A;
- Fig. 19
- are curves showing both the measured and calculated transmitting response of the FLEXDUCER
module of Fig. 16-A;
- Fig. 20
- shows the computed maximum acoustic power output and the mechanical Qm of a rectangular
sonar array, comprised of a plurality of FLEXDUCER modules of Fig. 16-A as a function
of the number of modules in the array;
- Fig. 21
- compares the measured housing vibration transmissibilities for a transducer module
comprised of FLEXBARs and a transducer module comprised of the equivalent bender-bars;
- Fig. 22
- shows the piezoceramic plate means (k₃₁) for driving a FLEXBAR;
- Fig. 23
- shows the piezoceramic stack means (k₃₃) for driving a FLEXBAR;
- Fig. 24
- shows the piezoceramic stripe-plate means (ksp) for driving a FLEXBAR;
- Fig. 25-A
- shows the drilled-hole means for mechanically tuning a FLEXBAR;
- Fig. 25-B
- shows the filled-hole means for mechanically tuning a FLEXBAR;
- Fig. 25-C
- shows the added-plate means for mechanically tuning a FLEXBAR;
- Fig. 26-A & Fig. 26-B
- show the slotted-plate means for mechanically tuning a FLEXBAR;
- Fig. 26-C
- shows the tuning-slug means for mechanically tuning a FLEXBAR;
- Fig. 27-A & Fig. 27-B
- show the fixed-pin means for nodal mounting of a FLEXBAR;
- Fig. 27-C
- shows the fixed-tab means for nodal mounting of a FLEXBAR; and
- Fig. 28
- shows the auto-nodal means for nodal mounting of a FLEXBAR.
PRINCIPLE OF THE FLEXBAR
[0010] The basic principle of the invention, the FLEXBAR sonar projector element, can be
readily understood by referring to Fig. 1 through Fig. 4. Fig. 1 depicts an ideal
elastic uniform free-free bar 1 excited by some means so as to vibrate freely in its
lowest, fundamental flexure mode. Under this condition two nodes 2 develop, which
represent points (or lines) of no vibration. The section of the bar between the nodal
points vibrates in opposite phase to the outer sections; i.e. when the center section
is flexing upward, the outer sections are flexing downward, and vice versa. Since
no external forces are acting on the bar, the total momentum (both translational and
rotational) must be zero; and this leads to the requirement that the total momentum
of the center section must be equal (and of opposite phase) to the sum of the total
momentum of end sections.
[0011] This requirement is sufficient to determine the location of the nodal points, as
shown in Fig. 1, and thus, the nodal spacing is ℓ = 0.552 x L, where L is the overall
length of the bar.
[0012] One of the interesting properties of the free-free bar is that it can be hung from
its nodal points 2 by threads 3 from overhead supports 4; then, when the bar is excited
in high amplitude vibrations at its fundamental frequency, the threads experience
no vibratory reaction forces, and are subjected only to the static force corresponding
to the weight of the bar.
[0013] Fig. 2 shows a schematic representation of a free-free bar as an underwater acoustic
source. The free-free bar 1 is mounted on its nodal points 2 by means of suitable
mounting brackets 5 in an appropriate housing 6. An acoustically transparent rubber
window 7 is bonded to the radiating surface of the bar and to the housing so as to
form a water-tight seal, while at the same time allowing the bar to vibrate relatively
freely. Air which may be at the same pressure as the water, depending on the depth,
fills the interior of the housing, resulting in acoustic radiation into the water
only.
[0014] Under these conditions, the free-free bar transducer radiates as a dipole, since
the center section is vibrating 180° out of phase with the outer sections. As the
center section of the bar moves up, it increases the water pressure as indicated by
the symbol +⃝; while at the same time the outer sections move down, decreasing the
adjacent water pressure, as indicated by the symbol ⊝. The reverse takes place on
the succeeding portion of the vibration, when the center section is moving down and
the outer sections are moving up. Thus much of the kinetic energy of the vibrating
bar is wasted by hydrodynamically sloshing water back and forth between the adjacent
zones. Such behavior interferes with the primary compressional acoustic waves and
results in the poor acoustic radiation loading characteristic of a dipole source.
[0015] Consider now Fig. 3, where the outer sections 8A and 8B of the free-free bar 8 of
length L are "bent" down at the nodal points 2 at right angles to the center section.
If such a modified free-free bar is set into vibratory motion, it will have substantially
the same resonant frequency and substantially the same location of nodal points as
the original free-free bar. This results from the fact that the total inertia about
the nodes of the "bent" ends sections are the same as the original straight end sections.
In effect, the free-free bar sees "phantom" straight end sections. The modified free-free
bar can also vibrate freely when suspended by threads.
[0016] The free-free bar can be further modified by shortening the "bent" end section and
increasing their cross-section and mass so as to maintain the same total inertia about
the nodal points. This further modified free-free bar will still vibrate at the same
fundamental resonant frequency as the original free-free bar, and with the same locations
of nodal points. Such a flexure bar is designated a "FLEXBAR".
[0017] Fig. 4 is a schematic representation of a FLEXBAR, as an underwater acoustic source.
The FLEXBAR 9 is mounted on its nodal points 2 by suitable mounting brackets 5 in
an appropriate housing 10. A combination cover-window 11 is bonded to the radiating
surface of the FLEXBAR so as to form a water-tight seal. The end-section masses have
clearance from the cover plate in those areas 12 beyond the nodal points so that the
FLEXBAR can vibrate freely. As before, the interior of the housing is air-filled so
that the FLEXBAR radiates only into the water.
[0018] In this configuration, the center section between nodes is the only section of the
FLEXBAR that is acoustically coupled to the water. The out-of-phase modified end sections
vibrate entirely in the air-filled housing and are effectively decoupled from the
water. This results in the desired monopole radiation, while at the same time the
FLEXBAR is nodally mounted and essentially dynamically balanced. Thus, the FLEXBAR
exhibits excellent radiaton characteristics and virtually no reaction forces on the
mountings and mechanical coupling to the housing.
[0019] This improvement of the free-free flexure bar has unexpected, profound, and far-reaching
consequences on the performance of low-frequency, high-power, broad-band sonar transducer
arrays.
[0020] As Fig. 4 shows, when the center section flexes upward the outer sections 8A and
8B flex inward therewith compressing the air under the center section. This assists
the upward flexing of the center section. When the center section flexes downward
and the outer sections flex outward, the same enhancing effect appears with opposite
phase.
[0021] The preferred embodiment of the invention is an electroacoustic underwater transducer
element that is basically a piezoceramic "free-free" flexure bar, but modified so
as to radiate as a "monopole" rather than as a "dipole", and retaining the unique
properties of being nodally mounted and dynamically balanced. One of the important
consequences is the fact that the reaction forces on the modified flexure bar mountings
and the concomitant structure-borne vibrations, are virtually eliminated.
A PREFERRED EMBODIMENT OF THE PIEZOCERAMIC FLEXBAR
[0022] A preferred embodiment of the FLEXBAR is shown in Fig. 5. It is of trilaminar construction;
the center lamina of which is a metal bar 13 of generally rectangular cross-section,
with a relatively thin center web 14 and enlarged ends 15. Electrical insulation 16
and 17 line the inner sections of the metal bar, forming a top and bottom opening.
Two outer laminae 18-A and 18-B consisting of a plurality of piezoceramic blocks with
suitable electrodes 19 and assembled with appropriate polarity, are placed in the
top and bottom openings. The whole assembly, including the metal bar 13, the insulation
16 and 17, and the piezoceramic blocks 18-A and 18-B are consolidated into a solid
composite bar by means of an electrically insulating cement. Electrical leads 20 are
connected to the piezoceramic block electrodes 19 with appropriate polarity, with
the leads 21-A and 21-B extending out from the inside bottom of the bar. Tuning masses
22 are attached to the bar end sections 15 by means of bolts 23. Metal mounting pins
24 with rubber tubing covers 25 are inserted into nodal holes 26 located on the center
line of the bar at the nodal planes 27. In order to minimize tensile strain in the
brittle piezoceramic blocks, they are subjected to a precompression mechanical bias
during assembly by means of the metal bias-blocks 28 ... said precompression being
measured by resistance strain gages 29 cemented to the center-web 14 both top and
bottom. Metal-clad plastic plates 30 are cemented to the top and bottom of the bar
to enhance its shock resistance. Finally, electrical conductors 20 leading from the
piezoceramic blocks are entirely imbedded in high dielectric strength cement in order
to avoid electrical breakdown and corona discharge under the high drive voltages.
[0023] Three different configurations of mechanical bias blocks were found useful in applying
precompression bias to the piezoceramic blocks. The first of these methods is biased
on the use of wedges as shown in Fig. 6-A and Fig. 6-B. Here, pairs of wedges 31 and
32 are inserted, top and bottom, at one end of the metal bar 13 between the piezoceramic
stacks 18-A and 18-B and both of the shoulders of the enlarged bar end section 15.
Electrical insulating pads 17 between the wedge-pairs 31 and 32 and the piezoceramic
stacks 18-A and 18-B insulate the stacks from the bar ground potential. Each wedge
has one parallel face and one inclined face and all inclined faces have the same incline
angle. The wedge-pairs are assembled with the inclined faces mated. More-or-less equal,
inward forces are applied along the main axis of the wedge-pairs (at right angle to
the main bar axis), forcing the piezoceramic stacks against the shoulders of the enlarged
bar end section 15 at the opposite end of the metal bar. This results in tension stress
in the bar center web 14 and compression stress in the piezoceramic stacks 18-A and
18-B. The amount of precompressional stress in the piezoceramic stack can be controlled
by the incline angle of the wedges, the force applied to the wedges, the cross-sectional
area of the center web and the tension modulus of the material of the center web.
The strain gages 29 shown in Fig. 5 are used to measure the tension force in the web,
which, of course, equals the compressive force in the piezoceramic stack. The whole
process is most easily accomplished if the piezoceramic stacks 18-A and 18-B are preassembled
with their insulation 16 and 17 cemented in place. The cement is then applied between
the center web 14 and the insulating plates 16. The stacks 18-A and 18-B are then
placed on the bar and put into compression. The cement joint between the web 14 and
the insulating plates 16 is allowed to set up with the stacks under compression, thus
avoiding an unwanted shear stress in this cement joint. The protruding end of the
wedges can then be cut off along the dotted lines 33.
[0024] An alternative means for applying precompression is shown in the sectional sketch
of Fig. 7. Here a pair of mechanical bias blocks 34 with tapered holes drilled into
each end of the block pair are inserted between the piezoceramic stack 18 (with end
insulating pad 17) and the shoulder of the enlarged end section 15 of the bar. The
blocks are forced apart by driving two taper-pins 35 into the tapered holes, resulting
in precompression of the piezoceramic stack (and tension in the bar center web). In
the somewhat similar method of Fig. 8, the tapered holes in the blocks 36 are threaded
and tapered, threaded plugs 37 are screwed into the blocks, forcing them apart and,
thus, precompressing the piezoceramic stack. As before, the protruding ends of the
taper-pins or threaded-plugs can be removed after the inner cement joints have fully
set-up.
[0025] The FLEXBAR shown in Fig. 5 can be set into flexural vibration by applying an alternating
electrical voltage to the terminals 21-A and 21-B. Since the piezoceramic stacks 18-A
and 18-B are oppositely polarized, one-half cycle of the resulting alternating current
causes the upper stack to expand and the lower stack to contract; and in the next
half of the cycle the opposite occurs. This results in the bar being driven in flexural
vibration at the frequency of the applied alternating current. The amplitude of vibration
is a maximum at the resonant frequency (lowest mode) of the FLEXBAR, which is given
by the approximate formular:

where:
- f₀ =
- the resonant frequency of the bar (Hz)
- a =
- the thickness of the bar (inches)
- l =
- the nodal length (inches)
- c =
- effective longitudinal velocity of the bar (in/sec)
[0026] Fig. 9-A, Fig. 9-B, and Fig. 9-C are, respectively; the top-view, the side-view,
and the end-view of an assembly drawing of a FLEXBAR designed for a resonant frequency
of ∼1000 Hz. The FLEXBAR 15 with a skeleton of brass has a nodal length of 190,5 mm
(7½"), an over-all length of 279,4 mm (11"), a thickness of 38,1 mm (1½"), and a width
of 57,1 mm (2¼"). The two ends of the bar have a reduced width of 44,45 mm (1 3/4")
to accommodate a mounting lug between adjacent FLEXBARs. Brass tuning weights 22 are
bolted to each end. Copper-clad glass-filled epoxy plates 30 are cemented to the top
and bottom of the bar in order to insulate the electrode ends and to "shock-harden"
the bar. The total weight of the FLEXBAR of this design is approximately 4,42 kg (9.75
lbs.).
OPERATIONAL CHARACTERISTICS OF THE FLEXBAR
[0027] Fig. 10 shows a typical measured relative (rms) displacement, in decibels, of the
center of the FLEXBAR of Fig. 9-B as a function of frequency. In this case the bar
was measured in air and exhibited resonance at the design frequency. The high mechanical
Qm ≃ 130 indicates that the bar has very low internal mechanical losses. Fig. 11 shows
the measured relative displacement along the same FLEXBAR driven at its resonant frequency.
The nodes are well defined and some 60 db below the center deflection. Fig. 12 shows
the measured total impedance vs. frequency of the same FLEXBAR with a typical resonance-antiresonance
at ∼1 KHz. The next higher mode at ∼2.75 KHz is nearly suppressed, but discernable,
and the third mode at ∼5.4 KHz, is also discernable. Above 10 KHz the bar breaks up
into a number of complex resonant modes.
[0028] One of the remarkable and unique properties of the FLEXBAR is its capability of being
mechanically tuned over approximately an octave, as shown in Fig. 13. This also represents
experimental data obtained for the FLEXBAR shown in Fig. 9-B. The resonant frequency
with no added "tuning" masses is ∼1350 Hz, and this frequency is systematically reduced
as mass is added. For a total added mass of 2500 grams (sum of mass at both ends).
The resonant frequency is reduced to ∼660 Hz, or approximately 1 octave lower. Also
shown in Fig. 13, is the effect of added mass on the location of the nodal points.
The effect is relatively small for such a wide range of frequencies representing approximately
± 12,7 mm (± 0.5 inches) from the location for the design frequency. Since the nodal
mounting pins 24 of Fig. 5 are decoupled from the vibrating FLEXBAR by means of the
compliant rubber sleeve 25, the small movement of the nodal point location has little
effect on the performance of the bar. For the design frequency of 1000 Hz, the total
added mass is approximately 1200 g, or 600 g on each end. As can be seen from Fig.
14, this wide range of added mass has negligible effect on the electromechanical coupling
coefficient of the FLEXBAR.
[0029] An important consequence of these unique properties is the fact that production runs
of FLEXBARs can be easily all tuned to the same nominal design frequency by adding
or subtracting small amounts of mass from the end tuning masses. This results in improved
quality control and reduced cost.
A FLEXBAR TRANSDUCER: THE FLEXDUCER
[0030] A FLEXBAR sonar transducer is comprised of one or more FLEXBARs, nodally mounted
in a suitable water-tight housing, and acoustically coupled to the water through a
sound-transparent rubber window. Fig. 15 is a schematic sketch showing the principal
parts comprising such a transducer: the cover plate 38 has a bonded sound-transparent
rubber window 39 with bolt holes 40; an ensemble of FLEXBARs 41 with nodal mounting
pins 42; and a flanged housing 43 with an electrical cable 44. In order to distinguish
such a FLEXBAR transducer from one comprised of bender-bar elements, it is named it
a "FLEXDUCER", and this terminology will be used throughout the rest of this specification.
Fig. 16-A, Fig. 16-B, and Fig. 16-C are, respectively, the top-view, the end-view,
and the side-view of a FLEXDUCER module comprised of 5 FLEXBARs of the design shown
in Fig. 9-B having element performance characteristics delinated above. Fig. 17-A,
Fig. 17-B, and Fig. 17-C are, respectively, the top-view, the side-view, and the end-view
of sectional sketches showing certain design details of the FLEXDUCER construction.
In this design, the FLEXBARs 41 are mounted by means of their rubber covered nodal
pins 42 to mounting lugs 46 rigidly attached (actually cast) to the cover plate 38.
Thus, all 5 of the FLEXBARs are preassembled to the cover plate, and the sound-transparent
rubber window 39 is then molded to the cover plate and the radiating face of the FLEXBARs.
The finished cover plate subassembly, after proper electrical connections are made
to the driving cable, is then mounted onto the flange of the housing 43 and secured
by bolts 45. An O-ring seal 44 prevents water leakage in the housing.
[0031] Fig. 18 shows a conventional equivalent circuit, that represents the response of
the FLEXDUCER; the circuit components being defined as follows:
- E =
- applied voltage
- I =
- Electrical current
- Cb =
- Electrical capacitance
- 1:N =
- Electromechanical transfer function
- Cm =
- Mechanical compliance of the bar between the nodes
- M₁ =
- Mass of the bar between nodes
- M₂ =
- Total mass of bar ends beyond nodes
- Rm =
- Mechanical resistance of the bar
- Mr =
- Radiation mass
- Rr =
- Radiation resistance
- F =
- Force applied to the water load
- U =
- Mechanical current (velocity)
[0032] Fig. 19 shows the calculated response of the FLEXDUCER using appropriate values for
the components of the equivalent circuit of Fig. 18 and the measured response. The
correlation is excellent and validates the equivalent circuit representation. The
efficiency was measured at ∼70%.
[0033] The FLEXDUCER of Fig. 16-B is intended to be a module of a large, high power plane
array with a nominal center frequency of 1 KHz. Since its dimensions (15" x 15") are
small compared to the wavelength (λ ≐ 60"), the acoustic power output will be stress
limited to ∼600 acoustic watts. Fig. 20 shows the maximum acoustic power output as
a function of the number of modules in a rectangular array. The transition from the
stress-limited to the field-limited output occurs at approximately 6 modules. For
40 modules, the FLEXDUCER array would be capable of 100 KW of acoustic power output.
The mechanical Qm drops from ∼3.5 for a single module to ∼35 for the full array of
40 modules due to the increase in radiation loading.
[0034] The importance of the nodal mounting of the FLEXBAR in the FLEXDUCER module and its
effectiveness in virtually eliminating structure-borne vibration is demonstrated by
the experimental data of Fig. 21. Here, a comparison of housing transmissibility is
made between the FLEXBAR module and an equivalent conventional bender-bar module.
In this case, the housing transmissibility is defined as the ratio of the vibration
amplitude of the bar at its center to the vibration amplitude of the housing resulting
from the vibration of the bar, in decibels; i.e., Transmissibility = 20 log (bar amplitude/housing
amplitude). As can be seen, the FLEXBAR module has an average transmissibility of
-60 dB over a whole octave from 700 - 1,400 Hz; i.e. the amplitude of vibration of
the housing is only 0.1% of that of the FLEXBAR. By contrast, the transmissibility
of the bender-bar module is on the average, only -14 dB; i.e. the amplitude of vibration
of the housing is 20% of that for the bender-bar. The significance of this difference
becomes clear if one considers a large, high-power array capable of an acoustic output
of 0.5 megawatts. The back radiation from the FLEXDUCER array would only be of the
order of 0.5 acoustic watts; while the bender-bar array would have back radiation
of ∼20,000 watts.
MEANS FOR DRIVING PIEZOCERAMIC FLEXBARS
[0035] There are e.g. three principal means for electromechanically driving piezoelectric
FLEXBARs. In the first of these shown in Fig. 22, the FLEXBAR is comprised of two
piezoceramic plates 47 with electrodes 48 on the main faces, and the polarization
vector P essentially perpendicular to the principal axis of the bar. Application of
an alternating voltage V to the terminals of the bar results in an electric field
vector E, either parallel or anti-parallel to the polarization vector. In turn, the
electric field, because of the electromechanical coupling, causes an expansion strain
+S in the upper plate and a contraction strain -S in the lower plate, both strains
being parallel to the main axis of the bar. On the next cycle of the driving voltage,
the mechanical strains are reversed and the FLEXBAR is driven into flexural vibration.
In this case where the strain is at right angles to the field, the electromechanical
coupling coefficient is typically k₃₁ ≃ 0.30.
[0036] In the second configuration, shown in Fig. 23, the electromechanical driving elements
are two stacks 49 of piezoceramic blocks 50 consolidated with an appropriate cement
(e.g. epoxy), and with electrodes 51 so oriented that the electric field E and the
mechanical strain S are in the same direction and parallel to the main axis of the
bar, as shown. This is the same means for driving the bar also depicted in Fig. 5.
In this case the electromechanical coupling coefficient is higher, typically k₃₃ ≃
0.60.
[0037] In the third configuration, shown in Fig. 24, the electromechanical driving elements
are two piezoceramic plates 52 with striped-electrodes 53 fused to the ceramic in
regularly spaced bands, the plates are polarized parallel to the longitudinal axis
of the bar, but in alternating directions as shown. Thus, in this configuration the
mechanical strain S and the electric field E are also substantially in the same direction
and parallel to the main axis of the bar. However, because of fringing of the electrical
field, the electromechanical coupling coefficient is less than that of the second
configuration, being typically k
sp ≃ 0.45.
MEANS FOR MECHANICAL TUNING OF FLEXBARS
[0038] One of the unique features of a FLEXBAR is the fact that it can be mechanically tuned
by varying the amount of the total moment of inertia of the end portions of the bar
beyond the nodal lines, symbolically designated as M₂ in the equivalent circuit of
Fig. 18. Three means of achieving this have been devised ; viz,: (1) by varying the
amount of the added-mass end pieces; (2) by varying the position of a portion of the
added-mass end pieces; and (3) by a combination of both (1) and (2). These means for
mechanical tuning apply equally well to piezoceramic FLEXBARs and FLEXBARs driven
by other means (e.g. electrodynamic drive, variable reluctance drive, etc.).
[0039] The mass M₂ can be reduced by simply drilling holes 54 in the added-mass end pieces
as shown in Fig. 25-A; or it can be increased by filling the holes with a high density
material such as lead 55 as shown in Fig. 25-B. Another way of varying the mass M₂
is shown in Fig. 25-C, where plates 56 are added or removed from the added-mass end
pieces. Reducing the added-mass, of course, increases the resonant frequency of the
bar; and increasing the added-mass reduces the resonant frequency.
[0040] The second means for mechanically tuning a FLEXBAR does not vary the added-mass,
but rather moves the centers-of-mass of the end pieces away from, or toward the nodal
points. This varies the total moment of inertia (linear plus rotational) of the end-pieces,
and changes the resonant frequency accordingly. In Fig. 26-A, for example, slotted
plates 57 are bolted in their extreme outward position, which lowers the resonant
frequency. In Fig. 26-B, the slotted plates 57 are in their extreme inward position,
resulting in a higher resonant frequency. Intermediate positions result in intermediate
resonant frequencies.
[0041] Another way of varying the moment of inertia of the end-pieces, and thus changing
the resonant frequency, is shown in Fig. 26-C. Here threaded tuning-slugs 58 located
in the added-masses 59 can be moved outward to lower the frequency, or inward to raise
the frequency. The tuning slugs can be locked into position by means of locknuts 60
or set screws 61. The percentage change in frequency can be increased by filling the
tuning-slugs with a higher density material such as lead.
[0042] Obviously, the resonant frequency of a FLEXBAR can be varied by means of a combination
of the above procedures.
MEANS FOR NODAL MOUNTING OF FLEXBARS
[0043] Two principal means for nodal mounting of FLEXBARs will be described. For a new bar
design, the location of the nodes must be first be determined. This is readily done
by driving a prototype FLEXBAR 63 at its lowest resonant mode and locating the nodes
64 by means of a probe accelerometer or phonograph pick-up (Fig. 27-A). Holes are
drilled at these nodal locations to accommodate the nodal pins 65 and their compliant
elastomer sheath 66 as shown in the cross-sectional Fig. 27-B. Compliant elastomer
washers 67 are inserted between the bar and the mountings 68. This combination isolates
the FLEXBAR from its mounting and decouples bar vibrations from the mounting structure.
An alternate to this method is shown in Fig. 27-C. In this variant integral tabs 69
at the nodal points extend out from the bar 63 and are encased in a compliant elastomer
sheath 66. This, together with the compliant elastomer washers 67, serve to isolate
the bar from the mounting 68. The vibration isolation of the nodal pins or nodal tabs,
by means of compliant members, is an important feature of the "fixed-nodal mounting"
since subsequent mechanical tuning and radiation loading can result in small movement
of the nodal locations determined from experimental measurements of FLEXBAR vibrations
in air. The compliant mounting accommodates to this change.
[0044] The second means for nodal mounting of FLEXBARs is called the "auto-nodal mounting"
and is shown in section view of Fig. 28. In this case, a flange 70 completely surrounds
the FLEXBAR 63 which is encased in a compliant elastomer 71 serving as a sonar window
and 72 serving as a compliant mount. The elastomer is bonded to both the flange and
to the bar so that the FLEXBAR is essentially "floating" in elastomer. The ends of
the bar are recessed with an intervening air space so that their vibration is decoupled
from the flange. Under these conditions, the FLEXBAR automatically determines its
own nodal location corresponding to a particular radiation loading.
1. An improved underwater acoustic transducer,
characterized by:
a) a free-free flexure bar;
b) means for electromechanically driving the said bar in flexural vibration over a
band of frequencies having as its central frequency a frequency, substantially corresponding
to the lowest free-free flexural mode of the said bar;
c) means for mounting said flexure bar substantially at the two nodal lines characteristic
of the said lowest free-free flexural vibrational mode of the said bar, said mountings
having elastomeric members partially isolating said mountings from the vibration of
the said flexure bar;
d) means for affixing said flexure bar and its said nodal mountings into a gas-filled
water-tight housing in such a manner that the flexure bar can vibrate freely on its
nodal mountings without substantial mechanical coupling to said mountings or said
housing;
e) means for mechano-acoustically coupling to the water only the central portion of
the outer surface of said mounted bar lying between the said two nodal lines so that
when electromechanically driven in flexural vibration, the said flexure bar will radiate
acoustic energy into the water from said central portion;
f) means for allowing those outer portions of said flexure bar lying outside of the
said two nodal lines to vibrate freely in the gas-filled interior of said housing
without mechanoacoustic coupling to the water.
2. The transducer of Claim 1, characterized by comprising a plurality of said free-free flexure bars.
3. The transducer of Claim 1 or 2, characterized in that the free-free flexure bar is comprised of two modified end sections lying outside
of the nodal lines of the said free-free flexure bars which are rigidly attached to
the central portion of the said free-free bar and extend at substantially right angles
to and on the opposite side of the central radiating surface of the said free-free
flexure bar, where said end sections would provide substantially the same total inertia,
both translational and rotational, taken about the nodal lines, as would be provided
by uniform end sections extending outside of the nodal lines and parallel to the central
radiating face of the free-free flexure bar.
4. The transducer of claim 3, characterized in that the said free-free flexure bar is comprised of said modified end sections which have
a portion of their surfaces that are contiguous with the central radiating surface
recessed so as to avoid vibrational interference with a transducer cover plate.
5. A vibratile element, suitable for use in a transducer according to one of the preceding
claims,
characterized by:
a) a free-free flexure bar;
b) means for electromechanically driving said bar in flexural vibration over a band
of frequencies having as its central frequency a frequency substantially corresponding
to the lowest free-free flexural vibrational mode of the said bar;
c) means for mounting said flexure bar substantially at the two nodal lines characteristic
of the said lowest free-free flexural vibrational mode of the said bar, said mountings
having elastomeric members partially isolating said mountings from the vibrations
of said flexure bar; two modified end sections lying outside of the nodal lines of
the said free-free flexure bars which are rigidly attached to the central portion
of said free-free bar and extend at substantially right angles to and on the same
side of central portion of said bar, where said end sections would provide substantially
the same total inertia, both translational and rotational, taken about the nodal lines,
as would be provided by uniform end sections extending outside of the nodal lines
and parallel to the central portion of said free-free flexure bar.
6. The vibratile element of claim 5, characterized by means for changing the mass of said modified end sections so as to change the frequency
substantially corresponding to the lowest free-free flexural vibrational mode of said
bar.
7. The vibratile element of claim 5, characterized by means for changing the moment of inertia taken about the nodal lines of said modified
end sections so as to change the frequency substantially corresponding to the lowest
free-free flexural vibrational mode of said bar.
8. A vibratile element suitable for mounting in an underwater acoustic transducer housing,
characterized by:
a) a free-free flexure bar having two modified end sections lying outside the two
nodal lines characteristic of the lowest free-free flexural vibrational mode of said
bar, said end sections being rigidly attached to the central portion of said flexural
bar and extending substantially at right angle to and in the same direction from the
central portion of said bar, where said end sections would provide substantially the
same total inertia, both translational and rotational, taken about the nodal lines,
as would be provided by uniform end sections extending outside of the nodal lines
of an unmodified, uniform free-free flexure bar;
b) means for electromechanically driving said modified bar in flexural vibration over
a band of frequencies having as its central frequency a frequency substantially corresponding
to the lowest free-free flexural vibrational mode of the said bar;
c) means for bonding or cementing compliant elastomeric layers between each side of
said modified flexure bar and corresponding parallel mounting structures attached
to the said transducer housing, in such a manner that said modified bar is suspended
in compliant elastomeric material and, when driven, is substantially free to vibrate
in flexure, seeking its own nodal lines irrespective of changes in the total inertia
of said end sections, or changes in radiation loading; and
d) means for acoustic coupling to the water, only the central face of said bar lying
between the nodal lines and opposite to the extension of said modified end sections,
leaving the other face of said bar and its said end sections decoupled from the water
end and free to vibrate in the air-filled interior of the said transducer housing.
9. An apparatus according to one of the claims 1 to 8, characterized in that the means for electromechanically driving said fibratile element in flexural vibration
is a piezoelectric means.
10. The apparatus of claim 9, characterized in that the piezoelectric means is one of a class of polarized piezoceramics.
11. The apparatus of claim 9 or 10, characterized in that the piezoelectric means comprise two piezoceramic plates provided with electrodes
on the main faces of said plates, whereat the polarization vector extends essentially
perpendicular to the principal axis of the bar (Fig. 22).
12. The apparatus of claim 9 or 10, characterized in that the piezoelectric means comprise at least two stacks of piezoceramic blocks with
electrodes oriented such that the electrical field between the electrodes and the
mechanical strain are in the same direction and parallel to the main axis of the bar
(Fig. 23).
13. The apparatus of claim 9 or 10, characterized in that the piezoelectric means are at least two piezoceramic plates with strip-shaped electrodes
in regularly spaced bands, the plates are polarized parallel to the longitudinal axis
of the bar, but in alternating directions (Fig. 24).
14. An apparatus according to one of the claims 1 to 8, characterized in that the means for electromechanically driving said vibratile element in flexural vibration
is a magnetostrictive means.
15. An apparatus according to one of the claims 1 to 8, characterized in that the means for electromechanically driving said vibratile element in flexural vibration
is a magnetic electrodynamic means.
16. An apparatus according to one of the claims 1 to 9, characterized in that the means for electromechanically driving said vibratile element in flexural vibration
is a variable magnetic reluctance means.
17. The apparatus of claim 10, characterized by means to subject the polarized piezoceramic to a substantially permanent precompression
mechanical bias in the course of fabrication of the said vibratile element.
18. The apparatus of claim 17, characterized in that a pair of tapered wedges are the means for obtaining the said mechanical bias (Fig.
6).
19. The apparatus of claim 17, characterized in that a pair of tapered pins and matching blocks are the means for obtaining the said mechanical
bias (Fig. 7).
20. The apparatus of claim 17, characterized in that a pair of tapered threaded bolts and matching block are the means for obtaining the
said mechanical bias (Fig. 8).
21. The apparatus according to one of the preceding claims, characterized by means for mechanically tuning the bar.
22. The apparatus of claim 21, characterized in that the mass of the end pieces of the bar is changeable (Fig. 25).
23. The apparatus of claim 21, characterized in that the position of the center-of-mass of the end pieces is changeable (Fig. 26).
24. The apparatus according to one of the preceding claims, characterized in that the bar at each nodal location has a hole for accommodating a nodal mounting pin
and a compliant elastomer sheath, and a compliant elastomer washer is inserted between
the bar and the mounting (Fig. 27B).
25. The apparatus according to one of the claims 1 to 23, characterized in that at each nodal point of the bar an integral tab extends out from the bar and is encased
in a compliant elastomer sheath, which together with a compliant elastomer washer
isolates the bar from the mounting (Fig. 27C).
26. The apparatus according to one of the claims 1 to 23, characterized in that a flange completely surrounds the bar, which is encased in a compliant elastomer,
such that the elastomer is bonded to both the flange and to the bar and the bar is
essentially floating on the elastomer.
27. The apparatus of claim 26, characterized in that the ends of the bar are recessed with an intervening air space for decoupling them
from the flange.