Electrodynamic Transducer For Low Frequency Broad Band Underwater Use

Abstract

An underwater, low frequency, high power transducer operates at much greater efficiencies than heretofore possible due to special relationships between a diaphragm mass and area. The data relating to the relationship are summarized by the graphs of FIGS. 3 and 4. The transducer structure includes a tubular housing having a diaphragm at either end. The internal pressure on the inside surface of the diaphragms is equalized to the external hydrostatic pressure in the water at the depth of operation.

Description

This invention relates to underwater transducers, and more particularly to underwater transducers capable of generating uniform acoustic power over a large portion of the lower audible frequency spectrum.

The invention is specifically concerned with the design of a compact transducer in which the diameter of the vibrating surface is in the range between a few inches and one foot and which is capable of generating acoustic power levels in excess of 1 watt over a broad portion of the lower audible frequency spectrum, down to frequencies in the order of 100 Hz or less.

In order to achieve a uniform transmitting response characteristic over the entire lower audible frequency range, a rigid vibratile diaphragm is flexibly mounted by a suspension system having sufficient compliance to resonate the vibrating system below the lowest frequency to be reproduced. The mechanical impedance of the vibrating system is mass controlled over the entire frequency region requiring flat response. The vibratile piston will be driven by electrodynamic forces generated in an attached coil of wire which is suspended in a magnetic field. This strucuture is similar to conventional dynamic speakers for home sound reproducing equipment.

Previous designs of electrodynamic underwater transducers have failed to provide significant acoustic power output levels. The acoustic power output has generally been limited to a small fraction of a watt. This low power limitation was inherent in previous designs because the vibratile diaphragm was either too small (generally only 2 or 3 inches diameter) and therefore incapable of making the large excursions necessary to generate power levels in the order of 1 watt or greater for frequencies in the neighborhood of 100 Hz; or, for larger size diaphragms, the efficiency was so low (in the neighborhood of 0.1 percent) that the electrical power loss in the voice coil would burn it out, if driven at the power levels required to produce acoustic power levels in the order of 1 watt or greater in the 100 Hz region.

The primary object of this invention is to overcome the inherent limitations in previously designed electrodynamic transducers for underwater generation of sound.

Another object of this invention is to provide electrodynamic transducers employing a vibratile piston several inches in diameter, capable of a wide range, uniform response, over the lower audible frequency range, down to the region of 100 Hz or less and having an efficiency in excess of 1 percent.

An additional object of this invention is to provide electrodynamic transducers for underwater use, capable of generating acoustic power levels in excess of 1 watt in the lower audible frequency region down to the vicinity of 100 Hz or less.

A still further object of this invention is to provide a compact electrodynamic transducer design in which two vibratile pistons are mounted to radiate from opposite ends of the axis of the structure, whereby each piston effectively becomes loaded as if it were mounted in an infinite baffle and, as such, each of the two pistons individually generates approximately twice the acoustic power for a given displacement that would result for the same piston operating singly and mounted on one face of an enclosing housing.

Another object of this invention is to specify the minimum relationships that must be satisfied between the mass of the voice coil and diameter of the vibratile piston in order that the efficiency of the transducer shall exceed 1 percent.

These and other objects, features and advantages of the invention will become more apparent from a study of the following description when taken in conjunction with the drawings, wherein:

FIG. 1 is an end view of a transducer incorporating one illustrative embodiment of my invention;

FIG. 2 is a cross-sectional view taken along the line 2--2 of FIG. 1;

FIG. 3 is a chart showing the relationship between the coil mass and transducer efficiency for pistons of various sizes; and

FIG. 4 is a chart showing the relationship between acoustic power output and frequency for diaphragms of various diameters vibrating at constant amplitude.

In the figures, the reference character 1 identifies a cylindrical core of magnetic conducting material which is accurately machined, at each end, to define the inside diameter of an annular air gap at each end of the core. A hollow cylindrical permanent magnet 2 is provided with end plates 3 and 3A of magnetic conducting material, such as soft iron. Each of the end plates has a hole machined through its center to define the outside diameter of the annular air gaps as illustrated in FIG. 2. The end plates 3 and 3A are provided with brass collars 4 and 4A which are attached by means of the screws 5. A clearance hole is machined through each collar 4 and 4A, so that the machined ends of the core piece 1 can be held in concentric alignment with the holes in the end plates 3 and 3A, to provide a uniform concentric air gap at each end of the magnetic assembly as illustrated in FIG. 2. A convenient means for insuring that the holes in the plate members 3 and 3A are concentric with the holes in the collars 4 and 4A is to mahcine the final hole sizes after attaching the collars 4 and 4A to the end plates 3 and 3A. The end plates 3 and 3A may be held to the ends of the magnet 2 by means of a suitable cement, such as epoxy. After assembling the magnetic structure, I prefer to fill the space between the core 1 and the permanent magnet 2 with a potting compound 6 which may be poured into the space through a small hole through either the wall of the magnet or the surface of one of the end plates 3.

At each end of the magnetic structure is attached a vibratile diaphragm assembly, one of which comprises a voice coil 7 wound on a tubular coil form 8. The coil form 8 is bonded to a mating surface 9 provided at the base of the diaphragm 10, as illustrated. The voice coil 7 comprises several layers of insulated wire wound over the coil form 8 and held together as a composite rigid assembly by a suitable cement, such as epoxy, as is well known in the art of loud speaker construction. The diaphragm structure comprises a truncated conically shaped waterproof diaphragm 10 which includes a corrugation 11 formed near the outer periphery to provide a flexible suspension means for enabling relatively large excursions of the diaphragm. A suitable material for the diaphragm structure 10 would be stainless steel which is rugged and resistive to the corrosive action of the underwater environment. The outer flat peripheral portion of the diaphragm 10 is nested within a recessed cavity 12 machined into the face of the structural frame member 13. To provide added stiffness for forming a piston portion at the central vibratile portion of the diaphragm structure, the conical cavity portion of diaphragm 10 is filled with a rigid potting compound 14, such as epoxy. The diaphragm 10 with its attached voice coil assembly 7 and 8 is mounted on the structural support member 13 by using proper locating fixtures to insure that the voice coil is located exactly along the center line of the structure. Two insulated conductors 15 and 16, which provide electrical connection to the coil 7, pass through a hole provided in structural member 13, as illustrated.

The diaphragm assembly mounted at the opposite end of the magnetic structure is identical to the diaphragm assembly just described. It comprises voice coil 7A and coil form 8A attached to diaphragm 10A, which is attached to frame member 13A similar to the previously described assembly. Frame member 13A includes a counterbored hole, through its face, to enable a watertight assembly of a waterproof cable 17 by means of the gland nut 18, washer 19, and rubber grommet 20, as shown. The conductors 15, 16, 15A and 16A, from the voice coils 7 and 7A are connected together and to the conductors in cable 17 in such phase that an electrical signal supplied to the cable will cause both diaphragms 10 and 10A to move together, simultaneously away or toward the center of the core piece 1, in accordance with the polarity of the a-c signals supplied through the cable 17.

The diaphragm assemblies 10 and 10A, together with their support members 13 and 13A, are attached to the end plates 3 and 3A and are held in place by the screws 21, as illustrated. At this point in the assembly, the structure comprises a pair of vibratile diaphragms assembled to opposite ends of a magnetic structure. They are capable of being driven by mechanical forces generated within their respective voice coils which are suspended in annular air gaps provided on opposite ends of a common magnetic circuit.

After the electrical connections are made between the conductors 15, 16, 15A, 16A and the conductors from the cable 17, a rubber boot 22 is stretched over and attached to the outer periphery of the structure 13 to provide a watertight seal to the internal transducer structure. The rubber boot 22 is sealed to the edge surfaces of members 13 and 13A by circumferential pressure applied by the metal bands 23, as illustrated. A sealed air volume 24 inside the flexible rubber boot 22 communicates with the clearance spaces 25 and 25A, as shown in FIG. 2. When the transducer is lowered in water, the flexible boot 22 compresses air volume 24 to equalize the internal pressure to the external water pressure. A rigid cylindrical sleeve 26 is attached to the outer peripheral ends of structural members 13 and 13A by means of the screws 27 to complete the assembly. A few small holes 28 through the wall of the cylindrical tubing 26 permit the entrance of water in the space 29 when the transducer is immersed in the sea. The purpose for providing the rigid sleeve 26 to enclose the rubber boot is to prevent the unprotected exposure to the sea of the low impedance pressure release surface, represented by the air backed rubber boot 22, which would otherwise reduce the efficiency of radiation of sound from the transducer.

The invention is concerned with the configuration of the dual diaphragm system which, when operating together, effectively performs as if each diaphragm was separately mounted in an infinite baffle, which results in an improved radiation resistance load on each diaphragm. In other words, by having the dual diaphragms operate as described, each diaphragm will individually have approximately twice the radiation resistance on its surface, as compared to the case where only a single diaphragm is operating from one end of a conventional magnetic structure. This means that the use of two diaphragms, with each diaphragm vibrating at the same amplitude, will generate approximately four times the acoustic power that would be generated by one diaphragm operating separately.

The basic invention resides primarily in the relationships that I have found necessary to be satisfied between the mass of the voice coil and the size of the diaphragm, in order to achieve the greatly improved efficiency and power generating capability which I have achieved over the prior art electrodynamic transducers designed to operate over a broad frequency range, at the lower region of the audible frequency spectrum, down to frequencies in the vicinity of 100 Hz. Electrodynamic transducers which have heretofore been designed for underwater use have efficiencies in the vicinity of 0.1 percent. Because of such low efficiencies, the acoustic power output is limited to a small fraction of a watt since there is a tremendous temperature rise in the voice coil, which occurs due to the high losses. By applying the teachings disclosed in this invention, I am able to very materially increase the efficiency and also the power output capability of an electrodynamic transducer operating under water over the lower audible frequency range.

In order to investigate the efficiency and power generating capability of the transducer structure which has been described, each diaphragm may be considered as being effectively mounted in an infinite baffle. Since the diameter of the diaphragm is small as compared to the wave length of sound at the low frequencies of interest, the dual diaphragm structure will radiate sound in an omnidirectional pattern. In order to support the conditions which will be claimed for achieving the improvements in electrodynamic low frequency transducers as stated (namely: the transducer is capable of generating acoustic power levels greater than 1 watt, and the efficiency of the inventive transducer is greater than 1 percent as compared to the prior art designs having efficiencies in the vicinity of 0.1 percent) a brief mathematical analysis will be presented together with specific numerical data to permit the selection of the necessary parameters to achieve the teachings of this invention.

It can be shown from fundamental principles such as presented in section 2.10 of the book by Olson and Massa, entitled Applied Acoustics, second edition, P. Blakiston's Son & Co., Philadelphia, 1939, that the acoustic impedance loading on the surface of a small piston mounted in an infinite baffle is given by the expression

z = .rho.c k.sup.2 r.sup.2 /2 + j8R.omega..rho./3.pi. (1)

where:

z = specific radiation impedance in mechanical ohms/cm.sup.2

.rho. = density of the medium in gms/cm.sup.3

c = velocity of sound in the medium in cm/sec

k = 2.pi./.lambda.

.lambda. = wavelength in cm = c/f

f = frequency in Hz

R = radius of piston in cm.

The total radiation impedance on the surface of a piston in an infinite baffle radiating low frequencies in water can be derived from Equation (1) and is given by

Z.sub.M = 1.04 .times. 10.sup..sup.-3 D.sup.4 f.sup.2 + j 30.4D.sup.3 f mechanical ohms (2)

from which,

R.sub.M = 1.04 .times. 10.sup..sup.-3 D.sup.4 f.sup.2 mech. ohms (3) X.sub.M = 30.4 D.sup.3 (4) ech. ohms

where:

D = piston diameter in inches

f = frequency in Hz.

Since the reactance X.sub.M in Equation (4) is equal to .omega.M.sub.W, where M.sub.W is the magnitude of the water load on the surface of the vibrating piston, it follows that

M.sub.W = 4.85 D.sup.3 grams. (5)

The motional impedance, which appears in series with the electrical impedance of the voice in an electrodynamic transducer, is equal to

Z.sub.EM = B.sup.2 L.sup.2 .times. 10.sup..sup.-9 / R.sub.M + j.omega.M.sub.o ohm (6)

where:

B = air gap flux density in gauss

L = length of conductor in voice coil, in cm

R.sub.M = radiation resistance in mech. ohms

M.sub.o = total mass of vibrating system in grams.

The largest portion of M.sub.o is the water load which is given by Equation (5). It is possible to keep the total mass of the piston plus voice coil to within about 50 percent of the water load mass; therefore, it will be assumed that M.sub.o is equal to about 1-1/2 times the value of M.sub.W in Equation (5). Therefore, for purposes of this analysis,

M.sub.o = 7.5D.sup.3 grams. (7)

Substituting the values of R.sub.M from Equation (3) and M.sub.o from Equation (7) into Equation (6), the motional impedance becomes

Z.sub.EM = B.sup.2 L.sup.2 .times. 10.sup.-.sup.9 /1.04 .times. 10.sup..sup.-3 D.sup.4 f.sup.2 + j47D.sup.3 f. (8)

By multiplying the numerator and denominator by the conjugate of the denominator, the expression for the motional impedance becomes

Z.sub.EM = B.sup.2 L.sup.2 .times. 10.sup..sup.-9 (1.04 .times. 10.sup..sup.-3 Df - j47)/D f (1.08 .times. 10.sup..sup.-6 D.sup.2 f.sup.2 + 2200). (9)

For the purposes of the transducer design covered by this invention, the diameter of the diaphragm is always less than one-fourth wavelength of the sound being generated in the water; therefore, the first term inside the bottom parantheses becomes negligibly small and expression for motional impedance reduces to

Z.sub.EM = B.sup.2 L.sup.2 .times. 10.sup..sup.-9 (1.04 .times. 10.sup..sup.-3 Df - j47/2200 D.sup.3 f (10)

from which the real part represents the motional resistance, which is equal to

R.sub.EM = 4.8 .times. 10.sup..sup.-16 B.sup.2 L.sup.2 /D.sup.2 ohm. (11)

Since the motional resistance in Equation (11) appears in series with the resistance of the voice coil, it follows that the efficiency of the electrodynamically driven piston mounted in an infinite baffle is given by

Eff. = R.sub.EM /R.sub.EM + R.sub.E .times. 100 percent (12)

where:

R.sub.E = voice coil resistance in ohms.

For a copper conductor of length L cms and mass M.sub.c grams,

R.sub.E = 15,2 .times. 10.sup..sup.-6 L.sup.2 /M.sub.c ohms. (13)

Substituting Equation (13) and Equation (11) into Equation (12), the efficiency becomes

Eff. = 3.15 .times. 10.sup..sup.-11 B.sup.2 M.sub.c /3.15 .times. 10.sup..sup.-11 B.sup.2 M.sub.c +D.sup.2 .times. 100 percent. (14)

To give a physical interpretation of the analytical conclusions developed above and to present specific design data that can be used by a transducer engineer to design low frequency underwater wide range transducers with efficiencies greater than 1 percent, in accordance with the teachings of the invention, a family of curves have been computed from Equation (14). These curves show the mass of copper conductor required in the voice coil design of an electrodynamic transducer as a function of efficiency for various pistons ranging from 2 to 10 inches in diameter. The data are shown in FIG. 3 and are based on an assumed value of air gap flux density equal to 12,000 gausses. This value of flux density is a reasonable maximum that can be obtained with the best grades of Alnico magnets that are commercially available. For lower values of flux density, the voice coil mass required for a fixed efficiency and piston diameter will increase in inverse proportion to the square of the flux density.

Using the assumed maximum value of 12,000 gausses in the air gap, it can be seen from the data in FIG. 3 that the requirement to be met for achieving a transducer efficiency greater than 1 percent is

M.sub.c >2.2D.sup.2 grams. (15)

For example, if a 7 inches diameter piston is chosen for the transducer diaphragm, it will be necessary to design a voice coil employing more than approximately 100 grams of copper to achieve an efficiency greater than 1 percent. If the flux density is reduced from the 12,000 gauss assumed value, then the voice coil has to employ a still greater quantity of copper.

It would seem from an inspection of the data in FIG. 3 that all that is necessary to design a high efficiency transducer with a relatively lightweight coil and corresponding lightweight magnetic structure is to use a small diameter piston. For example, a 2 inches diameter piston requires only 9 grams of copper in the drive coil to achieve an efficiency of 1 percent. This is correct as far as efficiency is concerned; however, a 2 inches diameter piston will not be able to generate much power at the lower audible frequencies due to the limitation in maximum amplitude of vibration which is imposed by the magnetic structure. In order for the transducer to generate an acoustic power level of at least 1 watt at 100 Hz, it will be necessary for the piston diameter to be not less than the minimum value required to prevent amplitudes of vibration from exceeding the linear range provided in the air gap design.

The acoustic power generated by a vibrating piston can be determined by multiplying Equation (3) by the square of the piston velocity. The acoustic power output from the piston is

P.sub.A = .omega..sup.2 A.sup.2 .times. 1.04 .times. 10.sup..sup.-3 D.sup.4 f.sup.2 .times. 10.sup..sup.-7 watts (16)

where:

A = piston amplitude in cm.

By combining terms, Equation (16) may be rewritten as

P.sub.A = 2.6d.sup.2 D.sup.4 f.sup.4 .times. 10.sup..sup.-14 watts (17)

where:

d = piston amplitude in mils.

The information represented by Equation (17) was used to produce the family of curves in FIG. 4 which show the acoustic power output generated over the frequency range 100 Hz -- 1,000 Hz by various pistons ranging in diameter from 1 to 10 inches when vibrated at an r.m.s. amplitude of 10 mils (which is equivalent to a peak-to-peak amplitude of 28 mils for a sinusoidal vibration). An inspection of the curves in FIG. 4 show that the 2 inches diameter piston mentioned earlier can only generate about 10 milliwatts of power at 100 Hz for the assumed 10 mils r.m.s. amplitude. It is also shown that, for a piston to be able to generate 1 watt acoustic power at 100 Hz at 10 mils r.m.s. amplitude, the piston diameter must be about 8 inches. If the maximum permissible amplitude were increased to 20 mils r.m.s. (56 mils peak-to-peak), a 6 inches diameter piston would be required to generate 1 watt output at 100 Hz. Even if the requirement is that each diaphragm of the dual structure shown in FIG. 2 generate only one-half watt each, in order for the complete transducer to generate 1 watt at 100 Hz, the piston diameter must be greater than 4 inches if the maximum peak-to-peak excursion of the voice coil is to be limited to approximate 60 mils, which is a fairly large excursion to accommodate and still maintain linearity in the transducer.

This invention has disclosed the design of a low frequency, electrodynamic, underwater transducer capable of greatly exceeding the efficiency and power generating capabilities of prior art designs. Specific design data has also been presented showing the relationships between the magnitudes of the various parameters which define the basic elements of the vibrating system and the acoustic performance of the transducer.

Although only a few specific examples have been discussed to illustrate the teachings of this invention, it is obvious that some variations may be made in the specified limits chosen to illustrate the invention, without departing materially from the conclusions which have been drawn. Other obvious changes in some of the details which have been mentioned may be made by those skilled in the art without departing substantially from the teachings of this invention. Therefore, I desire that my invention shall not be limited except insofar as is made necessary by the prior art and that the appended claims be construed to cover all equivalent structures.

Claims

1. An electrodynamic transducer for generating uniform acoustic power under water throughout the lower portion of the audible frequency spectrum down to the region in the vicinity of 100 Hz, said transducer comprising magnetic structure means defining a circular air gap, at least one vibratile diaphragm having a radiating face approximating a circular piston, flexible suspension means associated therewith, a coil of insulated electrical conductor wound and consolidated into a rigid cylindrical shell supported by one side of said vibratile diaphragm, the mass in grams of said conductor being greater than approximately twice the value of the square of the diameter in inches of said circular piston, the longitudinal axis of said coil being in alignment with the normal axis perpendicular to the radiating face of said vibratile diaphragm, frame means rigidly attached to said magnetic structure means, means for attaching said flexible suspension means to said frame means with said vibratile diaphragm being supported by said flexible suspension means in mechanical alignment with the coil concentrically positioned within said circular air gap, and waterproof housing means enclosing said air gap and said coil means together with said one side of said vibratile diaphragm.

2. The invention in claim 1 wherein the diameter of said circular piston

3. The invention in claim 1 wherein said waterproof housing includes a

4. An electrodynamic transducer for generating acoustic power under water throughout substantially all of the lower portion of the audible frequency spectrum, said transducer comprising a magnetic structure including a pair of air gaps with one air gap located on each opposite end of a common axis within said magnetic structure, a pair of vibratile diaphragm assembly means, each of said vibratile diaphragm assembly means being associated with a corresponding one of said air gaps and comprising a rigid piston portion surrounded by a flexible suspension means, drive coil means of insulated wire attached to said piston portion on each of said diaphragms, the mass in grams of each of said drive coil means being greater than approximately twice the value of the square of the diameter in inches of the piston portion of the attached diaphragm, each of said drive coils being supported in an operable position within one of said air gaps, and waterproof housing means including a flexible wall portion defining a sealed air volume for enclosing said magnetic structure and drive coil means, said vibratile diaphragm assemblies being sealed to said housing means by said flexible suspension means to provide a completely sealed air volume enclosure for said magnetic structure and diaphragm assembly means, said sealed air volume including communication means extending between said enclosed air volume and the internal enclosed surfaces of said

5. The invention in claim 4 and a rigid covering surrounding the outer surface of said flexible wall portion, said rigid covering having an opening therein for exposing said flexible wall to ambient external

6. The invention in claim 4 further characterized in that said piston portions of said vibratile diaphragms have diameters within the

7. An electrodynamic transducer for operating under water comprising an elongated magnetic circuit having an axial core, an annular air gap located at each opposite end of said axial core, two identical vibratile diaphragm assemblies, each diaphragm assembly having an internal and an external side, each diaphragm assembly further comprising a rigid piston portion surrounded by a peripheral waterproof flexible suspension means, and each diaphragm assembly including a drive coil of insulated wire rigidly attached to the center internal side of each vibratile diaphragm, the mass in grams of each of said drive coils being greater than approximately twice the value of the square of the diameter of the piston portion of said diaphragm assembly, a structural support means rigidly attached to each end of said elongated magnetic circuit, said waterproof flexible suspension means operably sealing the periphery of each vibratile diaphragm to each of said structural support means with the associated coil of each diaphragm operably located in one of said annular air gaps, a waterproof housing sealingly enclosing said magnetic structure and the internal sides of said vibratile diaphragm assemblies whereby a waterproof enclosure is achieved for the transducer assembly, and pressure compensating means including an air volume on the inside of said waterproof housing with communicating passageways extending from said air

8. The invention in claim 7 wherein the diameter of the active piston portions of said vibratile diaphragm assemblies lie in the range extending

9. The invention in claim 7 wherein said waterproof housing has a flexible tubular wall, a rigid tubular housing surrounding said flexible tubular housing, said rigid tubular housing including an opening for enabling the flow of water from the outside surface of said rigid housing to the inside surface of said rigid housing, thereby equalizing ambient pressures inside

10. The invention in claim 9 wherein the diameter of the active piston portions of said vibratile diaphragms lies within the approximate range of

11. The invention in claim 7 wherein the diameters of the piston portions of said vibratile diaphragm assemblies lie within the approximate range of 4 to 12 inches and the mass in grams of each of said drive coils is more than approximately twice the value of the square of the diameter in inches

12. A dual electrodynamic transducer comprising an elongated cylindrical housing sealed on both ends by a diaphragm assembly having a frustoconical section filled with a rigidifying substance and having a coil at least partially surrounding the truncated apex of said frustroconical section, the mass of said coil comprising an electric conductor having a mass in grams greater than approximately twice the value of the square of the diameter in inches of said rigidified portion of said diaphragm.