US3474268A - Piezoelectric ceramic transducer - Google Patents
Piezoelectric ceramic transducer Download PDFInfo
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- US3474268A US3474268A US544242A US3474268DA US3474268A US 3474268 A US3474268 A US 3474268A US 544242 A US544242 A US 544242A US 3474268D A US3474268D A US 3474268DA US 3474268 A US3474268 A US 3474268A
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- 239000000919 ceramic Substances 0.000 title description 22
- 239000004020 conductor Substances 0.000 description 47
- 239000000463 material Substances 0.000 description 23
- 238000007639 printing Methods 0.000 description 19
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- KDLHZDBZIXYQEI-UHFFFAOYSA-N Palladium Chemical compound [Pd] KDLHZDBZIXYQEI-UHFFFAOYSA-N 0.000 description 2
- 238000005452 bending Methods 0.000 description 2
- BASFCYQUMIYNBI-UHFFFAOYSA-N platinum Chemical compound [Pt] BASFCYQUMIYNBI-UHFFFAOYSA-N 0.000 description 2
- 239000000843 powder Substances 0.000 description 2
- 229910000679 solder Inorganic materials 0.000 description 2
- 239000007787 solid Substances 0.000 description 2
- VSYMNDBTCKIDLT-UHFFFAOYSA-N [2-(carbamoyloxymethyl)-2-ethylbutyl] carbamate Chemical compound NC(=O)OCC(CC)(CC)COC(N)=O VSYMNDBTCKIDLT-UHFFFAOYSA-N 0.000 description 1
- 229910052788 barium Inorganic materials 0.000 description 1
- DSAJWYNOEDNPEQ-UHFFFAOYSA-N barium atom Chemical compound [Ba] DSAJWYNOEDNPEQ-UHFFFAOYSA-N 0.000 description 1
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- JUWSSMXCCAMYGX-UHFFFAOYSA-N gold platinum Chemical compound [Pt].[Au] JUWSSMXCCAMYGX-UHFFFAOYSA-N 0.000 description 1
- 229910000464 lead oxide Inorganic materials 0.000 description 1
- HFGPZNIAWCZYJU-UHFFFAOYSA-N lead zirconate titanate Chemical class [O-2].[O-2].[O-2].[O-2].[O-2].[Ti+4].[Zr+4].[Pb+2] HFGPZNIAWCZYJU-UHFFFAOYSA-N 0.000 description 1
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- YEXPOXQUZXUXJW-UHFFFAOYSA-N oxolead Chemical compound [Pb]=O YEXPOXQUZXUXJW-UHFFFAOYSA-N 0.000 description 1
- 229910052763 palladium Inorganic materials 0.000 description 1
- 229910052697 platinum Inorganic materials 0.000 description 1
- 238000003825 pressing Methods 0.000 description 1
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Images
Classifications
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H9/00—Networks comprising electromechanical or electro-acoustic devices; Electromechanical resonators
- H03H9/46—Filters
- H03H9/54—Filters comprising resonators of piezoelectric or electrostrictive material
- H03H9/58—Multiple crystal filters
- H03H9/581—Multiple crystal filters comprising ceramic piezoelectric layers
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04R—LOUDSPEAKERS, MICROPHONES, GRAMOPHONE PICK-UPS OR LIKE ACOUSTIC ELECTROMECHANICAL TRANSDUCERS; DEAF-AID SETS; PUBLIC ADDRESS SYSTEMS
- H04R17/00—Piezoelectric transducers; Electrostrictive transducers
-
- H—ELECTRICITY
- H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
- H10N—ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
- H10N30/00—Piezoelectric or electrostrictive devices
- H10N30/20—Piezoelectric or electrostrictive devices with electrical input and mechanical output, e.g. functioning as actuators or vibrators
- H10N30/204—Piezoelectric or electrostrictive devices with electrical input and mechanical output, e.g. functioning as actuators or vibrators using bending displacement, e.g. unimorph, bimorph or multimorph cantilever or membrane benders
Definitions
- PIEZOELECTRIC CERAMIC TRANSDUCER Filed April 21, 1966 Sheets-Sheet 2 United States Patent O 3,474,268
- PIEZOELECTRIC CERAMIC TRANSDUCER Norman Rudnick, Piscataway, NJ. assignor to Gulton ndustries, Inc., Metuchen, NJ., a corporation of New ersey Filed Apr. 21, 1966, Ser. No. 544,242 Int. Cl. H01v 7/00 U.S. Cl. S- 8.5 8 Claims ABSTRACT OF THE DISCLOSURE
- a piezoelectric transducer having a homogeneous monolithic body having one electrode embedded in the center of the body and the other electrode completely surrounding the body except at one end thereof. The monolithic body operates in the shear mode.
- the present invention relates to bar or strip type piezoelectric ceramic transducers which are to produce a mechanical 4movement in response to the application of a voltage thereto, and has its most important (but not its only) application to transducers of this type which are to impart appreciable thrust or pulling forces at high rates as detemined by voltage pulses applied at relatively high random pulse repetition rates.
- Another object of the invention is to provide a bar or strip type ceramic piezoelectric transducer sandwich which produces a maximum deflection for a given voltage and for a given thickness and volume of piezoelectric material utilized.
- Still another object of the invention is to provide a ceramic piezoelectric transducer sandwich as described which is so thin that large voltage gradients are present ice and yet where arcing between the electrodes does not readily take place.
- a further object of the invention is to provide a ceramic transducer sandwich as described which, because of its mode of construction, can be easily manufactured in extremely thin cross-sections without warping and other problems and by mass production techniques.
- a still further object of the invention is to provide a thin ceramic transducer sandwich as described to which strong solder connections or other good contact connections can be readily made.
- Another object of the invention is to provide a ceramic transducer sandwich as described where the movement of the transducer unit is a longitudinal expansion or contraction thereof in response to a signal voltage applied across the thickness thereof.
- piezoelectric ceramic transducers generally produce very small mechanical displacements when electrically stressed unless operated under resonant conditions or in bending or flexural modes.
- the operation of piezoelectric transducers under resonant conditions has serious shortcomings.
- resonant operation may not be suitable because it may be difficult to design a transducer to operate at the desired frequency or because the transducer must be operated at random times.
- small forces opposing the motion thereof will suppress much of the amplified motion resulting from the resonant mode of operation thereof. Bending or iiexural modes of operation of a piezoelectric transducer unit achieve large displacements only at the sacrifice of the ability to apply strong thrust or pulling forces.
- the best electromechanical coupling in piezoelectric transducer units is attained when the displacements thereof are in line with the applied electric fields.
- the applied voltage must generally be very large to produce relatively large movements.
- relatively large movement accompanied by relatively large forces can be generated without requiring very large voltages.
- the transducer of the present invention is constructed to operate in the latter mode.
- two or more pairs 4of thin elongated strips of piezoelectric ceramic material are secured together with one or more electrode layers between each pair of strips.
- the electrode layer between the strips of each pair of strips of piezoelectric material is spaced appreciably from all margins of the sandwich except one which is most desirably one end margin of the piezoelectric sandwich.
- the electrode layers encompass most of the cross sectional area of the transducer unit in a plane parallel to the opposite faces (i.e.
- a first region of conductive material is applied to an end face of the piezoelectric sandwich to which the electrode layers between the strips of each pair of strips extend. This region of conductive material preferably extends a short distance around the sides of the piezoelectric sandwich materially to increase the area of conductive material occupied by the first region of said material which forms a terminal for the transducer unit of appreciable area, though occupying only an insignificant percentage of the area of the entire transducer unit.
- a second region of conductive material is preferably applied to the remaining surface area of the piezoelectric sandwich except for a narrow insulating gap separating the same from said lirst region of conductive material.
- the second region of conductive material will thus make electrical contact with any inner electrode layers extending to said other end margin of the piezoelectric sandwich.
- the second region of conductive material forms a terminal for the transducer unit and with any other inner electrode connected thereto, electrode means which cooperates with the inner electrode layers extending to the first region of'conductive material to elfect the desired displacement when a voltage is applied to the transducer unit.
- the piezoelectric sandwich is constructed so that the piezoelectric material throughout the sandwich forms a single, continuous, homogeneous monolithic body of such material extending between said regions of conductive material and around the edges of all of the inner electrodes except the edges thereof extending to the margins of the piezoelectric sandwich.
- the monolithic character of the piezoelectric sandwic'h can be achieved by superimposing thin sheets ⁇ of raw ceramic material held together with a binder and having the various aforesaid electrode layers silk screened or otherwise coated on the surfaces of the layers of ceramic material to be located within the sandwich, applying pressure to the raw ceramic sandwich and then firing the same to sinter the various sheets of raw ceramic material into a solid monolithic structure.
- the transducer unit described is formed into a piezoelectric unit by simply polarizing the piezoelectric ceramic mate- ⁇ rial by the application of a polarizing voltage between the terminals of the transducer unit.
- AL is the displacement in meters from the -unstrained length L
- V is applied voltage in volts
- d3 is the transverse piezoelectric strain coeiicient with units of meters/meter per volt/meter
- t is the thickness of the transducer in meters. It can be seen that the displacement can be increased without change in voltage by increasing the length and ⁇ decreasing the thickness.
- the transducer unit described above comprising two or more strips or layers of piezoelectric material secured together in a manner to form a continuous, homogeneous, monolithic piezoelectric body constitutes a multiplicity of piezoelectric elements electrically connected in parallel.
- Such a transducer unit can deliver the same displacement with a greater thrust at the same voltage than a single layer transducer unit.
- the applied voltages affect substantially all portions of the piezoelectric body for maximum response and arcing is prevented because the closely spaced edges of the electrodes are separated by a high di-electric ceramic material.
- the transducer unit of the invention described above can be mounted within a holder which confines the transducer on all sides except one end thereof. Then, when the voltage is applied to the terminals of the transducer unit, all of the displacement will occur at one end of the transducer element.
- the holder can include terminal strips which contact the aforesaid first and second regions of conductive material and lead to screw or other ter- 4 minals for connecting the ends of conductor wires. Alternatively, wires can be directly soldered to the regions of conductive material referred to.
- the amount of motion producible by the transducer unit yof the invention with presently available piezoelectric ceramic compositions makes it useful wherever small displacements are required ⁇ with a minimum of machinery and electrical input.
- Such applications lie in the areas of optical adjustments, switching. actions, pumping devices, and, in particular, rapid printing mechanisms.
- a 4.6 inch long, two-layered strip, 0.20 inch wide and 0.018 inch thick has a lowest resonant frequency of over 10,000 cycles per second.
- the voltage pulses fed thereto which are desirably fed at a pulse repetition rate well below the lowest resonant frequency thereof, can be ata 4rate of several hundreds and even thousands of pulses per second, which can provide repeated random thrusts ata rate far exceeding the rates attainable by conventional printing mechanisms.
- conventional printing mechanisms operate at -rates -of the order of 3 to 4 lines per second
- instruments using the piezoelectric transducer of the present invention can be operated to produce to 200 lines per second and higher.
- FIG. 1 is a perspective view of a rapid printing mechanism having a printing head with the transducer unit of the present invention incorporated therein;
- FIG. 2 is a greatly enlarged, fragmentary sectional view through the printing head of FIG. 1, taken along section line 2--2 thereof;
- FIG. 3 is another sectional view of the printing head of FIGS. 1 and 2, taken along section lineI 3 3 in FIG. 2;
- FIG. 4 is a perspective view of a transducer unit used in the printing head of FIGS. 1 through 3, and having one internal electrode;
- FIG. 5 is an enlarged horizontal longitudinal sectional view through the transducer unit of FIG. 4, taken along section line 5-5 therein;
- FIG. 6 is a greatly enlarged fragmentary, transverse sectional, perspective view of the transducer unit of FIGS. 4 and 5;
- FIG. 7 is a diagrammatic view of the transducer unit of FIG. 4 connected into an electrical circuit to operate the same;
- FIG. 8 is a curve showing exemplary bias and signal voltages applied to a transducer unit of the invention.
- FIGS. 9 through 13 are a series of views illustrating a preferred method of mass producing transducer units like that illustrated in FIGS. 4 through 6;
- FIG. 14 is a longitudinal vertical sectional view through a form of transducer unit of the present invention which utilizes a number of internal electrodes.
- FIG. 1 illustrates such a high speed printing mechanism which includes a printing head generally indicated by reference numeral 1 which carries on the inner face thereof a row of thin transducer units 2 which are mounted in closely spaced relation with their thin dimensions extending in the direction of the spacing thereof in individual cavities 5 in a housing ⁇ 6 forming part of lthe printing head.
- the vindividual transducer units 2 are most advantageously thin and elongated as shown in FIG. 4 and of rectangular cross-section. Each transducer unit is closely confined but not constricted against longitudinal sliding movement on three sides thereof, as shown in FIGS.
- each transducer unit 2 and 3 have an inner end projecting horizontally from the printing head housing 6 -where it is free to move longitudinally outwardly.
- a small piece of metal or other similar material 7 is preferably secured by an adhesive or otherwise on the projecting end face or edge of each transducer unit 2.
- the metal faced end of each transducer unit may be positioned to engage a printing element or, as illustrated, one side of a moving strip of paper whose other side passes by a stationary or moving raised indicia carrying member 12. As a transducer unit 2 is thrust outwardly momentarily, an imprint is made on the point of paper 10 engaged by (or opposite the) small end face of the transducer unit involved.
- the metal facing 7 on each transducer unit protects the end thereof from wear.
- each transducer unit has a pair of terminals formed by insulated regions of conductive material 8 and 9, as best shown in FIG. 4.
- the conductive region 8 preferably forms a narrow end cap around one end of the transducer unit and so covers the end face and a narrow strip on all side faces and edges of the transducer unit occupying only an insignificant fraction of the length of the transducer unit.
- the other region 9 of conductive material is spaced from the narrow region l8 of conductive material by a narrow insulating gap 10, and preferably occupies, except for the gap 10i, and the area encompassed by the conductive end cap 8, all remaining surface areas of the transducer unit, which is most of the surface area thereof.
- the regions 81 and 9 of conductive material form terminals for the transducer unit, the latter region also forming an outer displacement imparting electrode.
- the portions of the large region 9 of conductive material covering the opposite faces 11 and 13 of the transducer unit confronts the opposite faces of at least one inner electrode 15 imbedded Within a body of piezoelectric material 17 constituting most of the volume of the transducer unit 2.
- the inner electrode 15 is in a plane parallel to the opposite faces 11 and 13 of the piezoelectric body.
- the transducer unit 2 is pre-polarized in a direction transverse to the thickness thereof as shown by arrows 21 in FIG. 6 by application of a suitable dire-ct current voltage between the conductive regions or terminals 8 and 9 thereof.
- the piezoelectric body 17 forms a single, continuous, homogeneous monolithic body of piezoelectric material, so that the polarization referred to makes the entire volume of the piezoelectric body active in the piezoelectric process.
- the transducer unit When a signal voltage is applied across the terminals 8 and 9 in a direction to oppose this polarization, the transducer unit will contract in thickness which, in turn, results in an expansion of the length of the piezoelectric body, which is the desired movement in the high speed printing mechanism application of the invention illustrated in FIG. 1. If the aforesaid signal voltage reinforces the polarization, the transducer unit would expand in thickness and contract longitudinally.
- a biasing action voltage 23 (FIG. 7) is desirably applied in a direction of the original poling orientation, and a source of signal voltage 25 is connected in series with the biasing voltage source 23 between the transducer terminals 8 and 9, so that the signal voltage is superimposed on and opposes the biasing voltage, as illustrated Iby the curve of FIG. 8.
- the bias voltage source 23 will re-establish the original polarization, if any depoling action results from the signal voltage.
- the signal voltage may be raised substantially beyond the limits di-ctated by an unbiased transducer unit without de-poling the transducer or reversing its direction of polarization, thereby increasing the amount of elongation that can be produced.
- each transducer unit in the housing 6 in any suitable Way, such as by placing within the housing 6, which is shown as being made of a molded insulating plastic material, a pair of longitudinally spaced metal rings 25 and 27 which line each cavity 5 :and are respectively engaged b ⁇ y the insulated terminals 8 and 9 formed by the aforementioned regions of conductive material on the piezoelectric body of the associated transducer unit as best shown in FIG. 3.
- the rings 25 and 27 are connected by conductor strips 25 and 27 to the rear face of the housing 6 where they are engaged by suitable terminal posts or screws 31 and 33, respectively, to which the bared end of signal wires 35 and 37 and respectively connected.
- Each pair of signal wires 3S and 37 extend to the circuit including the biasing voltage source 23 and the signal voltage source 25, as shown in FIG. 7.
- the transducer units 2 can be made in a wide variety of sizes.
- the piezoelectric body had an over-all thickness of between 18 and 20 mils, a length of about 41/2 inches, and a width of about .2 inch.
- an elongation of over 1 mil resulted for a signal voltage of plus 400 volts.
- This voltage gradient could probably be raised to 30 volts per mil and higher without arcing problems.
- the monolithic character of the piezoelectric material forming the body 7 added materially to the strength, effectiveness and compactness of the transducer unit 1.
- FIGS. 9 through 12 illustrate the manner in which the transducer units 2 are preferably made.
- thin flexible at sheets 17a- 17b of raw piezoelectric ceramic material lare which are sized to form a number of transducer units.
- the formulation of the slip used contains appropriate proportion of binder and vehicle along with the ceramic powders needed to produce a piezoelectric body, such as one of the family of barium titanates or lead titanate-zirconates.
- An exemplary formula for the ceramic is a modified lead titan-ate zirconate Pb98 5La1.5(Ti46Zr54)03. Since the sheets are enforced by binder content, they may be made very thin without major problems in handling.
- the thickness of the sheets 17a-17b depends upon the desired thickness of the piezoelectric bodies desired, and consideration must be given to substantial shrinkage factors common in the firing of piezoelectric ceramic materials (shrinkage factors of 25% are not uncommon).
- the surface of one of the sheets 17a which is to confront the other sheet 17b has applied thereon metallic coatings 15a as shown in FIG. 9 which all extend to the same edge 17a' of the sheet 17a.
- the material which is coated on the sheet 17a may be a suspension of ne noble 4metal powder, such as platinum, palladium, platinum-gold mixture, or similar metal which will remain inert and survive subsequent firing at high temperatures.
- the sheet 17b is then placed on the coated side of the sheet 17a (FIG. l0) and the sheets 4are pressed to promote intimacy of contact and eliminate entrapped air from between the sheets.
- a printing pattern comprising lines 40 may be suitably screened or otherwise formed on the outside of the sheet 17b best shown in FIG.
- the laminate body should be cut to form separate individual transducer units
- the individual elements are then red at a suitable temperature, as, for example, in a kiln with a controlled atmosphere into which lead oxide vapors are introduced Initially, the transducer elements are heated slowly to drive off organic binders and the like. The units are then heated to a much higher temperature, for example, a temperature of 2350 degrees Fahrenheit to sinter the ceramic material and solidify the same to form a solid monolithic block.
- the internal metal electrodes 15 become a continuous, conducting film imbedded within the ceramic material and emerging only -at one end to provide access for external electrode connections as indicated previously.
- the resulting transducer unit comprises two electroded layers of monolithically bonded piezoelectric material which are electrically connected in parallel, as shown in FIG. 7.
- FIG. 14 illustrates a transducer unit 2' with an outer piezoelectric body 17 having three internal electrodes, the outer electrodes 15-15 extending to the narrow region of conductive material 8 and immediately confronting the large region of conductive material 9' for most of the length and width of the body 17.
- Another internal electrode 45 - is positioned in spaced relation between the electrodes 15-15' and extends to the end face of the piezoelectric body 17 opposite to that including the narrow region of conductive material 8.
- a piezoelectric transducer unit comprising: a thin plate-like body of piezoelectric ceramic material having opposite ends to which movement is to be imparted in a direction along a line extending between the ends thereof by application of a voltage acrossthe thickness thereof, said body of piezoelectric material having imbedded therein at least one inner electrode which is spaced from all margins of the body except one end edge thereof to which the electrode extends, said electrode encompassing most of the cross sectional area of the body in a plane transverse to the thickness of the body, a first region of conductive material at least on the outside edge of said piezoelectric body at said one end thereof which region of conductive material makes electrical contact with said inner electrode extending to the end edge, a second region of conductive material on the outside of said body and spaced by an insulating gap from said first region of conductive material, said first region of conductive material constituting one terminal of the transducer unit and said second region of conductive material constituting another terminal and an electrode of the transducer unit which immediately confronts, is
- the piezoelectric transducer unit of claim 1 wherein said first region of conductive material is located entirely in a small region at said one end of the piezoelectric body and said second region of conductive material extends for most of the length of the piezoelectric Ibody.
- transducer unit of claim 3 wherein said rst region of conductive material extends around the side o the piezoelectric body for a short distance representing an insignificant portion of the length of the body, to provide a much larger area of conductive material than the area of the end edge thereof.
- transducer unit of claim 2 wher-ein there are n parallel spaced inner electrodes like said one electrode within said piezoelectric body which extend to said one end thereof to make contact with said first region of conductive material, n being an even number, and there are n-l electrodes in spaced parallel relation to and interleaved with said n parallel electrodes, each of said n-l electrodes extending to a surface of the piezoelectric body which is covered by said second region of conductive material to make electrical Contact therewith, the portions of said second region of conductive material on said opposite faces of said piezoelectric body immediately confronting the outermost of said n electrodes.
- the transducer unit of claim 5 wherein the surface of the piezoelectric body to which said n-l inner electrodes extend is the end edge thereof opposite the end edge to which said n inner electrodes extend, and said second region of conductive material covering the former end edge in addition to the opposite faces of the piezoelectric body.
- the transducer unit of claim 1 wherein the piezoelectric body is an elongated body whose width is only a small fraction of the length thereof and whose thickness is only a small fraction of the width thereof.
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Description
Oct. 21, 1969 N. RUDNICK PIEZOELECTRIC CERAMIC TRANSDUCER 2 Sheets-Sheet 1 Oct. 21, 1969 lN. RuDNlcK 3,474,268
PIEZOELECTRIC CERAMIC TRANSDUCER Filed April 21, 1966 2 Sheets-Sheet 2 United States Patent O 3,474,268 PIEZOELECTRIC CERAMIC TRANSDUCER Norman Rudnick, Piscataway, NJ., assignor to Gulton ndustries, Inc., Metuchen, NJ., a corporation of New ersey Filed Apr. 21, 1966, Ser. No. 544,242 Int. Cl. H01v 7/00 U.S. Cl. S- 8.5 8 Claims ABSTRACT OF THE DISCLOSURE A piezoelectric transducer having a homogeneous monolithic body having one electrode embedded in the center of the body and the other electrode completely surrounding the body except at one end thereof. The monolithic body operates in the shear mode.
The present invention relates to bar or strip type piezoelectric ceramic transducers which are to produce a mechanical 4movement in response to the application of a voltage thereto, and has its most important (but not its only) application to transducers of this type which are to impart appreciable thrust or pulling forces at high rates as detemined by voltage pulses applied at relatively high random pulse repetition rates.
The production of a bar or strip type piezoelectric transd-ucer which must operate at appreciable force and displacement magnitudes and at high rates, such as hundreds or thousands of force pulsations per second, and at reasonably low voltages generally requires a very thin sandwich of two or more piezoelectric elements connected in parallel. Frequently, such a piezoelectric transducer must have a thickness well under 100 mils (like 20-30 mils or less). Prior to the present invention, due to the nature of the transducer constructions, it was exceedingly difiicult to manufacture such thin bar or strip type transducer sandwiches having the required ruggedness and sensitivity. Thus, it was heretofore the practice to manufacture ceramic transducers of the type referred to by first fabricating individual two terminal transducer elements and then cementing them together. The cementing of the transducer elements was disadvantageous because, among other reasons, it was difiicult to handle the thin transducer elements during the cementing process without breaking the same. Also, the ceramic transducer elements are formed by firing unusually thin strips of raw ceramic which easily warp during the firing process. Additionally, the adhesive used to cement the transducer element together added appreciably to the thickness of the resulting sandwich to reduce the displacement per unit thickness achieved with a given electric field. Moreover, the electrode configurations used created arcing, terminal soldering and contact problems, and the most effective use of the piezoelectric material was not achieved.
It is, accordingly, one of the objects of the invention to provide a very thin sensitive rugged bar or strip type ceramic piezoelectric transducer sandwich in which appreciable intermittent movement can be imparted thereto at high random rates by voltage pulses fed thereto at high pulse repetition rates and relatively modest voltage levels.
Another object of the invention is to provide a bar or strip type ceramic piezoelectric transducer sandwich which produces a maximum deflection for a given voltage and for a given thickness and volume of piezoelectric material utilized.
Still another object of the invention is to provide a ceramic piezoelectric transducer sandwich as described which is so thin that large voltage gradients are present ice and yet where arcing between the electrodes does not readily take place.
A further object of the invention is to provide a ceramic transducer sandwich as described which, because of its mode of construction, can be easily manufactured in extremely thin cross-sections without warping and other problems and by mass production techniques.
A still further object of the invention is to provide a thin ceramic transducer sandwich as described to which strong solder connections or other good contact connections can be readily made.
Another object of the invention is to provide a ceramic transducer sandwich as described where the movement of the transducer unit is a longitudinal expansion or contraction thereof in response to a signal voltage applied across the thickness thereof.
To best appreciate the significance of the present invention, it should be understood that piezoelectric ceramic transducers generally produce very small mechanical displacements when electrically stressed unless operated under resonant conditions or in bending or flexural modes. The operation of piezoelectric transducers under resonant conditions has serious shortcomings. For example, resonant operation may not be suitable because it may be difficult to design a transducer to operate at the desired frequency or because the transducer must be operated at random times. Also, with resonant operation of transducers small forces opposing the motion thereof will suppress much of the amplified motion resulting from the resonant mode of operation thereof. Bending or iiexural modes of operation of a piezoelectric transducer unit achieve large displacements only at the sacrifice of the ability to apply strong thrust or pulling forces.
The best electromechanical coupling in piezoelectric transducer units is attained when the displacements thereof are in line with the applied electric fields. In this case, however, the applied voltage must generally be very large to produce relatively large movements. In the case where the displacements involved are transverse to the applied electric field, relatively large movement accompanied by relatively large forces can be generated without requiring very large voltages. The transducer of the present invention is constructed to operate in the latter mode.
In the most advantageous form of the invention, two or more pairs 4of thin elongated strips of piezoelectric ceramic material are secured together with one or more electrode layers between each pair of strips. The electrode layer between the strips of each pair of strips of piezoelectric material is spaced appreciably from all margins of the sandwich except one which is most desirably one end margin of the piezoelectric sandwich. There is located between the contiguous pair of strips of piezoelectric material (where more than one pair is utilized) an electrode layer spaced appreciably from all margins of the sandwich except one which is most desirably at the opposite end of the piezoelectric sandwich from said one end. The electrode layers encompass most of the cross sectional area of the transducer unit in a plane parallel to the opposite faces (i.e. transverse to the thickness) of the transducer unit. A first region of conductive material is applied to an end face of the piezoelectric sandwich to which the electrode layers between the strips of each pair of strips extend. This region of conductive material preferably extends a short distance around the sides of the piezoelectric sandwich materially to increase the area of conductive material occupied by the first region of said material which forms a terminal for the transducer unit of appreciable area, though occupying only an insignificant percentage of the area of the entire transducer unit. A second region of conductive material is preferably applied to the remaining surface area of the piezoelectric sandwich except for a narrow insulating gap separating the same from said lirst region of conductive material. The second region of conductive material will thus make electrical contact with any inner electrode layers extending to said other end margin of the piezoelectric sandwich. The second region of conductive material forms a terminal for the transducer unit and with any other inner electrode connected thereto, electrode means which cooperates with the inner electrode layers extending to the first region of'conductive material to elfect the desired displacement when a voltage is applied to the transducer unit.
A feature of substantial importance is that the piezoelectric sandwich is constructed so that the piezoelectric material throughout the sandwich forms a single, continuous, homogeneous monolithic body of such material extending between said regions of conductive material and around the edges of all of the inner electrodes except the edges thereof extending to the margins of the piezoelectric sandwich. The monolithic character of the piezoelectric sandwic'h can be achieved by superimposing thin sheets `of raw ceramic material held together with a binder and having the various aforesaid electrode layers silk screened or otherwise coated on the surfaces of the layers of ceramic material to be located within the sandwich, applying pressure to the raw ceramic sandwich and then firing the same to sinter the various sheets of raw ceramic material into a solid monolithic structure. The transducer unit described is formed into a piezoelectric unit by simply polarizing the piezoelectric ceramic mate- `rial by the application of a polarizing voltage between the terminals of the transducer unit.
For a single, long, thin element of piezoelectric ceramic electrode on its two major faces and poled in the direction of its thickness, the relation between longitudinal displacement and applied voltage is:
Where AL is the displacement in meters from the -unstrained length L, V is applied voltage in volts, d3, is the transverse piezoelectric strain coeiicient with units of meters/meter per volt/meter, and t is the thickness of the transducer in meters. It can be seen that the displacement can be increased without change in voltage by increasing the length and `decreasing the thickness.
The transducer unit described above comprising two or more strips or layers of piezoelectric material secured together in a manner to form a continuous, homogeneous, monolithic piezoelectric body constitutes a multiplicity of piezoelectric elements electrically connected in parallel. Such a transducer unit can deliver the same displacement with a greater thrust at the same voltage than a single layer transducer unit. Also, in the monolithic multi-layered structure described, the applied voltages affect substantially all portions of the piezoelectric body for maximum response and arcing is prevented because the closely spaced edges of the electrodes are separated by a high di-electric ceramic material. Moreover, it is much stronger in its raw unfired state (as well as its completed state) than a single layered structure, so warping cannot readily occur during firing thereof, and it affords such mounting advantages as a grounded outer surface where needed and greater resistance to breaking where cementing or clamping of the transducer unit is required. Also, strong solder or other good electrical connections can readily be made thereto.
The transducer unit of the invention described above can be mounted within a holder which confines the transducer on all sides except one end thereof. Then, when the voltage is applied to the terminals of the transducer unit, all of the displacement will occur at one end of the transducer element. The holder can include terminal strips which contact the aforesaid first and second regions of conductive material and lead to screw or other ter- 4 minals for connecting the ends of conductor wires. Alternatively, wires can be directly soldered to the regions of conductive material referred to.
The amount of motion producible by the transducer unit yof the invention with presently available piezoelectric ceramic compositions makes it useful wherever small displacements are required `with a minimum of machinery and electrical input. Such applications lie in the areas of optical adjustments, switching. actions, pumping devices, and, in particular, rapid printing mechanisms. For example, a 4.6 inch long, two-layered strip, 0.20 inch wide and 0.018 inch thick, has a lowest resonant frequency of over 10,000 cycles per second. For application in a printing mechanism, the voltage pulses fed thereto,which are desirably fed at a pulse repetition rate well below the lowest resonant frequency thereof, can be ata 4rate of several hundreds and even thousands of pulses per second, which can provide repeated random thrusts ata rate far exceeding the rates attainable by conventional printing mechanisms. Whereas conventional printing mechanisms operate at -rates -of the order of 3 to 4 lines per second, instruments using the piezoelectric transducer of the present invention can be operated to produce to 200 lines per second and higher.
Fora clearer understanding of the present invention, reference should be made tothe drawings wherein:
FIG. 1 is a perspective view of a rapid printing mechanism having a printing head with the transducer unit of the present invention incorporated therein;
FIG. 2 is a greatly enlarged, fragmentary sectional view through the printing head of FIG. 1, taken along section line 2--2 thereof;
FIG. 3 is another sectional view of the printing head of FIGS. 1 and 2, taken along section lineI 3 3 in FIG. 2;
FIG. 4 is a perspective view of a transducer unit used in the printing head of FIGS. 1 through 3, and having one internal electrode;
FIG. 5 is an enlarged horizontal longitudinal sectional view through the transducer unit of FIG. 4, taken along section line 5-5 therein;
FIG. 6 is a greatly enlarged fragmentary, transverse sectional, perspective view of the transducer unit of FIGS. 4 and 5;
FIG. 7 is a diagrammatic view of the transducer unit of FIG. 4 connected into an electrical circuit to operate the same;
FIG. 8 is a curve showing exemplary bias and signal voltages applied to a transducer unit of the invention;
FIGS. 9 through 13, are a series of views illustrating a preferred method of mass producing transducer units like that illustrated in FIGS. 4 through 6; and
FIG. 14 is a longitudinal vertical sectional view through a form of transducer unit of the present invention which utilizes a number of internal electrodes.
As previously indicated, one of the most important applications of the present invention is in a high speed printing mechanism where the transducer elements are operated at very high speeds. FIG. 1 illustrates such a high speed printing mechanism which includes a printing head generally indicated by reference numeral 1 which carries on the inner face thereof a row of thin transducer units 2 which are mounted in closely spaced relation with their thin dimensions extending in the direction of the spacing thereof in individual cavities 5 in a housing `6 forming part of lthe printing head. The vindividual transducer units 2 are most advantageously thin and elongated as shown in FIG. 4 and of rectangular cross-section. Each transducer unit is closely confined but not constricted against longitudinal sliding movement on three sides thereof, as shown in FIGS. 2 and 3, and have an inner end projecting horizontally from the printing head housing 6 -where it is free to move longitudinally outwardly. A small piece of metal or other similar material 7 is preferably secured by an adhesive or otherwise on the projecting end face or edge of each transducer unit 2. The metal faced end of each transducer unit may be positioned to engage a printing element or, as illustrated, one side of a moving strip of paper whose other side passes by a stationary or moving raised indicia carrying member 12. As a transducer unit 2 is thrust outwardly momentarily, an imprint is made on the point of paper 10 engaged by (or opposite the) small end face of the transducer unit involved. The metal facing 7 on each transducer unit protects the end thereof from wear.
4Each transducer unit has a pair of terminals formed by insulated regions of conductive material 8 and 9, as best shown in FIG. 4. The conductive region 8 preferably forms a narrow end cap around one end of the transducer unit and so covers the end face and a narrow strip on all side faces and edges of the transducer unit occupying only an insignificant fraction of the length of the transducer unit. The other region 9 of conductive material is spaced from the narrow region l8 of conductive material by a narrow insulating gap 10, and preferably occupies, except for the gap 10i, and the area encompassed by the conductive end cap 8, all remaining surface areas of the transducer unit, which is most of the surface area thereof. The regions 81 and 9 of conductive material form terminals for the transducer unit, the latter region also forming an outer displacement imparting electrode. The portions of the large region 9 of conductive material covering the opposite faces 11 and 13 of the transducer unit confronts the opposite faces of at least one inner electrode 15 imbedded Within a body of piezoelectric material 17 constituting most of the volume of the transducer unit 2. As best shown in FIGS. 5 and 6, the inner electrode 15 is in a plane parallel to the opposite faces 11 and 13 of the piezoelectric body. It occupies most of the crosssectional area of the piezoelectric body in said plane and is spaced from all margins of the piezoelectric body 17 except the end thereof including the narrow region or lcap 8 of conductive material with which it makes electrical contact by extending to the end face 19 thereof (FIG. 5).
The transducer unit 2 is pre-polarized in a direction transverse to the thickness thereof as shown by arrows 21 in FIG. 6 by application of a suitable dire-ct current voltage between the conductive regions or terminals 8 and 9 thereof. As previously indicated, the piezoelectric body 17 forms a single, continuous, homogeneous monolithic body of piezoelectric material, so that the polarization referred to makes the entire volume of the piezoelectric body active in the piezoelectric process. When a signal voltage is applied across the terminals 8 and 9 in a direction to oppose this polarization, the transducer unit will contract in thickness which, in turn, results in an expansion of the length of the piezoelectric body, which is the desired movement in the high speed printing mechanism application of the invention illustrated in FIG. 1. If the aforesaid signal voltage reinforces the polarization, the transducer unit would expand in thickness and contract longitudinally. l
Where a longitudinal expansion of the transducer unit 2 is desired, a biasing action voltage 23 (FIG. 7) is desirably applied in a direction of the original poling orientation, and a source of signal voltage 25 is connected in series with the biasing voltage source 23 between the transducer terminals 8 and 9, so that the signal voltage is superimposed on and opposes the biasing voltage, as illustrated Iby the curve of FIG. 8. When the signal voltage is removed, it is apparent that the bias voltage source 23 will re-establish the original polarization, if any depoling action results from the signal voltage. If desired, because of the bias voltage, the signal voltage may be raised substantially beyond the limits di-ctated by an unbiased transducer unit without de-poling the transducer or reversing its direction of polarization, thereby increasing the amount of elongation that can be produced.
In the printing head application of the invention shown in FIGS. 1 through 3, electrical connection is made to the terminals 8 and 9 of each transducer unit in the housing 6 in any suitable Way, such as by placing within the housing 6, which is shown as being made of a molded insulating plastic material, a pair of longitudinally spaced metal rings 25 and 27 which line each cavity 5 :and are respectively engaged b`y the insulated terminals 8 and 9 formed by the aforementioned regions of conductive material on the piezoelectric body of the associated transducer unit as best shown in FIG. 3. The rings 25 and 27 are connected by conductor strips 25 and 27 to the rear face of the housing 6 where they are engaged by suitable terminal posts or screws 31 and 33, respectively, to which the bared end of signal wires 35 and 37 and respectively connected. Each pair of signal wires 3S and 37 extend to the circuit including the biasing voltage source 23 and the signal voltage source 25, as shown in FIG. 7.
The transducer units 2 can be made in a wide variety of sizes. For one printing head application, the piezoelectric body had an over-all thickness of between 18 and 20 mils, a length of about 41/2 inches, and a width of about .2 inch. With such a construction, with a bias of negative 200 volts, an elongation of over 1 mil resulted for a signal voltage of plus 400 volts. This produced a voltage gradient of 20 volts per mil and yet no arcing occurred. This voltage gradient could probably be raised to 30 volts per mil and higher without arcing problems. The monolithic character of the piezoelectric material forming the body 7 added materially to the strength, effectiveness and compactness of the transducer unit 1.
Refer now to FIGS. 9 through 12 which illustrate the manner in which the transducer units 2 are preferably made. As shown in FIG. 9, thin flexible at sheets 17a- 17b of raw piezoelectric ceramic material lare provided which are sized to form a number of transducer units. The formulation of the slip used contains appropriate proportion of binder and vehicle along with the ceramic powders needed to produce a piezoelectric body, such as one of the family of barium titanates or lead titanate-zirconates. An exemplary formula for the ceramic is a modified lead titan-ate zirconate Pb98 5La1.5(Ti46Zr54)03. Since the sheets are enforced by binder content, they may be made very thin without major problems in handling. The thickness of the sheets 17a-17b depends upon the desired thickness of the piezoelectric bodies desired, and consideration must be given to substantial shrinkage factors common in the firing of piezoelectric ceramic materials (shrinkage factors of 25% are not uncommon).
The surface of one of the sheets 17a which is to confront the other sheet 17b has applied thereon metallic coatings 15a as shown in FIG. 9 which all extend to the same edge 17a' of the sheet 17a. The material which is coated on the sheet 17a may be a suspension of ne noble 4metal powder, such as platinum, palladium, platinum-gold mixture, or similar metal which will remain inert and survive subsequent firing at high temperatures. The sheet 17b is then placed on the coated side of the sheet 17a (FIG. l0) and the sheets 4are pressed to promote intimacy of contact and eliminate entrapped air from between the sheets. A printing pattern comprising lines 40 may be suitably screened or otherwise formed on the outside of the sheet 17b best shown in FIG. 9 to indicate where the laminate body should be cut to form separate individual transducer units The individual elements are then red at a suitable temperature, as, for example, in a kiln with a controlled atmosphere into which lead oxide vapors are introduced Initially, the transducer elements are heated slowly to drive off organic binders and the like. The units are then heated to a much higher temperature, for example, a temperature of 2350 degrees Fahrenheit to sinter the ceramic material and solidify the same to form a solid monolithic block. The internal metal electrodes 15 become a continuous, conducting film imbedded within the ceramic material and emerging only -at one end to provide access for external electrode connections as indicated previously.
i. After the firing operation, a strip of adhesive material l42 (FIG. 11) Vis wound around each piezoelectric element intimate contact with the piezoelectric material. This .forms a strong bond between the silver and the ceramic. The tail 42 of the adhesivey strip 42 is grasped and unraveled, which leaves the aforementioned insulating gap 10. The resulting transducer unit comprises two electroded layers of monolithically bonded piezoelectric material which are electrically connected in parallel, as shown in FIG. 7.
As previously indicated, if a greater thrust or pulling force is desired, additional pairsof electroded piezoelectric layers are added to the transducer laminate during its fabrication. In such case, in order that the piezoelectric material of the body 17 be most effectively used, it is necessary thatA both sides of each internal electrode extending to the narrow region of conductive material 9 confront an electrode extending to the large region of conductive material 9. Assuming that the second region of conductive material 9 covers both faces 11 and 13 of the piezoelectric body as in the preferred form of the invention, there would be an odd number of internal electrodes imbedded within the body of piezoelectric material with an even number (n) of electrodes extending to the narrow region of conductive material 8 and (la-1) internal electrodes extending to the opposite ends of the piezoelectric body where they contact the large region of conductive material 9. Each of the latter electrodes is positioned between and spaced from a pair of the (n) electrodes extending to the region of conductive material 8. FIG. 14 illustrates a transducer unit 2' with an outer piezoelectric body 17 having three internal electrodes, the outer electrodes 15-15 extending to the narrow region of conductive material 8 and immediately confronting the large region of conductive material 9' for most of the length and width of the body 17. Another internal electrode 45 -is positioned in spaced relation between the electrodes 15-15' and extends to the end face of the piezoelectric body 17 opposite to that including the narrow region of conductive material 8.
It should be understood that numerous modifications may be made in the most preferred forms of the invention described above without deviating from the broader .aspects of the invention.
I claim:
1. A piezoelectric transducer unit comprising: a thin plate-like body of piezoelectric ceramic material having opposite ends to which movement is to be imparted in a direction along a line extending between the ends thereof by application of a voltage acrossthe thickness thereof, said body of piezoelectric material having imbedded therein at least one inner electrode which is spaced from all margins of the body except one end edge thereof to which the electrode extends, said electrode encompassing most of the cross sectional area of the body in a plane transverse to the thickness of the body, a first region of conductive material at least on the outside edge of said piezoelectric body at said one end thereof which region of conductive material makes electrical contact with said inner electrode extending to the end edge, a second region of conductive material on the outside of said body and spaced by an insulating gap from said first region of conductive material, said first region of conductive material constituting one terminal of the transducer unit and said second region of conductive material constituting another terminal and an electrode of the transducer unit which immediately confronts, is parallel to and is spaced from at least one face of said inner electrode over an extensive area thereof, said body of piezoelectric material being polarized in the direction of the thickness thereof, wherein application of a signal voltage across said terminals will effect contraction or expansion of the piezoelectric body transversely thereof resulting respectively in the expansion or contraction of the ends thereof, and said body of piezoelectric material being a single, continuous, homogeneous monolithic body of such material extending between `all of said electrodes and around all the edges of each inner electrode except the one edge extending to said one end of the piezoelectric body.
2. The piezoelectric transducer unit of claim 1 wherein said first region of conductive material is located entirely in a small region at said one end of the piezoelectric body and said second region of conductive material extends for most of the length of the piezoelectric Ibody.
3. The transducer unit of claim 2 wherein there s an odd number of inner electrodes in said body of piezoelectricmaterial, said second region of conductive material covers substantially all the surface areas of the piezoelectric body on all sides thereof, and the portions of said second region of conductive material on the opposite faces of the piezoelectric body each confronts a corresponding portion of an inner electrode which is electrically connected to said first region of conductive material at said one end of the piezoelectric body.
4. The transducer unit of claim 3 wherein said rst region of conductive material extends around the side o the piezoelectric body for a short distance representing an insignificant portion of the length of the body, to provide a much larger area of conductive material than the area of the end edge thereof.
5. The transducer unit of claim 2 wher-ein there are n parallel spaced inner electrodes like said one electrode within said piezoelectric body which extend to said one end thereof to make contact with said first region of conductive material, n being an even number, and there are n-l electrodes in spaced parallel relation to and interleaved with said n parallel electrodes, each of said n-l electrodes extending to a surface of the piezoelectric body which is covered by said second region of conductive material to make electrical Contact therewith, the portions of said second region of conductive material on said opposite faces of said piezoelectric body immediately confronting the outermost of said n electrodes.
6. The transducer unit of claim 5 wherein the surface of the piezoelectric body to which said n-l inner electrodes extend is the end edge thereof opposite the end edge to which said n inner electrodes extend, and said second region of conductive material covering the former end edge in addition to the opposite faces of the piezoelectric body.
7. The transducer unit of claim 1 wherein the piezoelectric body is an elongated body whose width is only a small fraction of the length thereof and whose thickness is only a small fraction of the width thereof.
8. The transducer unit of claim 7 wherein the surface of the piezoelectric body to which said n-l inner electrodes extend is the end edge thereof opposite the end edge to which said n inner electrodes extend, and said second region of conductive material covering the former end edge in addition to the opposite faces of the piezoelectric body.
References Cited UNITED STATES PATENTS 1,860,529 5/1932 Cady 310-8.6 2,269,403 1/ 1942 Williams S10-8.6 2,451,966 10/ 1948 Massa 310-86 3,115,588 12/1963 Hueter S10-8.6 3,258,617 6/1966 Hart B10-8.6 3,378,704 4/ 1968 Miller 310-85 I. D. MILLER, Primary Examiner I Us. C1. XR.
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
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US54424266A | 1966-04-21 | 1966-04-21 |
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US3474268A true US3474268A (en) | 1969-10-21 |
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Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
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US544242A Expired - Lifetime US3474268A (en) | 1966-04-21 | 1966-04-21 | Piezoelectric ceramic transducer |
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US3590287A (en) * | 1966-11-17 | 1971-06-29 | Clevite Corp | Piezoelectric thin multilayer composite resonators |
US4087716A (en) * | 1975-09-22 | 1978-05-02 | Siemens Aktiengesellschaft | Multi-layer element consisting of piezoelectric ceramic laminations and method of making same |
FR2427660A1 (en) * | 1978-05-29 | 1979-12-28 | Philips Nv | DEVICE FOR CONTROL OF A PIEZO-ELECTRIC POSITIONING ELEMENT |
FR2499805A1 (en) * | 1981-02-09 | 1982-08-13 | Nukem Gmbh | METHOD FOR PRODUCING AND / OR RECEIVING ULTRA-SOUND SIGNALS |
US4443729A (en) * | 1981-06-22 | 1984-04-17 | Rockwell International Corporation | Piezoceramic bender element having an electrode arrangement suppressing signal development in mount region |
US4471256A (en) * | 1982-06-14 | 1984-09-11 | Nippon Soken, Inc. | Piezoelectric actuator, and valve apparatus having actuator |
WO1988004475A1 (en) * | 1985-08-06 | 1988-06-16 | The Dow Chemical Company | Piezoelectric/pyroelectric elements and a process for making same |
US5430342A (en) * | 1993-04-27 | 1995-07-04 | Watson Industries, Inc. | Single bar type vibrating element angular rate sensor system |
US5475278A (en) * | 1991-04-15 | 1995-12-12 | Nec Corporation | Method for driving piezoelectric actuator |
US5760530A (en) * | 1992-12-22 | 1998-06-02 | The United States Of America As Represented By The Secretary Of The Air Force | Piezoelectric tactile sensor |
US6335856B1 (en) | 1999-03-05 | 2002-01-01 | L'etat Francais, Represente Par Le Delegue Ministeriel Pour L'armement | Triboelectric device |
US6515403B1 (en) * | 2001-07-23 | 2003-02-04 | Honeywell International Inc. | Co-fired piezo driver and method of making for a ring laser gyroscope |
US20040027035A1 (en) * | 2001-07-30 | 2004-02-12 | Ngk Insulators, Ltd. | Piezoelectric/electrostrictive element and piezoelectric/electrostrictive device and production method thereof |
US20050134144A1 (en) * | 2003-12-18 | 2005-06-23 | Palo Alto Research Center Incorporated | Poling system for piezoelectric diaphragm structures |
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US20040027035A1 (en) * | 2001-07-30 | 2004-02-12 | Ngk Insulators, Ltd. | Piezoelectric/electrostrictive element and piezoelectric/electrostrictive device and production method thereof |
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US20050134144A1 (en) * | 2003-12-18 | 2005-06-23 | Palo Alto Research Center Incorporated | Poling system for piezoelectric diaphragm structures |
US7176600B2 (en) * | 2003-12-18 | 2007-02-13 | Palo Alto Research Center Incorporated | Poling system for piezoelectric diaphragm structures |
WO2010019371A1 (en) * | 2008-08-14 | 2010-02-18 | Maki Voldi E | Method and apparatus for measurement of mechanical characteristics of a cement sample |
US20100042342A1 (en) * | 2008-08-14 | 2010-02-18 | Maki Jr Voldi E | Method and Apparatus for Measurement of Mechanical Characteristics of a Cement Sample |
US7942064B2 (en) | 2008-08-14 | 2011-05-17 | Maki Jr Voldi E | Method and apparatus for measurement of mechanical characteristics of a cement sample |
US9879615B2 (en) | 2015-12-16 | 2018-01-30 | General Electric Company | Machine-specific probabilistic control in gas turbine tuning for power output-emissions parameters, related control systems, computer program products and methods |
US9879612B2 (en) | 2015-12-16 | 2018-01-30 | General Electric Company | Combined probabilistic control in gas turbine tuning for power output-emissions parameters with scaling factor, related control systems, computer program products and methods |
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