Sensor Structure Incorporating Multiple Piezoelectric Generators

The present invention relates to piezoelectric sensors and in the preferred embodiment to piezoelectric angular rate sensor apparatus suitable for generating, in response to Coriolis acceleration forces, a signal containing angular rate information.

The concept of deriving angular rate information from piezoelectric generating devices is well known in the art. Such sensor devices are generally rotated about an axis perpendicular to the angular rate or rates to be sensed, the form of rotation either being continuous (i.e., spinning) or vibratory (i.e., oscillating). See for example U.S. Pat. Nos. 2,716,893 and 3,842,681. Moreover, such devices conventionally comprise two separate and distinct piezoelectric bender elements, each being independently mounted to a rotatable driveshaft so as to be substantially perpendicular to, and on opposing sides of, the driveshaft, each bender element further being oriented for generating a signal in response to a bending force parallel to the axis of rotation. Some prior art vibratory devices use four separate and distinct benders each being independently mounted at substantially 90.degree. intervals around the driveshaft.

Such devices exhibit deficiencies and problems which can make them unsuitable for some applications. For example, unacceptable differences in amplitude and/or phase between signals from the different bender elements may result if the individual bender elements are not electrically matched with one another or if the individual bender elements are not suitably aligned relative to one another and relative to the spin axis. These conditions can also result in contaminated signals because the device may not have an output stable with time and temperature and/or may not be immune to objectionable force components such as linear accelerations, vibrations and gravity, or such as vibration along the axis of rotation.

In accordance with the present invention, there is featured the provision of a piezoelectric sensor means which has improved characteristics in regard to the above identified problem areas. These and other features, objects, and advantages of the invention will become more apparent upon reference to the following specification, claims, and appended drawings in which:

FIG. 1 is a perspective view of a typical prior art piezoelectric rate sensor device;

FIG. 2 is a perspective view of a piezoelectric sensor embodiment incorporating many of the presently preferred features;

FIG. 3 is an equivalent circuit schematic representing the FIG. 2 apparatus and a preferred connection of the FIG. 2 sensor electrodes;

FIG. 4a is a perspective view representing the presently preferred inventive embodiment;

FIG. 4b is a sectional view of the sensor apparatus of FIG. 4a;

FIGS. 5 through 8 are perspective views representing examples of alternative sensor embodiments and features also within the inventive principles herein;

FIG. 9 is a perspective view representing a part which may be added to the FIG. 4a, 4b apparatus, thereby resulting in another alternative embodiment;

FIG. 10 is a sectional view representing the alternative embodiment achieved by adding the FIG. 9 apparatus to the FIG. 4a, 4b appartus;

FIG. 11a is a sectional view representing another alternative modification of the FIG. 4a, 4b apparatus, and

FIG. 11b is an equivalent circuit schematic representing the FIG. 11a apparatus.

Referring now to FIG. 1, the typical prior art embodiment therein shown comprises two separate and distinct piezoelectric bender elements 11 and 13, each being secured at one end to an opposite side of a spinning driveshaft 15, and each having an outward projecting free end to permit up-down element bending in response to Coriolis forces as the assembly spins. Such cantilevered bender element 11 typically comprises two layers 16 and 17 of polarized piezoelectric material and also two electrodes 19 and 21 located on exterior major surfaces of layers 16 and 17. Also in the prior art, a metal layer or coating 20 is sandwiched between layers 16 and 17. Similarly, cantilevered element 13 typically comprises two layers 22 and 23 of polarized piezoelectric material and two electrodes 25 and 27 located on exterior major surfaces of layers 22 and 23. As in element 11, element 13 further includes a metal layer 26 interiorly disposed between layers 22 and 23. Voltages generated in active layers 16, 17, 22, and 23 are combined in various ways to provide useful output signals and eliminate undesired signals.

In the angular rate sensing mode, and as the assembly spins while experienceing an angular rate normal to the spin axis, one bender element tends to flex through repeated up-down-up cycles while the other tends to flex out of phase through down-up-down cycles. Thus, as part of the usually preferred situation, for the condition where a constant angular rate is experienced about a single axis perpendicular to the spin axis, the two signals at the two respective electrode pairs, namely pair 19-21 and pair 25-27, would both be sine waves having identical peak amplitudes and frequencies and being out of phase exactly 180.degree.. As another part of the usually preferred case, the output signal between electrodes 19 and 25 would not reflect or be sensitive to forces parallel to the X-Y plane and would not on the average reflect reciprocating type vibrations of the shaft along the Z axis.

However, for several reasons, the FIG. 1 type of device has inherent deficiencies which can readily thwart accomplishment of these goals. For example, the two bender elements can have unmatched electrical characteristics due to a variety of factors. Such factors include (1) element-to-element differences in built-in stresses resulting from such things as variations in manufacturing conditions (2) element-to-element differences in sensitivity and temperature-dependence resulting from such things as batch-to-batch variations in materials (3) element-to-element differences in electrical characteristic changes with aging (4) element-to-element variations in polarization (5) element-to-element variations in the internal stresses resulting from different stresses imposed by the two independent mounts (6) non-repeatability of piezoelectric parameters within the same element due to temperature induced steady-state stresses in the mount regions. There is also the problem of improper alignment of the two bender elements relative to each other and relative to the driveshaft. Alignment is improper if (1) the two elements are not opposed suitably close to 180.degree. or (2) either element is not aligned suitably close to normal with the Z axis or (3) either element is "twisted" so that its bending axis is not parallel with the Z axis.

It should be apparent that, for purposes of facilitating explanation and description, three mutually perpendicular axes X, Y, and Z are superimposed on the illustrations of various sensor embodiments such that the Z axis is perpendicular to major surfaces and generally represents the axis about which the sensors spin.

Referring now to FIG. 2, the inventive embodiment 30 represented therein could in one respect (and as compared to the FIG. 1 prior art device) be partially described as a multiple bender embodiment fashioned according to a unitary structure. More particularly however, the sensor embodiment 30 represented in FIG. 2 is constructed of three flat rectangular plates of piezoelectric material arranged according to a laminated structure. Plates 31 and 33 are exteriorly disposed and plate 35 is interiorly disposed and sandwiched between plates 31 and 33. Located on the top major surface of plate 31 so as to electrically contact it are two electrodes 41 and 42. Relative to the Z axis, electrodes 41 and 42 are angularly displaced from one another such that their electrical "centers" are also angularly separated. In the preferred modes, such electrical center separation is a mechanical angle of 180.degree.. Moreover, each electrode is located and configured to exhibit certain aspects of symmetry. More particularly, each of electrodes 41 and 42 is disposed the same predetermined distance from, but on an opposite side of, the X-Z plane. Further, the major surface area contacted by electrode 41 is substantially symmetric about the Y-Z plane. Likewise, the major surface area contacted by electrode 42 is substantially symmetric about the Y-Z plane. Also, these two major surface contact areas are substantially symmetric with one another about the X-Z plane. Each of electrodes 41 and 42 is substantially rectangular in the FIG. 2 embodiment, their X dimension being substantially coextensive with the plate X dimension and their Y dimension being somewhat less than the plate Y dimension.

Still referring to FIG. 2, a third electrode 43 is interiorly disposed such that part of said electrode 43 is located between plates 31 and 35, and a further part of such electrode 43 is located between plates 33 and 35. In the FIG. 2 embodiment, such electrode 43 is located and configured to contact all of the bottom (i.e., interior) major surface of rectangular plate 31 and all of the top (i.e., interior) major surface of rectangular plate 33.

A fourth electrode 44 is exteriorly disposed at the FIG. 2 illustrated near end. In the FIG. 2 embodiment part of the fourth electrode occupies and contacts top major surface area of plate 31 and not occupied by electrode 41. Another substantially identical part of the fourth electrode is located to contact the bottom major surface of plate 33 directly below the top part of such fourth electrode. The fourth electrode 44 is substantially symmetric about the Y-Z plane and is electrically connected to the third electrode 43. A fifth electrode 45 is substantially the same as the fourth electrode 44 except electrode 45 is located at the FIG. 2 illustrated far end. Like the fourth electrode 44, the fifth electrode 45 is electrically connected to the third electrode 43 and is electrically isolated from the first and second electrodes 41 and 42. Electrodes 44 and 45 are substantially symmetric with one another about the X-Z plane.

A sixth electrode 46 is exteriorly disposed near the middle of the FIG. 2 illustrated sensor means. Part of such sixth electrode 46 occupies and contacts top major surface area of plate 31 between, and unoccupied by, first and second electrodes 41 and 42. The top major surface area contacted by this top part of electrode 46 is substantially symmetric about the Y-Z plane and is also substantially symmetric about the X-Z plane. Another part of the sixth electrode 46 is located on the bottom major surface of plate 33. The major surface area contacted by this bottom part of electrode 46, and the major surface area contacted by the top part of electrode 46, are substantially mirror images of one another about a plane parallel to the X-Y plane. The sixth electrode 46 is electrically connected to the third electrode 43 and is electrically isolated from the first and second electrodes 41 and 42.

Located to contact the bottom major surface of the bottom plate 33 are seventh and eighth electrodes 47 and 48. The bottom major surface contacted by the seventh electrode 47, and the top major surface area contacted by the first electrode 41 are substantially mirror images of one another about a plane parallel to the X-Y plane. Similarly, the bottom major surface contacted by the eighth electrode 48, and the top major surface area contacted by the second electrode 42, are substantially mirror images of one another about a plane parallel to the X-Y plane. The first, second, seventh, and eighth electrodes 41, 42, 47, and 48 are each electrically isolated from one another and also from the third, fourth, fifth, and sixth electrodes 43, 44, 45, and 46.

Each of piezoelectric plates 31, 33, and 35 uniformly and undirectionally polarized and, further, is polarized such that the direction of each plate's polarization is normal to the major surfaces, such direction also being normal in the FIG. 2 illustration to the X-Y plane. As illustrated in FIG. 2 by arrows 50 all three plates have a downward direction of polarization. For embodiments where it is intended for the voltages at the first and seventh electrodes 41 and 47 to be connected in parallel, then plates 31 and 33, when undirectionally polarized, should both be polarized upwardly or both downwardly. For embodiments where the voltages at the first and seventh electrodes 41 and 47 are intended to operate and be connected in series, then plates 31 and 33, when undirectionally polarized, should be polarized in opposite directions. For either case, interior plate 35 may be polarized uniformly in either an upward or downward direction. When it is intended to connect electrodes 42 and 48, they are typically connected in the same fashion that 41 and 47 are connected.

In use as a rate sensor, the FIG. 2 sensor 30 is typically secured to a spinnable shaft (not shown in FIG. 2) oriented and aligned coaxially with the Z axis. Attachment of sensor 30 to such shaft is typically accomplished by securing sixth electrode 46 to a shaft-mounted cross member (also not shown in FIG. 2). A hole through the center of the sensor 30 permits passage of the shaft therethrough.

FIG. 3 shows a typical electrode interconnection for the FIG. 2 sensor 30 being used as a signal generating rate sensor. As represented in FIG. 3, there are four distinct signal generating electrode-pairs. First and third electrodes 41 and 43 act as a signal generating electrode-pair G1, seventh and third electrodes 47 and 43 act as a further signal generating electrode-pair G2, second and third electrodes 42 and 43 act as another signal generating electrode-pair G3, and eighth and third electrodes 48 and 43 act as yet another signal generating electrode pair G4. The first and seventh electrodes 41 and 47 are electrically connected together so that the G1 and G2 electrode pairs operate in parallel. The second and eighth electrodes 42 and 48 are electrically connected together so that the G3 and G4 electrode pairs operate in parallel. The G1-G2 combination is connected in series with the G3-G4 combination and the voltage E.sub.O between electrodes 41 and 42 is used as the output signal. Typically, slip rings (not shown) are used to carry the signal to utilizing circuitry which is stationary (i.e., not rotating).

In use as a rate sensor, as the sensor 30 experiences an angular rate perpendicular to the spin axis Z, a Coriolis acceleration force is exerted on all elements of the mass of the sensor means. The useful acceleration term is parallel to the spin axis. Thus, the output voltage E.sub.0 is of the form

where K is a sensitivity constant for the sensor and where N is the spin frequency in radians per second. .theta. represents the angular displacement or tilt of the spin axis in the Y-Z plane and .psi. represents the angular displacement or tilt of the spin axis in the X-Z plane. .theta. and .psi. are respectively d.theta./dt and d.psi./dt and thus are angular rates about axes perpendicular to the spin axis. In the utilizing circuitry, the output voltage E.sub.O is phase detected and measured to determine the desired rates .theta. and .psi..

Connection of the electrodes according to FIG. 3 is suitable in preferred applications because the four generators G1, G2, G3, and G4 each generate a signal whose amplitude and phase are stable and predictable relative to the amplitude and phase of the other three signals. More particularly, both the G1 and G2 generated signals are AC signals whose electrical phase separation is substantially zero degrees and whose peak amplitudes are substantially equal. Also, both the G3 and G4 generated signals are AC signals whose electrical phase separation is substantially zero and whose peak amplitudes are substantially equal. Moreover, when the same Coriolis force magnitude is being sensed, the G1 and G3 generated AC signals are substantially equal in peak amplitude and are separated in electrical phase by substantially 180.degree.. The various symmetrics of the sensor structure and its electrodes and plates contribute significantly toward the producing of these presentaly preferred amplitude and phase relationships. These and other amplitude and phase relationships can also be achieved, for example, through different placement and/or configuration of electrodes. Such other relationships also find useful application since they are stable and determinable. Also, as will be seen from further description and explanations herein, bidirectional polarization can be employed in such a way that all four signals will be in-phase, i.e., separated in electrical phase by substantially 0.degree..

Turning now to FIG. 4a, the presently preferred embodiment 430 represented therein is constructed the same as the FIG. 2 embodiment with the basic exception that one is a circular or disc-shaped embodiment and the other is a rectangular or box-shaped embodiment. More particularly, the FIG. 4a embodiment 430 is a laminated structure comprising three flat piezoelectric plates 431, 433, and 435 which correspond directly in function to, respectively, plates 31, 33, and 35 in FIG. 2. The three plates 431, 433, and 435 are each uniformly polarized in a downward direction normal to the major surfaces. Also, the FIG. 4a embodiment includes first through eighth electrodes namely 441, 442, 443, 444, 445, 446, 447, and 448, which correspond directly in function and generally in location to, respectively, the eight FIG. 2 electrodes namely 41, 42, 43, 44, 45, 46, 47, and 48. The third electrode 443 in FIG. 4a is again interiorly disposed, having a part between plates 31 and 35 and another part between plates 33 and 35. Symmetries about the Y-Z plane of all electrodes are maintained. Symmetries among the first, second, seventh and eighth electrodes are maintained. Symmetry of the sixth electrode relative to the X-Z plane is maintained. The first, second, seventh, and eighth electrodes are maintained as the active electrodes, and the third, fourth, fifth, and sixth electrodes are again electrically connected together and act as points of a common potential. Inactive regions are again created at the central and end regions by the fourth, fifth, and sixth electrodes. As to differences, in the FIG. 4a embodiment 430 the piezoelectric plates 431, 433, and 435 are circular whereas the corresponding plates 31, 33, and 35 respectively, in the FIG. 2 embodiment 30 are rectangular. Also, in the FIG. 4a embodiment 430 the major surface areas contacted by the first, second, fourth, fifth, sixth, seventh, and eighth electrodes are bounded by various chords and arcs of the plate-defined circle, whereas in the FIG. 2 embodiment 30 the major surface areas contacted by these corresponding electrodes are bounded by the perimeters of various rectangles. Also, in the FIG. 4a embodiment, the upper and lower parts of the fourth electrode 444 are electrically connected together and also to the third electrode 443 by edge plating rather than by wires as represented in FIG. 2. Likewise for the upper and lower parts of the fifth electrode 445 and the upper and lower parts of the sixth electrode 446.

When in use as an angular rate sensor, the FIG. 4a sensor 430 is secured to a Z-axis-aligned spinnable shaft 71 via appropriate attachment of the sixth electrode 446 to a shaft-mounted cross member 73. Typical attachment is effected by soldering or adhesive bonding. It is of course desirable to maintain isolation between the active region electrodes and the driveshaft.

It is thus seen that the embodiments 30 and 430 are identical in concept and in principle of operation. However, the circular embodiment 430 is presently preferred because it offers increased efficiency and/or sensitivity when for a particular application it is desired that the maximum major surface dimension be restricted and small.

Either of the embodiments 30 or 430 may be formed as a monolithic structure. This involves drying a slurry of dielectric material into thin flat sheets, electroding the sheets, cutting the electroded green sheets to the desired shape, stacking the cut parts into a laminated structure, and then firing, poling, and cooling the structure. Alternatively, the embodiments may be constructed by bonding together preformed and electroded piezoceramic plates. In either case, completion of the desired electrode configurations may be achieved by applying electrode paste or paint, or removing, either chemically or mechanically, previously deposited electrode material. The manufacture of these embodiments is presently the same as described in my U.S. Pat. application Ser. No. 276,112 entitled "Piezoelectric Sensor" and assigned to the assignee hereof, said application also showing in its drawing a three layer piezoelectric device having interior and exterior electrodes. Said application elaborates further on certain details including device manufacture. Thus, for a more complete presentation, the teachings of said application Ser. No. 276,112 is hereby incorporated by reference into the present disclosure. The primary additional manufacturing step used to produce the embodiments 30 and 430 is to form the shaft-accomodating through-hole either mechanically or chemically. Of course, the hole may be omitted in some embodiments, such as those where the sensor means may be located at the end of the shaft.

It should also be noted that the uniformity of polarization of the piezoelectric material is an important aspect of the presently preferred embodiments. Internal stresses in the structure at extreme temperatures are minimized when the piezoelectric material is uniformly polarized. Accordingly, during manufacture, it is preferred that the exterior surface electrode configurations be established or altered after the piezoelectric material is poled in order to achieve uniformity of polarization at locations such as the fourth, fifth, and sixth electrode regions and also at locations such as the isolation gaps between electrodes associated with the active regions and electrodes associated with the inactive regions.

It should also be noted that the electrode arrangement of embodiments 30 and 430 electrically isolates a substantial portion of the end and central regions of each sensor apparatus, making the end regions and the central region inactive in the circuit and thus providing functional and/or structural symmetry and increased sensitivity and stability of the sensor means. More particularly, prior art piezoelectric sensors are typically bonded to or clamped in rigid mounting members. Because the piezoelectric parameters vary with steady-state stress, and because steady-state stress in the base or mount region of a sensor can change with temperature, it is preferred to virtually eliminate the signal developed in the mount region from the output signal of the sensor means, thereby improving long-term stability and repeatability of scale factor and impedance of the sensor means. In addition, changes in the elastic modulus of the bonding material at the interface change the distribution of stresses in the mount area of the bender element which in turn can change the effective length of the bender elements and thus affect scale factor. By removing the mount region from the active sensor regions, the effective length of the bender elements is more nearly defined by the configuration of the active electrode plating and is less influenced by variable strains in the mount and sensor-to-mount bond.

Turning now to FIG. 4b, therein is shown a sectional view of sensor 430 taken along the line 4b--4b of FIG. 4a. Typical presently preferred values (in inches) for the FIG. 4b-defined dimensions are as follows: r.sub.1 =0.075, r.sub.2 =0.105, r.sub.3 =0.25, r.sub.4 =0.28, r.sub.5 =0.5, r.sub.H =0.10, thickness, of plate 431=thickness of plate 433=0.01, thickness of plate 435=0.02. As indicated hereinabove, the sensor 430 is substantially symmetric about the X-Z plane and thus the various "r" dimensions and values are left-right symmetric about the center line in FIG. 4b. Electrode thickness is quite small and is exaggerated in all drawings for clarity of presentation. Typically, the thickness of each part of interior electrode 443 is less than 0.0005 inches. Also, typically, the thickness of each of the exterior electrodes is less than 0.001 inches. As also indicated hereinabove, each plate of sensor 430 is uniformly polarized downwardly and normal to the major surfaces. Such polarization is represented by the arrows in FIG. 4b.

As should now be apparent, the inventive principles herein may be variously embodied. FIGS. 5 through 11 represent embodiments which are exemplary of such alternatives. Each illustrated alternative includes three or more electrodes arranged on a base member of two or more piezoelectric plates. Many of the electrode and plate components in the FIGS. 5, 6, 7, and 8 embodiments correspond in function to similar electrode and plate components in the FIGS. 2 and 4a embodiments. To indicate such correspondence, each three digit numerical designator assigned to a component in FIGS. 5 through 8 uses the figure number as its most significant digit and uses as its least significant two digits the same two digit designator assigned to the corresponding component in FIG. 2. A similar scheme of designation was employed in FIGS. 4a and b.

Turning now to FIG. 5, therein is represented an embodiment which indicates that laminated embodiments using only two piezoelectric plates may be realized. The FIG. 5 embodiment includes first through eighth electrodes, namely, 541, 542, 543, 544, 545, 546, 547, and 548, and a laminated structure comprising two uniformly polarized piezoelectric plates 531 and 533. The third electrode 543 is sandwiched between plates 531 and 533.

Turning now to FIG. 6, therein is represented an embodiment employing two piezoelectric plates 631 and 633, and only first, second, and third electrodes 641, 642, and 643. FIG. 6 thus indicates that for some applications, a suitable embodiment need not include the shorted, inactive regions near the ends and the center.

The FIG. 7 apparatus, quite similarly to the FIG. 6 apparatus, employs two piezoelectric plates 731 and 733, and first, second, and third electrodes 741, 742, and 743. In FIG. 7 however, the first and second electrodes 741 and 742 are located to contact different exterior major surfaces of the plates 731 and 733. The third electrode 743 is interiorly disposed between plate 731 and plate 733 so as to contact same in areas suitable to maintain the formation of a first electrode pair and a second electrode pair.

FIG. 8 illustrates an alternative embodiment featuring more than two active electrodes on either or both exterior major surfaces. More particularly, FIG. 8 represents an embodiment quite similar to a wider or squarer version of the FIG. 5 apparatus which has been further modified to divide each one of the four active electrodes into two active electrodes. The resulting FIG. 8 apparatus this has eight active electrodes, namely, 841a, 841b, 842a, 842b, 847a, 847b, 848a, and 848b. Electrodes 847b, and 848b, not seen in FIG. 8, reside on the underside of plate 833 beneath, respectively, electrodes 841b and 842b. Each a-b pair could be interconnected to serve as a single electrode, the result being a FIG. 5 type of apparatus with only four electrically distinct generators. It is contemplated as preferable, however, to bring out the signal from each of the eight active electrodes and thus maintain eight distinct generators. Further, it is contemplated that for some applications, either one of electrodes 841a or 841b could serve by itself and without connection to the other as a "first electrode", that is, one analogous to the first electrode of FIGS. 2, 4a, or 5. Likewise, either one of 842a or 842b could serve by itself and without connection to the other as a "second electrode". Similarly for 847a, 847b, 848a, and 848b when they are employed. The FIG. 8 type of apparatus could thus be employed, for example, to effect additional redundancy.

FIG. 9 represents a small weight 91 whose configuration and makeup make it particularly suitable for adding mass at the ends of the sensor 430. More particularly, weight 91 comprises a single flat piezoelectric layer 93 which preferably bears, on at least one major surface, an electrode or metal layer 95. The shape of the weight 91 is generally that of a minor segment of a circle and, more particularly, matches the shape and size of the top and bottom portions of electrode 444 (and also 445) of sensor 430 illustrated in FIG. 4a.

Four of the weights 91, namely, 91a, 91b, 91c, and 91d, may be added to sensor 430 as illustrated in FIG. 10. Typically, the four weights are bonded to electrodes 444 and 445 (both top and bottom portions thereof) with solder or adhesive. (Note that the FIG. 10 sectional view of sensor 430 is from the same aspect as FIG. 4b.)

It is contemplated as preferable that the four weights also be uniformly polarized normal to major surfaces as illustrated in FIG. 10. It is further contemplated as preferable as illustrated in FIG. 10 that both major surfaces of the weights be electrically connected via edge plating to the interior electrode 443. A typical thickness of weight 91 is about half the thickness of sensor 430. Alternatively the weights could be made from suitable metal preferrably matched in temperature coefficient with the ceramic.

Turning now to FIG. 11a, therein is represented a further alternative which indicates that another mode of polarization may be employed for the embodiments herein. More particularly, FIG. 11a represents a sensor 430bp which, except for polarization of the three individual piezoelectric plates, is identical to the sensor 430 shown in FIGS. 4a and 4b. (Note that the FIG. 11a sectional view of the sensor is from the same aspect as FIG. 4b.) Like the three piezoelectric plates of sensor 430 in FIG. 4b, each individual one of the three plates of sensor 430bp is still uniformly polarized normal to its major surfaces. However, whereas the three plates of the FIG. 4b sensor 430 are each unidirectionally polarized, each of the three plates of sensor 430bp is bidirectionally polarized. More particularly, the portions of plates 431bp, 433bp, and 435bp lying on one side of the X-Z plane are uniformly polarized upwardly, and the portions of plates 431bp, 433bp and 435bp lying on the other side of the X-Z plane are uniformly polarized downwardly. Such polarization is represented by arrows 450bp. There is of course a polarization discontinuity in the central inactive region along the X axis but the FIG. 11a polarization is nevertheless considered uniform for purposes of definition herein.

One advantage of the polarization shown in FIG. 11a is that for rate measuring applications, all of the voltages generated at electrodes 441, 447, 448, and 442 with respect to the common electrode 443 are in-phase since the left-hand side of the FIG. 11a apparatus is strained oppositely from the right-hand side due to the coriolis accelerations. FIG. 11b, which is an equivalent circuit schematic of the FIG. 11a apparatus, indicates such phase relationship with arrows. Having the voltages nominally in-phase with respect to a common electrode that may also be connected to the support structure is advantageous in some signal processing applications.

It of course will be apparent to those skilled in the art that suitable combinations of the above described individual variations and modifications will yield additional variations and modifications, and also that the variations and modifications herein presented are not exhaustive of those within the scope of the present invention.

The various disclosed features are thus seen to afford improvement in the areas of (i) matching electrical characteristics of a plurality of unmounted and shaft-mounted bender elements, (ii) mechanically aligning a plurality of bender elements relative to one another and relative to a driveshaft, and (iii) electrical accuracy, sensitivity, and stability of bender elements. Each structure is built on a single base comprising a plurality of plates arranged according to a laminated structure. Being built on such a single base, electrical parameters and characteristics of the different benders in a unit are more nearly matched than typical prior art discrete-component type benders. That is, each bender of a unit originates at the same time from the same batch of materials and under the same manufacturing conditions. Furthermore, the highly preferred feature of uniform polarity can be more nearly realized. Furthermore, being built on such a single base, appropriate mechanical alignment of benders is stable and accurate. About the only misalignment which can occur in mounting one of the multiple bender sensors to the driveshaft is the misalignment wherein the sensor is secured so that the major surfaces are not exactly perpendicular to the driveshaft. Even then however, the opposing benders are still substantially parallel and on the average cancel out effects of forces normal to the spin axis. Furthermore, additional stability of electrical characteristics is afforded in the preferred embodiments by the end and central inactive regions. Also, even further electrical stability is afforded in the preferred embodiments by the three-layer laminated structure.

Thus, while various embodiments of the present invention have been shown and/or described, it is apparent that changes and modifications may be made therein without departing from the invention in its broader aspects. The aim of the appended claims, therefore, is to cover all such changes and modifications as fall within the true spirit and scope of the invention.